From 2080903b9e6bd01e3f64cc4c7c62ea1b3af0aa6a Mon Sep 17 00:00:00 2001
From: rohanarun <rohanarun@gmail.com>
Date: Sun, 11 Oct 2026 20:55:33 -0400
Subject: [PATCH] Compose rank-sector factory and112-port restriction:
 conditional kappa0.001467289440740487

---
 research/ranksector112-async/ADAPTATIONS.json |     5 +
 .../ranksector112-async/EXACT-ARITHMETIC.json |   130 +
 research/ranksector112-async/EXPECTED.json    |    25 +
 research/ranksector112-async/MANIFEST.json    |   224 +
 research/ranksector112-async/README.md        |     9 +
 .../REUSE-SOURCE522-INPUTS.json               |    72 +
 .../code/audit_112_independent.py             |   280 +
 .../code/audit_async_invoice.py               |   100 +
 .../code/audit_global_restriction.py          |   307 +
 .../code/transport_owners.py                  |    32 +
 .../ranksector112-async/data/OWNERS.json.gz   |   Bin 0 -> 467018 bytes
 research/ranksector112-async/data/PLAN.json   | 12227 +++
 .../validation/COMPOSITION-RECEIPT.json       |    54 +
 .../validation/LOCAL-RECEIPT.json             |    36 +
 .../validation/PACKAGED-REPLAY.json           |    98 +
 .../validation/SOURCE522-RECEIPT.json         |    88 +
 .../validation/SOURCE523-RECEIPT.json         |   102 +
 .../validation/audit/ASYNC-AUDIT.json         |    57 +
 .../validation/audit/EXACT-ASSEMBLY.json      |   127 +
 .../validation/audit/GLOBAL-PREFIX.json       |    13 +
 .../audit/GLOBAL-RESTRICTION-AUDIT.json       |    77 +
 .../audit/INDEPENDENT112-RAW-AUDIT.json       |    98 +
 .../validation/audit/OWNERS-AND-PROFILE.json  |    35 +
 .../validation/audit/PREFIX-AND-INVOICE.json  |    69 +
 .../vendor/pr522/EXPECTED.json                |     6 +
 .../ranksector112-async/vendor/pr522/LICENSE  |   201 +
 .../vendor/pr522/MANIFEST.json                |   293 +
 .../vendor/pr522/NOTICE.md                    |    13 +
 .../vendor/pr522/PORTABILITY.md               |    11 +
 .../ranksector112-async/vendor/pr522/PROOF.md |    13 +
 .../vendor/pr522/README.md                    |    23 +
 .../vendor/pr522/RESEARCH.md                  |    18 +
 .../vendor/pr522/SOURCES.json                 |   146 +
 .../vendor/pr522/code/assemble.py             |    42 +
 .../vendor/pr522/code/audit_async.py          |   149 +
 .../vendor/pr522/code/audit_async_invoice.py  |   100 +
 .../vendor/pr522/code/audit_kernel_scalar.py  |    55 +
 .../vendor/pr522/code/build_kernel92.py       |    42 +
 .../vendor/pr522/code/build_pair35.py         |    58 +
 .../vendor/pr522/code/build_ranksector.py     |    56 +
 .../vendor/pr522/code/construct_partial.py    |   309 +
 .../vendor/pr522/code/construct_ranksector.py |   329 +
 .../vendor/pr522/code/emit_async.py           |    89 +
 .../vendor/pr522/code/run_portable.py         |    15 +
 .../vendor/pr522/evidence/EXACT-ASSEMBLY.json |   127 +
 .../evidence/INDEPENDENT-FINAL-REVIEW.json    |    43 +
 .../evidence/INDEPENDENT-NOMINATION.json      |    29 +
 .../pr522/evidence/INDEPENDENT-PREFIX.json    |    15 +
 .../evidence/PAIR35-COMMUTATOR-SCREEN.json    |     1 +
 .../pr522/evidence/PORTABLE-REPLAY.json       |    88 +
 .../pr522/evidence/PREFIX-AND-INVOICE.json    |    69 +
 .../RANKSECTOR-COMMUTATOR-SCREEN.json         |     1 +
 .../pr522/evidence/TRANSPORT-CONTROLS.json    |    17 +
 .../vendor/pr522/inputs/ASYNC-6.json          | 12807 +++
 .../vendor/pr522/inputs/ASYNC-OWNERS.json.gz  |   Bin 0 -> 460813 bytes
 .../pr522/inputs/KERNEL84-SELECTION.json      |   664 +
 .../pr522/inputs/KERNEL92-SELECTION.json      |   551 +
 .../vendor/pr522/inputs/PAIR-SELECTION.json   |   575 +
 .../vendor/pr522/inputs/PAIR-SPEC.json        |     1 +
 .../vendor/pr522/inputs/PR493-EXPECTED.json   |    91 +
 .../vendor/pr522/inputs/RETIME-FRAMES.json.gz |   Bin 0 -> 5905 bytes
 .../hamming/PACKET-PROGRAMS.json.gz           |   Bin 0 -> 3400 bytes
 .../complex-network/hamming/PROTOTYPE.json    | 21364 +++++
 .../work/complex-nine-native/DATA-PHASES.json | 73604 ++++++++++++++++
 .../GLOBAL-TEMPLATE.json.gz                   |   Bin 0 -> 415067 bytes
 .../verified/gcert1-e8-retimed.json.gz        |   Bin 0 -> 23365 bytes
 .../inputs/work/odd-stages/clifford_exact.py  |   149 +
 .../pr361/code/engines/base_two_moment.py     |    63 +
 .../inputs/work/pr361/code/engines/moment.py  |   113 +
 .../inputs/work/pr361/code/engines/outer.py   |    58 +
 .../e8-bit/data/bit/bitE8-r865.json.gz        |   Bin 0 -> 33865 bytes
 .../vendor/pr522/references/PR493-NOTICE.md   |    11 +
 .../pr522/research-notes/CORRELATED-REPAIR.md |    13 +
 .../pr522/research-notes/PORTABLE-REPLAY.md   |     7 +
 .../pr522/research-notes/RANKSECTOR-PROOF.md  |    56 +
 .../research-notes/RANKSECTOR-SOURCES.json    |    25 +
 .../pr522/research-notes/ROOT-WORD-PROOF.md   |    29 +
 .../research-notes/ROOT-WORD-SOURCES.json     |    23 +
 .../research-notes/ROUNDING-SOURCES.json      |    21 +
 .../pr522/research-notes/SWITCH-SCREEN.json   | 15758 ++++
 .../pr522/research-notes/SWITCH-SOURCES.json  |    22 +
 .../pr522/research-notes/Y-SWITCH-PROOF.md    |    11 +
 .../research-notes/transvection-window.cpp    |    24 +
 .../pr522/vendor/audit_scalar_invoice.py      |    82 +
 .../code/adapters_gk.py                       |    59 +
 .../e8-complex-gauge-kernel/code/audit_gk.py  |   189 +
 .../e8-complex-gauge-kernel/code/emit_gk.py   |   156 +
 .../e8-complex-gauge-kernel/code/gk_common.py |    94 +
 .../e8-complex-gauge-kernel/code/gk_word.py   |   194 +
 .../code/integrate_gk.py                      |   123 +
 .../code/onehost_gk.py                        |   111 +
 .../e8-complex-gauge-kernel/code/replay_gk.py |   280 +
 .../data/selections/gauge80-kernel42.json     |   470 +
 .../code/complex_phases_full.py               |    39 +
 .../vendor/clifford_exact.py                  |   149 +
 .../vendor/pr522/verify.py                    |    64 +
 .../vendor/pr522/verify.sh                    |    10 +
 .../vendor/pr523/ADAPTATIONS.json             |    35 +
 .../vendor/pr523/EXPECTED.json                |    26 +
 .../ranksector112-async/vendor/pr523/LICENSE  |   201 +
 .../vendor/pr523/LOCAL-VALIDATION.json        |   149 +
 .../vendor/pr523/MANIFEST.json                |   501 +
 .../vendor/pr523/NOTICE.md                    |    51 +
 .../vendor/pr523/PORTABILITY.md               |    54 +
 .../ranksector112-async/vendor/pr523/PROOF.md |   199 +
 .../vendor/pr523/README.md                    |   271 +
 .../vendor/pr523/REPRODUCTION.json            |    17 +
 .../vendor/pr523/SOURCES.json                 |   118 +
 .../vendor/pr523/code/assemble.py             |    42 +
 .../pr523/code/audit_112_independent.py       |   280 +
 .../vendor/pr523/code/audit_async.py          |   149 +
 .../vendor/pr523/code/audit_async_invoice.py  |   100 +
 .../pr523/code/audit_global_restriction.py    |   297 +
 .../vendor/pr523/code/audit_local112.py       |   144 +
 .../pr523/code/audit_port112_transport.py     |   108 +
 .../vendor/pr523/code/build_port112.py        |   128 +
 .../vendor/pr523/code/emit_async.py           |    90 +
 .../vendor/pr523/code/emit_local112.py        |   156 +
 .../vendor/pr523/code/phases_local112.py      |    39 +
 .../vendor/pr523/code/restrict_global.py      |   173 +
 .../vendor/pr523/evidence/ASYNC-AUDIT.json    |    57 +
 .../vendor/pr523/evidence/COLD-REPLAY.json    |   102 +
 .../vendor/pr523/evidence/COLD-STEPS.json     |    72 +
 .../vendor/pr523/evidence/EXACT-ASSEMBLY.json |   127 +
 .../vendor/pr523/evidence/GLOBAL-PREFIX.json  |    13 +
 .../evidence/GLOBAL-RESTRICTION-AUDIT.json    |    77 +
 .../evidence/INDEPENDENT112-RAW-AUDIT.json    |    95 +
 .../pr523/evidence/OWNERS-AND-PROFILE.json    |    35 +
 .../pr523/evidence/PREDECESSOR-REPLAY.json    |    78 +
 .../pr523/evidence/PREFIX-AND-INVOICE.json    |    69 +
 .../pr523/evidence/PUBLIC-SNAPSHOT.json       |   103 +
 .../pr523/evidence/SERIALIZATION-CHECKS.json  |   118 +
 .../evidence/hosted/ACTUAL-SIGMAS.json.gz     |   Bin 0 -> 183116 bytes
 .../evidence/hosted/GLOBAL-TEMPLATE.json.gz   |   Bin 0 -> 912721 bytes
 .../vendor/pr523/evidence/hosted/HOSTED.json  |    46 +
 .../evidence/local/CANONICAL-WORD.json.gz     |   Bin 0 -> 84988 bytes
 .../evidence/local/CLIFFORD-RECIPES.json      |     1 +
 .../pr523/evidence/local/CLIFFORD-REVIEW.json |    21 +
 .../pr523/evidence/local/FULL-WORD.json.gz    |   Bin 0 -> 39283 bytes
 .../local/INDEPENDENT-LOCAL-REPLAY.json       |    62 +
 .../vendor/pr523/evidence/local/LEMMA-A.json  |   136 +
 .../pr523/evidence/local/LOCAL-CHECKS.json    |    40 +
 .../evidence/local/LOCAL-PROGRAMS.json.gz     |   Bin 0 -> 217265 bytes
 .../pr523/evidence/local/PORT-MAPPING.json    |   354 +
 .../evidence/local/RESIDUAL-ADAPTERS.json     |     1 +
 .../pr523/evidence/local/RESTRICTION.json     |     1 +
 .../pr523/evidence/local/TRANSPORT.json       |   123 +
 .../vendor/pr523/inputs/ASYNC112-PLAN.json    | 12226 +++
 .../vendor/pr523/inputs/OWNERS112.json.gz     |   Bin 0 -> 462249 bytes
 .../vendor/pr523/proof/GLOBAL-RESTRICTION.md  |   125 +
 .../vendor/pr523/proof/INDEPENDENT-REVIEW.md  |   120 +
 .../vendor/pr523/proof/LOCAL-RESTRICTION.md   |   111 +
 .../vendor/pr523/vendor/pr514/EXPECTED.json   |     8 +
 .../vendor/pr523/vendor/pr514/LICENSE         |   201 +
 .../vendor/pr523/vendor/pr514/MANIFEST.json   |   277 +
 .../vendor/pr523/vendor/pr514/NOTICE.md       |     9 +
 .../vendor/pr523/vendor/pr514/PORTABILITY.md  |    11 +
 .../vendor/pr523/vendor/pr514/PROOF.md        |    27 +
 .../vendor/pr523/vendor/pr514/README.md       |    38 +
 .../vendor/pr523/vendor/pr514/RESEARCH.md     |    16 +
 .../vendor/pr523/vendor/pr514/SNAPSHOT.md     |     5 +
 .../vendor/pr523/vendor/pr514/SOURCES.json    |    92 +
 .../pr523/vendor/pr514/code/assemble.py       |    42 +
 .../pr523/vendor/pr514/code/audit_async.py    |   149 +
 .../vendor/pr514/code/audit_async_invoice.py  |   100 +
 .../vendor/pr514/code/audit_kernel_scalar.py  |    55 +
 .../pr523/vendor/pr514/code/build_kernel92.py |    42 +
 .../vendor/pr514/code/construct_partial.py    |   309 +
 .../pr523/vendor/pr514/code/emit_async.py     |    89 +
 .../pr523/vendor/pr514/code/run_portable.py   |    15 +
 .../vendor/pr514/evidence/ASYNC-AUDIT.json    |    60 +
 .../vendor/pr514/evidence/EXACT-ASSEMBLY.json |   127 +
 .../INDEPENDENT-NOMINATION-REVIEW.json        |    35 +
 .../vendor/pr514/evidence/KERNEL-SCALAR.json  |   104 +
 .../pr514/evidence/OWNERS-AND-PROFILE.json    |    38 +
 .../pr514/evidence/PORTABLE-REPLAY.json       |    78 +
 .../pr514/evidence/PREFIX-AND-INVOICE.json    |    69 +
 .../pr523/vendor/pr514/evidence/RESULT.json   |    78 +
 .../pr514/evidence/TRANSPORT-CONTROLS.json    |    14 +
 .../pr523/vendor/pr514/inputs/ASYNC-6.json    | 12123 +++
 .../vendor/pr514/inputs/ASYNC-OWNERS.json.gz  |   Bin 0 -> 460906 bytes
 .../pr514/inputs/KERNEL84-SELECTION.json      |   664 +
 .../pr514/inputs/KERNEL92-SELECTION.json      |   551 +
 .../vendor/pr514/inputs/PR493-EXPECTED.json   |    91 +
 .../vendor/pr514/inputs/RETIME-FRAMES.json.gz |   Bin 0 -> 5905 bytes
 .../hamming/PACKET-PROGRAMS.json.gz           |   Bin 0 -> 3400 bytes
 .../complex-network/hamming/PROTOTYPE.json    | 21364 +++++
 .../work/complex-nine-native/DATA-PHASES.json | 73604 ++++++++++++++++
 .../GLOBAL-TEMPLATE.json.gz                   |   Bin 0 -> 415067 bytes
 .../verified/gcert1-e8-retimed.json.gz        |   Bin 0 -> 23365 bytes
 .../inputs/work/odd-stages/clifford_exact.py  |   149 +
 .../pr361/code/engines/base_two_moment.py     |    63 +
 .../inputs/work/pr361/code/engines/moment.py  |   113 +
 .../inputs/work/pr361/code/engines/outer.py   |    58 +
 .../e8-bit/data/bit/bitE8-r865.json.gz        |   Bin 0 -> 33865 bytes
 .../vendor/pr514/references/PR493-NOTICE.md   |    11 +
 .../pr514/research-notes/COALESCING-GATE.json |  3174 +
 .../pr514/research-notes/COALESCING-PROOF.md  |    19 +
 .../research-notes/COMPLEX-SOURCE-HASHES.json |    41 +
 .../pr514/research-notes/HOSTING-RESEARCH.md  |    40 +
 .../research-notes/KERNEL-MACHINE-SOURCES.md  |    35 +
 .../research-notes/KERNEL-SOURCE-HASHES.json  |    49 +
 .../research-notes/MACHINE-TRANSFORMATIONS.md |    31 +
 .../research-notes/REPEATED-AXIS-LEMMA.md     |    27 +
 .../pr514/research-notes/REPLAY-REPAIRS.md    |     7 +
 .../RESTORATION-AND-CSE-SCREEN.json           |    22 +
 .../pr514/research-notes/coalescing_gate.py   |    26 +
 .../pr514/vendor/audit_scalar_invoice.py      |    82 +
 .../code/adapters_gk.py                       |    59 +
 .../e8-complex-gauge-kernel/code/audit_gk.py  |   189 +
 .../e8-complex-gauge-kernel/code/emit_gk.py   |   156 +
 .../e8-complex-gauge-kernel/code/gk_common.py |    94 +
 .../e8-complex-gauge-kernel/code/gk_word.py   |   194 +
 .../code/integrate_gk.py                      |   123 +
 .../code/onehost_gk.py                        |   111 +
 .../e8-complex-gauge-kernel/code/replay_gk.py |   280 +
 .../data/selections/gauge80-kernel42.json     |   470 +
 .../code/complex_phases_full.py               |    39 +
 .../vendor/clifford_exact.py                  |   149 +
 .../vendor/pr523/vendor/pr514/verify.py       |    62 +
 .../vendor/pr523/vendor/pr514/verify.sh       |    10 +
 .../vendor/pr523/verify.py                    |   158 +
 research/ranksector112-async/verify.py        |   157 +
 223 files changed, 279007 insertions(+)
 create mode 100644 research/ranksector112-async/ADAPTATIONS.json
 create mode 100644 research/ranksector112-async/EXACT-ARITHMETIC.json
 create mode 100644 research/ranksector112-async/EXPECTED.json
 create mode 100644 research/ranksector112-async/MANIFEST.json
 create mode 100644 research/ranksector112-async/README.md
 create mode 100644 research/ranksector112-async/REUSE-SOURCE522-INPUTS.json
 create mode 100644 research/ranksector112-async/code/audit_112_independent.py
 create mode 100644 research/ranksector112-async/code/audit_async_invoice.py
 create mode 100644 research/ranksector112-async/code/audit_global_restriction.py
 create mode 100644 research/ranksector112-async/code/transport_owners.py
 create mode 100644 research/ranksector112-async/data/OWNERS.json.gz
 create mode 100644 research/ranksector112-async/data/PLAN.json
 create mode 100644 research/ranksector112-async/validation/COMPOSITION-RECEIPT.json
 create mode 100644 research/ranksector112-async/validation/LOCAL-RECEIPT.json
 create mode 100644 research/ranksector112-async/validation/PACKAGED-REPLAY.json
 create mode 100644 research/ranksector112-async/validation/SOURCE522-RECEIPT.json
 create mode 100644 research/ranksector112-async/validation/SOURCE523-RECEIPT.json
 create mode 100644 research/ranksector112-async/validation/audit/ASYNC-AUDIT.json
 create mode 100644 research/ranksector112-async/validation/audit/EXACT-ASSEMBLY.json
 create mode 100644 research/ranksector112-async/validation/audit/GLOBAL-PREFIX.json
 create mode 100644 research/ranksector112-async/validation/audit/GLOBAL-RESTRICTION-AUDIT.json
 create mode 100644 research/ranksector112-async/validation/audit/INDEPENDENT112-RAW-AUDIT.json
 create mode 100644 research/ranksector112-async/validation/audit/OWNERS-AND-PROFILE.json
 create mode 100644 research/ranksector112-async/validation/audit/PREFIX-AND-INVOICE.json
 create mode 100644 research/ranksector112-async/vendor/pr522/EXPECTED.json
 create mode 100644 research/ranksector112-async/vendor/pr522/LICENSE
 create mode 100644 research/ranksector112-async/vendor/pr522/MANIFEST.json
 create mode 100644 research/ranksector112-async/vendor/pr522/NOTICE.md
 create mode 100644 research/ranksector112-async/vendor/pr522/PORTABILITY.md
 create mode 100644 research/ranksector112-async/vendor/pr522/PROOF.md
 create mode 100644 research/ranksector112-async/vendor/pr522/README.md
 create mode 100644 research/ranksector112-async/vendor/pr522/RESEARCH.md
 create mode 100644 research/ranksector112-async/vendor/pr522/SOURCES.json
 create mode 100644 research/ranksector112-async/vendor/pr522/code/assemble.py
 create mode 100644 research/ranksector112-async/vendor/pr522/code/audit_async.py
 create mode 100644 research/ranksector112-async/vendor/pr522/code/audit_async_invoice.py
 create mode 100644 research/ranksector112-async/vendor/pr522/code/audit_kernel_scalar.py
 create mode 100644 research/ranksector112-async/vendor/pr522/code/build_kernel92.py
 create mode 100644 research/ranksector112-async/vendor/pr522/code/build_pair35.py
 create mode 100644 research/ranksector112-async/vendor/pr522/code/build_ranksector.py
 create mode 100644 research/ranksector112-async/vendor/pr522/code/construct_partial.py
 create mode 100644 research/ranksector112-async/vendor/pr522/code/construct_ranksector.py
 create mode 100644 research/ranksector112-async/vendor/pr522/code/emit_async.py
 create mode 100644 research/ranksector112-async/vendor/pr522/code/run_portable.py
 create mode 100644 research/ranksector112-async/vendor/pr522/evidence/EXACT-ASSEMBLY.json
 create mode 100644 research/ranksector112-async/vendor/pr522/evidence/INDEPENDENT-FINAL-REVIEW.json
 create mode 100644 research/ranksector112-async/vendor/pr522/evidence/INDEPENDENT-NOMINATION.json
 create mode 100644 research/ranksector112-async/vendor/pr522/evidence/INDEPENDENT-PREFIX.json
 create mode 100644 research/ranksector112-async/vendor/pr522/evidence/PAIR35-COMMUTATOR-SCREEN.json
 create mode 100644 research/ranksector112-async/vendor/pr522/evidence/PORTABLE-REPLAY.json
 create mode 100644 research/ranksector112-async/vendor/pr522/evidence/PREFIX-AND-INVOICE.json
 create mode 100644 research/ranksector112-async/vendor/pr522/evidence/RANKSECTOR-COMMUTATOR-SCREEN.json
 create mode 100644 research/ranksector112-async/vendor/pr522/evidence/TRANSPORT-CONTROLS.json
 create mode 100644 research/ranksector112-async/vendor/pr522/inputs/ASYNC-6.json
 create mode 100644 research/ranksector112-async/vendor/pr522/inputs/ASYNC-OWNERS.json.gz
 create mode 100644 research/ranksector112-async/vendor/pr522/inputs/KERNEL84-SELECTION.json
 create mode 100644 research/ranksector112-async/vendor/pr522/inputs/KERNEL92-SELECTION.json
 create mode 100644 research/ranksector112-async/vendor/pr522/inputs/PAIR-SELECTION.json
 create mode 100644 research/ranksector112-async/vendor/pr522/inputs/PAIR-SPEC.json
 create mode 100644 research/ranksector112-async/vendor/pr522/inputs/PR493-EXPECTED.json
 create mode 100644 research/ranksector112-async/vendor/pr522/inputs/RETIME-FRAMES.json.gz
 create mode 100644 research/ranksector112-async/vendor/pr522/inputs/work/complex-network/hamming/PACKET-PROGRAMS.json.gz
 create mode 100644 research/ranksector112-async/vendor/pr522/inputs/work/complex-network/hamming/PROTOTYPE.json
 create mode 100644 research/ranksector112-async/vendor/pr522/inputs/work/complex-nine-native/DATA-PHASES.json
 create mode 100644 research/ranksector112-async/vendor/pr522/inputs/work/complex-nine-native/GLOBAL-TEMPLATE.json.gz
 create mode 100644 research/ranksector112-async/vendor/pr522/inputs/work/higher-stage-e8/verified/gcert1-e8-retimed.json.gz
 create mode 100644 research/ranksector112-async/vendor/pr522/inputs/work/odd-stages/clifford_exact.py
 create mode 100644 research/ranksector112-async/vendor/pr522/inputs/work/pr361/code/engines/base_two_moment.py
 create mode 100644 research/ranksector112-async/vendor/pr522/inputs/work/pr361/code/engines/moment.py
 create mode 100644 research/ranksector112-async/vendor/pr522/inputs/work/pr361/code/engines/outer.py
 create mode 100644 research/ranksector112-async/vendor/pr522/inputs/work/pr370-source/research/e8-bit/data/bit/bitE8-r865.json.gz
 create mode 100644 research/ranksector112-async/vendor/pr522/references/PR493-NOTICE.md
 create mode 100644 research/ranksector112-async/vendor/pr522/research-notes/CORRELATED-REPAIR.md
 create mode 100644 research/ranksector112-async/vendor/pr522/research-notes/PORTABLE-REPLAY.md
 create mode 100644 research/ranksector112-async/vendor/pr522/research-notes/RANKSECTOR-PROOF.md
 create mode 100644 research/ranksector112-async/vendor/pr522/research-notes/RANKSECTOR-SOURCES.json
 create mode 100644 research/ranksector112-async/vendor/pr522/research-notes/ROOT-WORD-PROOF.md
 create mode 100644 research/ranksector112-async/vendor/pr522/research-notes/ROOT-WORD-SOURCES.json
 create mode 100644 research/ranksector112-async/vendor/pr522/research-notes/ROUNDING-SOURCES.json
 create mode 100644 research/ranksector112-async/vendor/pr522/research-notes/SWITCH-SCREEN.json
 create mode 100644 research/ranksector112-async/vendor/pr522/research-notes/SWITCH-SOURCES.json
 create mode 100644 research/ranksector112-async/vendor/pr522/research-notes/Y-SWITCH-PROOF.md
 create mode 100644 research/ranksector112-async/vendor/pr522/research-notes/transvection-window.cpp
 create mode 100644 research/ranksector112-async/vendor/pr522/vendor/audit_scalar_invoice.py
 create mode 100644 research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/adapters_gk.py
 create mode 100644 research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/audit_gk.py
 create mode 100644 research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/emit_gk.py
 create mode 100644 research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/gk_common.py
 create mode 100644 research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/gk_word.py
 create mode 100644 research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/integrate_gk.py
 create mode 100644 research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/onehost_gk.py
 create mode 100644 research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/replay_gk.py
 create mode 100644 research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/data/selections/gauge80-kernel42.json
 create mode 100644 research/ranksector112-async/vendor/pr522/vendor/complex/split-centres-global/code/complex_phases_full.py
 create mode 100644 research/ranksector112-async/vendor/pr522/vendor/complex/split-centres-global/vendor/clifford_exact.py
 create mode 100644 research/ranksector112-async/vendor/pr522/verify.py
 create mode 100644 research/ranksector112-async/vendor/pr522/verify.sh
 create mode 100644 research/ranksector112-async/vendor/pr523/ADAPTATIONS.json
 create mode 100644 research/ranksector112-async/vendor/pr523/EXPECTED.json
 create mode 100644 research/ranksector112-async/vendor/pr523/LICENSE
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diff --git a/research/ranksector112-async/ADAPTATIONS.json b/research/ranksector112-async/ADAPTATIONS.json
new file mode 100644
index 0000000000..0dcfcfc713
--- /dev/null
+++ b/research/ranksector112-async/ADAPTATIONS.json
@@ -0,0 +1,5 @@
+{
+  "audit_async_invoice.py": "Recompute actual scalar prefix with unchanged algorithm; update expected regression values from21/206 to25/210 for source522. Full strict bounds and charged512 retained.",
+  "audit_112_independent.py": "Replace old514 fixed width multiset with exact ordered width equality to freshly rebuilt source522; raw column/frame/ownership checks unchanged.",
+  "audit_global_restriction.py": "Replace old514 compensation count and bank spectrum fixtures with independently bound new canonical compensation length and literal old source522 bank-route recount. All actual scalar, frame, hash and corruption controls retained. Initial fixture failure preserved in PR477."
+}
diff --git a/research/ranksector112-async/EXACT-ARITHMETIC.json b/research/ranksector112-async/EXACT-ARITHMETIC.json
new file mode 100644
index 0000000000..b34aa3c40d
--- /dev/null
+++ b/research/ranksector112-async/EXACT-ARITHMETIC.json
@@ -0,0 +1,130 @@
+{
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+    },
+    {
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+      "cutoff_log2": "173456267857927793965636576496375774666101"
+    }
+  ],
+  "scope": "Arithmetic assumes inherited row allowance20161 and bit coefficient6464. Actual new-factory scalar/phase/owner/prefix/finite-invoice admission remains required. No verified bound claim."
+}
diff --git a/research/ranksector112-async/EXPECTED.json b/research/ranksector112-async/EXPECTED.json
new file mode 100644
index 0000000000..ab442895a1
--- /dev/null
+++ b/research/ranksector112-async/EXPECTED.json
@@ -0,0 +1,25 @@
+{
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+  "strict_constraints": 47
+}
diff --git a/research/ranksector112-async/MANIFEST.json b/research/ranksector112-async/MANIFEST.json
new file mode 100644
index 0000000000..99024d4088
--- /dev/null
+++ b/research/ranksector112-async/MANIFEST.json
@@ -0,0 +1,224 @@
+{
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diff --git a/research/ranksector112-async/README.md b/research/ranksector112-async/README.md
new file mode 100644
index 0000000000..b161db159b
--- /dev/null
+++ b/research/ranksector112-async/README.md
@@ -0,0 +1,9 @@
+# Rank-sector factory on 112 ports
+
+Completed finite composition: conditional kappa0.001467289440740487 (+0.6408797 percent over pinned PR523). Complex b0.001469445542668988969610. Fresh source522 and source523 full replays pass. Changed112-port local scalar/phase/wrapper checks, global data restriction, independent owner/controller and raw audits, finite invoice and exact assembly pass. Completed receipts and audit files are under validation/.
+
+This composes PR522's rank-sector99 factory with PR523's exact coordinate-port restriction. All helper roles are reassigned by width dominance and residual offsets compacted, retaining the complete invocation order and physical family identities. All these changed-word checks passed on the actual emitted composition; old quoted gains are not added.
+
+Immutable source packages are included under vendor/pr522 and vendor/pr523, with all their source notices/licenses. Source522 head e9f8075b5212e9bddf361097dbb022dcd052e0bb; source523 head a900f98be8ff2c09d3292b5112d4731dbd0c8438. Credits: Dugongue #522/#518/#514 factory/retiming/gauges; icekylinx #523 puncturing and actual 112-port audits; eumemic #507/#493, #484/#496/#505/#473 and all retained ancestors. New composition and owner transport by Rohan Arun with OpenAI Codex assistance.
+
+The unchanged bit493 operator is cited and its histogram repriced. All-size compiler, common-label/mutable-basis realization, normalized Lemma A, restored-row, precision/tape and analytic-transfer interfaces remain assumed. No unconditional theorem, practical runtime crossover, global optimum, fresh Lean proof or CI pass is claimed. Run `python -B verify.py --work /absolute/new/output`. Default rebuilds source522; explicit `--reuse-source522` validates every published pin, then reruns all changed-local and global stages. Packaged replay passed with explicit byte-pinned completed-source522 reuse and fresh changed-local/global reconstruction; see validation/PACKAGED-REPLAY.json. No cold combined wrapper or CI pass claimed.
diff --git a/research/ranksector112-async/REUSE-SOURCE522-INPUTS.json b/research/ranksector112-async/REUSE-SOURCE522-INPUTS.json
new file mode 100644
index 0000000000..70de2a5c77
--- /dev/null
+++ b/research/ranksector112-async/REUSE-SOURCE522-INPUTS.json
@@ -0,0 +1,72 @@
+{
+  "RESULT.json": "3e9578a84ece9f913e3cdc9c0bc9827348f1ef2068b13dcae6e05975d898c541",
+  "STEPS.json": "1d7d7b76a571f541eef981e2ec4b59404d7078271898ae1d9c03410067b7bee9",
+  "adapters.log": "540bb8ff395313f998c0c0de6dba7cfbd8725ceff1e762194520742b123d2d47",
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+  "audit/EXACT-ASSEMBLY.json": "817029b90f3f525334fc994a84aec33b246f33333f7551d50720d3142e1b6131",
+  "audit/GLOBAL-PREFIX.json": "c65b85f9543c507525a637656d34cd96277158f2e52f20bbd8922f1ac453bd6b",
+  "audit/KERNEL-SCALAR.json": "c2b515a7ecce1a575830ae6f0e84b78537141e8052bd24129a315f8cc93338b8",
+  "audit/OWNERS-AND-PROFILE.json": "fc3702a89ef9640d77e987004cdf50d6f98ebaa3812cfe35562fbc188066f3ef",
+  "audit/PREFIX-AND-INVOICE.json": "b4379c3dcafdae3afa0370cfc0c1e01b30470147bf42beb16e6a836ef9870347",
+  "base/ASYNC-6.json": "9b4b8f125a19ec5741050ca62167c0a4ea2e7f80880f4635c1b6e6c99ea506e8",
+  "base/BIT-PRICE.json": "73f1b82f7f122711c763518f99553d925ae69395f1e4b9b1481070f1d4734190",
+  "base/LEMMA-A.json": "9ba336d40bae9ad52f85d0bf57946e4a115062c657ebbb01884a1a8db3270fb4",
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+  "base/reference-pair35/factory_constructor.py": "c9769df09b337458a04110b116969db3d1b03fce33bcd687a99ee3061ff22c29",
+  "base/split-centres/CANONICAL-WORD.json.gz": "eb7e6e1e8b33ecdcc0f8be3e10900694569937647b58faa85da5faf306e38177",
+  "base/split-centres/CLIFFORD-RECIPES.json": "105b44e6af0784ab99b85ce8f2375f2fde8b0393ad09a09ad38be01e568bcea9",
+  "base/split-centres/CLIFFORD-REVIEW.json": "f94ff7c04a3dae914846e473bfc23e33d26b5c0540230493390d874be8f26a3c",
+  "base/split-centres/CONSTRUCTION.json": "20325bd9dafa8f474bc743cfeeae9ecb51c139bc7167e9a9aeefae1132f64fad",
+  "base/split-centres/FULL-WORD.json.gz": "7634aadc00147ceee52dce60a5271f2c102ccd6703f67b5419e11d7ecafe1101",
+  "base/split-centres/GLOBAL-TEMPLATE.json.gz": "d228fe3e1895e1e8d3097bf27501e2f19d54ab07c8bef351045bf48a35f2b607",
+  "base/split-centres/INDEPENDENT-REPLAY.json": "fbccbfb963d997b99536dd609e8d38f16cc3f6ff4cb9fb1c92fd5edd19d4b31e",
+  "base/split-centres/INTEGRATION.json": "efe0d50b13332997b75bdae6465029e8d4cafc3cf6040e4866a5a73e091db6a9",
+  "base/split-centres/LOCAL-CHECKS.json": "8f0596ec728381082cb294f3fc27610e98e78a83b0f6e1576512ba13450ea160",
+  "base/split-centres/LOCAL-PROGRAMS.json.gz": "95813b328608ddbd56829efab33d25c9b284f320198c1dfb90afa9bf88b9f35c",
+  "base/split-centres/RESIDUAL-ADAPTERS.json": "06a889a51fd2833dd465ed9c660b35fa8f68496ff7ed34c931d17c4f7551e1b2",
+  "base/split-centres/RETIMED-BASE.json.gz": "318a858c1f45c0e8fb1cb96ff1577bc555eb2c921ab421d98d90bedbbaa1c74c",
+  "base/split-centres/SCALAR-FRAME-AUDIT.json": "b2ba14163f7f4596f8adbfafefb2ee87f878f14eb43603dc44bf186f9026b83a",
+  "base/split-centres/SELECTION.json": "e818377083be1b581da718ae4cdb0741f074df313c0813e4239377b3754f25a5",
+  "base/split-centres/factory/FULL-DISCOVERY.json": "32d7738232c065ab83294760b5bcba129ab33daf24cab4b0e2e01373db6a5419",
+  "base/split-centres/factory/FULL-WORD.json.gz": "bfdf3db4279ded5f8c114a17fc73e80eaf2108a656f5f3f841bbf81e819cc7d7",
+  "base/split-centres/factory-construction.log": "32d7738232c065ab83294760b5bcba129ab33daf24cab4b0e2e01373db6a5419",
+  "base/work/complex-network/hamming/PACKET-PROGRAMS.json.gz": "d833ae0390d165d7da0c639a3c7aeb77156c2ddb52447087cb49b9d03b19e9b9",
+  "base/work/complex-network/hamming/PROTOTYPE.json": "327d2a868043e846381aa58a33053c24425e8cad522ff401b10ec8af1d649a3f",
+  "base/work/complex-nine-native/DATA-PHASES.json": "f621f6d4296cb215f334830356c5f79fe10d6d04d15b3ccda76ba0885ab67d0a",
+  "base/work/complex-nine-native/GLOBAL-TEMPLATE.json.gz": "1b84904a31a733aab9bfdda3f528c06719f590d2133a43687a8bded955dc991e",
+  "base/work/higher-stage-e8/verified/gcert1-e8-retimed.json.gz": "77b0c0fa19ef3da1c7316010e13493aa5eea1a50c3506eddc08f7480e659878b",
+  "base/work/odd-stages/clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962",
+  "base/work/pr361/code/engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+  "base/work/pr361/code/engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+  "base/work/pr361/code/engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c",
+  "base/work/pr370-source/research/e8-bit/data/bit/bitE8-r865.json.gz": "1fb726ea3818fe0837cceb0dd22a71a0814f064e5e781628104610d6468e0e55",
+  "construct-kernel92.log": "dbd3e4241512f675bcdc0195ee7a26949aa1014bfbc6ae3dda99e16171744bbe",
+  "construct-pair35.log": "b1d0efb26afac94acdbcf8523031459d0c2969db81d4f2abcee93b9ad288241f",
+  "construct-ranksector.log": "a04259ecc63627c4d9929799f5941fc57c9d54a21395f992b7846aed000bc96e",
+  "emit-async.log": "bda51aa7d706b353bb54cd31c9ee0533eff362fa153ec13b62ee627d5707e60c",
+  "emit-local.log": "72c26cba832ac574f08f0d09b14cec1ff7903ced9ac528091c1c3f2ef56bf384",
+  "hosted/ACTUAL-SIGMAS.json.gz": "0c87bb00123781751e8cfdfeb97d88d29c2fbf6e7c15287cb9118544445e369b",
+  "hosted/GLOBAL-TEMPLATE.json.gz": "b80e6142ccae5c91f0b9b703fbf0753987a50dee01926e867b95aa78d3650e2e",
+  "hosted/HOSTED.json": "bda51aa7d706b353bb54cd31c9ee0533eff362fa153ec13b62ee627d5707e60c",
+  "independent-async.log": "88c53e113fcbb28f9335374eadb42409c5d6719a57de65d6a3061af68cb52868",
+  "invoice.log": "b4379c3dcafdae3afa0370cfc0c1e01b30470147bf42beb16e6a836ef9870347",
+  "kernel-scalar-controls.log": "ba10c3fa0011c1fcd42e080affb7e19eac860995b22f7667b137b61c95da37d7",
+  "parent-integration.log": "7e13c81c421bbf125f7d2c2db8365f72db0579c5e89326e5de0c58049550724c",
+  "parent-replay.log": "04a057c55168c3dbfe452a4fc62fc90f55f1844d9e8c62e48e78e59b58ae1137",
+  "partial-factory.log": "9b66eb63b65fc0a5c7f57d3c18df9d12bfa509d1f7e9f0d41ff256e8433982e6",
+  "phases.log": "93f6a3c5b25599ec9e0ea756bdd9024b43497e1e70639713a5ca90d6f7d3dd7c",
+  "scalar.log": "c4f7e5a07a0553b843721bcb66397875a653c498833883945d14d3754fcea4f6",
+  "two-moments-assembly.log": "e36bd84f172355e18b2358e77f41a1c5178d00657ce98b28f4136b2b3a13a90a"
+}
diff --git a/research/ranksector112-async/code/audit_112_independent.py b/research/ranksector112-async/code/audit_112_independent.py
new file mode 100644
index 0000000000..e9eba06889
--- /dev/null
+++ b/research/ranksector112-async/code/audit_112_independent.py
@@ -0,0 +1,280 @@
+"""Independent raw-artifact audit of the 112-port restriction and whole owners.
+Prepared for icekylinx with GPT-6 Astra assistance.
+
+Does not import an emitter, hosting optimizer, nominated profile, nominated
+windows, or the adapted PR514 checker.  Inputs are the original checked local
+and global artifacts, the new literal local word/program, and 40,320 owners.
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+from collections import Counter, defaultdict
+from functools import lru_cache
+import argparse, gzip, hashlib, json, time
+
+ap=argparse.ArgumentParser()
+ap.add_argument('--original-base',type=Path,required=True)
+ap.add_argument('--local',type=Path,required=True)
+ap.add_argument('--owners',type=Path,required=True)
+ap.add_argument('--out',type=Path,required=True)
+a=ap.parse_args(); start_time=time.monotonic()
+
+def read(p):
+    data=p.read_bytes()
+    return json.loads(gzip.decompress(data) if p.suffix=='.gz' else data)
+def digest(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+def out(name,z):(a.out/name).write_text(json.dumps(z,indent=2,sort_keys=True)+'\n')
+a.out.mkdir(parents=True,exist_ok=True)
+old=read(a.original_base/'split-centres/CANONICAL-WORD.json.gz')
+new=read(a.local/'CANONICAL-WORD.json.gz')
+programs=read(a.local/'LOCAL-PROGRAMS.json.gz')
+parent=read(a.original_base/'split-centres/GLOBAL-TEMPLATE.json.gz')
+phase=read(a.original_base/'work/complex-nine-native/DATA-PHASES.json')
+roles=read(a.owners)
+V=new['v'];R=new['R'];N=2*V+R;H=new['h'];M=parent['m'];T=8
+assert (old['v'],V,R,H,M)==(120,112,560,9,73)
+
+# Infer the restriction from actual labels, not its producer's mapping file.
+assert len(set(new['ports']))==V and set(new['ports'])<set(old['ports'])
+kept=[i for i,q in enumerate(old['ports']) if q in set(new['ports'])]
+assert [old['ports'][i] for i in kept]==new['ports']
+rmp={oldi:newi for newi,oldi in enumerate(kept)}
+rmp.update({120+oldi:V+newi for newi,oldi in enumerate(kept)})
+rmp.update({240+h:2*V+h for h in range(R)})
+removed=set(range(240+R))-set(rmp)
+assert len(removed)==16 and new['frames']==old['frames']
+removed_ops=Counter()
+for name in ('A','B','precondition','compensation','cut','cleanup'):
+    result=[]
+    for event in old[name]:
+        rs=event[1:3] if event[0]=='add' else event[1:2]
+        if any(r in removed for r in rs):
+            assert name=='cut' and event[0]=='add'
+            assert event[1]==120+event[2] and event[3:5]==[1,1]
+            removed_ops[name]+=1
+            continue
+        z=event.copy();z[1]=rmp[z[1]]
+        if z[0]=='add':z[2]=rmp[z[2]]
+        result.append(z)
+    assert result==new[name],('not a literal restriction',name)
+assert removed_ops=={'cut':8}
+for name in ('start','final'):
+    assert new[name]==[old[name][r] for r in sorted(rmp,key=rmp.get)]
+assert new['centers']==[rmp[r] for r in old['centers'] if r in rmp]
+assert new['center_frames']==[f for r,f in zip(old['centers'],old['center_frames']) if r in rmp]
+assert new['target_levels']=={str(rmp[120+int(t)]-V):f for t,f in old.get('target_levels',{}).items()}
+frames=new['frames']
+
+@lru_cache(None)
+def subspace(i):
+    s={0}
+    for x in frames[i]:s|={y^x for y in s}
+    assert len(s)==1<<len(frames[i])
+    return frozenset(s)
+
+# Replay each literal local instruction, including all independent dirt columns.
+# Recursive events contribute one child only after their actual endpoint frames
+# have been checked. Scalar events are replayed as exact rational sparse rows.
+local_results={}
+for orientation,events in programs.items():
+    state={('L',r):{r:Q(1)} for r in range(N)}
+    cur={('L',r):new['start'][r] for r in range(N)}
+    private=set(); profile=Counter(); current_phase=None; macros=0
+    entries={r for r in range(2*V,N) if new['start'][r]!=0}
+    adapters_seen=set();residual_seen=set();last_scalar=-1;first_post=None
+    for event_index,event in enumerate(events):
+        tag=event[0]
+        if tag=='phase':current_phase=event[1];continue
+        if tag=='climb':
+            _,part,r,fr,to,rank=event
+            assert current_phase==part and cur['L',r]==fr
+            assert subspace(fr)<subspace(to) and rank==len(frames[to])-len(frames[fr])
+            cur['L',r]=to;profile[rank]+=1
+        elif tag=='center':
+            _,k,fr,to,rank=event;reg=('C',k)
+            assert current_phase=='centers' and reg in private and cur[reg]==fr
+            assert subspace(fr)<subspace(to) or subspace(to)<subspace(fr)
+            assert rank==abs(len(frames[to])-len(frames[fr]))
+            cur[reg]=to;profile[rank]+=1
+        elif tag=='adapter':
+            _,kind,r,f=event
+            assert (kind,r) not in adapters_seen;adapters_seen.add((kind,r))
+            if kind=='old_to_new':
+                assert current_phase=='entry_adapters' and r not in entries and f==new['start'][r]
+            else:
+                assert kind=='new_to_old' and current_phase=='exit_adapters' and f==new['final'][r]
+        elif tag=='residual_adapter':
+            _,kind,r,f=event
+            assert r in entries and f==new['start'][r] and (kind,r) not in residual_seen
+            residual_seen.add((kind,r))
+            if kind=='pre':assert current_phase=='entry_adapters'
+            else:
+                assert kind=='post' and current_phase=='full_frame_cleanup'
+                if first_post is None:first_post=event_index
+        elif tag=='scalar':
+            _,e,f=event;op=e[0];t=tuple(e[1]);macros+=1;last_scalar=event_index
+            if op in ('clear','copy'):
+                if op=='clear':
+                    if t in private:assert cur[t]==f;private.remove(t)
+                    state[t]={};cur[t]=f
+                else:
+                    source=tuple(e[2]);assert cur[source]==f
+                    assert not state.get(t,{}) and t not in private
+                    state[t]=state[source].copy();cur[t]=f;private.add(t)
+            else:
+                if t[0]=='C' and t not in private:
+                    assert not state.get(t,{})
+                    private.add(t);cur[t]=f
+                assert cur[t]==f,(orientation,current_phase,'target-frame',t,cur[t],f)
+                if op=='scale':
+                    q=Q(e[2],e[3]);assert q
+                    state[t]={j:q*x for j,x in state[t].items()}
+                else:
+                    assert op=='add';s=tuple(e[2]);assert t!=s and cur[s]==f
+                    q=Q(e[3],e[4]);row=state[t]
+                    for j,x in tuple(state[s].items()):
+                        z=row.get(j,Q(0))+q*x
+                        if z:row[j]=z
+                        else:row.pop(j,None)
+        else:raise AssertionError(('unknown local event',tag))
+    assert not private and all(not row for reg,row in state.items() if reg[0]=='C')
+    assert adapters_seen=={('old_to_new',r) for r in range(N) if r not in entries}|{('new_to_old',r) for r in range(N)}
+    assert residual_seen=={(kind,r) for kind in ('pre','post') for r in entries}
+    assert first_post is not None and first_post>last_scalar
+    for r in range(N):
+        desired={r:Q(1)}
+        if orientation=='forward' and V<=r<2*V:desired[r-V]=Q(1)
+        if orientation=='backward' and r<V:desired[V+r]=Q(-1)
+        assert state['L',r]==desired,(orientation,r)
+        assert cur['L',r]==new['final'][r]
+    local_results[orientation]={'events':len(events),'scalar_macros':macros,'columns':N,'profile':dict(sorted(profile.items()))}
+assert set(local_results)=={'forward','backward'}
+local=Counter(local_results['forward']['profile'])
+assert local==Counter(local_results['backward']['profile'])
+assert local==Counter({int(r):n for r,n in new['local_profile'].items()})
+widths=[H-len(frames[new['start'][2*V+h]]) for h in range(R)]
+assert widths==[H-len(old['frames'][old['start'][2*old['v']+h]]) for h in range(R)], 'bind every width to freshly reconstructed source522'
+old_adapters=read(a.original_base/'split-centres/RESIDUAL-ADAPTERS.json')['recipes']
+new_adapters=read(a.local/'RESIDUAL-ADAPTERS.json')['recipes']
+for f in {new['start'][2*V+h] for h,w in enumerate(widths) if w<H}:
+    assert new_adapters[str(f)]==old_adapters[str(f)]
+
+# Derive the complete invocation order directly from its controller formula.
+order=sorted(((s,rep) for s in range(9) for rep in range(T)),key=lambda z:(7*z[0]+6*z[1],z[0],z[1]))
+pos_call={}; timeline=[]; blocks={};s=None
+for event in parent['execution_schedule']:
+    if event['kind'] in ('bank_padding_cover_sweep','translate_every_live_family'):continue
+    if event['kind']=='local_cover_sweep':s=event['stage'];blocks[s]=[]
+    assert s is not None;blocks[s].append(event)
+for tm,(stage,rep) in enumerate(order):
+    for e in blocks[stage]:
+        if e['kind']=='local_cover_sweep':pos_call[stage,rep]=len(timeline)
+        timeline.append((rep,e))
+assert len(pos_call)==72
+stage_pairs={e['stage']:e['pair'] for e in parent['recipe'] if e['kind']=='local'}
+child_rank={}
+for child in parent['idle_children']:
+    i=child['child'];r=child['rank']
+    assert i not in child_rank or child_rank[i]==r
+    child_rank[i]=r
+child_pair={};child_side={};windows={};last_touch={}
+for pos,(rep,e) in enumerate(timeline):
+    kind=e['kind']
+    if kind=='local_cover_sweep':last_touch[rep,stage_pairs[e['stage']]]=pos
+    elif kind=='bridge':
+        last_touch[rep,e['src']]=pos;last_touch[rep,e['dst']]=pos
+    elif kind=='idle_cover_sweep':
+        pair=e['pair']
+        for side,i in enumerate(e['child_indices']):
+            if i in child_rank:
+                child_pair[i]=pair;child_side[i]=side
+                windows[rep,i]=(last_touch.get((rep,pair),-1),pos)
+assert len(windows)==T*len(child_rank)
+
+# Construct the actual orthogonal port charts by a transvection. Each chosen
+# pending vector is checked as a vector, not merely a nominal offset.
+phase_by_q={z['q']:z for z in phase['recipes']}
+assert len(phase_by_q)==120
+charts=[];idle_vectors={}
+for port,q in enumerate(new['ports']):
+    z=next(i for i in range(H) if not(q>>i)&1)
+    a0=q^(1<<z);assert a0.bit_count()%2==0
+    local_order=[z]+[i for i in range(H) if i!=z]
+    # Only q needs to be first. Match the inherited chart's remaining order
+    # by swapping z with 0, which is part of the fixed chart convention.
+    local_order=list(range(H));local_order[0],local_order[z]=local_order[z],local_order[0]
+    B=[(1<<i)^(a0 if (a0>>i)&1 else 0) for i in local_order]+[1<<i for i in range(H,M)]
+    assert B[0]==q and len(set(B))==M
+    assert all(((x&y).bit_count()&1)==int(i==j) for i,x in enumerate(B) for j,y in enumerate(B))
+    charts.append(B)
+    pr=phase_by_q[q]
+    for i,rank in child_rank.items():
+        axes=pr['idle_children'][i]['orthogonal_axes']
+        assert len(axes)==rank==pr['idle_children'][i]['rank'] and all(x in B for x in axes)
+        assert len(set(axes))==rank
+        idle_vectors[port,i]=axes
+
+# Every complete invocation contains all active data owners and exactly one
+# assigned whole physical owner for every helper. Check full-family exclusion.
+by_call=defaultdict(list);used=defaultdict(set);role_ids=set();family_roles=Counter();chart_hashes=set()
+for role in roles:
+    s,rep,h=role['stage'],role['replica'],role['helper']
+    assert (s,rep,h) not in role_ids;role_ids.add((s,rep,h))
+    assert 0<=h<R and role['time']==order.index((s,rep))
+    fam=role['family'];orep,remainder=divmod(fam,8*V)
+    pairside,port=divmod(remainder,V);pair,side=divmod(pairside,2)
+    assert 0<=orep<T and role['owner_replica']==orep and role['port']==port
+    assert role['copy']==orep*V+port
+    i=role['child'];off=role['offset'];width=role['width']
+    assert pair==child_pair[i] and side==child_side[i]
+    assert width==widths[h] and 0<=off and off+width<=child_rank[i]
+    lo,hi=windows[orep,i];assert lo<pos_call[s,rep]<hi
+    occupied=set(range(off,off+width));key=(orep,i,port)
+    assert not used[key]&occupied
+    used[key]|=occupied;family_roles[fam]+=1;by_call[s,rep].append(fam)
+    B=charts[port];actual=idle_vectors[port,i][off:off+width]
+    assert len(actual)==width
+    first=[B.index(x) for x in actual]
+    spectators=[j for j in range(M) if j not in first][:H-width]
+    orderB=first+spectators+[j for j in range(M) if j not in first+spectators]
+    assert len(orderB)==len(set(orderB))==M and len(first+spectators)==H
+    sigma=[B[j] for j in orderB]
+    assert sigma[:width]==actual
+    # All pairwise products inherit the already checked orthonormal basis.
+    assert len(set(sigma))==M and set(sigma)==set(B)
+    chart_hashes.add(hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest())
+assert role_ids=={(s,rep,h) for s in range(9) for rep in range(T) for h in range(R)}
+for (s,rep),helpers in by_call.items():
+    active={rep*(8*V)+(2*stage_pairs[s]+side)*V+p for side in (0,1) for p in range(V)}
+    assert len(active)==2*V and len(helpers)==R and len(set(helpers))==R
+    assert not active&set(helpers)
+    assert len(active|set(helpers))==N
+
+# Recount every paid child from the literal local programs and the unused
+# source idle axes. Never consume a nominated histogram or residual count.
+paid=Counter({r:n*len(order) for r,n in local.items()});remainders=Counter();covered=0
+for orep in range(T):
+    for port in range(V):
+        for i,rank in child_rank.items():
+            cells=used[orep,i,port]
+            assert cells==set(range(len(cells)))
+            covered+=len(cells);left=rank-len(cells)
+            assert left>=0
+            if left:paid[left]+=1;remainders[left]+=1
+stock=T*8*V;mass=sum(r*n for r,n in paid.items());deficit=M*stock-mass
+assert covered==len(order)*sum(widths)
+assert deficit==T*((9-1)*V-9*sum(len(frames[f]) for f in new['center_frames']))
+assert M*M>2*max(paid)**2
+result={
+ 'status':'PASS_INDEPENDENT_RAW_112_RESTRICTION_LOCAL_COLUMNS_CHARTS_WINDOWS_OWNERS_AND_PROFILE',
+ 'inputs':{str(p):digest(p) for p in [a.original_base/'split-centres/CANONICAL-WORD.json.gz',a.original_base/'split-centres/GLOBAL-TEMPLATE.json.gz',a.original_base/'work/complex-nine-native/DATA-PHASES.json',a.local/'CANONICAL-WORD.json.gz',a.local/'LOCAL-PROGRAMS.json.gz',a.local/'RESIDUAL-ADAPTERS.json',a.owners]},
+ 'local':local_results,'deleted_scalar_operations':dict(removed_ops),'deleted_canonical_ports':sorted(set(range(120))-set(kept)),
+ 'v':V,'helpers':R,'live':stock,'physical':stock+len(new['centers'])+R+2,
+ 'deficit':deficit,'rank_mass':mass,'paid_profile':dict(sorted(paid.items())),
+ 'residual_widths':dict(Counter(widths)),'whole_owner_roles':len(roles),'invocations':len(order),
+ 'all_owners_per_call_distinct':N,'pending_axes_covered':covered,'idle_remainders':dict(sorted(remainders.items())),
+ 'actual_orthogonal_charts':len(chart_hashes),'same_local_frames_and_residual_wrappers_as_PR514':True,
+ 'no_nominated_profile_or_windows_used':True,'no_emitter_or_hosting_checker_imported':True,
+ 'seconds':time.monotonic()-start_time,
+ 'scope':'Independent finite restriction, all rational scalar columns, nested local frames, fixed whole-owner schedule, actual port charts and paid histogram. The inherited all-size/compiler, common-label realization, precision/tape and analytic transfer interfaces remain conditions.'}
+out('INDEPENDENT112-RAW-AUDIT.json',result)
+print(json.dumps(result,indent=2))
diff --git a/research/ranksector112-async/code/audit_async_invoice.py b/research/ranksector112-async/code/audit_async_invoice.py
new file mode 100644
index 0000000000..7d1583cbfd
--- /dev/null
+++ b/research/ranksector112-async/code/audit_async_invoice.py
@@ -0,0 +1,100 @@
+"""Async PR484 scalar/prefix lowering and finite overcharge recount. OpenAI Codex.
+Reads emitted programs, canonical word and raw routes, importing no supplier code.
+Inherited all-size compiler admissibility is a condition, not inferred here.
+"""
+from pathlib import Path
+from fractions import Fraction as F
+from collections import Counter
+import gzip,json,math,hashlib
+import sys
+O=Path(sys.argv[1]);V=Path(sys.argv[2]);HOSTED=Path(sys.argv[3])
+def read(p):return json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+w=read(V/'split-centres/CANONICAL-WORD.json.gz');p=read(V/'split-centres/LOCAL-PROGRAMS.json.gz');old=read(V/'split-centres/GLOBAL-TEMPLATE.json.gz');new=read(HOSTED/'GLOBAL-TEMPLATE.json.gz');integ=read(V/'split-centres/INTEGRATION.json');checks=read(V/'split-centres/LOCAL-CHECKS.json');prior=read(V/'split-centres/INDEPENDENT-REPLAY.json');owners=read(O/'OWNERS-AND-PROFILE.json')
+VV=w['v'];R=w['R'];N=2*VV+R;M=73;L=9;T=8;K=4
+assert VV==112 and w['h']==9
+PAYLOAD=512
+control=read(O/'ASYNC-AUDIT.json')
+raw=gzip.decompress((HOSTED/'GLOBAL-TEMPLATE.json.gz').read_bytes());th=hashlib.sha256(raw).hexdigest()
+assert th==control['complex_template_sha256']==owners['template_sha256']
+assert control['one_owner_per_complete_invocation'] and control['complete_invocations']==72
+assert new['local_programs']==old['local_programs'] and new['recipe']==old['recipe']
+assert Counter(c['orientation']for c in new['calls'])==Counter(c['orientation']for c in old['calls'])
+local={}
+for ori,evs in p.items():
+ rows={('L',i):{i:F(1)}for i in range(N)};env={('L',i):F(1)for i in range(N)};peak=F(1);real=macros=0;paid=Counter();workops=0
+ for e in evs:
+  if e[0]=='climb':paid[e[5]]+=1
+  elif e[0]=='center':paid[e[4]]+=1
+  elif e[0]=='scalar':
+   macros+=1;x=e[1];op=x[0];a=tuple(x[1]);count=0
+   if op=='clear':rows[a]={};env[a]=F(0);count=1
+   elif op=='copy':rows[a]=dict(rows[tuple(x[2])]);env[a]=env[tuple(x[2])];count=1
+   elif op=='scale':
+    q=F(x[2],x[3]);num,den=abs(q.numerator),q.denominator
+    assert num and num&(num-1)==0 and den&(den-1)==0
+    rows[a]={j:q*v for j,v in rows[a].items()};env[a]*=abs(q)
+    count=abs(num.bit_length()-den.bit_length())+int(q<0)
+   elif op=='add':
+    b=tuple(x[2]);q=F(x[3],x[4]);num,den=abs(q.numerator),q.denominator
+    assert a!=b and num>0 and den&(den-1)==0
+    # Lower actual coefficient to cleared Horner work. Every intermediate
+    # magnitude envelope is explicitly included, before denominator halvings.
+    acc=0;count=1
+    for i,ch in enumerate(bin(num)[2:]):
+     if i:acc*=2;count+=1;peak=max(peak,acc*env[b])
+     if ch=='1':acc+=1;count+=1;peak=max(peak,acc*env[b])
+    v=F(acc)
+    for i in range(den.bit_length()-1):v/=2;count+=1;peak=max(peak,v*env[b])
+    assert v==abs(q);count+=2 # signed accumulation and private work clear
+    env[a]=env.get(a,F(0))+abs(q)*env[b];rr=rows.setdefault(a,{})
+    for j,z in list(rows[b].items()):
+     value=rr.get(j,F(0))+q*z
+     if value:rr[j]=value
+     else:rr.pop(j,None)
+    workops+=count
+   else:raise AssertionError(op)
+   real+=2*count;peak=max(peak,env[a])
+ assert all(not row for reg,row in rows.items()if reg[0]=='C')
+ for i in range(N):
+  expected={i:F(1)}
+  if ori=='forward'and VV<=i<(2*VV):expected[i-VV]=F(1)
+  if ori=='backward'and i<VV:expected[i+VV]=F(-1)
+  assert rows['L',i]==expected
+ assert peak==F(prior['local'][ori]['prefix_l1_upper']) and peak<2**192
+ assert real==checks[ori]['real_component_primitive_bound']and macros==checks[ori]['scalar_macros']
+ assert dict(paid)=={int(r):z for r,z in checks[ori]['paid_profile'].items()}
+ local[ori]=dict(events=len(evs),macros=macros,real_component_primitives=real,prefix_l1=str(peak),prefix_bits=peak.numerator.bit_length()-peak.denominator.bit_length()+1,coefficient_work_primitive_count=workops,all_exact_columns=N,all_560_dirty_helper_columns_restored=True,private_centres_and_coefficient_work_cleared=True)
+centres=len(w['centers']);widths=[9-len(w['frames'][f])for f in w['start'][(2*VV):]];enter=sum(x<9 for x in widths)
+children=sum(checks['forward']['paid_profile'].values());macros=max(x['macros']for x in local.values());compiler=64*(M+1)**3
+adapters=16*(macros+children+N+centres)+64*M
+primitive_bound=max(x['real_component_primitives']for x in local.values())+adapters*compiler
+bridges=sum(e['kind']=='bridge'for e in old['recipe']);bridgeadd=2*VV*T*bridges;assert sum(e['kind']=='bridge'for e in new['execution_schedule'])==T*bridges
+shifts=K*VV*T;moves=2*K*VV*T
+oldW=old['live'];oldP=old['physical'];oldNB=(oldW-2*VV*K*T)//L
+scalar=sum(local[c['orientation']]['real_component_primitives']for c in old['calls'])
+nonlocal_items=4*VV*T*L+2*VV*T*L+2*L*T*R+sum(e['replicas']for e in old['idle_children'])+L*oldNB+bridgeadd+shifts+moves+oldW+oldP+2*L*T*enter*144
+outside=8*nonlocal_items+64*M
+pervertex=scalar+bridgeadd+shifts+moves+oldW+(72*adapters+outside)*compiler+64*oldP
+invoice=integ['finite_invoice'];assert (primitive_bound,adapters,pervertex,compiler)==(invoice['local_primitive_bound'],invoice['local_adapters'],invoice['pervertex'],invoice['compiler'])
+# Independent hosted stock rebase, retaining the larger unhosted operation
+# overcharge; only the stock and mass in the common router/literal change.
+W=new['live'];P=new['physical'];mass=owners['rank_mass'];profile=owners['paid_profile']
+assert M*W-mass==2560 and P==W+R+centres+2
+rebase=pervertex-oldP*65+P*65-oldW+W;used=max(rebase,pervertex)
+r=M//2;group=2**(r*r)
+for i in range(1,r+1):group*=2**(2*i)-1
+stock=group*P;smass=group*mass;logical=group*used+64;router=compiler*(logical+1)*(stock+1)**2
+G,E,C0=2**30000,2**100000,2**210000;B=smass+E;literal=2*G*stock**2+8*smass+4*stock+4+32*M;row=2*stock.bit_length()+9909+252+2*PAYLOAD;maxchild=max(map(int,profile))
+ineq=dict(local_primitive_bound=primitive_bound<2**48,logical=logical<2**6050,router=router<G,literal=literal<E,mass=B<2**100001,precision=32*M*B*B<C0,tape=2*B+18<C0,row=row<20161,halving=M*M>2*maxchild*maxchild)
+assert all(ineq.values())
+localbits=max(x['prefix_bits']for x in local.values());input_l2_bits=(M+1)//2
+bridge_sweeps=sum(e['kind']=='bridge'for e in new['execution_schedule'])
+required_prefix=localbits+input_l2_bits+len(new['calls'])+bridge_sweeps+4
+assert localbits==25 and bridge_sweeps==72 and required_prefix==210 and required_prefix<PAYLOAD
+assert owners['explicit_idle_remainder_children']<=owners['source_idle_children_charged']
+assert new['physical']<=old['physical'] and new['live']<=old['live'] and not new['bank_padding']['families']
+out=dict(status='PASS_INDEPENDENT_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE',template_sha256=th,global_prefix_bits=required_prefix,charged_prefix_bits=PAYLOAD,complete_invocation_sweeps=72,bridge_sweeps=bridge_sweeps,row_prefix_extra=2*PAYLOAD,local=local,entering_helpers=enter,entrance_rank=sum(9-x for x in widths),local_adapters=adapters,local_primitive_bound=primitive_bound,wrapper_elementary_factors_charged=2*72*enter*144,compiler=compiler,unhosted_pervertex=pervertex,hosted_rebased_pervertex=rebase,conservative_pervertex_used=used,finite=dict(physical_stock_bits=stock.bit_length(),router_bits=router.bit_length(),literal_bits=literal.bit_length(),physical_row_coefficient=row,retained_row_coefficient=20161,required_C0_bits=(32*M*B*B).bit_length(),halving_integer_inequality=[M*M,2*maxchild*maxchild],G_exponent=30000,E_exponent=100000,C0_exponent=210000),strict_checks=ineq,scope='Exact finite recount conditional on inherited all-size compiler/precision/tape and analytic-transfer contracts. Signed accumulation uses the supplier scalar primitive convention. Async prefix counts all72individual bridges and72complete invocations;512bits are charged, and an additional2*512 enters the two-level physical row bound.')
+(O/'PREFIX-AND-INVOICE.json').write_text(json.dumps(out,indent=2)+'\n');print(json.dumps(out,indent=2),flush=True)
+
+prefix=dict(status='PASS_ASYNC_GLOBAL_PREFIX',template_sha256=th,global_prefix_bits=required_prefix,retained_payload_bits=PAYLOAD,complete_invocation_cover_sweeps=len(new['calls']),bridge_factor_two_sweeps=bridge_sweeps,local_scalar_coefficient_work_prefix_bits=localbits,stream_input_sup_to_l2_bits=input_l2_bits,primitive_arithmetic_margin_bits=4,controller_audit_sha256=hashlib.sha256((O/'ASYNC-AUDIT.json').read_bytes()).hexdigest(),proof=f'Each complete normalized invocation has unitary helper endpoints and a data shear with at most two unitary summands. Distinct full orthogonal owner charts act by right-translation bijections on the retained cover group. Thus the maximum full-stream L2 norm grows by at most2per complete local cover sweep and individual bridge. All72local sweeps and72individual bridge sweeps are counted. Unit-modulus phases, idle children, terminal translations and normalized spectator endpoints are unitary. The independently replayed scalar/Horner envelope costs {localbits} bits, initial sup-to-L2 conversion {input_l2_bits} bits, primitive margin 4 bits: total {required_prefix} < {PAYLOAD}. All-size child/compiler and precision/tape interfaces remain inherited.')
+(O/'GLOBAL-PREFIX.json').write_text(json.dumps(prefix,indent=2)+'\n')
diff --git a/research/ranksector112-async/code/audit_global_restriction.py b/research/ranksector112-async/code/audit_global_restriction.py
new file mode 100644
index 0000000000..3fafe9fbf0
--- /dev/null
+++ b/research/ranksector112-async/code/audit_global_restriction.py
@@ -0,0 +1,307 @@
+"""Independently check the 112-port global data restriction of PR514.
+
+Uses only the serialized old/new artifacts and the Python standard library.
+Imports neither the restriction emitter nor the local/global emitters.
+Usage: python audit_global_restriction.py OLD_BASE NEW_BASE REPORT.json
+
+The verified object here is the restricted data/controller interface.  The
+final complete whole-owner placement and its finite invoice are separate
+audits.  In particular, no execution of the parent's obsolete rank-one-only
+bank-padding display field is asserted here.
+"""
+from pathlib import Path
+from collections import Counter
+import argparse
+import copy
+import gzip
+import hashlib
+import json
+import sys
+
+
+def need(condition, message):
+    if not condition:
+        raise AssertionError(message)
+
+
+def read(path):
+    data = path.read_bytes()
+    return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data)
+
+
+def filehash(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def objhash(value):
+    return hashlib.sha256(json.dumps(value, sort_keys=True,
+                                    separators=(',', ':')).encode()).hexdigest()
+
+
+parser = argparse.ArgumentParser(description=__doc__,
+                                 formatter_class=argparse.RawDescriptionHelpFormatter)
+parser.add_argument('old_base', type=Path, help='Replayed pinned PR514 base directory')
+parser.add_argument('new_base', type=Path, help='Restricted 112-port base directory')
+parser.add_argument('report', type=Path, help='Destination JSON audit receipt')
+args = parser.parse_args()
+if sys.version_info < (3, 10):
+    parser.error('Python 3.10 or later is required for exact integer bit_count')
+OLD, NEW, REPORT = (p.resolve() for p in (args.old_base, args.new_base, args.report))
+OS, NS = OLD / 'split-centres', NEW / 'split-centres'
+old = read(OS / 'GLOBAL-TEMPLATE.json.gz')
+oldcan = read(OS / 'CANONICAL-WORD.json.gz')
+oldphase = read(OLD / 'work/complex-nine-native/DATA-PHASES.json')
+can = read(NS / 'CANONICAL-WORD.json.gz')
+checks = read(NS / 'LOCAL-CHECKS.json')
+programs = read(NS / 'LOCAL-PROGRAMS.json.gz')
+local_replay = read(NS / 'INDEPENDENT-REPLAY.json')
+local_phase = read(NS / 'CLIFFORD-REVIEW.json')
+restriction = read(NS / 'RESTRICTION.json')
+transport = read(NS / 'TRANSPORT.json')
+state = dict(template=read(NS / 'GLOBAL-TEMPLATE.json.gz'),
+             phase=read(NEW / 'work/complex-nine-native/DATA-PHASES.json'),
+             mapping=read(NS / 'PORT-MAPPING.json'),
+             invoice=read(NS / 'INTEGRATION.json'))
+
+bindings = {
+    'canonical': filehash(NS / 'CANONICAL-WORD.json.gz'),
+    'canonical_content': hashlib.sha256(gzip.decompress((NS / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest(),
+    'programs': filehash(NS / 'LOCAL-PROGRAMS.json.gz'),
+    'local_phase': filehash(NS / 'CLIFFORD-RECIPES.json'),
+    'adapters': filehash(NS / 'RESIDUAL-ADAPTERS.json'),
+    'old_template': filehash(OS / 'GLOBAL-TEMPLATE.json.gz'),
+    'old_template_content': hashlib.sha256(gzip.decompress((OS / 'GLOBAL-TEMPLATE.json.gz').read_bytes())).hexdigest(),
+    'old_phase': filehash(OLD / 'work/complex-nine-native/DATA-PHASES.json'),
+    'phase': filehash(NEW / 'work/complex-nine-native/DATA-PHASES.json'),
+}
+need(local_replay['canonical_word_sha256'] == local_phase['canonical_word_sha256']
+     == transport['canonical_sha256'] == bindings['canonical'],
+     'Local independent receipts must bind this canonical word')
+need(local_replay['local_programs_sha256'] == bindings['programs'],
+     'Local replay must bind this expanded program')
+need(local_phase['recipe_sha256'] == bindings['local_phase']
+     and local_phase['all_child_equalities_include_global_phase'],
+     'Local phase receipt must include the scalar phase')
+need(transport['independently_recomputed_helper_compensations_match'] == len(can['compensation']) == len(oldcan['compensation']),
+     'Arbitrary helper dirt transport was not independently certified')
+for orientation, program in programs.items():
+    need(objhash(program) == checks[orientation]['sha256'], 'Local program hash')
+    need(local_replay['local'][orientation]['all_exact_columns'] == 784
+         and local_replay['local'][orientation]['private_work_erased'],
+         'Local replay must cover all data/helper columns and cleanup')
+    need(local_replay['paid_profiles'][orientation]
+         == checks[orientation]['paid_profile'], 'Local paid profiles')
+
+
+def audit(s):
+    t, ph, mp, inv = (s[k] for k in ('template', 'phase', 'mapping', 'invoice'))
+    nto = mp['new_to_old']
+    omitted = [i for i in range(120) if i not in nto]
+    need(len(nto) == len(set(nto)) == 112 and nto == sorted(nto), 'Port injection')
+    need(omitted == [0, 13, 22, 35, 40, 51, 54, 119], 'Exactly the eight axis ports')
+    need(omitted == restriction['removed_canonical_source_indices'], 'Local/global selection')
+    need({str(p): i for i, p in enumerate(nto)} == mp['old_to_new'], 'Inverse port map')
+    otn = {p: i for i, p in enumerate(nto)}
+    need((can['h'], can['v'], can['R'], len(can['centers'])) == (9, 112, 560, 8),
+         'Local dimensions and private center count')
+    need(can['ports'] == [oldcan['ports'][p] for p in nto], 'Actual binary port labels')
+    need(can['frames'] == oldcan['frames']
+         and can['start'][224:] == oldcan['start'][240:]
+         and can['final'][224:] == oldcan['final'][240:], 'Helper frames unchanged')
+    need(t['m'] == 73 and (t['live'], t['physical']) == (12208, 12778),
+         'Live and private stock')
+    need(t['private_namespace'] == dict(centers=[12208, 12216],
+                                      reserved_tableau=[12216, 12776],
+                                      coefficient=[12776, 12778]), 'Private ranges')
+    need(t['local_programs'] == programs, 'Use the new verified local program')
+    for key in ('recipe', 'loop_order', 'cover', 'adapter_policy', 'route_semantics',
+                'expanded_scalar_interface'):
+        need(t[key] == old[key], 'Inherited controller field ' + key)
+    need('each local invocation completes before the next' in t['loop_order'].lower(),
+         'Complete invocations must remain indivisible')
+    need(t['exact_data_phase_recipe_sha256'] == bindings['phase']
+         and t['exact_local_clifford_recipe_sha256'] == bindings['local_phase']
+         and t['residual_adapter_sha256'] == bindings['adapters'], 'Global recipe hashes')
+    provenance = t['port_restriction']
+    need(provenance['new_to_old'] == nto
+         and provenance['parent_global_template_content_sha256'] == bindings['old_template_content']
+         and provenance['parent_data_phase_sha256'] == bindings['old_phase']
+         and provenance['canonical_word_content_sha256'] == bindings['canonical_content'], 'Provenance')
+
+    # The old polynomial verification applies to each selected literal recipe.
+    # This comparison includes every axis, every Z4 translation, and the
+    # terminal correction; it is stronger than comparing only rank histograms.
+    need(ph['m'] == 73 and ph['ports'] == 112 and len(ph['recipes']) == 112,
+         'Data phase dimensions')
+    for key in ('status', 'cover_correction', 'global_phase_argument'):
+        need(ph[key] == oldphase[key], 'Inherited phase statement ' + key)
+    need(ph['source_parent_sha256'] == bindings['old_phase'], 'Parent phase provenance')
+    for p, op in enumerate(nto):
+        got = copy.deepcopy(ph['recipes'][p])
+        need(got['port'] == p and got['q'] == can['ports'][p], 'Phase port labels')
+        got['port'] = op
+        need(got == oldphase['recipes'][op], 'Exact per-port phase recipe restriction')
+        q = can['ports'][p]
+        z = next(i for i in range(9) if not ((q >> i) & 1))
+        a = q ^ (1 << z)
+        order = list(range(9))
+        order[0], order[z] = order[z], order[0]
+        basis = [(1 << i) ^ (a if (a >> i) & 1 else 0) for i in order]
+        basis += [1 << i for i in range(9, 73)]
+        need(all(((x & y).bit_count() & 1) == (i == j)
+                 for i, x in enumerate(basis) for j, y in enumerate(basis)),
+             'Orthogonal 73-dimensional port chart')
+        for child in got['idle_children']:
+            axes = child['orthogonal_axes']
+            need(len(axes) == len(set(axes)) == child['rank']
+                 and set(axes) <= set(basis), 'Literal idle child axes')
+    need(ph['terminal_omission_controls_rejected'] == 112, 'Terminal control count')
+
+    # The source event list acts separately at every port after a complete
+    # verified local invocation.  Preserve all events and all replica order.
+    schedule = copy.deepcopy(old['execution_schedule'])
+    correction = dict(old['cover_final_correction'], families=[0, 12208],
+                      charged_calls_per_cover=12208)
+    for event in schedule:
+        if event['kind'] == 'bank_padding_cover_sweep':
+            event['families'] = [7168, 12208]
+        elif event['kind'] == 'translate_every_live_family':
+            event.update(correction)
+    need(t['execution_schedule'] == schedule and t['cover_final_correction'] == correction,
+         'Exact inherited event order and terminal cover correction')
+    want_idle = []
+    for child in old['idle_children']:
+        if child['port'] in otn:
+            want_idle.append(dict(child, port=otn[child['port']]))
+    need(t['idle_children'] == want_idle and len(want_idle) == 2016,
+         'Every selected idle child with unchanged multiplicity')
+    need(t['bank_padding'] == dict(old['bank_padding'], families=list(range(7168, 12208))),
+         'Inherited bank metadata and exact renumbering')
+
+    need(len(t['calls']) == len(old['calls']) == 72, 'Number of complete invocations')
+    need([(c['stage'], c['replica']) for c in t['calls']]
+         == [(s, r) for s in range(9) for r in range(8)], 'Invocation order')
+    bank_cells = {}
+    paid = Counter()
+    helper_roles = 0
+    data_roles = 0
+    for call, parent in zip(t['calls'], old['calls']):
+        for key in ('orientation', 'stage', 'replica', 'pair', 'window'):
+            need(call[key] == parent[key], 'Inherited call ' + key)
+        need(call['local_program_sha256'] == checks[call['orientation']]['sha256'],
+             'Call-local word binding')
+        owners = call['owners']
+        need(len(owners) == 784, 'Local owner count')
+        rep, pair, stage = (call[k] for k in ('replica', 'pair', 'stage'))
+        for side in range(2):
+            for p, op in enumerate(nto):
+                need(owners[112 * side + p]
+                     == [896 * rep + 112 * (2 * pair + side) + p, [1, stage, p]],
+                     'Literal new data family')
+                need(parent['owners'][120 * side + op]
+                     == [960 * rep + 120 * (2 * pair + side) + op, [1, stage, op]],
+                     'Literal source data family')
+                data_roles += 1
+        multiplicities = Counter(f for f, route in owners)
+        for h, (family, route) in enumerate(owners[224:]):
+            oldfamily, oldroute = parent['owners'][240 + h]
+            need(family == oldfamily - 512 and route == oldroute, 'Helper bank route unchanged')
+            need(7168 <= family < 12208, 'Bank owner stock bounds')
+            width = 9 - len(can['frames'][can['start'][224 + h]])
+            need(route[0] == 2, 'Bank routing kind')
+            if width < 9:
+                need(multiplicities[family] == 1, 'Entering helper has one whole owner')
+                need(len(route) == 4 and route[2] == width
+                     and len(route[3]) == 9 - width, 'Entering width and spectators')
+            off = 9 * route[1] if len(route) == 2 else route[1]
+            cells = set(range(off, off + width))
+            need(0 <= off and off + width <= 73, 'Bank residual interval')
+            previous = bank_cells.setdefault(family, set())
+            need(not previous & cells, 'Disjoint bank residual intervals')
+            previous.update(cells)
+            helper_roles += 1
+        paid.update({int(r): n for r, n in checks[call['orientation']]['paid_profile'].items()})
+    need(helper_roles == 40320 and data_roles == 16128, 'All literal owner roles')
+    need(set(bank_cells) == set(range(7168, 12208)), 'Every retained bank accounted for')
+    pads = Counter()
+    for cells in bank_cells.values():
+        need(cells == set(range(len(cells))), 'Bank used cells form the literal prefix')
+        leftover = 73 - len(cells)
+        need(0 < leftover <= 51, 'One legal complementary bank child suffices')
+        pads[leftover] += 1
+    old_bank_cells = {}
+    for original_call in old['calls']:
+        for h, (family, route) in enumerate(original_call['owners'][240:]):
+            width = 9 - len(oldcan['frames'][oldcan['start'][240 + h]])
+            offset = 9 * route[1] if len(route) == 2 else route[1]
+            cells = set(range(offset, offset + width))
+            previous = old_bank_cells.setdefault(family, set())
+            need(not previous & cells, 'Original bank residuals must be disjoint')
+            previous.update(cells)
+    expected_pads = Counter(73 - len(cells) for cells in old_bank_cells.values())
+    need(pads == expected_pads, 'Actual bank spectrum must equal source522 literal bank routes')
+    paid.update(pads)
+    for child in t['idle_children']:
+        need(child['rank'] == ph['recipes'][child['port']]['idle_children'][child['child']]['rank'],
+             'Paid idle rank equals literal phase recipe')
+        paid[child['rank']] += child['replicas']
+    mass = sum(r * n for r, n in paid.items())
+    need(mass == 888624 and 73 * 12208 - mass == 2560, 'Unhosted rank-mass identity')
+    need(inv['live'] == 12208 and inv['physical'] == 12778
+         and inv['rank_mass'] == mass and inv['deficit'] == 2560,
+         'Invoice stock and rank mass')
+    need(inv['global_profile'] == {str(r): n for r, n in paid.items()}
+         and inv['bank_remainder_profile'] == {str(r): n for r, n in pads.items()},
+         'Invoice must use literal remainders, not obsolete bank display rank')
+    return dict(retained_ports=112, deleted_canonical_ports=omitted, data_owner_roles=data_roles,
+                helper_owner_roles=helper_roles, complete_invocations=72,
+                exact_port_phase_recipes=112, exact_stage_alignments=1008,
+                exact_idle_axis_recipes=2240, paid_idle_children=2016,
+                replicated_paid_idle_children=sum(x['replicas'] for x in want_idle),
+                bank_families=5040, bank_remainder_profile=dict(sorted(pads.items())),
+                unhosted_paid_profile=dict(sorted(paid.items())),
+                unhosted_rank_mass=mass, unhosted_live=12208, unhosted_physical=12778,
+                deficit=2560)
+
+
+result = audit(state)
+need(objhash(state['template']) == state['invoice']['global_template_sha256'],
+     'Invoice template content hash')
+controls = []
+
+
+def reject(name, mutation):
+    changed = copy.deepcopy(state)
+    mutation(changed)
+    try:
+        audit(changed)
+    except (AssertionError, KeyError, IndexError, ValueError, TypeError):
+        controls.append(name)
+    else:
+        raise AssertionError('Accepted negative control: ' + name)
+
+
+reject('duplicate selected port', lambda s: s['mapping']['new_to_old'].__setitem__(0, 2))
+reject('wrong phase port label', lambda s: s['phase']['recipes'][0].__setitem__('q', 1))
+reject('wrong inherited idle axis', lambda s: s['phase']['recipes'][0]['idle_children'][0]['orthogonal_axes'].__setitem__(0, 1))
+reject('missing terminal port correction', lambda s: s['phase']['recipes'][0].__setitem__('terminal_Y_translation', 0))
+reject('wrong data owner family', lambda s: s['template']['calls'][0]['owners'][0].__setitem__(0, 1))
+reject('wrong canonical data route', lambda s: s['template']['calls'][0]['owners'][0][1].__setitem__(2, 1))
+reject('stale local program hash', lambda s: s['template']['calls'][0].__setitem__('local_program_sha256', 'old'))
+reject('changed entering bank owner', lambda s: s['template']['calls'][0]['owners'][224].__setitem__(0, 7168))
+reject('missing complete invocation', lambda s: s['template']['calls'].pop())
+reject('missing paid idle child', lambda s: s['template']['idle_children'].pop())
+reject('missing cover correction', lambda s: s['template']['execution_schedule'].pop())
+reject('understated private reserve', lambda s: s['template'].__setitem__('physical', 12777))
+reject('unpaid bank remainder', lambda s: s['invoice']['global_profile'].__setitem__('17', 0))
+
+report = dict(status='PASS_INDEPENDENT_GLOBAL_DATA_PORT_RESTRICTION',
+              **result, source_bindings=bindings, negative_controls_rejected=controls,
+              local_scalar_replay_receipt_sha256=filehash(NS / 'INDEPENDENT-REPLAY.json'),
+              local_phase_receipt_sha256=filehash(NS / 'CLIFFORD-REVIEW.json'),
+              template_content_sha256=objhash(state['template']),
+              scope='Exact restriction of all inherited global data routes, phase recipes, complete-call order, idle axes and terminal corrections. Local arbitrary-dirt identities are supplied by the newly hash-bound independent local replay. Actual bank remainders are recounted for the conservative parent invoice. Final whole-owner placement, executable global program, finite compilation and outer exponent require their separate fresh audits.')
+REPORT.parent.mkdir(parents=True, exist_ok=True)
+REPORT.write_text(json.dumps(report, indent=2) + '\n')
+print(json.dumps({k: report[k] for k in ('status', 'retained_ports', 'data_owner_roles',
+      'helper_owner_roles', 'unhosted_rank_mass', 'deficit', 'negative_controls_rejected')}, indent=2))
diff --git a/research/ranksector112-async/code/transport_owners.py b/research/ranksector112-async/code/transport_owners.py
new file mode 100644
index 0000000000..2987070140
--- /dev/null
+++ b/research/ranksector112-async/code/transport_owners.py
@@ -0,0 +1,32 @@
+"""Transport PR523 slots to PR522 widths, retaining whole-family ownership.
+Discovery only; run the independent physical verifier on the result.
+"""
+from pathlib import Path
+from collections import defaultdict,Counter
+import json,gzip,hashlib,sys
+SOURCE,LOCAL,OUT=map(Path,sys.argv[1:4]);OUT.mkdir(exist_ok=False)
+read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+plan=read(SOURCE/'inputs/ASYNC112-PLAN.json');roles=read(SOURCE/'inputs/OWNERS112.json.gz');can=read(LOCAL/'CANONICAL-WORD.json.gz');v=can['v'];widths=[can['h']-len(can['frames'][f])for f in can['start'][2*v:]];oldwidths=plan['baseline_widths'];assert all(a<=b for a,b in zip(sorted(widths),sorted(oldwidths)))
+bycall=defaultdict(list);groups=defaultdict(list)
+for z in roles:bycall[z['time']].append(z);groups[z['owner_replica'],z['child'],z['port']].append(z)
+left={g:plan['windows'][f'{g[0]},{g[1]}'][0]-sum(z['width']for z in zs)for g,zs in groups.items()}
+for t,zs in sorted(bycall.items()):
+ avail=list(zs)
+ for h in sorted(range(len(widths)),key=lambda h:(-widths[h],h)):
+  w=widths[h];possible=[z for z in avail if z['width']>=w];assert possible
+  def key(z):
+   g=z['owner_replica'],z['child'],z['port'];return(z['width']-w,left[g]if z['width']==w else-left[g],z['family'])
+  z=min(possible,key=key);avail.remove(z);g=z['owner_replica'],z['child'],z['port'];left[g]+=z['width']-w;z['helper']=h;z['width']=w
+ assert not avail and len({z['family']for z in zs})==len(widths)
+for g,zs in groups.items():
+ off=0
+ for z in sorted(zs,key=lambda z:z['offset']):z['offset']=off;off+=z['width']
+ assert off<=plan['windows'][f'{g[0]},{g[1]}'][0]
+H=Counter({int(r):len(plan['order'])*n for r,n in can['local_profile'].items()})
+for k,(rank,window)in plan['windows'].items():
+ rep,child=map(int,k.split(','))
+ for port in range(v):
+  remainder=rank-sum(z['width']for z in groups.get((rep,child,port),[]))
+  if remainder:H[remainder]+=1
+plan.update(baseline_widths=widths,profile=dict(sorted(H.items())),status='NEW_LITERAL_WIDTH_DOMINANCE_TRANSPORT_PENDING_GLOBAL_AUDIT')
+(OUT/'PLAN.json').write_text(json.dumps(plan,indent=2)+'\n');raw=json.dumps(sorted(roles,key=lambda z:(z['time'],z['helper'])),sort_keys=True,separators=(',',':')).encode();(OUT/'OWNERS.json.gz').write_bytes(gzip.compress(raw,mtime=0));print('NOMINATED',len(roles),dict(sorted(H.items())))
diff --git a/research/ranksector112-async/data/OWNERS.json.gz b/research/ranksector112-async/data/OWNERS.json.gz
new file mode 100644
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diff --git a/research/ranksector112-async/validation/COMPOSITION-RECEIPT.json b/research/ranksector112-async/validation/COMPOSITION-RECEIPT.json
new file mode 100644
index 0000000000..5feaa540f6
--- /dev/null
+++ b/research/ranksector112-async/validation/COMPOSITION-RECEIPT.json
@@ -0,0 +1,54 @@
+{
+  "status": "PASS_RANKSECTOR112_FINITE_COMPOSITION",
+  "kappa": "1467289440740487/1000000000000000000",
+  "kappa_decimal": "0.001467289440740487",
+  "complex_lower": "146944554266898896961/100000000000000000000000",
+  "complex_template_sha256": "87a2c10f5638bddbb7748803bdc0b63ed027c499bbee0e6f14edb01565adaf30",
+  "steps": [
+    {
+      "name": "restrict-global",
+      "returncode": 0,
+      "seconds": 1.0724410420516506,
+      "log_sha256": "2caf353a2ef3d9e55ac110dccb47666f9a59071929af3d795c5d5cdc34a8869d"
+    },
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+      "returncode": 0,
+      "seconds": 4.493412124924362,
+      "log_sha256": "bf554fcc690142b7af9551b5a46e9ed80421ddbe812aeea63b51dc61178fff7f"
+    },
+    {
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+      "seconds": 2.128549750079401,
+      "log_sha256": "5b4fc2c4e8f30c9374751fa5b52349eb9195267971893fe10a9f4575cad0544c"
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+      "log_sha256": "23e2810f2a33ccb8c88093029de35b3200156525c82c31df837adf09c7946ecf"
+    },
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+      "seconds": 2.2766572919208556,
+      "log_sha256": "7fe91918ee21ba0b3af80f71529d4b326781d861bf20fca5e98feb5ee7bdf918"
+    },
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+      "log_sha256": "7a05caa05a857c27d11a3e12a4e5dc4d3519c3aad15669579dbdf8bea1c72fdf"
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+      "log_sha256": "d9544803f98f1b48e57757258e46ad213d5ac4a6c5759afa09eb0433547b07a1"
+    }
+  ],
+  "source522_receipt_sha256": "3e9578a84ece9f913e3cdc9c0bc9827348f1ef2068b13dcae6e05975d898c541",
+  "local_receipt_sha256": "2489865213856e70f3d0e8bfa69bc4474e50d020738eb58fcfeb826d73631999",
+  "scope": "Fresh source522 complex replay, changed local112 checks, global restriction, independent actual whole owners, invoice and exact assembly. Bit493 operator cited/repriced; inherited all-size and analytic interfaces remain conditional."
+}
diff --git a/research/ranksector112-async/validation/LOCAL-RECEIPT.json b/research/ranksector112-async/validation/LOCAL-RECEIPT.json
new file mode 100644
index 0000000000..16c44159d8
--- /dev/null
+++ b/research/ranksector112-async/validation/LOCAL-RECEIPT.json
@@ -0,0 +1,36 @@
+{
+  "status": "PASS_RANKSECTOR112_LOCAL_ONLY",
+  "steps": [
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+      "returncode": 0,
+      "seconds": 0.1482715830206871
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+    {
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+  ],
+  "scope": "Fresh restricted local scalar transport, both orientation column/frame checks, exact phases and residual wrappers. Global ownership and exact composition remain separate."
+}
diff --git a/research/ranksector112-async/validation/PACKAGED-REPLAY.json b/research/ranksector112-async/validation/PACKAGED-REPLAY.json
new file mode 100644
index 0000000000..12f2c6660b
--- /dev/null
+++ b/research/ranksector112-async/validation/PACKAGED-REPLAY.json
@@ -0,0 +1,98 @@
+{
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+  "deficit": 2560,
+  "global_profile": {
+    "1": 177552,
+    "2": 13104,
+    "3": 40455,
+    "4": 6373,
+    "5": 20492,
+    "6": 9007,
+    "7": 183,
+    "8": 158,
+    "48": 230
+  },
+  "strict_constraints": 47,
+  "improvement_over_source522": "21692052061268/467404428185561",
+  "whole_owner_roles": 40320,
+  "all_own_stages": 13,
+  "pinned_predecessor_stages": 15,
+  "source522_mode": "byte-pinned-completed-source522-reuse",
+  "package_manifest_sha256": "61356d1ba32133b90484bd1911478083717a19db6187d80459ff3d64e6b62fcb",
+  "seconds": 125.05487037508283,
+  "steps": [
+    {
+      "stage": "02-restrict-local",
+      "exit": 0,
+      "seconds": 0.14696391695179045
+    },
+    {
+      "stage": "03-exact-word-transport",
+      "exit": 0,
+      "seconds": 0.16542383399792016
+    },
+    {
+      "stage": "04-emit-local",
+      "exit": 0,
+      "seconds": 0.46319116698578
+    },
+    {
+      "stage": "05-independent-local",
+      "exit": 0,
+      "seconds": 1.879943292005919
+    },
+    {
+      "stage": "06-exact-local-phases",
+      "exit": 0,
+      "seconds": 99.89293637499213
+    },
+    {
+      "stage": "07-residual-wrappers",
+      "exit": 0,
+      "seconds": 0.5527796249371022
+    },
+    {
+      "stage": "08-restrict-global-data",
+      "exit": 0,
+      "seconds": 1.0188599169487134
+    },
+    {
+      "stage": "09-independent-global-restriction",
+      "exit": 0,
+      "seconds": 4.497085832990706
+    },
+    {
+      "stage": "10-emit-whole-owners",
+      "exit": 0,
+      "seconds": 2.136576500022784
+    },
+    {
+      "stage": "11-independent-hosted-program",
+      "exit": 0,
+      "seconds": 10.6742982090218
+    },
+    {
+      "stage": "12-independent-raw-reconstruction",
+      "exit": 0,
+      "seconds": 2.361917416099459
+    },
+    {
+      "stage": "13-scalar-prefix-and-finite-invoice",
+      "exit": 0,
+      "seconds": 1.0109542909776792
+    },
+    {
+      "stage": "14-two-moments-and-global-assembly",
+      "exit": 0,
+      "seconds": 0.24490983306895941
+    }
+  ],
+  "scope": "Finite complex restriction, exact local phases, whole physical owners, complete fee inventory, two rational moments and 47 outer inequalities checked. The unchanged PR493 bit operator, all-size compiler, common-label/mutable-basis realization, normalized Lemma A, restored-row, precision/tape and analytic-transfer contracts remain dependencies. No unconditional theorem or new Lean certification."
+}
diff --git a/research/ranksector112-async/validation/SOURCE522-RECEIPT.json b/research/ranksector112-async/validation/SOURCE522-RECEIPT.json
new file mode 100644
index 0000000000..a1bc5e252b
--- /dev/null
+++ b/research/ranksector112-async/validation/SOURCE522-RECEIPT.json
@@ -0,0 +1,88 @@
+{
+  "status": "PASS_CONDITIONAL_ASYNCHRONOUS_COMPLEX_DERIVATIVE",
+  "kappa": "1402213284556683/1000000000000000000",
+  "kappa_decimal": "0.001402213284556683",
+  "complex_lower": "1404182247558147721001/1000000000000000000000000",
+  "bit_lower": "391360506745414227149/250000000000000000000000",
+  "template_sha256": "d69ff4e565e93d2379fafc62b12ebc200486b7f701077b05d22997a445ae2a11",
+  "strict_constraints": 47,
+  "scope": "New complex program independently replayed. The unchanged PR493 bit operator and inherited all-size compiler, common-label, Lemma A realization, restored-row, precision/tape and analytic-transfer contracts remain dependencies. No unconditional multiplication bound or fresh Lean certification is claimed.",
+  "stages": [
+    {
+      "stage": "partial-factory",
+      "exit": 0,
+      "seconds": 0.20327587495557964
+    },
+    {
+      "stage": "construct-kernel92",
+      "exit": 0,
+      "seconds": 0.6937963750679046
+    },
+    {
+      "stage": "construct-pair35",
+      "exit": 0,
+      "seconds": 0.5949640839826316
+    },
+    {
+      "stage": "construct-ranksector",
+      "exit": 0,
+      "seconds": 0.5945867910049856
+    },
+    {
+      "stage": "kernel-scalar-controls",
+      "exit": 0,
+      "seconds": 8.651234999997541
+    },
+    {
+      "stage": "scalar",
+      "exit": 0,
+      "seconds": 0.742384040961042
+    },
+    {
+      "stage": "emit-local",
+      "exit": 0,
+      "seconds": 0.4210075419396162
+    },
+    {
+      "stage": "phases",
+      "exit": 0,
+      "seconds": 101.8168482920155
+    },
+    {
+      "stage": "adapters",
+      "exit": 0,
+      "seconds": 0.5938915000297129
+    },
+    {
+      "stage": "parent-integration",
+      "exit": 0,
+      "seconds": 0.6343775000423193
+    },
+    {
+      "stage": "parent-replay",
+      "exit": 0,
+      "seconds": 3.272448208066635
+    },
+    {
+      "stage": "emit-async",
+      "exit": 0,
+      "seconds": 2.190103832981549
+    },
+    {
+      "stage": "independent-async",
+      "exit": 0,
+      "seconds": 11.134319250006229
+    },
+    {
+      "stage": "invoice",
+      "exit": 0,
+      "seconds": 1.0618699580663815
+    },
+    {
+      "stage": "two-moments-assembly",
+      "exit": 0,
+      "seconds": 0.2559707909822464
+    }
+  ],
+  "package_manifest_sha256": "115cee362577680784b93bf749e75796239febffceb2a634f5a0cddcfe97fd75"
+}
diff --git a/research/ranksector112-async/validation/SOURCE523-RECEIPT.json b/research/ranksector112-async/validation/SOURCE523-RECEIPT.json
new file mode 100644
index 0000000000..997344b1d3
--- /dev/null
+++ b/research/ranksector112-async/validation/SOURCE523-RECEIPT.json
@@ -0,0 +1,102 @@
+{
+  "status": "PASS_CONDITIONAL_PUNCTURED112_GLOBAL_KAPPA",
+  "kappa": "182243220215421/125000000000000000",
+  "kappa_decimal": "0.001457945761723368",
+  "complex_lower": "1460074471110324279467/1000000000000000000000000",
+  "bit_lower": "391360506745414227149/250000000000000000000000",
+  "template_sha256": "2ae6ac3aff97a861d037ee51d6dcdd7bfe79ecbb0d8f1e186754428abc997a99",
+  "live": 7168,
+  "physical": 7738,
+  "deficit": 2560,
+  "global_profile": {
+    "1": 182232,
+    "2": 11520,
+    "3": 41514,
+    "4": 6336,
+    "5": 24726,
+    "6": 4896,
+    "7": 132,
+    "8": 72,
+    "48": 230
+  },
+  "strict_constraints": 47,
+  "improvement_over_pinned514": "66422302131539/1391523459591829",
+  "whole_owner_roles": 40320,
+  "all_own_stages": 14,
+  "pinned_predecessor_stages": 13,
+  "package_manifest_sha256": "e353b0e9d76cf6253d502f7410d17c228180e98bb6e56072eb869a1d923c3c17",
+  "seconds": 260.20254633401055,
+  "steps": [
+    {
+      "stage": "01-pinned514-full-replay",
+      "exit": 0,
+      "seconds": 132.74850291700568
+    },
+    {
+      "stage": "02-restrict-local",
+      "exit": 0,
+      "seconds": 0.1693020419916138
+    },
+    {
+      "stage": "03-exact-word-transport",
+      "exit": 0,
+      "seconds": 0.18928362510632724
+    },
+    {
+      "stage": "04-emit-local",
+      "exit": 0,
+      "seconds": 0.525245749973692
+    },
+    {
+      "stage": "05-independent-local",
+      "exit": 0,
+      "seconds": 2.2412997089559212
+    },
+    {
+      "stage": "06-exact-local-phases",
+      "exit": 0,
+      "seconds": 100.59046891599428
+    },
+    {
+      "stage": "07-residual-wrappers",
+      "exit": 0,
+      "seconds": 0.48223083303309977
+    },
+    {
+      "stage": "08-restrict-global-data",
+      "exit": 0,
+      "seconds": 1.1344536669785157
+    },
+    {
+      "stage": "09-independent-global-restriction",
+      "exit": 0,
+      "seconds": 4.846456832950935
+    },
+    {
+      "stage": "10-emit-whole-owners",
+      "exit": 0,
+      "seconds": 2.152218583971262
+    },
+    {
+      "stage": "11-independent-hosted-program",
+      "exit": 0,
+      "seconds": 11.282583542051725
+    },
+    {
+      "stage": "12-independent-raw-reconstruction",
+      "exit": 0,
+      "seconds": 2.3557603750377893
+    },
+    {
+      "stage": "13-scalar-prefix-and-finite-invoice",
+      "exit": 0,
+      "seconds": 1.2375561249209568
+    },
+    {
+      "stage": "14-two-moments-and-global-assembly",
+      "exit": 0,
+      "seconds": 0.2418515000026673
+    }
+  ],
+  "scope": "Finite complex restriction, exact local phases, whole physical owners, complete fee inventory, two rational moments and 47 outer inequalities checked. The unchanged PR493 bit operator, all-size compiler, common-label/mutable-basis realization, normalized Lemma A, restored-row, precision/tape and analytic-transfer contracts remain dependencies. No unconditional theorem or new Lean certification."
+}
diff --git a/research/ranksector112-async/validation/audit/ASYNC-AUDIT.json b/research/ranksector112-async/validation/audit/ASYNC-AUDIT.json
new file mode 100644
index 0000000000..b4a548943d
--- /dev/null
+++ b/research/ranksector112-async/validation/audit/ASYNC-AUDIT.json
@@ -0,0 +1,57 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS",
+  "template_sha256": "87a2c10f5638bddbb7748803bdc0b63ed027c499bbee0e6f14edb01565adaf30",
+  "complex_template_sha256": "87a2c10f5638bddbb7748803bdc0b63ed027c499bbee0e6f14edb01565adaf30",
+  "complex_live": 7168,
+  "complex_profile": {
+    "1": 177552,
+    "2": 13104,
+    "3": 40455,
+    "4": 6373,
+    "5": 20492,
+    "6": 9007,
+    "7": 183,
+    "8": 158,
+    "48": 230
+  },
+  "complex_hosted_residuals": 40320,
+  "physical": 7738,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "entering_helper_roles": 12888,
+  "cross_replica_helper_roles": 31430,
+  "one_owner_per_complete_invocation": true,
+  "helper_busy_family_window_checks": 40320,
+  "complete_invocations": 72,
+  "actual_orthogonal_73column_maps": 3448,
+  "actual_sigma_stream_sha256": "7401fa168ca1aa450ebb743722cab6447e21b098babc44490ba93f77734883f3",
+  "all_actual_residual_and_spectator_charts": true,
+  "idle_remainders": 6914,
+  "mutations_rejected": [
+    "wrong call time",
+    "alias two whole owners",
+    "helper on active data family",
+    "owner in private namespace",
+    "unbound change of owner replica",
+    "omit complete invocation",
+    "reorder invocation replicas",
+    "interleave local invocations",
+    "change local instruction stream",
+    "wrong residual width",
+    "wrong spectator coordinate",
+    "omit spectator route",
+    "overlap residual footprint",
+    "omit idle remainder",
+    "underpay idle remainder",
+    "omit bridge touch",
+    "remove one-owner rule",
+    "duplicate frozen role",
+    "understate physical reserve"
+  ],
+  "widths": {
+    "7": 18,
+    "8": 161,
+    "9": 381
+  },
+  "scope": "Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses unchanged source local program and normalized residual-wrapper identities; all-size compilation and complete coefficient invoice are separate inherited obligations."
+}
diff --git a/research/ranksector112-async/validation/audit/EXACT-ASSEMBLY.json b/research/ranksector112-async/validation/audit/EXACT-ASSEMBLY.json
new file mode 100644
index 0000000000..18a9f686c8
--- /dev/null
+++ b/research/ranksector112-async/validation/audit/EXACT-ASSEMBLY.json
@@ -0,0 +1,127 @@
+{
+  "status": "PASS_ASYNC_COMPLEX_AND_CITED_BIT_EXACT_ASSEMBLY",
+  "complex_lower": "146944554266898896961/100000000000000000000000",
+  "complex_decimal": "0.00146944554266898896961",
+  "next_b_rejected": "1469445542668988969611/1000000000000000000000000",
+  "exact_moment_receipts": [
+    {
+      "endpoint": "146944554266898896961/100000000000000000000000",
+      "mercator": [
+        "-1529377618637656443230046730340509031952367/6739986666787659948666753771754907668409286105635143120275902562304",
+        "-3058755237275312886460093460681018063904733/13479973333575319897333507543509815336818572211270286240551805124608"
+      ],
+      "base_two": [
+        "-2269118284998798006841/10000000000000000000000000000000000000000000000",
+        "-2269108284998798006711/10000000000000000000000000000000000000000000000"
+      ],
+      "accept": true
+    },
+    {
+      "endpoint": "1469445542668988969611/1000000000000000000000000",
+      "mercator": [
+        "10484554499095637330930451310020194340024575/3369993333393829974333376885877453834204643052817571560137951281152",
+        "41938217996382549323721805240080777360098301/13479973333575319897333507543509815336818572211270286240551805124608"
+      ],
+      "base_two": [
+        "31111491715377670058549/10000000000000000000000000000000000000000000000",
+        "31111501715377670058679/10000000000000000000000000000000000000000000000"
+      ],
+      "accept": false
+    }
+  ],
+  "bit_lower": "391360506745414227149/250000000000000000000000",
+  "bit_result_sha256": "3494ba83280cc86548fe0cc6695c50d23e6b6ffca85aeb1a33337c1196e280cb",
+  "bit_template_sha256": "e37b52e4861c39154b5891460fb45df8651c92cd68961078f8f06596f057c822",
+  "bit_prefix_bits": 2176,
+  "bit_charged_three_level_coefficient_bits": 6464,
+  "external_row_allowance": 20161,
+  "kappa": "1467289440740487/1000000000000000000",
+  "kappa_decimal": "0.001467289440740487",
+  "binding_component": "complex",
+  "strict_outer_constraints": {
+    "bit_positive": "146944554266898895373312849914507934630014197271950112363658580306902650867407541221233414688342532869485709231387165534505148440659787503622898225022858872473633539642335292220526488207152847585345858152395657842014202768388804358904696565508041743390382031662282348420869728479312321/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_above_bit": "1587687150085492065369985802728049887636341419693097349132592458778766585311657467130514290768612834465494851559340212496377101774977141127526366460357664707779473511792847152414654141847604342157985797231611195641095303434491958256609617968337717651579130271520687679/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_below_one_over32": "2978055445733101103039/100000000000000000000000",
+    "beta_positive": "1/1000000000000000000",
+    "beta_below_one": "999999999999999999/1000000000000000000",
+    "leaf_saving_above_bit": "1440742595818593168408985802728049887636341419693097349132592458778766585311657467130514290768612834465494851559340212496377101774977141127526366460357664707779473511792847152414654141847604342157985797231611195641095303434491958256609617968337717651579130271520687679/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_positive": "73472277133449447539711870690355071941694248721467121551815092881501213070045190303714056476763725213509439927351049897766864988942728217306300671851641932613918544798308773636629704461241131572146440869044981335661243231798744337438145514365216512790494450323099430820052832577373812079130271520687679/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_internal": "146944554266898895373312849914507934630014197271950112363658580306902650867407541221233414688342532869485709231387165534505148440659787503622898225022858872473633539642335292220526488207152847585345858152395657842014202768388804358904696565508041743390382031662282348420869728479312321/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
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+    "q_below_reservations": "1/4000000000000000000",
+    "lambda_above_tau": "146944554266898895373312849914507934630014197271950112363658580306902650867407541221233414688342532869485709231387165534505148440659787503622898225022858872473633539642335292220526488207152847585345858152395657842014202768388804358904696565508041743390382031662282348420869728479312321/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_above_sigma": "1734631704352390960743298652642557822266355616965047461496251039085669236179065008351747705456955367334980560790727378030882250215636928631149264685380523580253107051435182444635180630054757189743331655384006853483109506202880762615514314533845759394969512303182970027420869728479312321/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_above_internal": "146944554266898895373312849914507934630014197271950112363658580306902650867407541221233414688342532869485709231387165534505148440659787503622898225022858872473633539642335292220526488207152847585345858152395657842014202768388804358904696565508041743390382031662282348420869728479312321/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "lambda_prime_above_lambda": "146944554266898895373312849914507934630014197271950112363658580306902650867407541221233414688342532869485709231387165534505148440659787503622898225022858872473633539642335292220526488207152847585345858152395657842014202768388804358904696565508041743390382031662282348420869728479312321/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_leaf": "867315852176195479577805751278532878448184907118498786929954809696285943523236274786490560072648950102233135011057271782693699328148358067386081455201691226363370295538758868427853559130955018664338756768201255662561854485634783487209505549676900569179947167422626187920869728479312321/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_reservations": "1/4000000000000000000",
+    "lambda_prime_below_one": "73472277133449447539711870690355071941694248721467121551815092881501213070045190303714056476763725213509439927351049897766864988942728217306300671851641932613918544798308773636629704461241131572146440869044981335661243231798744337438145514365216512790494450323099430820052832577373812079130271520687679/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
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+      "cutoff_log2": "374538950686619088001481508130444347"
+    },
+    {
+      "gap": "1440642595818593168408985802728049887636341419693097349132592458778766585311657467130514290768612834465494851559340212496377101774977141127526366460357664707779473511792847152414654141847604342157985797231611195641095303434491958256609617968337717651579130271520687679/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "173456267857927793965636576496375774666101"
+    }
+  ],
+  "complex_template_sha256": "87a2c10f5638bddbb7748803bdc0b63ed027c499bbee0e6f14edb01565adaf30",
+  "owner_audit_sha256": "03d2870ca03c106f651efdf79b1846a531535ff671c34f3f69dda77fa2b59df6",
+  "invoice_sha256": "7a05caa05a857c27d11a3e12a4e5dc4d3519c3aad15669579dbdf8bea1c72fdf",
+  "bit_scope": "PR493 published profile and operator reused as a pinned dependency; this verifier reprices its published profile but does not reconstruct that unchanged bit operator.",
+  "scope": "Conditional finite witness. Inherited compiler, precision/tape and analytic-transfer contracts remain assumed; changed-host operator admission recorded separately."
+}
diff --git a/research/ranksector112-async/validation/audit/GLOBAL-PREFIX.json b/research/ranksector112-async/validation/audit/GLOBAL-PREFIX.json
new file mode 100644
index 0000000000..d754fbe6ac
--- /dev/null
+++ b/research/ranksector112-async/validation/audit/GLOBAL-PREFIX.json
@@ -0,0 +1,13 @@
+{
+  "status": "PASS_ASYNC_GLOBAL_PREFIX",
+  "template_sha256": "87a2c10f5638bddbb7748803bdc0b63ed027c499bbee0e6f14edb01565adaf30",
+  "global_prefix_bits": 210,
+  "retained_payload_bits": 512,
+  "complete_invocation_cover_sweeps": 72,
+  "bridge_factor_two_sweeps": 72,
+  "local_scalar_coefficient_work_prefix_bits": 25,
+  "stream_input_sup_to_l2_bits": 37,
+  "primitive_arithmetic_margin_bits": 4,
+  "controller_audit_sha256": "23e2810f2a33ccb8c88093029de35b3200156525c82c31df837adf09c7946ecf",
+  "proof": "Each complete normalized invocation has unitary helper endpoints and a data shear with at most two unitary summands. Distinct full orthogonal owner charts act by right-translation bijections on the retained cover group. Thus the maximum full-stream L2 norm grows by at most2per complete local cover sweep and individual bridge. All72local sweeps and72individual bridge sweeps are counted. Unit-modulus phases, idle children, terminal translations and normalized spectator endpoints are unitary. The independently replayed scalar/Horner envelope costs 25 bits, initial sup-to-L2 conversion 37 bits, primitive margin 4 bits: total 210 < 512. All-size child/compiler and precision/tape interfaces remain inherited."
+}
diff --git a/research/ranksector112-async/validation/audit/GLOBAL-RESTRICTION-AUDIT.json b/research/ranksector112-async/validation/audit/GLOBAL-RESTRICTION-AUDIT.json
new file mode 100644
index 0000000000..d7fd2d9e9a
--- /dev/null
+++ b/research/ranksector112-async/validation/audit/GLOBAL-RESTRICTION-AUDIT.json
@@ -0,0 +1,77 @@
+{
+  "status": "PASS_INDEPENDENT_GLOBAL_DATA_PORT_RESTRICTION",
+  "retained_ports": 112,
+  "deleted_canonical_ports": [
+    0,
+    13,
+    22,
+    35,
+    40,
+    51,
+    54,
+    119
+  ],
+  "data_owner_roles": 16128,
+  "helper_owner_roles": 40320,
+  "complete_invocations": 72,
+  "exact_port_phase_recipes": 112,
+  "exact_stage_alignments": 1008,
+  "exact_idle_axis_recipes": 2240,
+  "paid_idle_children": 2016,
+  "replicated_paid_idle_children": 16128,
+  "bank_families": 5040,
+  "bank_remainder_profile": {
+    "1": 3429,
+    "9": 1449,
+    "17": 162
+  },
+  "unhosted_paid_profile": {
+    "1": 180981,
+    "2": 13104,
+    "3": 37152,
+    "4": 6336,
+    "5": 17424,
+    "6": 8928,
+    "7": 72,
+    "8": 5448,
+    "9": 1449,
+    "16": 3584,
+    "17": 162,
+    "32": 3584,
+    "48": 3584
+  },
+  "unhosted_rank_mass": 888624,
+  "unhosted_live": 12208,
+  "unhosted_physical": 12778,
+  "deficit": 2560,
+  "source_bindings": {
+    "canonical": "7c03982b550c2823d5cddd376bd4e816404930c7a137d78f050f2af174b030bf",
+    "canonical_content": "99d06e986447f7c71bea6df3ebd0df77356aec6f4c2b0a12183946faf77434b4",
+    "programs": "6289cdb4b08b89d39efb9ce85495e9578dbe890875588c6a8315b64756bd195d",
+    "local_phase": "6970f7ccf30f6748674cd86bf062df441d754d8ebda2a333664bf396c34a1c09",
+    "adapters": "06a889a51fd2833dd465ed9c660b35fa8f68496ff7ed34c931d17c4f7551e1b2",
+    "old_template": "d228fe3e1895e1e8d3097bf27501e2f19d54ab07c8bef351045bf48a35f2b607",
+    "old_template_content": "65c1b7abdfe0c82bf40c5ee3a7f169c986811a29d97b565272b92839cc687f80",
+    "old_phase": "f621f6d4296cb215f334830356c5f79fe10d6d04d15b3ccda76ba0885ab67d0a",
+    "phase": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa"
+  },
+  "negative_controls_rejected": [
+    "duplicate selected port",
+    "wrong phase port label",
+    "wrong inherited idle axis",
+    "missing terminal port correction",
+    "wrong data owner family",
+    "wrong canonical data route",
+    "stale local program hash",
+    "changed entering bank owner",
+    "missing complete invocation",
+    "missing paid idle child",
+    "missing cover correction",
+    "understated private reserve",
+    "unpaid bank remainder"
+  ],
+  "local_scalar_replay_receipt_sha256": "eae3ca2abd975b0b778311209ab9ea97a1e719a123c2fe5587224ea60aab5fc0",
+  "local_phase_receipt_sha256": "a35ca0eb3ea50040769e22583aa3712fd66f8e4541e2d7882651244817b54cd2",
+  "template_content_sha256": "b3c6ad4972a38c811833794f7320fe785526b8298bb80508bb6bb96721a22484",
+  "scope": "Exact restriction of all inherited global data routes, phase recipes, complete-call order, idle axes and terminal corrections. Local arbitrary-dirt identities are supplied by the newly hash-bound independent local replay. Actual bank remainders are recounted for the conservative parent invoice. Final whole-owner placement, executable global program, finite compilation and outer exponent require their separate fresh audits."
+}
diff --git a/research/ranksector112-async/validation/audit/INDEPENDENT112-RAW-AUDIT.json b/research/ranksector112-async/validation/audit/INDEPENDENT112-RAW-AUDIT.json
new file mode 100644
index 0000000000..6f73a08ede
--- /dev/null
+++ b/research/ranksector112-async/validation/audit/INDEPENDENT112-RAW-AUDIT.json
@@ -0,0 +1,98 @@
+{
+  "actual_orthogonal_charts": 3448,
+  "all_owners_per_call_distinct": 784,
+  "deficit": 2560,
+  "deleted_canonical_ports": [
+    0,
+    13,
+    22,
+    35,
+    40,
+    51,
+    54,
+    119
+  ],
+  "deleted_scalar_operations": {
+    "cut": 8
+  },
+  "helpers": 560,
+  "idle_remainders": {
+    "3": 3303,
+    "4": 37,
+    "5": 3068,
+    "6": 79,
+    "7": 111,
+    "8": 86,
+    "48": 230
+  },
+  "inputs": {
+    "/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/pr522-independent-full314/base/split-centres/CANONICAL-WORD.json.gz": "eb7e6e1e8b33ecdcc0f8be3e10900694569937647b58faa85da5faf306e38177",
+    "/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/pr522-independent-full314/base/split-centres/GLOBAL-TEMPLATE.json.gz": "d228fe3e1895e1e8d3097bf27501e2f19d54ab07c8bef351045bf48a35f2b607",
+    "/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/pr522-independent-full314/base/work/complex-nine-native/DATA-PHASES.json": "f621f6d4296cb215f334830356c5f79fe10d6d04d15b3ccda76ba0885ab67d0a",
+    "/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/ranksector112-local-admission/local/CANONICAL-WORD.json.gz": "7c03982b550c2823d5cddd376bd4e816404930c7a137d78f050f2af174b030bf",
+    "/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/ranksector112-local-admission/local/LOCAL-PROGRAMS.json.gz": "6289cdb4b08b89d39efb9ce85495e9578dbe890875588c6a8315b64756bd195d",
+    "/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/ranksector112-local-admission/local/RESIDUAL-ADAPTERS.json": "06a889a51fd2833dd465ed9c660b35fa8f68496ff7ed34c931d17c4f7551e1b2",
+    "/Volumes/SP AI 01_16/CodexWorkspaces/imb-retime2/frontier390/ranksector112-owner-transport/OWNERS.json.gz": "303248081467c4816b50ca2c05da478a3c971a8f43a6de19fd32b8e497e0bbbc"
+  },
+  "invocations": 72,
+  "live": 7168,
+  "local": {
+    "backward": {
+      "columns": 784,
+      "events": 22036,
+      "profile": {
+        "1": 2466,
+        "2": 182,
+        "3": 516,
+        "4": 88,
+        "5": 242,
+        "6": 124,
+        "7": 1,
+        "8": 1
+      },
+      "scalar_macros": 16660
+    },
+    "forward": {
+      "columns": 784,
+      "events": 22036,
+      "profile": {
+        "1": 2466,
+        "2": 182,
+        "3": 516,
+        "4": 88,
+        "5": 242,
+        "6": 124,
+        "7": 1,
+        "8": 1
+      },
+      "scalar_macros": 16660
+    }
+  },
+  "no_emitter_or_hosting_checker_imported": true,
+  "no_nominated_profile_or_windows_used": true,
+  "paid_profile": {
+    "1": 177552,
+    "2": 13104,
+    "3": 40455,
+    "4": 6373,
+    "5": 20492,
+    "6": 9007,
+    "7": 183,
+    "8": 158,
+    "48": 230
+  },
+  "pending_axes_covered": 348696,
+  "physical": 7738,
+  "rank_mass": 520704,
+  "residual_widths": {
+    "7": 18,
+    "8": 161,
+    "9": 381
+  },
+  "same_local_frames_and_residual_wrappers_as_PR514": true,
+  "scope": "Independent finite restriction, all rational scalar columns, nested local frames, fixed whole-owner schedule, actual port charts and paid histogram. The inherited all-size/compiler, common-label realization, precision/tape and analytic transfer interfaces remain conditions.",
+  "seconds": 1.9106298750266433,
+  "status": "PASS_INDEPENDENT_RAW_112_RESTRICTION_LOCAL_COLUMNS_CHARTS_WINDOWS_OWNERS_AND_PROFILE",
+  "v": 112,
+  "whole_owner_roles": 40320
+}
diff --git a/research/ranksector112-async/validation/audit/OWNERS-AND-PROFILE.json b/research/ranksector112-async/validation/audit/OWNERS-AND-PROFILE.json
new file mode 100644
index 0000000000..c15e0d4131
--- /dev/null
+++ b/research/ranksector112-async/validation/audit/OWNERS-AND-PROFILE.json
@@ -0,0 +1,35 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE",
+  "template_sha256": "87a2c10f5638bddbb7748803bdc0b63ed027c499bbee0e6f14edb01565adaf30",
+  "paid_profile": {
+    "1": 177552,
+    "2": 13104,
+    "3": 40455,
+    "4": 6373,
+    "5": 20492,
+    "6": 9007,
+    "7": 183,
+    "8": 158,
+    "48": 230
+  },
+  "live": 7168,
+  "physical": 7738,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "hosted_residuals": 40320,
+  "banked_residuals": 0,
+  "all_784_owners_per_call_distinct": true,
+  "actual_helper_owner_charts": 40320,
+  "actual_73column_sigmas": 3448,
+  "cross_replica_helper_roles": 31430,
+  "explicit_idle_remainder_children": 6914,
+  "source_idle_children_charged": 16128,
+  "source_artifacts": {
+    "split-centres/CANONICAL-WORD.json.gz": "7c03982b550c2823d5cddd376bd4e816404930c7a137d78f050f2af174b030bf",
+    "split-centres/LOCAL-PROGRAMS.json.gz": "6289cdb4b08b89d39efb9ce85495e9578dbe890875588c6a8315b64756bd195d",
+    "split-centres/LOCAL-CHECKS.json": "274285d55b55848582f12c22789cea20958ae0af59e88f010fd0593f8374f840",
+    "split-centres/RESIDUAL-ADAPTERS.json": "06a889a51fd2833dd465ed9c660b35fa8f68496ff7ed34c931d17c4f7551e1b2",
+    "work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa"
+  },
+  "controller_audit_sha256": "23e2810f2a33ccb8c88093029de35b3200156525c82c31df837adf09c7946ecf"
+}
diff --git a/research/ranksector112-async/validation/audit/PREFIX-AND-INVOICE.json b/research/ranksector112-async/validation/audit/PREFIX-AND-INVOICE.json
new file mode 100644
index 0000000000..b2b6dcac10
--- /dev/null
+++ b/research/ranksector112-async/validation/audit/PREFIX-AND-INVOICE.json
@@ -0,0 +1,69 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE",
+  "template_sha256": "87a2c10f5638bddbb7748803bdc0b63ed027c499bbee0e6f14edb01565adaf30",
+  "global_prefix_bits": 210,
+  "charged_prefix_bits": 512,
+  "complete_invocation_sweeps": 72,
+  "bridge_sweeps": 72,
+  "row_prefix_extra": 1024,
+  "local": {
+    "backward": {
+      "events": 22036,
+      "macros": 16660,
+      "real_component_primitives": 169678,
+      "prefix_l1": "57889301/2",
+      "prefix_bits": 25,
+      "coefficient_work_primitive_count": 83919,
+      "all_exact_columns": 784,
+      "all_560_dirty_helper_columns_restored": true,
+      "private_centres_and_coefficient_work_cleared": true
+    },
+    "forward": {
+      "events": 22036,
+      "macros": 16660,
+      "real_component_primitives": 169630,
+      "prefix_l1": "737611",
+      "prefix_bits": 20,
+      "coefficient_work_primitive_count": 83887,
+      "all_exact_columns": 784,
+      "all_560_dirty_helper_columns_restored": true,
+      "private_centres_and_coefficient_work_cleared": true
+    }
+  },
+  "entering_helpers": 179,
+  "entrance_rank": 197,
+  "local_adapters": 341824,
+  "local_primitive_bound": 8864978638542,
+  "wrapper_elementary_factors_charged": 3711744,
+  "compiler": 25934336,
+  "unhosted_pervertex": 1450414476891552,
+  "hosted_rebased_pervertex": 1450414476558912,
+  "conservative_pervertex_used": 1450414476891552,
+  "finite": {
+    "physical_stock_bits": 2641,
+    "router_bits": 7984,
+    "literal_bits": 35282,
+    "physical_row_coefficient": 16467,
+    "retained_row_coefficient": 20161,
+    "required_C0_bits": 200012,
+    "halving_integer_inequality": [
+      5329,
+      4608
+    ],
+    "G_exponent": 30000,
+    "E_exponent": 100000,
+    "C0_exponent": 210000
+  },
+  "strict_checks": {
+    "local_primitive_bound": true,
+    "logical": true,
+    "router": true,
+    "literal": true,
+    "mass": true,
+    "precision": true,
+    "tape": true,
+    "row": true,
+    "halving": true
+  },
+  "scope": "Exact finite recount conditional on inherited all-size compiler/precision/tape and analytic-transfer contracts. Signed accumulation uses the supplier scalar primitive convention. Async prefix counts all72individual bridges and72complete invocations;512bits are charged, and an additional2*512 enters the two-level physical row bound."
+}
diff --git a/research/ranksector112-async/vendor/pr522/EXPECTED.json b/research/ranksector112-async/vendor/pr522/EXPECTED.json
new file mode 100644
index 0000000000..91343a36ef
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/EXPECTED.json
@@ -0,0 +1,6 @@
+{
+  "kappa": "1402213284556683/1000000000000000000",
+  "complex_lower": "1404182247558147721001/1000000000000000000000000",
+  "bit_lower": "391360506745414227149/250000000000000000000000",
+  "template_sha256": "d69ff4e565e93d2379fafc62b12ebc200486b7f701077b05d22997a445ae2a11"
+}
diff --git a/research/ranksector112-async/vendor/pr522/LICENSE b/research/ranksector112-async/vendor/pr522/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
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diff --git a/research/ranksector112-async/vendor/pr522/MANIFEST.json b/research/ranksector112-async/vendor/pr522/MANIFEST.json
new file mode 100644
index 0000000000..1b0039ba73
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/MANIFEST.json
@@ -0,0 +1,293 @@
+{
+  "format": "sha256-lf-text-v1",
+  "files": {
+    "code/assemble.py": {
+      "mode": "lf-text",
+      "sha256": "9db68cad2738d76052b25c8bdf6485edd6f14025bf47107d2425b10a2bdf69e0"
+    },
+    "code/audit_async.py": {
+      "mode": "lf-text",
+      "sha256": "009494faa5470f2cf7099eef97b203ea59d0a2d703db7f9f5af49b78cf6fd56f"
+    },
+    "code/audit_async_invoice.py": {
+      "mode": "lf-text",
+      "sha256": "75e30d516069140c958063e45905c84ad7e04c2029654592e5fa7c8725a7feba"
+    },
+    "code/audit_kernel_scalar.py": {
+      "mode": "lf-text",
+      "sha256": "7a0e306013e8a198f2a77a0d582aab6cf14b5520756345143205272b9f1b0f3f"
+    },
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+    },
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+    }
+  }
+}
diff --git a/research/ranksector112-async/vendor/pr522/NOTICE.md b/research/ranksector112-async/vendor/pr522/NOTICE.md
new file mode 100644
index 0000000000..abe6e510dc
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/NOTICE.md
@@ -0,0 +1,13 @@
+# Scoped attribution
+
+Prepared with OpenAI Codex assistance. Apache-2.0; see LICENSE. Original authorship notices in included vendor code are retained.
+
+PR507 directly supplies the partial-own factory, 84-pivot reference and its retiming map. PR484 supplies the gauge/kernel construction and wrappers; PR496 supplies whole-owner pooling and invoice ancestry. PR493 supplies the unchanged cited bit operator. PR495 supplies body-frame retiming, with PR501 and PR502 integrating it. PR473's single-gauge proposal inspired our coordinated four-gauge collapse; its updated schedule was also considered. PR505 contains our prior asynchronous complete-invocation scheduling. PR506 supplies a related public comparison and portability feedback. PR477's experiment log informed bounded route selection.
+
+Earlier retained ancestry includes PR433/425/370 for geometry and the scalar/phase compiler, PR458 for whole-owner spectator wrappers, PR361/315 for exact moments and outer arithmetic, and PR434/417/435/440/401/408/416 for response-kernel and gauge methods. SOURCES.json separates direct ingredients, ancestry, comparisons and excluded interfaces; credits do not mean their gains were added independently.
+
+Our contribution here is the actual combined reconstructed 99-pivot word and literal whole-owner allocation, with complete fresh checks of the changed complex program. OpenAI math, the Problem 1.8 implementation and the installed machine compiler sources informed the documented research adaptations. No fresh Lean certification is claimed.
+
+Additional direct inspiration: OpenAI math sparse interpolation, unit-flow/matching, rational Schur history and exact pruning. The source and adaptation ledgers distinguish these roles. Recent PR509-513 were inspected as context, not counted as additional numerical gains.
+
+This derivative changes the coordinate-total factory by a rank-factor construction, retaining the99-pivot pair35 ancestry and unchanged whole-owner witness. Additional OpenAI source families this round: Cotype rank factors, UniformKServer rounding, SwitchChain switches and DukePrimeDegree root commutators. See their exact hashes and scope in research-notes/. PR514-517 and the updatedPR511 are acknowledged as described in SOURCES.json.
diff --git a/research/ranksector112-async/vendor/pr522/PORTABILITY.md b/research/ranksector112-async/vendor/pr522/PORTABILITY.md
new file mode 100644
index 0000000000..b6e9671200
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/PORTABILITY.md
@@ -0,0 +1,11 @@
+# Portable replay and browser uploads
+
+No hidden file is required. MANIFEST.json binds every included file except itself. Each entry declares either exact raw-byte hashing (gzip and other binary inputs) or SHA-256 after converting CRLF to LF (recognized text files). This accepts only the platform newline distinction; it does not ignore whitespace, JSON values, source code or any other content. An omitted file or changed token still fails.
+
+verify.py copies static work inputs into its new output directory, canonicalizes recognized text there, and creates an LF copy of the frozen asynchronous plan. Only those canonical copies enter runtime raw-byte template hashes. Each child executes through code/run_portable.py, which preserves argv, import path and working directory while forcing generated Path.write_text output to UTF-8/LF. Generated adapter JSON therefore has the same embedded hash on Windows and Linux.
+
+Gzip transport bytes are manifest-bound. Newly generated gzip container headers can vary across Python versions; the expected final template hash binds decompressed canonical content instead. Mathematical input fields are checked independently. The normalized local word omits only two irrelevant inherited display floats and a checked redundant dimension field.
+
+The package is tested locally with assertions enabled. Optimized Python is rejected. The final portability test changes every recognized package text file to CRLF and runs the complete verifier against the frozen expected result. This is a Windows line-ending test, not a claim that Linux or Python 3.14 ran locally.
+
+Upload batches contain at most 40 files each, have no hidden files, and reproduce the same research/rank-sector-async directory. Upload each batch's research folder at your fork's repository root, on one fresh branch. Do not upload the part folder itself. After all batches are committed, open one PR from that branch. Nothing in the verifier publishes, deletes files or modifies a fork.
diff --git a/research/ranksector112-async/vendor/pr522/PROOF.md b/research/ranksector112-async/vendor/pr522/PROOF.md
new file mode 100644
index 0000000000..647ef2c1dc
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/PROOF.md
@@ -0,0 +1,13 @@
+# Sufficient rank-sector construction
+
+In each of fourteen blocks, the twelve retired rows have clean source rank eight. Choose eight independent rows. Their coefficient matrix on the eight source coordinates is invertible. Let A be that matrix. Extend the four desired coordinate-sum rows to an invertible eight-row output matrix M, then emit the elementary factorization of M A^-1 at the existing legal rank-four frame. On the clean source sector this gives (M A^-1) A x=Mx. The remaining four physical rows are kept, not deleted or cleared.
+
+The clean calculation is not the arbitrary-input certificate. The new factory's complete dirty response is recomputed; the exact 99-pivot compensation, frame checks and inverse cleanup are rebuilt. Every independent dirty/source/target column is checked in both forward and inverse-transpose orientations. All 99 omitted-correction controls reject. All scalar coefficients satisfy the existing dyadic compiler contract, and all nonlinear precision consequences are included in the actual prefix invoice.
+
+Four unused retired rows in each block stay at rank three until full-frame cleanup. Their old rank-one rise to four followed by a rank-five rise to nine is replaced by one rank-six rise. Hence the local delta is -56 rank-one children, -56 rank-five children and +56 rank-six children. Rank mass is unchanged. For every exponent p in (0,1), strict concavity gives 6^p < 1+5^p, so this is a universal strict improvement of the local moment in that range. No entropy approximation is needed for this comparison.
+
+The normalized selected word is SHA-256 d966e1481e0c09e4b7a0607429411046c6b3663ee83e6b8833958a745b82e337. Its residual inventory is unchanged in order: 18 width-seven, 161 width-eight and 381 width-nine helpers. Therefore the previous complete-owner assignment is a concrete feasible witness without a new allocation oracle. Every emitted physical chart and residual wrapper is nevertheless regenerated from this new provider and independently checked.
+
+Eight replicas execute nine complete calls in order (7*stage+6*replica,stage,replica), finishing each before the next. Each helper has one whole owner whose idle interval contains the invocation, and every complementary residual is paid before the owner's next touch. Induction using the inherited complete invocation contract preserves the original endpoint and restores spectators. No helper is split across families and no scalar gate crosses an unfinished invocation.
+
+The full profile is {1: 178128, 2: 13104, 3: 40196, 4: 6336, 5: 21032, 6: 8928, 7: 164, 8: 1224, 48: 796}; its rank sum is 73*7680-2496. Maximum recursive rank is 48 and 73^2>2*48^2. The fresh invoice derives the prefix from the actual new scalar program, not the previous provider's fixture. Two exact rational moment engines and all 47 strict outer inequalities establish conditional kappa=1402213284556683/1000000000000000000, b=1404182247558147721001/1000000000000000000000000, c=391360506745414227149/250000000000000000000000. Adjacent-price and malformed-assembly controls reject. All-size and analytic interfaces remain stated dependencies.
diff --git a/research/ranksector112-async/vendor/pr522/README.md b/research/ranksector112-async/vendor/pr522/README.md
new file mode 100644
index 0000000000..157bd44860
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/README.md
@@ -0,0 +1,23 @@
+# Rank-factor coordinate totals with asynchronous whole owners
+
+Conditional kappa = **0.001402213284556683**, exactly `1402213284556683/1000000000000000000`: **0.613517% above our preceding checked construction**, 0.001393662920776407. The complex supplier binds at b = `1404182247558147721001/1000000000000000000000000`; the unchanged cited PR493 bit supplier has c = `391360506745414227149/250000000000000000000000`.
+
+The new local construction computes each block's four coordinate totals inside an independent eight-row sector. The preceding factory raised all twelve retired rows to the rank-four frame. Four rows per block can instead remain untouched until cleanup, fusing 56 rank-one/rank-five recursive pairs into 56 rank-six children. All 560 helper registers, all 99 response cancellations and the entire ordered width inventory remain. Arbitrary dirty inputs are retained and compensated, not erased.
+
+The actual local paid profile is {1:2474,2:182,3:516,4:88,5:242,6:124,7:1,8:17}. The global profile, including all idle remainders, is `{1: 178128, 2: 13104, 3: 40196, 4: 6336, 5: 21032, 6: 8928, 7: 164, 8: 1224, 48: 796}`. The existing literal allocation of 40,320 whole helper uses is preserved, then re-emitted and independently checked against the new provider. Rank deficit 2,496, ambient dimension 73, live stock 7,680 and physical stock 8,258 are unchanged.
+
+## Reproduce
+
+Python 3.11 or later, standard library only:
+
+```text
+python -B verify.py --work /absolute/path/to/a-new-output-directory
+```
+
+Choose a new directory outside this package and keep assertions enabled. No network, optimizer, C++ compiler or Lean is needed. Fifteen stages reconstruct the factory, check 800 arbitrary-dirt columns in both orientations plus 99 omitted-correction controls, audit exact Gaussian phases and physical wrappers, independently verify every owner and remainder, recount the scalar-prefix/row invoice, and run two rational moment engines and all 47 strict outer constraints. The bit operator is a cited dependency, not reverified here.
+
+## Four new source-inspired routes
+
+The selected gain comes from the Cotype rank-factor adaptation. Three other distinct OpenAI-source techniques were concretely screened: UniformKServer correlated owner repairs, SwitchChain degree-preserving output-pair switches, and DukePrimeDegree paid root-commutator rewrites. They did not add savings. Their sufficient transformation rules, source hashes and bounded outcomes are preserved in RESEARCH.md and research-notes/. Four techniques tested does not mean four numerical gains, four imported Lean theorems or a claim of global novelty.
+
+This remains a finite conditional construction. All-size compilation, common-label/mutable-basis transport, normalized Lemma A realization, restored-row, precision/tape and analytic-transfer interfaces remain dependencies. No unconditional multiplication theorem or new Lean certification is claimed. The snapshot was frozen through PR517 before packaging; see SOURCES.json and NOTICE.md. No publication is performed by the verifier.
diff --git a/research/ranksector112-async/vendor/pr522/RESEARCH.md b/research/ranksector112-async/vendor/pr522/RESEARCH.md
new file mode 100644
index 0000000000..96d49a32cc
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/RESEARCH.md
@@ -0,0 +1,18 @@
+# Four new OpenAI-source adaptations
+
+OpenAI math source snapshot: adc7f1241b42e322a6451854ab7e4b4c146bf78a. These sources were inspected, not freshly compiled or instantiated in Lean.
+
+| Source family | Concrete sufficient construction | Outcome |
+| --- | --- | --- |
+| Analysis/Cotype/RankFactors | Extract an independent sector, reconstruct the exact requested row map there, retain arbitrary-dirt rows outside it | Selected construction; 56 pairs of recursive calls fused, full replay passed |
+| UniformKServer/TreeRounding and RoundingKernel | Jointly repair several owner bins while preserving role identities, invocation marginals, capacities and explicitly charged parked mass | 200,000 strict-repair triples plus a bounded neutral sweep found no improved full leftover profile |
+| Probability/SwitchChain/FourVertexSwitch and PairTradeSwitch | Switch Y-borrowing output matchings and reconstruct their inverse basis/scatter | Inherited retiming was incompatible; 27 raw-frame candidates were legal but lost the paid moment |
+| DukePrimeDegree/Geometry/RootCommutator | Reorder elementary shears with the explicit product-coefficient correction and pay every gate/frame change | Adjacent and 128-event windows found no lower-cost nominee; 603 candidate profiles on pair35 and 547 on the new provider |
+
+The Cotype source proves exact rank-pairing factors and their contraction identity. Our coordinate-total construction is a separate finite row-sector adaptation; the source theorem itself is not a multiplication speedup. The initial displacement-kernel/telescoping idea was also screened and helped identify the small requested output space, but is not relabeled as the winning rank-factor theorem.
+
+The minimum-retained-subset screen found that each block requires eight selected retired rows in the tested subset model, using modular exact rank checks. This does not rule out new linear combinations, altered packet construction or different interfaces. The successful universal moment inequality and full finite witness, not a barrier, are the result delivered here.
+
+The other screens are bounded discovery evidence, not universal no-go results. Floating moment screens nominate or reject research candidates; only the selected full rational replay certifies the reported exponent. No approximate quantum operation, unconstructed decomposition, unpaid scalar correction or hypothetical solver is assumed.
+
+PR517's exact packing ceiling freezes a different 84-pivot word and does not bound this 99-pivot rank-sector word. It usefully distinguishes a small allocation gap from a genuinely changed local construction. PR515 is an alternative bit-side method, not substituted for the stronger retained supplier. PR516 is draft formal realization context and does not remove our stated conditional assumptions automatically. PR511 updates provenance, not kappa. All are credited in SOURCES.json; unchanged public verifiers were not rerun.
diff --git a/research/ranksector112-async/vendor/pr522/SOURCES.json b/research/ranksector112-async/vendor/pr522/SOURCES.json
new file mode 100644
index 0000000000..08cf67b4ad
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/SOURCES.json
@@ -0,0 +1,146 @@
+{
+  "snapshot": "79 recent/updated PR conversations; frozen through PR517 before packaging.",
+  "direct": [
+    {
+      "pr": 496,
+      "head": "00cf70efd6a8637531deafef698157ca83e249ee",
+      "role": "whole-owner parent, invoice and assembly ancestry"
+    },
+    {
+      "pr": 484,
+      "head": "035845ce95f31d0a2dcfb42b8c8e13411271fa5f",
+      "role": "PR496 pinned gauge80-kernel42 parent, not newer moving head"
+    },
+    {
+      "pr": 493,
+      "head": "c3a9a436b84fe44fdc223a5784d84736d1c2d3c7",
+      "role": "unchanged cited R489 bit supplier"
+    },
+    {
+      "pr": 502,
+      "head": "4d30b8322184598e65e90a92389e17e1baedd9eb",
+      "role": "retiming transfer constructor and PR495 schedule fixture"
+    },
+    {
+      "pr": 501,
+      "head": "1dc056496fdbbc74073ed26d948a2dc235dbf356",
+      "role": "parallel retiming integration; credited, no duplicated gain"
+    },
+    {
+      "pr": 473,
+      "head": "628b454d3df00367d2d4f78de7d4eb9cbcbd47ca",
+      "role": "single-helper gauge withdrawal inspiration"
+    },
+    {
+      "pr": 507,
+      "head": "8d4444cf8a16d500cbb94add6e4fa8bcfb9c7d5e",
+      "role": "partial-own factory, 84-pivot reference and retiming map"
+    },
+    {
+      "pr": 505,
+      "head": "4ee769c8e28837482272b5f4742497da8e2fc9d4",
+      "role": "our prior complete-invocation asynchronous scheduling"
+    },
+    {
+      "pr": 506,
+      "head": "a4948baee6c7ea35323db74ff636620c6af2925a",
+      "role": "public asynchronous retiming comparison and portability feedback"
+    }
+  ],
+  "openai_math": {
+    "repository": "https://github.com/openai/math",
+    "revision": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
+    "status": "source inspection and mathematical adaptation; no new Lean audit"
+  },
+  "other_inspirations": [
+    497,
+    458,
+    442,
+    434,
+    433,
+    425,
+    417,
+    435,
+    440,
+    401,
+    408,
+    416,
+    370,
+    361,
+    315,
+    495,
+    503,
+    504
+  ],
+  "excluded": {
+    "494": "under-review split-residual interface not used",
+    "491": "withdrawn GL sampling argument not used",
+    "499": "larger claim inherits disputed split-residual interface; not used"
+  },
+  "related_updated": [
+    {
+      "pr": 473,
+      "head": "94b3c908fb7628142817d995155368aba2eae841",
+      "role": "new nonuniform scheduling comparison; earlier pinned gauge proposal remains a separate source"
+    },
+    {
+      "pr": 477,
+      "head": "2f23f46f1f9e4599168d40096fbacce4973a2978",
+      "role": "experiment log consulted to avoid repeating old searches"
+    }
+  ],
+  "recent_context": [
+    {
+      "pr": 509,
+      "head": "7b9c720ecc9f483c383e7cd9c2ab81f06ee5df59",
+      "role": "abstract Lemma G proof; no new numerical ingredient"
+    },
+    {
+      "pr": 510,
+      "head": "64edee18af02aab0c1696b677a0287dd0146381b",
+      "role": "nonbinding bit improvement; not substituted"
+    },
+    {
+      "pr": 511,
+      "head": "79f7c03c7f820ab89955b75ef239cbaccc627e6e",
+      "role": "formal dispatcher context"
+    },
+    {
+      "pr": 512,
+      "head": "73d367fe754cf5921cd954221133b20ac752f932",
+      "role": "asynchronous partial-own comparison"
+    },
+    {
+      "pr": 513,
+      "head": "005dd3f4e3cba8d1761abc4ab391aaf6d14d6f73",
+      "role": "formal completed-bank context"
+    }
+  ],
+  "this_round": [
+    {
+      "pr": 514,
+      "head": "246bfacd4cb4072836ae3147099f548bb728229f",
+      "role": "publication of earlier92-pivot baseline; inherited ancestry"
+    },
+    {
+      "pr": 515,
+      "head": "6590606e733768f6a7004b3f55ae35f988ba515f",
+      "role": "alternative bit copy deletion and chain optimization; comparison only"
+    },
+    {
+      "pr": 516,
+      "head": "871b1c51e53918c5e6c945dfe8ef45546c17da56",
+      "role": "draft paid-wrapper/asynchronous formal realization; not recompiled or instantiated here"
+    },
+    {
+      "pr": 517,
+      "head": "65518fcff5a7bd490365273ae5469a82aac14853",
+      "role": "old84-pivot coordinated witness and restricted packing ceiling; route-selection context"
+    },
+    {
+      "pr": 511,
+      "head": "9a20ad04be54b1c0fa26bd4ceb689f9ea220eab5",
+      "role": "provenance update; no new numerical ingredient"
+    }
+  ]
+}
diff --git a/research/ranksector112-async/vendor/pr522/code/assemble.py b/research/ranksector112-async/vendor/pr522/code/assemble.py
new file mode 100644
index 0000000000..de2a375d13
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/code/assemble.py
@@ -0,0 +1,42 @@
+"""Two exact moment engines and strict outer composition of a new PR484 rehosting
+with the unchanged published PR493 bit supplier. Prepared by OpenAI Codex; arithmetic
+engines are pinned inherited PR361/Mercator and independent base-two code.
+Usage: assemble_candidate.py AUDIT_OUT PARENT_VARIANT HOSTED BIT_RESULT
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+import json,gzip,sys,hashlib,importlib.util
+O,V,H,B=map(Path,sys.argv[1:5]);sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+def load(n):
+ p=V/'work/pr361/code/engines'/(n+'.py');s=importlib.util.spec_from_file_location('candidate_'+n,p);m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m
+M,Other,Outer=[load(n)for n in ['moment','base_two_moment','outer']]
+owner=json.loads((O/'OWNERS-AND-PROFILE.json').read_text());inv=json.loads((O/'PREFIX-AND-INVOICE.json').read_text());host=json.loads((H/'HOSTED.json').read_text());bit=json.loads(B.read_text())["eleven"];P={int(r):n for r,n in owner['paid_profile'].items()};m,W=73,owner['live'];assert m*W-sum(r*n for r,n in P.items())==2496
+rc=M.certify(P,m,W,True);b=Q(rc['lower']);bp=Q(rc['upper']);assert bp-b==Q(1,10**24)
+fallback=32*m*m*sum(P.values());receipts=[]
+for z,accept in[(b,True),(bp,False)]:
+ ml,mh=M.moment(P,m,W,z,True);a,c=Other.moment(m,W,list(P.items()),z);d,e=Other.moment(m,W,[(1,fallback)],z);a+=d/10**16;c+=e/10**16
+ assert (mh<1 and c<1)if accept else(ml>1 and a>1)
+ receipts.append(dict(endpoint=str(z),mercator=[str(ml-1),str(mh-1)],base_two=[str(a-1),str(c-1)],accept=accept))
+# Reprice the cited unchanged bit histogram, clearly separate from bit operator verification.
+bitP={int(r):n for r,n in bit['profile'].items()};bitc=Q(bit['bit_lower']);bitnext=bitc+Q(1,10**24)
+for zz,accepted in [(bitc,True),(bitnext,False)]:
+ bl,bh=M.moment(bitP,78,9600,zz,True)
+ ol,oh=Other.moment(78,9600,list(bitP.items()),zz)
+ fl,fh=Other.moment(78,9600,[(1,32*78*78*sum(bitP.values()))],zz)
+ assert (bh<1 and oh+fh/10**16<1) if accepted else (bl>1 and ol+fl/10**16>1)
+c=Q(bit['bit_lower']);eta=beta=Q(1,10**18);grid=Q(1,10**18);s=min(c,(1-beta)*b)-Q(1,10**24)
+assert 0<s<c and s<(1-beta)*b
+coeff=int(bit['bit']['charged_three_level_coefficient_bits']);row=max(20161,int(bit['bit']['row_coefficient']),inv['finite']['physical_row_coefficient']);chain=[Q(384599,10**10)];cuts=[]
+def ceil(x):return -(-x.numerator//x.denominator)
+for i in range(6):
+ old=chain[-1];a=(1-s)*s+s*old;gap=min(s-a,1-a-s,1-a-s*(1-old),1-s);assert old<a<s<1-a and gap>0
+ cut=max(ceil(36/gap**2),ceil(2*(4+coeff)/gap));assert cut*gap**2>=36 and cut*gap>=2*(4+coeff);cuts.append(dict(gap=str(gap),cutoff_log2=str(cut)));chain.append(a)
+q=chain[-1]*(1-2*eta);margin=(1-eta)*q/(1+q);ticks=margin/grid;kap=grid*((ticks.numerator-1)//ticks.denominator)
+bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1},'rows':{'degree_gap':Q(10**6)-Q(51*row,25)}}
+a=Outer.assembly(chain[-1],b,bridge,kap,eta=eta,beta=beta);assert len(a['strict_constraints'])==47 and all(x>0 for x in a['strict_constraints'].values());controls=[]
+for name,k,e,be in [('next_grid',kap+grid,eta,beta),('zero_eta',kap,Q(0),beta),('zero_beta',kap,eta,Q(0)),('unit_beta',kap,eta,Q(1))]:
+ try:Outer.assembly(chain[-1],b,bridge,k,eta=e,beta=be)
+ except AssertionError:controls.append(name)
+ else:raise AssertionError(name)
+res=dict(status='PASS_ASYNC_COMPLEX_AND_CITED_BIT_EXACT_ASSEMBLY',complex_lower=str(b),complex_decimal=rc['lower'],next_b_rejected=str(bp),exact_moment_receipts=receipts,bit_lower=str(c),bit_result_sha256=sha(B),bit_template_sha256=bit['emitted_program_sha256'],bit_prefix_bits=bit['bit']['charged_prefix_bits'],bit_charged_three_level_coefficient_bits=coeff,external_row_allowance=row,kappa=str(kap),kappa_decimal=f'{float(kap):.18f}',binding_component='bit'if c<(1-beta)*b else'complex',strict_outer_constraints={k:str(v)for k,v in a['strict_constraints'].items()},outer_controls=controls,bootstrap=cuts,complex_template_sha256=host['template_sha256'],owner_audit_sha256=sha(O/'OWNERS-AND-PROFILE.json'),invoice_sha256=sha(O/'PREFIX-AND-INVOICE.json'),bit_scope='PR493 published profile and operator reused as a pinned dependency; this verifier reprices its published profile but does not reconstruct that unchanged bit operator.',scope='Conditional finite witness. Inherited compiler, precision/tape and analytic-transfer contracts remain assumed; changed-host operator admission recorded separately.')
+(O/'EXACT-ASSEMBLY.json').write_text(json.dumps(res,indent=2)+'\n');print(res['status'],'b',res['complex_decimal'],'kappa',res['kappa_decimal'],flush=True)
diff --git a/research/ranksector112-async/vendor/pr522/code/audit_async.py b/research/ranksector112-async/vendor/pr522/code/audit_async.py
new file mode 100644
index 0000000000..43642d1aa0
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/code/audit_async.py
@@ -0,0 +1,149 @@
+"""OpenAI Codex independent serialized ASYNCHRONOUS controller/spectator audit.
+Imports no emitter, optimizer, expander, edge-coloring, or source hosting code.
+CLI: VERIFIED_VARIANT POOLED_HOSTED OUT.json
+The local provider is read from VERIFIED_VARIANT, never from a baseline width histogram.
+"""
+import sys,json,gzip,hashlib,copy
+from pathlib import Path
+from collections import Counter,defaultdict
+BASE,OUT,REPORT=map(lambda p:Path(p).resolve(),sys.argv[1:4]);read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+parent=read(BASE/'split-centres/GLOBAL-TEMPLATE.json.gz');canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz');checks=read(BASE/'split-centres/LOCAL-CHECKS.json');ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json');ct=read(OUT/'GLOBAL-TEMPLATE.json.gz');summary=read(OUT/'HOSTED.json');V=canon['v'];R=canon['R'];N=2*V+R;CENTRES=len(canon['centers']);assert V==120 and canon['h']==9; width=[9-len(canon['frames'][canon['start'][2*V+h]])for h in range(R)];prank={e['child']:e['rank']for e in parent['idle_children']};M=73;T=8;DATA=7680;PHYSICAL=DATA+CENTRES+R+2;CALLS=72;HOSTED=CALLS*R
+
+def orthobasis(port):
+ q=canon['ports'][port];z=next(i for i in range(9)if(q>>i)&1==0);a=q^(1<<z);order=list(range(9));order[z],order[0]=order[0],order[z]
+ b=[(1<<i)^(a if a>>i&1 else 0)for i in order]+[1<<i for i in range(9,73)]
+ assert len(b)==73 and all((x&y).bit_count()%2==int(i==j)for i,x in enumerate(b)for j,y in enumerate(b));return b
+bases=[orthobasis(p)for p in range(120)]
+# Bind the selected provider's actual normalization recipes, including newly
+# selected entrance frames; a baseline recipe registry cannot silently survive.
+required_artifacts={'split-centres/CANONICAL-WORD.json.gz','split-centres/LOCAL-PROGRAMS.json.gz','split-centres/LOCAL-CHECKS.json','split-centres/RESIDUAL-ADAPTERS.json','work/complex-nine-native/DATA-PHASES.json'}
+assert required_artifacts <= set(summary['source_artifacts'])
+adapter_path=BASE/'split-centres/RESIDUAL-ADAPTERS.json'
+assert hashlib.sha256(adapter_path.read_bytes()).hexdigest()==parent['residual_adapter_sha256']
+adapters=read(adapter_path)['recipes']
+for h,w in enumerate(width):
+ if w<9:
+  f=canon['start'][240+h];a=adapters[str(f)]
+  assert a['frame']==f and a['vectors']==canon['frames'][f] and a['rank']==w and a['entrance_rank']==9-w
+
+def audit(t):
+ assert(t['live'],t['physical'])==(DATA,PHYSICAL)
+ assert t['local_programs']==parent['local_programs']and t['recipe']==parent['recipe']and 'each local invocation completes before the next' in t['loop_order'].lower()
+ assert len(t['calls'])==72 and t['hosting']['max_helpers_per_physical_family_per_call']==1 and t['hosting']['banks']==[0]*9
+ for key in('exact_data_phase_recipe_sha256','exact_local_clifford_recipe_sha256','residual_adapter_sha256','adapter_policy'):assert t[key]==parent[key]
+ # Independently project the literal schedule onto every data replica.
+ src=parent['execution_schedule'];assert t['async_schedule']['source_schedule']==src
+ assert t['async_schedule']['source_call_order']==[[c['stage'],c['replica']]for c in parent['calls']]
+ order=[(c['stage'],c['replica'])for c in t['calls']]
+ assert [list(x)for x in order]==t['async_schedule']['order'] and len(set(order))==72
+ all_local=[];perrep={r:[]for r in range(8)};globals_=[]
+ for e in t['execution_schedule']:
+  j=e['source_event'];old=copy.deepcopy(src[j])
+  if 'replica'in e:
+   r=e['replica'];assert 0<=r<8 and j<30;perrep[r].append(j)
+   expected=old|dict(source_event=j,replica=r,replicas=[r],time=e['time'])
+   assert e==expected
+   assert 0<=e['time']<72 and order[e['time']][1]==r
+   if e['kind']=='local_cover_sweep':
+    assert order[e['time']]==(e['stage'],r);all_local.append((e['stage'],r,e['time']))
+  else:
+   globals_.append(j);expected=old|dict(source_event=j)
+   if e['kind']=='bank_padding_cover_sweep':expected['families']=[7680,7680]
+   if e['kind']=='translate_every_live_family':expected.update(families=[0,7680],charged_calls_per_cover=7680)
+   assert e==expected
+ assert all(v==list(range(30))for v in perrep.values()) and globals_==[30,31]
+ assert all_local==[(st,r,i)for i,(st,r)in enumerate(order)]
+ assert all('replica'in e for e in t['execution_schedule'][:-2])
+ assert [e['source_event']for e in t['execution_schedule'][-2:]]==[30,31]
+ # Local cover calls are indivisible; a block then runs the source events
+ # up to that replica's next local invocation.
+ block=-1
+ for e in t['execution_schedule'][:-2]:
+  if e['kind']=='local_cover_sweep':block+=1
+  assert e['time']==block
+ assert t['bank_padding']==dict(parent['bank_padding'],families=[])
+ assert t['cover_final_correction']==dict(parent['cover_final_correction'],families=[0,7680],charged_calls_per_cover=7680)
+ assert t['private_namespace']=={'centers':[DATA,DATA+CENTRES],'reserved_tableau':[DATA+CENTRES,DATA+CENTRES+R],'coefficient':[DATA+CENTRES+R,PHYSICAL]}
+ # Actual physical touch intervals include every individual bridge.
+ pairs={};sides={};windows={};last={};callpos={};stagepair={e['stage']:e['pair']for e in parent['recipe']if e['kind']=='local'}
+ for pos,e in enumerate(t['execution_schedule']):
+  if 'replica'not in e:continue
+  rep=e['replica']
+  if e['kind']=='local_cover_sweep':
+   pair=stagepair[e['stage']];callpos[e['stage'],rep]=pos;last[rep,pair]=pos
+  elif e['kind']=='bridge':last[rep,e['src']]=last[rep,e['dst']]=pos
+  elif e['kind']=='idle_cover_sweep':
+   for side,i in enumerate(e['child_indices']):
+    if i not in prank:continue
+    pairs[i]=e['pair'];sides[i]=side;windows[rep,i]=(last.get((rep,e['pair']),-1),pos)
+ used=defaultdict(set);roles={};paid=Counter();sigmas={};digest=hashlib.sha256();entering=0;cross=0;touches=defaultdict(list)
+ for call in t['calls']:
+  old=next(z for z in parent['calls']if(z['stage'],z['replica'])==(call['stage'],call['replica']))
+  assert {k:v for k,v in call.items()if k not in('owners','time')}=={k:v for k,v in old.items()if k!='owners'}
+  s,rep,pair=call['stage'],call['replica'],call['pair'];assert call['time']==t['async_schedule']['order'].index([s,rep]);own=call['owners'];assert len(own)==N and len({f for f,rt in own})==N and all(0<=f<DATA for f,rt in own)
+  assert own[:240]==old['owners'][:240]
+  for h,(family,route)in enumerate(own[240:]):
+   w=width[h];typ,i,off=route[:3];ownerrep,sub=divmod(family,960);fampair,sub=divmod(sub,240);side,port=divmod(sub,120)
+   assert windows[ownerrep,i][0]<callpos[s,rep]<windows[ownerrep,i][1] and fampair==pairs[i] and side==sides[i] and 0<=off and off+w<=prank[i]
+   B=bases[port];pend=[int(x)for x in ph['recipes'][port]['idle_children'][i]['orthogonal_axes']];assert len(pend)==prank[i]
+   occ=[B.index(v)for v in pend[off:off+w]];sp=[j for j in range(M)if j not in occ][:9-w]
+   assert route==([3,i,off]if w==9 else[4,i,off,w,sp]);assert len(set(occ+sp))==9
+   order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert sorted(order)==list(range(M));sigma=[B[j]for j in order]
+   assert sigma[:w]==pend[off:off+w]and sigma[w:9]==[B[j]for j in sp]
+   sh=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sh]=sigma;digest.update(json.dumps([s,rep,h,family,sh],separators=(',',':')).encode()+b'\n')
+   key=(i,ownerrep,port);cells=set(range(off,off+w));assert not used[key]&cells;used[key]|=cells
+   role=(s,rep,h);assert role not in roles;roles[role]=dict(stage=s,replica=rep,helper=h,family=family,owner_replica=ownerrep,child=i,copy=ownerrep*120+port,port=port,offset=off,width=w)
+   touches[family].append((s,rep,h));entering+=w<9;cross+=rep!=ownerrep
+  for r,n in checks[call['orientation']]['paid_profile'].items():paid[int(r)]+=n
+ assert set(roles)=={(s,rep,h)for s in range(9)for rep in range(8)for h in range(R)}
+ # The frozen pooled metadata must bind the actual serialized owner maps.
+ assert len(t['hosting']['pooled_slots'])==HOSTED
+ for z in t['hosting']['pooled_slots']:
+  key=(z['stage'],z['replica'],z['helper']);assert key in roles
+  assert {k:z[k]for k in roles[key]}==roles[key]
+ assert len({(z['stage'],z['replica'],z['helper'])for z in t['hosting']['pooled_slots']})==HOSTED
+ rem={};wanted=[]
+ for old in parent['idle_children']:
+  i,port=old['child'],old['port']
+  for rep in range(T):
+   u=used[i,rep,port];assert u==set(range(len(u)));r=old['rank']-len(u)
+   if r:
+    f=rep*960+(2*pairs[i]+sides[i])*120+port;wanted.append(dict(child=i,port=port,replica=rep,replicas=1,family=f,rank=r,hosted=len(u),pending_offset=len(u)));paid[r]+=1
+ assert t['idle_children']==wanted
+ mass=sum(r*n for r,n in paid.items());assert73=73*7680-mass;assert assert73==2496 and 73**2>2*max(paid)**2
+ return dict(profile=dict(sorted(paid.items())),mass=mass,hosted=HOSTED,entering=entering,cross_replica=cross,sigma_digest=digest.hexdigest(),sigmas=sigmas,idle_remainders=len(wanted),busy_family_checks=len(roles),invocations=72)
+
+r=audit(ct);raw=gzip.decompress((OUT/'GLOBAL-TEMPLATE.json.gz').read_bytes());assert hashlib.sha256(raw).hexdigest()==summary['template_sha256'];assert r['profile']=={int(k):v for k,v in summary['global_profile'].items()};assert r['sigmas']==read(OUT/'ACTUAL-SIGMAS.json.gz');assert r['sigma_digest']==summary['sigma_stream_sha256']
+assert all(hashlib.sha256((BASE/name).read_bytes()).hexdigest()==value for name,value in summary['source_artifacts'].items())
+controls=[]
+def reject(name,mut):
+ q=copy.deepcopy(ct);mut(q)
+ try:audit(q)
+ except(AssertionError,KeyError,IndexError,ValueError,TypeError):controls.append(name)
+ else:raise AssertionError('ACCEPTED '+name)
+reject('wrong call time',lambda q:q['calls'][0].__setitem__('time',71))
+enter=lambda q:next(o for c in q['calls']for o in c['owners'][240:]if o[1][0]==4)
+reject('alias two whole owners',lambda q:q['calls'][0]['owners'].__setitem__(241,q['calls'][0]['owners'][240]))
+reject('helper on active data family',lambda q:q['calls'][0]['owners'][240].__setitem__(0,q['calls'][0]['owners'][0][0]))
+reject('owner in private namespace',lambda q:q['calls'][0]['owners'][240].__setitem__(0,7680))
+reject('unbound change of owner replica',lambda q:q['calls'][0]['owners'][240].__setitem__(0,(q['calls'][0]['owners'][240][0]+960)%7680))
+reject('omit complete invocation',lambda q:q['calls'].pop())
+reject('reorder invocation replicas',lambda q:q['calls'].__setitem__(0,q['calls'][1]))
+reject('interleave local invocations',lambda q:q.__setitem__('loop_order','interleaved local instructions'))
+reject('change local instruction stream',lambda q:q['local_programs']['forward'].pop())
+reject('wrong residual width',lambda q:enter(q)[1].__setitem__(3,enter(q)[1][3]-1))
+reject('wrong spectator coordinate',lambda q:enter(q)[1][4].__setitem__(0,72))
+reject('omit spectator route',lambda q:enter(q).__setitem__(1,enter(q)[1][:3]))
+reject('overlap residual footprint',lambda q:q['calls'][0]['owners'][240][1].__setitem__(2,100))
+reject('omit idle remainder',lambda q:q['idle_children'].pop())
+reject('underpay idle remainder',lambda q:q['idle_children'][0].__setitem__('rank',0))
+reject('omit bridge touch',lambda q:q['execution_schedule'].pop(next(i for i,e in enumerate(q['execution_schedule'])if e['kind']=='bridge')))
+reject('remove one-owner rule',lambda q:q['hosting'].pop('max_helpers_per_physical_family_per_call'))
+reject('duplicate frozen role',lambda q:q['hosting']['pooled_slots'].__setitem__(1,q['hosting']['pooled_slots'][0]))
+reject('understate physical reserve',lambda q:q.__setitem__('physical',PHYSICAL-1))
+report=dict(status='PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS',template_sha256=summary['template_sha256'],complex_template_sha256=summary['template_sha256'],complex_live=7680,complex_profile=r['profile'],complex_hosted_residuals=HOSTED,physical=PHYSICAL,rank_mass=r['mass'],deficit=2496,entering_helper_roles=r['entering'],cross_replica_helper_roles=r['cross_replica'],one_owner_per_complete_invocation=True,helper_busy_family_window_checks=r['busy_family_checks'],complete_invocations=r['invocations'],actual_orthogonal_73column_maps=len(r['sigmas']),actual_sigma_stream_sha256=r['sigma_digest'],all_actual_residual_and_spectator_charts=True,idle_remainders=r['idle_remainders'],mutations_rejected=controls,widths=dict(sorted(Counter(width).items())),scope='Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses unchanged source local program and normalized residual-wrapper identities; all-size compilation and complete coefficient invoice are separate inherited obligations.')
+REPORT.write_text(json.dumps(report,indent=2)+'\n');print(json.dumps(report,indent=2))
+
+owners=dict(status='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE',template_sha256=summary['template_sha256'],paid_profile=r['profile'],live=7680,physical=PHYSICAL,rank_mass=r['mass'],deficit=2496,hosted_residuals=HOSTED,banked_residuals=0,all_800_owners_per_call_distinct=True,actual_helper_owner_charts=HOSTED,actual_73column_sigmas=len(r['sigmas']),cross_replica_helper_roles=r['cross_replica'],explicit_idle_remainder_children=r['idle_remainders'],source_idle_children_charged=sum(x['replicas']for x in parent['idle_children']),source_artifacts=summary['source_artifacts'],controller_audit_sha256=hashlib.sha256(REPORT.read_bytes()).hexdigest())
+(REPORT.parent/'OWNERS-AND-PROFILE.json').write_text(json.dumps(owners,indent=2)+'\n')
+
diff --git a/research/ranksector112-async/vendor/pr522/code/audit_async_invoice.py b/research/ranksector112-async/vendor/pr522/code/audit_async_invoice.py
new file mode 100644
index 0000000000..baca4c6dbb
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/code/audit_async_invoice.py
@@ -0,0 +1,100 @@
+"""Async PR484 scalar/prefix lowering and finite overcharge recount. OpenAI Codex.
+Reads emitted programs, canonical word and raw routes, importing no supplier code.
+Inherited all-size compiler admissibility is a condition, not inferred here.
+"""
+from pathlib import Path
+from fractions import Fraction as F
+from collections import Counter
+import gzip,json,math,hashlib
+import sys
+O=Path(sys.argv[1]);V=Path(sys.argv[2]);HOSTED=Path(sys.argv[3])
+def read(p):return json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+w=read(V/'split-centres/CANONICAL-WORD.json.gz');p=read(V/'split-centres/LOCAL-PROGRAMS.json.gz');old=read(V/'split-centres/GLOBAL-TEMPLATE.json.gz');new=read(HOSTED/'GLOBAL-TEMPLATE.json.gz');integ=read(V/'split-centres/INTEGRATION.json');checks=read(V/'split-centres/LOCAL-CHECKS.json');prior=read(V/'split-centres/INDEPENDENT-REPLAY.json');owners=read(O/'OWNERS-AND-PROFILE.json')
+VV=w['v'];R=w['R'];N=2*VV+R;M=73;L=9;T=8;K=4
+assert VV==120 and w['h']==9
+PAYLOAD=512
+control=read(O/'ASYNC-AUDIT.json')
+raw=gzip.decompress((HOSTED/'GLOBAL-TEMPLATE.json.gz').read_bytes());th=hashlib.sha256(raw).hexdigest()
+assert th==control['complex_template_sha256']==owners['template_sha256']
+assert control['one_owner_per_complete_invocation'] and control['complete_invocations']==72
+assert new['local_programs']==old['local_programs'] and new['recipe']==old['recipe']
+assert Counter(c['orientation']for c in new['calls'])==Counter(c['orientation']for c in old['calls'])
+local={}
+for ori,evs in p.items():
+ rows={('L',i):{i:F(1)}for i in range(N)};env={('L',i):F(1)for i in range(N)};peak=F(1);real=macros=0;paid=Counter();workops=0
+ for e in evs:
+  if e[0]=='climb':paid[e[5]]+=1
+  elif e[0]=='center':paid[e[4]]+=1
+  elif e[0]=='scalar':
+   macros+=1;x=e[1];op=x[0];a=tuple(x[1]);count=0
+   if op=='clear':rows[a]={};env[a]=F(0);count=1
+   elif op=='copy':rows[a]=dict(rows[tuple(x[2])]);env[a]=env[tuple(x[2])];count=1
+   elif op=='scale':
+    q=F(x[2],x[3]);num,den=abs(q.numerator),q.denominator
+    assert num and num&(num-1)==0 and den&(den-1)==0
+    rows[a]={j:q*v for j,v in rows[a].items()};env[a]*=abs(q)
+    count=abs(num.bit_length()-den.bit_length())+int(q<0)
+   elif op=='add':
+    b=tuple(x[2]);q=F(x[3],x[4]);num,den=abs(q.numerator),q.denominator
+    assert a!=b and num>0 and den&(den-1)==0
+    # Lower actual coefficient to cleared Horner work. Every intermediate
+    # magnitude envelope is explicitly included, before denominator halvings.
+    acc=0;count=1
+    for i,ch in enumerate(bin(num)[2:]):
+     if i:acc*=2;count+=1;peak=max(peak,acc*env[b])
+     if ch=='1':acc+=1;count+=1;peak=max(peak,acc*env[b])
+    v=F(acc)
+    for i in range(den.bit_length()-1):v/=2;count+=1;peak=max(peak,v*env[b])
+    assert v==abs(q);count+=2 # signed accumulation and private work clear
+    env[a]=env.get(a,F(0))+abs(q)*env[b];rr=rows.setdefault(a,{})
+    for j,z in list(rows[b].items()):
+     value=rr.get(j,F(0))+q*z
+     if value:rr[j]=value
+     else:rr.pop(j,None)
+    workops+=count
+   else:raise AssertionError(op)
+   real+=2*count;peak=max(peak,env[a])
+ assert all(not row for reg,row in rows.items()if reg[0]=='C')
+ for i in range(N):
+  expected={i:F(1)}
+  if ori=='forward'and 120<=i<240:expected[i-120]=F(1)
+  if ori=='backward'and i<120:expected[i+120]=F(-1)
+  assert rows['L',i]==expected
+ assert peak==F(prior['local'][ori]['prefix_l1_upper']) and peak<2**192
+ assert real==checks[ori]['real_component_primitive_bound']and macros==checks[ori]['scalar_macros']
+ assert dict(paid)=={int(r):z for r,z in checks[ori]['paid_profile'].items()}
+ local[ori]=dict(events=len(evs),macros=macros,real_component_primitives=real,prefix_l1=str(peak),prefix_bits=peak.numerator.bit_length()-peak.denominator.bit_length()+1,coefficient_work_primitive_count=workops,all_exact_columns=N,all_560_dirty_helper_columns_restored=True,private_centres_and_coefficient_work_cleared=True)
+centres=len(w['centers']);widths=[9-len(w['frames'][f])for f in w['start'][240:]];enter=sum(x<9 for x in widths)
+children=sum(checks['forward']['paid_profile'].values());macros=max(x['macros']for x in local.values());compiler=64*(M+1)**3
+adapters=16*(macros+children+N+centres)+64*M
+primitive_bound=max(x['real_component_primitives']for x in local.values())+adapters*compiler
+bridges=sum(e['kind']=='bridge'for e in old['recipe']);bridgeadd=2*VV*T*bridges;assert sum(e['kind']=='bridge'for e in new['execution_schedule'])==T*bridges
+shifts=K*VV*T;moves=2*K*VV*T
+oldW=old['live'];oldP=old['physical'];oldNB=(oldW-2*VV*K*T)//L
+scalar=sum(local[c['orientation']]['real_component_primitives']for c in old['calls'])
+nonlocal_items=4*VV*T*L+2*VV*T*L+2*L*T*R+sum(e['replicas']for e in old['idle_children'])+L*oldNB+bridgeadd+shifts+moves+oldW+oldP+2*L*T*enter*144
+outside=8*nonlocal_items+64*M
+pervertex=scalar+bridgeadd+shifts+moves+oldW+(72*adapters+outside)*compiler+64*oldP
+invoice=integ['finite_invoice'];assert (primitive_bound,adapters,pervertex,compiler)==(invoice['local_primitive_bound'],invoice['local_adapters'],invoice['pervertex'],invoice['compiler'])
+# Independent hosted stock rebase, retaining the larger unhosted operation
+# overcharge; only the stock and mass in the common router/literal change.
+W=new['live'];P=new['physical'];mass=owners['rank_mass'];profile=owners['paid_profile']
+assert M*W-mass==2496 and P==W+R+centres+2
+rebase=pervertex-oldP*65+P*65-oldW+W;used=max(rebase,pervertex)
+r=M//2;group=2**(r*r)
+for i in range(1,r+1):group*=2**(2*i)-1
+stock=group*P;smass=group*mass;logical=group*used+64;router=compiler*(logical+1)*(stock+1)**2
+G,E,C0=2**30000,2**100000,2**210000;B=smass+E;literal=2*G*stock**2+8*smass+4*stock+4+32*M;row=2*stock.bit_length()+9909+252+2*PAYLOAD;maxchild=max(map(int,profile))
+ineq=dict(local_primitive_bound=primitive_bound<2**48,logical=logical<2**6050,router=router<G,literal=literal<E,mass=B<2**100001,precision=32*M*B*B<C0,tape=2*B+18<C0,row=row<20161,halving=M*M>2*maxchild*maxchild)
+assert all(ineq.values())
+localbits=max(x['prefix_bits']for x in local.values());input_l2_bits=(M+1)//2
+bridge_sweeps=sum(e['kind']=='bridge'for e in new['execution_schedule'])
+required_prefix=localbits+input_l2_bits+len(new['calls'])+bridge_sweeps+4
+assert 0 < localbits <= 192 and len(new['calls']) == 72 and bridge_sweeps == 72 and required_prefix < PAYLOAD
+assert owners['explicit_idle_remainder_children']<=owners['source_idle_children_charged']
+assert new['physical']<=old['physical'] and new['live']<=old['live'] and not new['bank_padding']['families']
+out=dict(status='PASS_INDEPENDENT_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE',template_sha256=th,global_prefix_bits=required_prefix,charged_prefix_bits=PAYLOAD,complete_invocation_sweeps=72,bridge_sweeps=bridge_sweeps,row_prefix_extra=2*PAYLOAD,local=local,entering_helpers=enter,entrance_rank=sum(9-x for x in widths),local_adapters=adapters,local_primitive_bound=primitive_bound,wrapper_elementary_factors_charged=2*72*enter*144,compiler=compiler,unhosted_pervertex=pervertex,hosted_rebased_pervertex=rebase,conservative_pervertex_used=used,finite=dict(physical_stock_bits=stock.bit_length(),router_bits=router.bit_length(),literal_bits=literal.bit_length(),physical_row_coefficient=row,retained_row_coefficient=20161,required_C0_bits=(32*M*B*B).bit_length(),halving_integer_inequality=[M*M,2*maxchild*maxchild],G_exponent=30000,E_exponent=100000,C0_exponent=210000),strict_checks=ineq,scope='Exact finite recount conditional on inherited all-size compiler/precision/tape and analytic-transfer contracts. Signed accumulation uses the supplier scalar primitive convention. Async prefix counts all72individual bridges and72complete invocations;512bits are charged, and an additional2*512 enters the two-level physical row bound.')
+(O/'PREFIX-AND-INVOICE.json').write_text(json.dumps(out,indent=2)+'\n');print(json.dumps(out,indent=2),flush=True)
+
+prefix=dict(status='PASS_ASYNC_GLOBAL_PREFIX',template_sha256=th,global_prefix_bits=required_prefix,retained_payload_bits=PAYLOAD,complete_invocation_cover_sweeps=len(new['calls']),bridge_factor_two_sweeps=bridge_sweeps,local_scalar_coefficient_work_prefix_bits=localbits,stream_input_sup_to_l2_bits=input_l2_bits,primitive_arithmetic_margin_bits=4,controller_audit_sha256=hashlib.sha256((O/'ASYNC-AUDIT.json').read_bytes()).hexdigest(),proof=f'Each complete normalized invocation has unitary helper endpoints and a data shear with at most two unitary summands. Distinct full orthogonal owner charts act by right-translation bijections on the retained cover group. Thus the maximum full-stream L2 norm grows by at most2per complete local cover sweep and individual bridge. All72local sweeps and72individual bridge sweeps are counted. Unit-modulus phases, idle children, terminal translations and normalized spectator endpoints are unitary. The independently replayed scalar/Horner envelope costs {localbits} bits, initial sup-to-L2 conversion {input_l2_bits} bits, primitive margin 4 bits: total {required_prefix} < {PAYLOAD}. All-size child/compiler and precision/tape interfaces remain inherited.')
+(O/'GLOBAL-PREFIX.json').write_text(json.dumps(prefix,indent=2)+'\n')
diff --git a/research/ranksector112-async/vendor/pr522/code/audit_kernel_scalar.py b/research/ranksector112-async/vendor/pr522/code/audit_kernel_scalar.py
new file mode 100644
index 0000000000..4373bb9bd5
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/code/audit_kernel_scalar.py
@@ -0,0 +1,55 @@
+"""Independent exact scalar witness for a selected complex kernel word.
+Uses immutable correct-word compensation for omission controls; no repaired
+compensation is silently supplied to a mutant. No physical-hosting claim.
+"""
+import sys,json,gzip,hashlib,copy
+from pathlib import Path
+from fractions import Fraction as Q
+from collections import Counter
+p=Path(__file__).resolve().parent
+path=Path(sys.argv[1]);selection=Path(sys.argv[2]);out=Path(sys.argv[3]);w=json.loads(gzip.decompress(path.read_bytes()));sel=json.loads(selection.read_text());n=240+w['report']['R']
+def ident():return[{r:Q(1)}for r in range(n)]
+def apply(e,rows):
+ if e[0]=='scale':
+  _,t,a,b,*_=e;q=Q(a,b);rows[t]={j:q*x for j,x in rows[t].items()};return
+ _,t,s,a,b,*_=e;q=Q(a,b)
+ for j,x in list(rows[s].items()):
+  z=rows[t].get(j,Q(0))+q*x
+  if z:rows[t][j]=z
+  else:rows[t].pop(j,None)
+def inv(e,dual=False):
+ e=copy.deepcopy(e)
+ if e[0]=='add':
+  e[3]*=-1
+  if dual:e[1],e[2]=e[2],e[1]
+ else:e[2],e[3]=e[3],e[2]
+ return e
+def replay(es):
+ rows=ident()
+ for e in es:apply(e,rows)
+ return rows
+main=w['A']+w['cut']+w['B'];mx=replay(main);dirty=[{}for _ in range(n)]
+for r in range(120,240):dirty[r]={j:x for j,x in mx[r].items()if j>=240}
+for e in w['precondition']:apply(e,dirty)
+comp=[]
+for r in range(120,240):
+ for j,x in sorted(dirty[r].items()):
+  assert not w.get('start_extra',{}).get(str(j)),('nonzero-frame compensation',j)
+  comp.append(['add',r,j,-x.numerator,x.denominator,[]])
+cleanup=[inv(e)for e in reversed(w['A']+w['B'])if not 120<=e[1]<240]
+assert[e[:-1]for e in cleanup]==[e[:-1]for e in w['cleanup']]
+program=w['precondition']+comp+main+cleanup;expected=ident()
+for t in range(120):expected[120+t][t]=Q(1)
+assert replay(program)==expected
+back=ident()
+for t in range(120):back[t][120+t]=Q(-1)
+assert replay([inv(e,True)for e in program])==back
+controls={}
+for cl in sel['kernel']:
+ for h in cl['pivots']:
+  aa=[e for e in w['A']if not(e[0]=='add'and e[2]==240+h and e[1]>=240 and e[-1]==cl['E'])]
+  assert len(aa)<len(w['A']);cc=[inv(e)for e in reversed(aa+w['B'])if not 120<=e[1]<240]
+  assert replay(w['precondition']+comp+aa+w['cut']+w['B']+cc)!=expected
+  controls[str(h)]='REJECTED_OMITTED_KERNEL_CORRECTION'
+r=dict(status='PASS_EXACT_RATIONAL_FORWARD_AND_INVERSE_TRANSPOSE',word_sha256=hashlib.sha256(path.read_bytes()).hexdigest(),selection_sha256=hashlib.sha256(selection.read_bytes()).hexdigest(),columns_each_orientation=n,compensations=len(comp),program_operations=len(program),kernel_pivots=len(controls),controls=controls,scope='Exact local scalar identity and preserved frame-zero compensation; physical owner routing, complete invoice and outer kappa separate.')
+out.write_text(json.dumps(r,indent=2)+'\n');print(r['status'],n,len(controls))
diff --git a/research/ranksector112-async/vendor/pr522/code/build_kernel92.py b/research/ranksector112-async/vendor/pr522/code/build_kernel92.py
new file mode 100644
index 0000000000..f5e68e01f9
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/code/build_kernel92.py
@@ -0,0 +1,42 @@
+"""Reconstruct the selected 92-pivot partial-own complex word.
+Apache-2.0. Prepared with OpenAI Codex assistance; retain PR507/484 notices.
+Usage: python -B build_kernel92.py GK_CODE PARTIAL_BASE KERNEL84_SELECTION
+       RETIME_MAP KERNEL92_SELECTION NEW_OUTPUT_DIR
+No discovery search runs. Actual physical allocation is independently checked.
+"""
+from pathlib import Path
+import json,gzip,sys,copy,hashlib
+from collections import Counter
+if not __debug__:raise RuntimeError('Assertions must remain enabled')
+code,basefile,s84file,mapfile,s92file,out=map(Path,sys.argv[1:]);assert not out.exists();sys.dont_write_bytecode=True;sys.path.insert(0,str(code));import gk_word as g
+read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+base=read(basefile);s84=read(s84file);s92=read(s92file);fm=read(mapfile)
+assert base['report']['R']==560 and len(base['A'])==2680 and len(base['B'])==840
+assert sum(len(c['pivots'])for c in s84['kernel'])==84
+assert sum(len(c['pivots'])for c in s92['kernel'])==92
+wanted=copy.deepcopy(s84['gauge'])
+for h in ['540','541','542','543']:wanted[h]=[408,102]
+assert s92['gauge']==wanted
+w84=g.build(base,s84);r=copy.deepcopy(w84)
+for part in ['A','B']:
+ seen=set()
+ for i,old,new in fm[part]:
+  assert i not in seen and r[part][i][-1]==old,(part,i);seen.add(i);r[part][i][-1]=new
+ assert [e[:-1]for e in r[part]]==[e[:-1]for e in w84[part]]
+assert r['A'][:671]==w84['A'][:671]
+assert g.profile(r)==Counter({int(k):v for k,v in fm['expected_local_profile'].items()})
+ret=copy.deepcopy(base)
+for part in ['A','B']:
+ tail=r[part][-len(base[part]):];assert [e[:-1]for e in tail]==[e[:-1]for e in base[part]];ret[part]=copy.deepcopy(tail)
+ret['cleanup']=[g.inverse(e,g.FULL)for e in reversed(ret['A']+ret['B'])if not 120<=e[1]<240]
+w=g.build(ret,s92);H=g.profile(w);widths=g.widths_of(w)
+assert H=={1:2539,2:160,3:530,4:88,5:298,6:68,7:1,8:17}
+assert Counter(widths)=={7:18,8:154,9:388}
+# Normalize only the established inherited floating display fields and redundant R.
+norm=copy.deepcopy(w);assert norm.get('R',norm['report']['R'])==norm['report']['R']==560;norm.pop('R',None)
+for k in ['complex_coarse_float','gain_percent_float']:norm['report'].pop(k,None)
+semantic=hashlib.sha256(json.dumps(norm,sort_keys=True,separators=(',',':')).encode()).hexdigest()
+assert semantic=='c6e758b324d3566e8443b3fd3d739c4d01e1928eadbee40f5c36973404b0640b'
+out.mkdir(parents=True);(out/'FULL-WORD.json.gz').write_bytes(g.dump(w));(out/'SELECTION.json').write_text(json.dumps(s92,indent=2)+'\n');(out/'RETIMED-BASE.json.gz').write_bytes(g.dump(ret))
+receipt=dict(status='PASS_EXACT_SOURCE_BOUND_KERNEL92_RECONSTRUCTION',sources={label:hashlib.sha256(path.read_bytes()).hexdigest()for label,path in [('partial_base',basefile),('kernel84_selection',s84file),('frame_map',mapfile),('kernel92_selection',s92file),('gk_word.py',code/'gk_word.py'),('gk_common.py',code/'gk_common.py')]},normalized_word_sha256=semantic,word_sha256=hashlib.sha256((out/'FULL-WORD.json.gz').read_bytes()).hexdigest(),profile=dict(H),widths=dict(Counter(widths)),widths_ordered=widths,pivots=92,entrance_rank=sum(9-x for x in widths),scope='Exact local source construction; arbitrary-dirt scalar, physical phases/owners and final outer assembly checked separately.')
+(out/'CONSTRUCTION.json').write_text(json.dumps(receipt,indent=2)+'\n');print(receipt['status'])
diff --git a/research/ranksector112-async/vendor/pr522/code/build_pair35.py b/research/ranksector112-async/vendor/pr522/code/build_pair35.py
new file mode 100644
index 0000000000..0cfd8ae40a
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/code/build_pair35.py
@@ -0,0 +1,58 @@
+"""Rebuild the frozen blockwise evaluation-pair factory and 99-pivot word.
+Apache-2.0. Adapted with OpenAI Codex assistance; retain PR507/484 notices.
+Usage: python -B build_pair35.py PR507_CONSTRUCTOR HAMMING GK_CODE
+       OLD_PARTIAL_BASE RETIMED_PARTIAL_BASE PAIR_SPEC KERNEL_SELECTION NEW_OUT
+No optimizer or discovery search runs. Physical routing and outer price are separate.
+"""
+from pathlib import Path
+from collections import Counter
+from fractions import Fraction
+import sys,json,gzip,hashlib,copy,difflib,subprocess
+if not __debug__:raise RuntimeError('Assertions must remain enabled')
+source,hamming,code,oldfile,retfile,specfile,selfile,out=map(Path,sys.argv[1:])
+assert not out.exists()
+sha=lambda p:hashlib.sha256(p.read_bytes().replace(b'\r\n',b'\n') if p.suffix in {'.py','.json'} else p.read_bytes()).hexdigest()
+assert sha(source)=='8b9a7f1bb69626d76fec9e915134cec7199a70b53656723ce49ecc47f4644afd'
+assert sha(specfile)=='751fad3214c819635216df2dab77b682c6a1798d1d71a959ba4e7392aab9b8c0'
+assert sha(selfile)=='e818377083be1b581da718ae4cdb0741f074df313c0813e4239377b3754f25a5'
+read=lambda f:json.loads(gzip.decompress(f.read_bytes())if f.suffix=='.gz'else f.read_bytes())
+spec=read(specfile);assert len(spec)==14
+assert [k for k,v in sorted(spec.items())if v==[1,1]]==['0,2,4,6','0,3,4,7']
+assert all(v==([1,1]if k in ['0,2,4,6','0,3,4,7']else[0,0])for k,v in spec.items())
+s=source.read_text();old_token='[(1,1)[parity]]';assert s.count(old_token)==1
+s=s.replace(old_token,"[json.loads(Path(sys.argv[3]).read_text())[','.join(map(str,c))][parity]]")
+out.mkdir(parents=True);patched=out/'factory_constructor.py';patched.write_text(s,encoding='utf-8')
+with(out/'factory-construction.log').open('w')as log:
+ subprocess.run([sys.executable,'-B',str(Path(__file__).with_name('run_portable.py')),str(patched),str(hamming),str(out/'factory'),str(specfile)],stdout=log,stderr=subprocess.STDOUT,check=True)
+sys.dont_write_bytecode=True;sys.path.insert(0,str(code));import gk_word as g
+b=read(out/'factory/FULL-WORD.json.gz');old=read(oldfile);ret=read(retfile);selection=read(selfile)
+assert b['report']['R']==old['report']['R']==ret['report']['R']==560
+transferred={}
+for part in ['A','B']:
+ assert [e[:-1]for e in old[part]]==[e[:-1]for e in ret[part]]
+ aa=[tuple(e[:-1])for e in old[part]];bb=[tuple(e[:-1])for e in b[part]];count=0
+ for ia,ib,n in difflib.SequenceMatcher(a=aa,b=bb,autojunk=False).get_matching_blocks():
+  for d in range(n):
+   assert old[part][ia+d][:-1]==b[part][ib+d][:-1]
+   if old[part][ia+d][-1]!=ret[part][ia+d][-1]:b[part][ib+d][-1]=copy.deepcopy(ret[part][ia+d][-1]);count+=1
+ transferred[part]=count
+b['cleanup']=[g.inverse(e,g.FULL)for e in reversed(b['A']+b['B'])if not 120<=e[1]<240]
+w=g.build(b,selection);profile=g.profile(w);widths=g.widths_of(w)
+assert profile=={1:2530,2:182,3:516,4:88,5:298,6:68,7:1,8:17}
+assert Counter(widths)=={7:18,8:161,9:381}
+assert sum(len(c['pivots'])for c in selection['kernel'])==99
+counts={}
+for part in ['A','B','cut','cleanup','precondition']:
+ counts[part]=len(w.get(part,[]))
+ for e in w.get(part,[]):
+  assert e[0]in['add','scale']
+  q=Fraction(e[3],e[4])if e[0]=='add'else Fraction(e[2],e[3])
+  assert q.denominator&(q.denominator-1)==0,(part,e)
+  if e[0]=='scale':assert abs(q.numerator)>0 and abs(q.numerator)&(abs(q.numerator)-1)==0,(part,e)
+norm=copy.deepcopy(w);assert norm.get('R',560)==norm['report']['R']==560;norm.pop('R',None)
+for k in ['complex_coarse_float','gain_percent_float']:norm['report'].pop(k,None)
+semantic=hashlib.sha256(json.dumps(norm,sort_keys=True,separators=(',',':')).encode()).hexdigest()
+assert semantic=='bf26b8c3709039eb027430218f8b9bd3c369eb9c584e4ebfc2f9e350bab93f19'
+(out/'FULL-WORD.json.gz').write_bytes(g.dump(w));(out/'RETIMED-BASE.json.gz').write_bytes(g.dump(b));(out/'SELECTION.json').write_bytes(selfile.read_bytes())
+receipt=dict(status='PASS_SOURCE_BOUND_PAIR35_CONSTRUCTION_AND_DYADIC_GATE',sources={label:sha(f)for label,f in [('public_constructor',source),('prototype',hamming/'PROTOTYPE.json'),('packet_programs',hamming/'PACKET-PROGRAMS.json.gz'),('old_partial',oldfile),('retimed_partial',retfile),('pair_spec',specfile),('selection',selfile),('gk_word.py',code/'gk_word.py'),('gk_common.py',code/'gk_common.py')]},normalized_word_sha256=semantic,word_sha256=sha(out/'FULL-WORD.json.gz'),profile=dict(profile),widths=dict(Counter(widths)),widths_ordered=widths,pivots=99,transferred_frames=transferred,dyadic_event_counts=counts,scope='Exact local source, relation, frame and scalar compiler compatibility; complete arbitrary-dirt and physical provider replay remain separate.')
+(out/'CONSTRUCTION.json').write_text(json.dumps(receipt,indent=2)+'\n');print(receipt['status'])
diff --git a/research/ranksector112-async/vendor/pr522/code/build_ranksector.py b/research/ranksector112-async/vendor/pr522/code/build_ranksector.py
new file mode 100644
index 0000000000..a53740c2ee
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/code/build_ranksector.py
@@ -0,0 +1,56 @@
+"""Reconstruct the rank-sector coordinate-total supplier from frozen sources.
+Apache-2.0. Prepared with OpenAI Codex assistance; retain inherited PR507/484 notices.
+Usage: python -B build_ranksector.py HAMMING GK_CODE OLD_PAIR_BASE
+       RETIMED_PAIR_BASE PAIR_SPEC KERNEL_SELECTION NEW_OUT
+The adjacent construct_ranksector.py is a pinned source file, not an optimizer.
+"""
+from pathlib import Path
+from fractions import Fraction
+from collections import Counter
+import sys,json,gzip,copy,hashlib,difflib,subprocess
+if not __debug__:raise RuntimeError('Assertions must remain enabled')
+hamming,code,oldfile,retfile,specfile,selfile,out=map(Path,sys.argv[1:]);assert not out.exists()
+source=Path(__file__).resolve().with_name('construct_ranksector.py')
+rawsha=lambda f:hashlib.sha256(f.read_bytes()).hexdigest()
+lf=lambda f:f.read_bytes().replace(b'\r\n',b'\n').replace(b'\r',b'\n')
+textsha=lambda f:hashlib.sha256(lf(f)).hexdigest()
+assert textsha(source)=='0b535b717ea3d15cf7e86b096a9a95fc92d71748cd5f937d1989001a3d2ec996'
+assert textsha(specfile)=='751fad3214c819635216df2dab77b682c6a1798d1d71a959ba4e7392aab9b8c0'
+assert textsha(selfile)=='e818377083be1b581da718ae4cdb0741f074df313c0813e4239377b3754f25a5'
+read=lambda f:json.loads(gzip.decompress(f.read_bytes())if f.suffix=='.gz'else f.read_bytes())
+old=read(oldfile);ret=read(retfile);selection=read(selfile)
+assert old['report']['R']==ret['report']['R']==560
+out.mkdir(parents=True)
+with(out/'factory-construction.log').open('w')as log:
+ subprocess.run([sys.executable,'-B',str(Path(__file__).with_name('run_portable.py')),str(source),str(hamming),str(out/'factory'),str(specfile)],stdout=log,stderr=subprocess.STDOUT,check=True)
+sys.dont_write_bytecode=True;sys.path.insert(0,str(code));import gk_word as g
+b=read(out/'factory/FULL-WORD.json.gz');assert b['report']['R']==560
+transferred={}
+for part in ['A','B']:
+ assert [e[:-1]for e in old[part]]==[e[:-1]for e in ret[part]]
+ aa=[tuple(e[:-1])for e in old[part]];bb=[tuple(e[:-1])for e in b[part]];count=0
+ for ia,ib,n in difflib.SequenceMatcher(a=aa,b=bb,autojunk=False).get_matching_blocks():
+  for d in range(n):
+   assert old[part][ia+d][:-1]==b[part][ib+d][:-1]
+   if old[part][ia+d][-1]!=ret[part][ia+d][-1]:b[part][ib+d][-1]=copy.deepcopy(ret[part][ia+d][-1]);count+=1
+ transferred[part]=count
+b['cleanup']=[g.inverse(e,g.FULL)for e in reversed(b['A']+b['B'])if not 120<=e[1]<240]
+w=g.build(b,selection);profile=g.profile(w);widths=g.widths_of(w)
+assert profile=={1:2474,2:182,3:516,4:88,5:242,6:124,7:1,8:17}
+assert Counter(widths)=={7:18,8:161,9:381}
+assert sum(len(c['pivots'])for c in selection['kernel'])==99
+counts={}
+for part in ['A','B','cut','cleanup','precondition']:
+ counts[part]=len(w.get(part,[]))
+ for e in w.get(part,[]):
+  assert e[0]in['add','scale']
+  q=Fraction(e[3],e[4])if e[0]=='add'else Fraction(e[2],e[3]);n=abs(q.numerator);d=q.denominator
+  assert not d&(d-1),(part,e)
+  if e[0]=='scale':assert n>0 and not n&(n-1),(part,e)
+norm=copy.deepcopy(w);assert norm.get('R',560)==norm['report']['R']==560;norm.pop('R',None)
+for k in ['complex_coarse_float','gain_percent_float']:norm['report'].pop(k,None)
+semantic=hashlib.sha256(json.dumps(norm,sort_keys=True,separators=(',',':')).encode()).hexdigest()
+assert semantic=='d966e1481e0c09e4b7a0607429411046c6b3663ee83e6b8833958a745b82e337'
+(out/'FULL-WORD.json.gz').write_bytes(g.dump(w));(out/'RETIMED-BASE.json.gz').write_bytes(g.dump(b));(out/'SELECTION.json').write_bytes(lf(selfile))
+receipt=dict(status='PASS_SOURCE_BOUND_RANKSECTOR_AND_DYADIC_GATE',sources={label:rawsha(f)for label,f in [('prototype',hamming/'PROTOTYPE.json'),('packet_programs',hamming/'PACKET-PROGRAMS.json.gz'),('old_pair_base',oldfile),('retimed_pair_base',retfile)]},lf_source_hashes={label:textsha(f)for label,f in [('ranksector_constructor',source),('pair_spec',specfile),('selection',selfile),('gk_word.py',code/'gk_word.py'),('gk_common.py',code/'gk_common.py')]},normalized_word_sha256=semantic,word_sha256=rawsha(out/'FULL-WORD.json.gz'),profile=dict(profile),widths=dict(Counter(widths)),widths_ordered=widths,pivots=99,transferred_frames=transferred,dyadic_event_counts=counts,scope='Exact local source, rank-factor decoder, response relations, frame chains and dyadic contract; independent all-column, physical and outer replay remain separate.')
+(out/'CONSTRUCTION.json').write_text(json.dumps(receipt,indent=2)+'\n');print(receipt['status'])
diff --git a/research/ranksector112-async/vendor/pr522/code/construct_partial.py b/research/ranksector112-async/vendor/pr522/code/construct_partial.py
new file mode 100644
index 0000000000..69500f6513
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/code/construct_partial.py
@@ -0,0 +1,309 @@
+# Adapted by OpenAI Codex for isolated structural research.
+# Modified from PR425 by icekylinx with Codex assistance.
+"""Full discovery word for Hamming packets with borrowed X and Y registers.
+
+This changes the scalar architecture. It is not accepted by the old restricted
+gx interface: source bases may change until full-frame cleanup, and targets use
+an explicitly inverted output basis. No supplier admission is asserted.
+"""
+import copy,gzip,json,math,time
+import itertools as it
+from collections import Counter,defaultdict
+from fractions import Fraction as Q
+from pathlib import Path
+
+import sys
+INPUT=Path(sys.argv[1]);OUT=Path(sys.argv[2]);OUT.mkdir(parents=True,exist_ok=False);D=json.loads((INPUT/'PROTOTYPE.json').read_text())
+P=D['binary_ports'];R=D['root_lines'];v=120;h=9
+modules=json.load(gzip.open(INPUT/'PACKET-PROGRAMS.json.gz'))
+
+def basis(vectors):
+    b={}
+    for x in vectors:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+def inside(a,b):return basis(a+b)==b
+def hyper(p):return basis([x for x in range(1,512) if (x&p).bit_count()%2==0])
+FULL=basis([1<<i for i in range(9)])
+G=[[sum(x*y for x,y in zip(a,b))//2 for b in R] for a in R]
+blocks={tuple(z['receipt']['block']):z for z in modules}
+frame={next(i for i,x in enumerate(r) if x):s for s,r in enumerate(R) if sum(x!=0 for x in r)==1}
+cur=[(p,) for p in P]+[()]*v;rows=[{r:Q(1)} if r<v else {} for r in range(2*v)]
+A=[];B=[];H=Counter();by={k:Counter() for k in 'xysc'};phase=A
+
+def alloc():
+    n=len(cur);cur.append(());rows.append({});return n
+def climb(r,F):
+    assert inside(cur[r],F),('frame violation',r,cur[r],F)
+    dr=len(F)-len(cur[r])
+    if dr:H[dr]+=1;by['x' if r<v else 'y' if r<2*v else 's'][dr]+=1
+    cur[r]=F
+def add(t,s,q,F):
+    assert t!=s;q=Q(q)
+    if not q:return
+    climb(t,F);climb(s,F);phase.append(['add',t,s,q.numerator,q.denominator,list(F)])
+    for j,x in list(rows[s].items()):
+        z=rows[t].get(j,Q(0))+q*x
+        if z:rows[t][j]=z
+        else:rows[t].pop(j,None)
+def scale(t,q,F):
+    q=Q(q);assert q
+    if q==1:return
+    climb(t,F);phase.append(['scale',t,q.numerator,q.denominator,list(F)])
+    rows[t]={j:q*x for j,x in rows[t].items()}
+def swap(a,b,F):
+    if a==b:return
+    add(a,b,1,F);add(b,a,-1,F);add(a,b,1,F);scale(b,-1,F)
+def linear(regs,M,F):
+    """Apply an invertible rational square matrix by elementary operations."""
+    n=len(regs);a=[list(map(Q,row)) for row in M];undo=[]
+    for col in range(n):
+        k=next(i for i in range(col,n) if a[i][col])
+        if k!=col:a[k],a[col]=a[col],a[k];undo.append(('swap',k,col))
+        q=a[col][col]
+        if q!=1:a[col]=[x/q for x in a[col]];undo.append(('scale',col,1/q))
+        for i in range(n):
+            if i==col or not a[i][col]:continue
+            q=-a[i][col];a[i]=[x+q*y for x,y in zip(a[i],a[col])];undo.append(('add',i,col,q))
+    assert a==[[Q(i==j) for j in range(n)] for i in range(n)]
+    old=[dict(rows[r]) for r in regs]
+    for op in reversed(undo):
+        if op[0]=='swap':swap(regs[op[1]],regs[op[2]],F)
+        elif op[0]=='scale':scale(regs[op[1]],1/op[2],F)
+        else:add(regs[op[1]],regs[op[2]],-op[3],F)
+    for i,r in enumerate(regs):
+        expected=defaultdict(Q)
+        for j,q in enumerate(M[i]):
+            for k,x in old[j].items():expected[k]+=q*x
+        assert rows[r]=={k:x for k,x in expected.items() if x}
+
+# All original-source loads precede source borrowing.
+own={};fl={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines']
+    for s in ids:
+        own[s]=alloc()
+
+packets={};retired={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines'];mp={i:s for i,s in enumerate(ids)}
+    mp.update({i:alloc() for i in range(8,24)})
+    for event_index,(e,F) in enumerate(zip(z['events'],z['event_frames'])):
+        t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+        # 16 source copies and 24 two-shear operations precede face assembly.
+        if event_index==39:
+            for parity in (0,1):
+                tet=sorted(s for s in ids if sum(R[s][i]<0 for i in c)%2==parity)
+                matching=[[(tet[0],tet[1]),(tet[2],tet[3])],[(tet[0],tet[2]),(tet[1],tet[3])],[(tet[0],tet[3]),(tet[1],tet[2])]][(1,1)[parity]]
+                for pair in matching:
+                    rs=sorted(r for r in mp.values() if set(rows[r])==set(pair))
+                    assert len(rs)==2,(pair,rs)
+                    for s,r in zip(pair,rs):
+                        assert len(cur[r])==2
+                        add(own[s],r,1,cur[r])
+    keys=[(p,epsilon) for p in it.combinations(c,2) for epsilon in (-1,1)]
+    for key,(reg,alpha) in zip(keys,z['outputs']):
+        a=mp[reg];alpha=Q(alpha);F=cur[a]
+        b=alloc();add(b,a,1,F)
+        consumers=sorted(d for d in blocks if d!=c and set(key[0])<=set(d))
+        assert len(consumers)==2
+        for target,rr in zip(consumers,(a,b)):packets[c,key[0],key[1],target]=(rr,alpha)
+    retired[c]=[mp[r] for r in z['dead_registers']]
+
+# Four coordinate sums per code block, reconstructed in the retired register
+# stock at its legal rank-four frame. The remaining eight rows retain a basis.
+block_totals={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines'];regs=retired[c];F=basis([P[s] for s in ids])
+    assert len(regs)==12 and len(F)==4
+    for col,s in enumerate(ids):
+        k=next(i for i in range(col,len(regs)) if rows[regs[i]].get(s,Q(0)))
+        swap(regs[k],regs[col],F)
+        scale(regs[col],1/rows[regs[col]][s],F)
+        for i in range(len(regs)):
+            if i!=col and rows[regs[i]].get(s,Q(0)):add(regs[i],regs[col],-rows[regs[i]][s],F)
+    assert all(rows[regs[i]]=={s:Q(1)} for i,s in enumerate(ids))
+    assert all(not rows[r] for r in regs[8:])
+    for i,reg in zip(c,regs[8:]):
+        for j,s in enumerate(ids):add(reg,regs[j],R[s][i],F)
+        block_totals[c,i]=reg
+
+# Eight global coordinate sums, with a single copy each for the centers. The
+# other copy is exactly the correction needed by the eight frame-line targets.
+global_totals={};centers=[]
+for i in range(8):
+    regs=[block_totals[c,i] for c in sorted(blocks) if i in c]
+    F=hyper(P[frame[i]]);a=regs[0]
+    for b in regs[1:]:add(a,b,1,F)
+    global_totals[i]=a
+    centers.append(a)
+centers += [frame[i] for i in range(8)]
+center_frames=[cur[r] for r in centers]
+assert list(map(len,center_frames))==[8]*8+[1]*8
+
+# Own-block and coordinate-frame corrections, one stream per code target.
+own_out={};tetrads={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines']
+    tet=[sorted(s for s in ids if sum(R[s][i]<0 for i in c)%2==parity) for parity in (0,1)]
+    tetrads[c]=tet
+    for parity,targets in enumerate(tet):
+        sources=tet[1-parity];xs=[own[s] for s in sources]
+        F=basis([P[s] for s in sources])
+        # Current own registers are an invertible pair-partial basis T*x.
+        T=[[rows[x].get(s,Q(0)) for s in sources] for x in xs]
+        n=len(T);aug=[r+[Q(i==j) for j in range(n)] for i,r in enumerate(T)]
+        for col in range(n):
+            k=next(i for i in range(col,n) if aug[i][col]);aug[k],aug[col]=aug[col],aug[k]
+            q=aug[col][col];aug[col]=[x/q for x in aug[col]]
+            for i in range(n):
+                if i!=col:
+                    q=aug[i][col];aug[i]=[a-q*b for a,b in zip(aug[i],aug[col])]
+        inv=[r[n:] for r in aug]
+        M=[[sum(Q(G[t][s])*inv[k][j] for k,s in enumerate(sources)) for j in range(n)] for t in targets]
+        assert all(q.denominator&(q.denominator-1)==0 for row in M for q in row)
+        linear(xs,M,F)
+        for t,x in zip(targets,xs):own_out[t]=x
+
+# Cross-block M packets, shared by four targets, then two-output pair transforms.
+Ms={};consumers=defaultdict(list);pairs=[]
+for c in sorted(blocks):
+    for p in it.combinations(c,2):
+        ds=sorted(d for d in blocks if d!=c and set(p)<=set(d))
+        for epsilon in (-1,1):
+            (a,alpha),(b,beta)=[packets[d,p,epsilon,c] for d in ds]
+            F=basis(cur[a]+cur[b]);add(a,b,beta/alpha,F)
+            Ms[c,p,epsilon]=(a,alpha)
+    i,j,k,l=c;partitions=[((i,j),(k,l)),((i,k),(j,l)),((i,l),(j,k))]
+    for parity,tet in enumerate(tetrads[c]):
+        for pi,(p,q) in enumerate(partitions):
+            groups=defaultdict(list)
+            for t in tet:groups[R[t][p[0]]*R[t][p[1]]].append(t)
+            for eps,ts in sorted(groups.items()):
+                assert len(ts)==2;a,b=sorted(ts)
+                e2=R[a][q[0]]*R[a][q[1]]
+                assert e2==R[b][q[0]]*R[b][q[1]]
+                keys=[(c,p,eps),(c,q,e2)];pid=len(pairs)
+                selected=(pi==parity)  # different first partitions in the two tetrads
+                pairs.append({'targets':(a,b),'keys':keys,'selected':selected,
+                              'matrix':[[R[t][p[0]],R[t][q[0]]] for t in (a,b)]})
+                for key in keys:consumers[key].append(pid)
+slots={}
+for key,uses in sorted(consumers.items()):
+    assert len(uses)==2
+    a,alpha=Ms[key];ordinary=[i for i in uses if not pairs[i]['selected']]
+    for j,pid in enumerate(ordinary):
+        if j==0:r=a
+        else:r=alloc();add(r,a,1,cur[a])
+        slots[pid,key]=(r,alpha)
+
+assert len(cur)-240==560,(len(cur)-240)
+
+# The selected target pairs borrow Y as the first packet destination. Their
+# two-shear output basis is compensated at frame zero and in the scatter table.
+phase=B;selected=[];output_basis=[]
+for pid,pair in enumerate(pairs):
+    if not pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    (a,alpha),(b,beta)=Ms[key1],Ms[key2]
+    add(v+t,a,-Q(mat[0][0],2)*alpha,cur[a])
+    add(v+u,b,-Q(mat[0][1],2)*beta,cur[b])
+    selected.append((pid,t,u,mat))
+for pid,t,u,mat in selected:
+    F=basis(cur[v+t]+cur[v+u]);assert all((P[s]&p).bit_count()%2==0 for s in (t,u) for p in F)
+    add(v+t,v+u,1,F);add(v+u,v+t,-Q(1,2),F)
+    z=-Q(2*mat[1][0],mat[0][0]);scale(v+u,z,F)
+    output_basis.append((t,u,z))
+
+for pid,pair in enumerate(pairs):
+    if pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    (a,alpha),(b,beta)=slots[pid,key1],slots[pid,key2]
+    F=basis(cur[a]+cur[b]);aa,ab=Q(mat[0][0])*alpha,Q(mat[0][1])*beta
+    ba,bb=Q(mat[1][0])*alpha,Q(mat[1][1])*beta
+    add(a,b,ab/aa,F);q=ba/(bb-ba*ab/aa);add(b,a,q,F)
+    add(v+t,a,-aa/2,hyper(P[t]));add(v+u,b,-(bb-ba*ab/aa)/2,hyper(P[u]))
+for t,r in own_out.items():add(v+t,r,-Q(1,2),hyper(P[t]))
+
+side=[dict(rows[v+t]) for t in range(v)]
+for t in range(v):
+    expected={s:-Q(G[t][s],2) for s in range(v) if s!=t and G[t][s] and s not in frame.values()} if t not in frame.values() else {}
+    assert side[t]==expected,('side identity',t)
+
+# Correct the eight-center scatter through the inverse two-output basis.
+scatter=[[Q(r[i],4) if t not in frame.values() else Q(0) for i in range(8)]+[Q(t==frame[i]) for i in range(8)] for t,r in enumerate(R)]
+precondition=[]
+for t,u,z in output_basis:
+    a,b=scatter[t].copy(),scatter[u].copy()
+    scatter[t]=[x/2-y/z for x,y in zip(a,b)]
+    scatter[u]=[x/2+y/z for x,y in zip(a,b)]
+    precondition.extend([['scale',v+u,(1/z).numerator,(1/z).denominator,[]],
+                         ['add',v+u,v+t,1,2,[]],['add',v+t,v+u,-1,1,[]]])
+
+for r in range(len(cur)):climb(r,hyper(P[r-v]) if v<=r<2*v else FULL)
+H[8]+=8;H[1]+=8;by['c'][8]+=8;by['c'][1]+=8
+n=len(cur);Rcount=n-240
+assert sum(r*z for r,z in H.items())==9*Rcount+240*8+72
+
+def apply(event,matrix):
+    if event[0]=='add':
+        _,t,s,a,b,*_=event;q=Q(a,b)
+        for j,x in list(matrix[s].items()):
+            z=matrix[t].get(j,Q(0))+q*x
+            if z:matrix[t][j]=z
+            else:matrix[t].pop(j,None)
+    else:
+        _,t,a,b,*_=event;q=Q(a,b);matrix[t]={j:q*x for j,x in matrix[t].items()}
+def inverse(e,F=None):
+    e=copy.deepcopy(e)
+    if e[0]=='add':e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    if F is not None:e[-1]=list(F)
+    return e
+cut=[]
+for t,rr in enumerate(scatter):
+    for i,q in enumerate(rr):
+        if q:cut.append(['add',v+t,centers[i],q.numerator,q.denominator,None])
+cleanup=[inverse(e,FULL) for e in reversed(A+B) if not v<=e[1]<2*v]
+
+# Exact clean replay checks the changed decoder and restored source basis.
+matrix=[{r:Q(1)} if r<v else {} for r in range(n)]
+for e in A+cut+B+cleanup:apply(e,matrix)
+assert all(matrix[r]==({r:Q(1)} if r<v else {r-v:Q(1)} if r<2*v else {}) for r in range(n))
+
+m=73;T=8;L=9;W=7680+L*Rcount;globalH=Counter({r:z*L*T for r,z in H.items()})
+for r in (16,8,32,8,48,8,48,32,16):globalH[r]+=240*T
+globalH[1]+=L*Rcount
+assert m*W-sum(r*z for r,z in globalH.items())==2496
+# Discovery-only approximate display annotations use explicit left-to-right
+# accumulation for stable results across Python sum() implementations. These
+# floats are not acceptance inputs; complete profiles receive exact pricing.
+low,high=0.,.003
+for _ in range(60):
+    q=(low+high)/2
+    moment=0.0
+    for r,z in globalH.items():moment+=r*z/(m*W)*(m/r)**q
+    moment+=32*m*sum(globalH.values())/(10**16*W)*m**q
+    if moment<1:low=q
+    else:high=q
+report={'status':'EXACT_CLEAN_FULL_WORD_DISCOVERY_NOT_ADMITTED',
+        'h':9,'v':120,'R':Rcount,'cst':72,'local_profile':dict(sorted(H.items())),
+        'global_profile':dict(sorted(globalH.items())),'m':m,'W':W,
+        'complex_coarse_float':(low+high)/2,'baseline_b':0.000999388595603943,
+        'gain_percent_float':100*((low+high)/2/0.000999388595603943-1),
+        'scalar_operations_A':len(A),'scalar_operations_B':len(B),
+        'borrowed_output_pairs':len(output_basis),'centre_ranks':list(map(len,center_frames)),'source_columns_exact':120,
+        'source_and_helper_cleanup_exact_on_clean_columns':True,
+        'retained_center_rows_exact':True,
+        'remaining':['full arbitrary-dirt program and independent replay','exact complex phases and global template','finite invoice and coefficient lowering','two rational prices and outer assembly']}
+full={'report':report,'ports':P,'root_lines':R,'A':A,'B':B,'centers':centers,'scatter':[[str(x) for x in r] for r in scatter],
+      'cut':cut,'cleanup':cleanup,'precondition':precondition,'center_frames':center_frames}
+(OUT/'FULL-WORD.json.gz').write_bytes(gzip.compress(json.dumps(full,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+(OUT/'FULL-DISCOVERY.json').write_text(json.dumps(report,indent=2)+'\n')
+print(json.dumps(report,indent=2),flush=True)
diff --git a/research/ranksector112-async/vendor/pr522/code/construct_ranksector.py b/research/ranksector112-async/vendor/pr522/code/construct_ranksector.py
new file mode 100644
index 0000000000..7d6bb02bfc
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/code/construct_ranksector.py
@@ -0,0 +1,329 @@
+# Adapted by OpenAI Codex for isolated structural research.
+# Modified from PR425 by icekylinx with Codex assistance.
+"""Full discovery word for Hamming packets with borrowed X and Y registers.
+
+This changes the scalar architecture. It is not accepted by the old restricted
+gx interface: source bases may change until full-frame cleanup, and targets use
+an explicitly inverted output basis. No supplier admission is asserted.
+"""
+import copy,gzip,json,math,time
+import itertools as it
+from collections import Counter,defaultdict
+from fractions import Fraction as Q
+from pathlib import Path
+
+import sys
+INPUT=Path(sys.argv[1]);OUT=Path(sys.argv[2]);OUT.mkdir(parents=True,exist_ok=False);D=json.loads((INPUT/'PROTOTYPE.json').read_text())
+P=D['binary_ports'];R=D['root_lines'];v=120;h=9
+modules=json.load(gzip.open(INPUT/'PACKET-PROGRAMS.json.gz'))
+
+def basis(vectors):
+    b={}
+    for x in vectors:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+def inside(a,b):return basis(a+b)==b
+def hyper(p):return basis([x for x in range(1,512) if (x&p).bit_count()%2==0])
+FULL=basis([1<<i for i in range(9)])
+G=[[sum(x*y for x,y in zip(a,b))//2 for b in R] for a in R]
+blocks={tuple(z['receipt']['block']):z for z in modules}
+frame={next(i for i,x in enumerate(r) if x):s for s,r in enumerate(R) if sum(x!=0 for x in r)==1}
+cur=[(p,) for p in P]+[()]*v;rows=[{r:Q(1)} if r<v else {} for r in range(2*v)]
+A=[];B=[];H=Counter();by={k:Counter() for k in 'xysc'};phase=A
+
+def alloc():
+    n=len(cur);cur.append(());rows.append({});return n
+def climb(r,F):
+    assert inside(cur[r],F),('frame violation',r,cur[r],F)
+    dr=len(F)-len(cur[r])
+    if dr:H[dr]+=1;by['x' if r<v else 'y' if r<2*v else 's'][dr]+=1
+    cur[r]=F
+def add(t,s,q,F):
+    assert t!=s;q=Q(q)
+    if not q:return
+    climb(t,F);climb(s,F);phase.append(['add',t,s,q.numerator,q.denominator,list(F)])
+    for j,x in list(rows[s].items()):
+        z=rows[t].get(j,Q(0))+q*x
+        if z:rows[t][j]=z
+        else:rows[t].pop(j,None)
+def scale(t,q,F):
+    q=Q(q);assert q
+    if q==1:return
+    climb(t,F);phase.append(['scale',t,q.numerator,q.denominator,list(F)])
+    rows[t]={j:q*x for j,x in rows[t].items()}
+def swap(a,b,F):
+    if a==b:return
+    add(a,b,1,F);add(b,a,-1,F);add(a,b,1,F);scale(b,-1,F)
+def linear(regs,M,F):
+    """Apply an invertible rational square matrix by elementary operations."""
+    n=len(regs);a=[list(map(Q,row)) for row in M];undo=[]
+    for col in range(n):
+        k=next(i for i in range(col,n) if a[i][col])
+        if k!=col:a[k],a[col]=a[col],a[k];undo.append(('swap',k,col))
+        q=a[col][col]
+        if q!=1:a[col]=[x/q for x in a[col]];undo.append(('scale',col,1/q))
+        for i in range(n):
+            if i==col or not a[i][col]:continue
+            q=-a[i][col];a[i]=[x+q*y for x,y in zip(a[i],a[col])];undo.append(('add',i,col,q))
+    assert a==[[Q(i==j) for j in range(n)] for i in range(n)]
+    old=[dict(rows[r]) for r in regs]
+    for op in reversed(undo):
+        if op[0]=='swap':swap(regs[op[1]],regs[op[2]],F)
+        elif op[0]=='scale':scale(regs[op[1]],1/op[2],F)
+        else:add(regs[op[1]],regs[op[2]],-op[3],F)
+    for i,r in enumerate(regs):
+        expected=defaultdict(Q)
+        for j,q in enumerate(M[i]):
+            for k,x in old[j].items():expected[k]+=q*x
+        assert rows[r]=={k:x for k,x in expected.items() if x}
+
+# All original-source loads precede source borrowing.
+own={};fl={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines']
+    for s in ids:
+        own[s]=alloc()
+
+packets={};retired={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines'];mp={i:s for i,s in enumerate(ids)}
+    mp.update({i:alloc() for i in range(8,24)})
+    for event_index,(e,F) in enumerate(zip(z['events'],z['event_frames'])):
+        t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+        # 16 source copies and 24 two-shear operations precede face assembly.
+        if event_index==39:
+            for parity in (0,1):
+                tet=sorted(s for s in ids if sum(R[s][i]<0 for i in c)%2==parity)
+                matching=[[(tet[0],tet[1]),(tet[2],tet[3])],[(tet[0],tet[2]),(tet[1],tet[3])],[(tet[0],tet[3]),(tet[1],tet[2])]][((json.loads(Path(sys.argv[3]).read_text())[','.join(map(str,c))][parity]) if len(sys.argv)==4 else tuple(map(int,sys.argv[3:5]))[parity])]
+                for pair in matching:
+                    rs=sorted(r for r in mp.values() if set(rows[r])==set(pair))
+                    assert len(rs)==2,(pair,rs)
+                    for s,r in zip(pair,rs):
+                        assert len(cur[r])==2
+                        add(own[s],r,1,cur[r])
+    keys=[(p,epsilon) for p in it.combinations(c,2) for epsilon in (-1,1)]
+    for key,(reg,alpha) in zip(keys,z['outputs']):
+        a=mp[reg];alpha=Q(alpha);F=cur[a]
+        b=alloc();add(b,a,1,F)
+        consumers=sorted(d for d in blocks if d!=c and set(key[0])<=set(d))
+        assert len(consumers)==2
+        for target,rr in zip(consumers,(a,b)):packets[c,key[0],key[1],target]=(rr,alpha)
+    retired[c]=[mp[r] for r in z['dead_registers']]
+
+# Four coordinate sums per code block, reconstructed in the retired register
+# stock at its legal rank-four frame. The remaining eight rows retain a basis.
+block_totals={}
+def rowrank(a):
+    a=[list(map(Q,r))for r in a];i=0
+    for j in range(len(a[0])if a else 0):
+        k=next((k for k in range(i,len(a))if a[k][j]),None)
+        if k is None:continue
+        a[i],a[k]=a[k],a[i];q=a[i][j];a[i]=[x/q for x in a[i]]
+        for k in range(i+1,len(a)):
+            q=a[k][j]
+            if q:a[k]=[x-q*y for x,y in zip(a[k],a[i])]
+        i+=1
+    return i
+def invmat(T):
+    n=len(T);a=[list(map(Q,r))+[Q(i==j)for j in range(n)]for i,r in enumerate(T)]
+    for col in range(n):
+        k=next(i for i in range(col,n)if a[i][col]);a[k],a[col]=a[col],a[k];q=a[col][col];a[col]=[x/q for x in a[col]]
+        for i in range(n):
+            if i!=col:
+                q=a[i][col];a[i]=[x-q*y for x,y in zip(a[i],a[col])]
+    return[r[n:]for r in a]
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines'];regs=retired[c];F=basis([P[s]for s in ids]);chosen=[];T=[]
+    for r in regs:
+        t=[rows[r].get(x,Q(0))for x in ids]
+        if rowrank(T+[t])>len(T):chosen.append(r);T.append(t)
+    assert len(chosen)==8
+    U=[[Q(R[s][i])for s in ids]for i in c];assert rowrank(U)==4
+    for j in range(8):
+        t=[Q(k==j)for k in range(8)]
+        if rowrank(U+[t])>len(U):U.append(t)
+    assert len(U)==8
+    V=invmat(T);M=[[sum(U[i][k]*V[k][j]for k in range(8))for j in range(8)]for i in range(8)]
+    linear(chosen,M,F)
+    for i,r in zip(c,chosen[:4]):
+        assert rows[r]=={s:Q(R[s][i])for s in ids};block_totals[c,i]=r
+
+# Eight global coordinate sums, with a single copy each for the centers. The
+# other copy is exactly the correction needed by the eight frame-line targets.
+global_totals={};centers=[]
+for i in range(8):
+    regs=[block_totals[c,i] for c in sorted(blocks) if i in c]
+    F=hyper(P[frame[i]]);a=regs[0]
+    for b in regs[1:]:add(a,b,1,F)
+    global_totals[i]=a
+    centers.append(a)
+centers += [frame[i] for i in range(8)]
+center_frames=[cur[r] for r in centers]
+assert list(map(len,center_frames))==[8]*8+[1]*8
+
+# Own-block and coordinate-frame corrections, one stream per code target.
+own_out={};tetrads={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines']
+    tet=[sorted(s for s in ids if sum(R[s][i]<0 for i in c)%2==parity) for parity in (0,1)]
+    tetrads[c]=tet
+    for parity,targets in enumerate(tet):
+        sources=tet[1-parity];xs=[own[s] for s in sources]
+        F=basis([P[s] for s in sources])
+        # Current own registers are an invertible pair-partial basis T*x.
+        T=[[rows[x].get(s,Q(0)) for s in sources] for x in xs]
+        n=len(T);aug=[r+[Q(i==j) for j in range(n)] for i,r in enumerate(T)]
+        for col in range(n):
+            k=next(i for i in range(col,n) if aug[i][col]);aug[k],aug[col]=aug[col],aug[k]
+            q=aug[col][col];aug[col]=[x/q for x in aug[col]]
+            for i in range(n):
+                if i!=col:
+                    q=aug[i][col];aug[i]=[a-q*b for a,b in zip(aug[i],aug[col])]
+        inv=[r[n:] for r in aug]
+        M=[[sum(Q(G[t][s])*inv[k][j] for k,s in enumerate(sources)) for j in range(n)] for t in targets]
+        assert all(q.denominator&(q.denominator-1)==0 for row in M for q in row)
+        linear(xs,M,F)
+        for t,x in zip(targets,xs):own_out[t]=x
+
+# Cross-block M packets, shared by four targets, then two-output pair transforms.
+Ms={};consumers=defaultdict(list);pairs=[]
+for c in sorted(blocks):
+    for p in it.combinations(c,2):
+        ds=sorted(d for d in blocks if d!=c and set(p)<=set(d))
+        for epsilon in (-1,1):
+            (a,alpha),(b,beta)=[packets[d,p,epsilon,c] for d in ds]
+            F=basis(cur[a]+cur[b]);add(a,b,beta/alpha,F)
+            Ms[c,p,epsilon]=(a,alpha)
+    i,j,k,l=c;partitions=[((i,j),(k,l)),((i,k),(j,l)),((i,l),(j,k))]
+    for parity,tet in enumerate(tetrads[c]):
+        for pi,(p,q) in enumerate(partitions):
+            groups=defaultdict(list)
+            for t in tet:groups[R[t][p[0]]*R[t][p[1]]].append(t)
+            for eps,ts in sorted(groups.items()):
+                assert len(ts)==2;a,b=sorted(ts)
+                e2=R[a][q[0]]*R[a][q[1]]
+                assert e2==R[b][q[0]]*R[b][q[1]]
+                keys=[(c,p,eps),(c,q,e2)];pid=len(pairs)
+                selected=(pi==parity)  # different first partitions in the two tetrads
+                pairs.append({'targets':(a,b),'keys':keys,'selected':selected,
+                              'matrix':[[R[t][p[0]],R[t][q[0]]] for t in (a,b)]})
+                for key in keys:consumers[key].append(pid)
+slots={}
+for key,uses in sorted(consumers.items()):
+    assert len(uses)==2
+    a,alpha=Ms[key];ordinary=[i for i in uses if not pairs[i]['selected']]
+    for j,pid in enumerate(ordinary):
+        if j==0:r=a
+        else:r=alloc();add(r,a,1,cur[a])
+        slots[pid,key]=(r,alpha)
+
+assert len(cur)-240==560,(len(cur)-240)
+
+# The selected target pairs borrow Y as the first packet destination. Their
+# two-shear output basis is compensated at frame zero and in the scatter table.
+phase=B;selected=[];output_basis=[]
+for pid,pair in enumerate(pairs):
+    if not pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    (a,alpha),(b,beta)=Ms[key1],Ms[key2]
+    add(v+t,a,-Q(mat[0][0],2)*alpha,cur[a])
+    add(v+u,b,-Q(mat[0][1],2)*beta,cur[b])
+    selected.append((pid,t,u,mat))
+for pid,t,u,mat in selected:
+    F=basis(cur[v+t]+cur[v+u]);assert all((P[s]&p).bit_count()%2==0 for s in (t,u) for p in F)
+    add(v+t,v+u,1,F);add(v+u,v+t,-Q(1,2),F)
+    z=-Q(2*mat[1][0],mat[0][0]);scale(v+u,z,F)
+    output_basis.append((t,u,z))
+
+for pid,pair in enumerate(pairs):
+    if pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    (a,alpha),(b,beta)=slots[pid,key1],slots[pid,key2]
+    F=basis(cur[a]+cur[b]);aa,ab=Q(mat[0][0])*alpha,Q(mat[0][1])*beta
+    ba,bb=Q(mat[1][0])*alpha,Q(mat[1][1])*beta
+    add(a,b,ab/aa,F);q=ba/(bb-ba*ab/aa);add(b,a,q,F)
+    add(v+t,a,-aa/2,hyper(P[t]));add(v+u,b,-(bb-ba*ab/aa)/2,hyper(P[u]))
+for t,r in own_out.items():add(v+t,r,-Q(1,2),hyper(P[t]))
+
+side=[dict(rows[v+t]) for t in range(v)]
+for t in range(v):
+    expected={s:-Q(G[t][s],2) for s in range(v) if s!=t and G[t][s] and s not in frame.values()} if t not in frame.values() else {}
+    assert side[t]==expected,('side identity',t)
+
+# Correct the eight-center scatter through the inverse two-output basis.
+scatter=[[Q(r[i],4) if t not in frame.values() else Q(0) for i in range(8)]+[Q(t==frame[i]) for i in range(8)] for t,r in enumerate(R)]
+precondition=[]
+for t,u,z in output_basis:
+    a,b=scatter[t].copy(),scatter[u].copy()
+    scatter[t]=[x/2-y/z for x,y in zip(a,b)]
+    scatter[u]=[x/2+y/z for x,y in zip(a,b)]
+    precondition.extend([['scale',v+u,(1/z).numerator,(1/z).denominator,[]],
+                         ['add',v+u,v+t,1,2,[]],['add',v+t,v+u,-1,1,[]]])
+
+for r in range(len(cur)):climb(r,hyper(P[r-v]) if v<=r<2*v else FULL)
+H[8]+=8;H[1]+=8;by['c'][8]+=8;by['c'][1]+=8
+n=len(cur);Rcount=n-240
+assert sum(r*z for r,z in H.items())==9*Rcount+240*8+72
+
+def apply(event,matrix):
+    if event[0]=='add':
+        _,t,s,a,b,*_=event;q=Q(a,b)
+        for j,x in list(matrix[s].items()):
+            z=matrix[t].get(j,Q(0))+q*x
+            if z:matrix[t][j]=z
+            else:matrix[t].pop(j,None)
+    else:
+        _,t,a,b,*_=event;q=Q(a,b);matrix[t]={j:q*x for j,x in matrix[t].items()}
+def inverse(e,F=None):
+    e=copy.deepcopy(e)
+    if e[0]=='add':e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    if F is not None:e[-1]=list(F)
+    return e
+cut=[]
+for t,rr in enumerate(scatter):
+    for i,q in enumerate(rr):
+        if q:cut.append(['add',v+t,centers[i],q.numerator,q.denominator,None])
+cleanup=[inverse(e,FULL) for e in reversed(A+B) if not v<=e[1]<2*v]
+
+# Exact clean replay checks the changed decoder and restored source basis.
+matrix=[{r:Q(1)} if r<v else {} for r in range(n)]
+for e in A+cut+B+cleanup:apply(e,matrix)
+assert all(matrix[r]==({r:Q(1)} if r<v else {r-v:Q(1)} if r<2*v else {}) for r in range(n))
+
+m=73;T=8;L=9;W=7680+L*Rcount;globalH=Counter({r:z*L*T for r,z in H.items()})
+for r in (16,8,32,8,48,8,48,32,16):globalH[r]+=240*T
+globalH[1]+=L*Rcount
+assert m*W-sum(r*z for r,z in globalH.items())==2496
+# Discovery-only approximate display annotations use explicit left-to-right
+# accumulation for stable results across Python sum() implementations. These
+# floats are not acceptance inputs; complete profiles receive exact pricing.
+low,high=0.,.003
+for _ in range(60):
+    q=(low+high)/2
+    moment=0.0
+    for r,z in globalH.items():moment+=r*z/(m*W)*(m/r)**q
+    moment+=32*m*sum(globalH.values())/(10**16*W)*m**q
+    if moment<1:low=q
+    else:high=q
+report={'status':'EXACT_CLEAN_FULL_WORD_DISCOVERY_NOT_ADMITTED',
+        'h':9,'v':120,'R':Rcount,'cst':72,'local_profile':dict(sorted(H.items())),
+        'global_profile':dict(sorted(globalH.items())),'m':m,'W':W,
+        'complex_coarse_float':(low+high)/2,'baseline_b':0.000999388595603943,
+        'gain_percent_float':100*((low+high)/2/0.000999388595603943-1),
+        'scalar_operations_A':len(A),'scalar_operations_B':len(B),
+        'borrowed_output_pairs':len(output_basis),'centre_ranks':list(map(len,center_frames)),'source_columns_exact':120,
+        'source_and_helper_cleanup_exact_on_clean_columns':True,
+        'retained_center_rows_exact':True,
+        'remaining':['full arbitrary-dirt program and independent replay','exact complex phases and global template','finite invoice and coefficient lowering','two rational prices and outer assembly']}
+full={'report':report,'ports':P,'root_lines':R,'A':A,'B':B,'centers':centers,'scatter':[[str(x) for x in r] for r in scatter],
+      'cut':cut,'cleanup':cleanup,'precondition':precondition,'center_frames':center_frames}
+(OUT/'FULL-WORD.json.gz').write_bytes(gzip.compress(json.dumps(full,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+(OUT/'FULL-DISCOVERY.json').write_text(json.dumps(report,indent=2)+'\n')
+print(json.dumps(report,indent=2),flush=True)
diff --git a/research/ranksector112-async/vendor/pr522/code/emit_async.py b/research/ranksector112-async/vendor/pr522/code/emit_async.py
new file mode 100644
index 0000000000..9ffe035202
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/code/emit_async.py
@@ -0,0 +1,89 @@
+"""OpenAI Codex whole-owner cross-replica derivative of pinned PR484.
+CLI: SOURCE484_PACKAGE VERIFIED_VARIANT ASYNC-OWNERS.json.gz ASYNC-PLAN.json OUT
+No optimizer or unpublished word builder runs. The frozen map explicitly names
+one whole helper per family per complete invocation, plus borrowed spectators.
+"""
+import sys,json,gzip,hashlib,copy
+from pathlib import Path
+from collections import Counter,defaultdict
+SOURCE,BASE,MAP,PLAN,OUT=map(lambda p:Path(p).resolve(),sys.argv[1:6]);assert not OUT.exists();OUT.mkdir(parents=True)
+sys.path.insert(0,str(SOURCE/'code'));import onehost_gk as OH
+read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+plan=read(PLAN);call_order=[tuple(x)for x in plan['order']];assert len(call_order)==len(set(call_order))==72;at={x:i for i,x in enumerate(call_order)}
+parent=read(BASE/'split-centres/GLOBAL-TEMPLATE.json.gz');t=copy.deepcopy(parent);canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz');checks=read(BASE/'split-centres/LOCAL-CHECKS.json');ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json');roles=read(MAP);DATA=7680;T=8;V=120;M=73;R=560
+assert(len(roles),len(canon['start']),len(ph['recipes']))==(40320,800,120)
+widths=[9-len(canon['frames'][canon['start'][240+h]])for h in range(R)];assert widths==plan['baseline_widths'], 'source-bound selected provider widths'
+rank={z['child']:z['rank']for z in parent['idle_children']};side={};pairs={}
+for e in parent['execution_schedule']:
+ if e['kind']=='idle_cover_sweep':
+  for sd,ch in enumerate(e['child_indices']):side[ch]=sd;pairs[ch]=e['pair']
+bycall=defaultdict(dict);used=defaultdict(set);sigmas={};digest=hashlib.sha256();entering=0
+for z in roles:
+ s,rep,h=z['stage'],z['replica'],z['helper'];i,cp,off,w,f=z['child'],z['copy'],z['offset'],z['width'],z['family'];orp,port=divmod(cp,V)
+ assert 0<=s<9 and 0<=rep<T and 0<=h<R and w==widths[h] and 0<=orp<T
+ assert f==orp*960+(2*pairs[i]+side[i])*120+port
+ assert(h not in bycall[s,rep])and off>=0 and off+w<=rank[i]
+ assert z['time']==at[s,rep] and z['time'] in plan['windows'][f'{orp},{i}'][1]
+ B=OH.idle_basis(canon['ports'][port]);pending=list(map(int,ph['recipes'][port]['idle_children'][i]['orthogonal_axes']));assert len(pending)==rank[i]
+ occ=[B.index(v)for v in pending[off:off+w]];sp=OH.spectators(canon['ports'][port],pending,off,w)if w<9 else[]
+ order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert len(order)==len(set(order))==M
+ sigma=[B[j]for j in order];sigmahash=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sigmahash]=sigma
+ route=[4,i,off,w,sp]if w<9 else[3,i,off];bycall[s,rep][h]=[f,route];entering+=w<9
+ cells=set(range(off,off+w));assert not used[i,orp,port]&cells;used[i,orp,port]|=cells
+ digest.update(json.dumps([s,rep,h,f,sigmahash],separators=(',',':')).encode()+b'\n')
+for c in t['calls']:
+ k=(c['stage'],c['replica']);assert set(bycall[k])==set(range(R))
+ c['owners']=c['owners'][:240]+[bycall[k][h]for h in range(R)];assert len({f for f,r in c['owners']})==800 and all(f<DATA for f,r in c['owners'])
+newidle=[];paid=Counter()
+for c in t['calls']:
+ for r,n in checks[c['orientation']]['paid_profile'].items():paid[int(r)]+=n
+for old in parent['idle_children']:
+ i,port=old['child'],old['port']
+ for rep in range(T):
+  u=used[i,rep,port];assert u==set(range(len(u)));left=old['rank']-len(u)
+  if left:
+   f=rep*960+(2*pairs[i]+side[i])*120+port;newidle.append(dict(child=i,port=port,replica=rep,replicas=1,family=f,rank=left,hosted=len(u),pending_offset=len(u)));paid[left]+=1
+assert M*DATA-sum(r*n for r,n in paid.items())==2496
+C=len(canon['centers']);physical=DATA+C+R+2
+assert parent['physical']-parent['live']==C+R+2
+# Local circuits, exact phase recipes, normalized wrappers and data routes stay
+# byte-identical; only full-family helper placement and idle remainders change.
+t.update(version='complex484-asynchronous-replica-whole-owner-v1',live=DATA,physical=physical,idle_children=newidle,private_namespace={'centers':[DATA,DATA+C],'reserved_tableau':[DATA+C,DATA+C+R],'coefficient':[physical-2,physical]})
+t['hosting']=dict(rule='one-helper-per-physical-family-per-complete-invocation',max_helpers_per_physical_family_per_call=1,scope='asynchronously interleaved data replicas; each whole helper occurs once per(stage,invocation replica)',pooled_slots=roles,banks=[0]*9,owner_map_sha256=hashlib.sha256(MAP.read_bytes()).hexdigest(),idle_remainder_semantics='Each idle_children item acts once, on its explicit replica/family, at pending_offset with the stated rank; replicas=1.')
+t['route_semantics']['helper']='Whole physical family may belong to another replica; actual orthogonal port basis followed by residual/spectator coordinate permutation. Entering helpers have paid wrappers around the complete invocation; at most one helper and no active data wire uses that family in that invocation. Route[4,child,offset,width,spectators], width9 route[3,child,offset].'
+t['bank_padding']['families']=[];t['cover_final_correction']['families']=[0,DATA];t['cover_final_correction']['charged_calls_per_cover']=DATA
+for e in t['execution_schedule']:
+ if e['kind']=='bank_padding_cover_sweep':e['families']=[DATA,DATA]
+ elif e['kind']=='translate_every_live_family':e.update(t['cover_final_correction'])
+# Expand the retained controller into one-replica blocks; each block consists
+# of its full local cover sweep and every following replica-local event before
+# its next local sweep. Final whole-stock correction remains after all replicas.
+blocks={};globals_=[];st=None
+for ei,e in enumerate(parent['execution_schedule']):
+ if e['kind']in('bank_padding_cover_sweep','translate_every_live_family'):
+  globals_.append((ei,e));continue
+ if e['kind']=='local_cover_sweep':st=e['stage'];blocks[st]=[]
+ assert st is not None
+ blocks[st].append((ei,e))
+new_schedule=[]
+for tm,(s,rep)in enumerate(call_order):
+ for ei,e in blocks[s]:
+  ne=copy.deepcopy(e);ne.update(replica=rep,replicas=[rep],source_event=ei,time=tm)
+  new_schedule.append(ne)
+for ei,e in globals_:
+ ne=copy.deepcopy(e);ne['source_event']=ei
+ if e['kind']=='bank_padding_cover_sweep':ne['families']=[DATA,DATA]
+ else:ne.update(t['cover_final_correction'])
+ new_schedule.append(ne)
+t['execution_schedule']=new_schedule
+cmap={(c['stage'],c['replica']):c for c in t['calls']}
+t['calls']=[dict(cmap[s,rep],time=tm)for tm,(s,rep)in enumerate(call_order)]
+t['loop_order']='Follow the explicit asynchronous execution_schedule. Each local invocation completes before the next, including its entire cover sweep and normalization wrappers. Per-replica source event order is preserved; each idle remainder executes before that replica next touches its family.'
+t['async_schedule']=dict(order=[list(x)for x in call_order],source_plan_sha256=hashlib.sha256(PLAN.read_bytes()).hexdigest(),source_schedule=parent['execution_schedule'],source_call_order=[[c['stage'],c['replica']]for c in parent['calls']],scope='Only independent replica controllers are interleaved. Owner windows are measured on the owner replica timeline; no within-cover or within-invocation interleaving.')
+assert dict(sorted(paid.items()))=={int(k):v for k,v in plan['profile'].items()}
+assert M*M>2*max(paid)**2
+
+assert t['local_programs']==parent['local_programs']
+raw=json.dumps(t,sort_keys=True,separators=(',',':')).encode();(OUT/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+res=dict(status='EMITTED_ASYNCHRONOUS_WHOLE_OWNER_COMPLEX_TEMPLATE',template_sha256=hashlib.sha256(raw).hexdigest(),parent_template_sha256=hashlib.sha256(gzip.decompress((BASE/'split-centres/GLOBAL-TEMPLATE.json.gz').read_bytes())).hexdigest(),live=DATA,physical=physical,global_profile=dict(sorted(paid.items())),rank_mass=sum(r*n for r,n in paid.items()),deficit=2496,maxchild=max(paid),hosted_residuals=len(roles),banks_per_stage=[0]*9,entering_helper_roles=entering,unique_actual_73column_sigmas=len(sigmas),sigma_stream_sha256=digest.hexdigest(),cross_replica_helper_roles=sum(z['replica']!=z['owner_replica']for z in roles),asynchronous_order_sha256=hashlib.sha256(json.dumps(call_order,separators=(',',':')).encode()).hexdigest(),source_artifacts={p.relative_to(BASE).as_posix():hashlib.sha256(p.read_bytes()).hexdigest()for p in [BASE/'split-centres/CANONICAL-WORD.json.gz',BASE/'split-centres/LOCAL-PROGRAMS.json.gz',BASE/'split-centres/LOCAL-CHECKS.json',BASE/'split-centres/RESIDUAL-ADAPTERS.json',BASE/'work/complex-nine-native/DATA-PHASES.json']},scope='New emitted complete-invocation placement; independent controller/spectator/normalization and complete finite invoice admission required.')
+(OUT/'HOSTED.json').write_text(json.dumps(res,indent=2)+'\n');(OUT/'ACTUAL-SIGMAS.json.gz').write_bytes(gzip.compress(json.dumps(sigmas,separators=(',',':')).encode(),mtime=0));print(json.dumps(res,indent=2))
diff --git a/research/ranksector112-async/vendor/pr522/code/run_portable.py b/research/ranksector112-async/vendor/pr522/code/run_portable.py
new file mode 100644
index 0000000000..dcfe7128e1
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/code/run_portable.py
@@ -0,0 +1,15 @@
+"""Run one retained verifier with UTF-8/LF text outputs on every platform.
+This changes output serialization only; no mathematical operation is replaced.
+"""
+from pathlib import Path
+import runpy,sys
+if not __debug__:
+    raise RuntimeError('Assertions must remain enabled')
+original_write_text=Path.write_text
+def write_text_lf(self,data,encoding=None,errors=None,newline=None):
+    return original_write_text(self,data,encoding=encoding or 'utf-8',errors=errors,newline='\n')
+Path.write_text=write_text_lf
+script=Path(sys.argv[1]).resolve()
+sys.argv=sys.argv[1:]
+sys.path.insert(0,str(script.parent))
+runpy.run_path(str(script),run_name='__main__')
diff --git a/research/ranksector112-async/vendor/pr522/evidence/EXACT-ASSEMBLY.json b/research/ranksector112-async/vendor/pr522/evidence/EXACT-ASSEMBLY.json
new file mode 100644
index 0000000000..63368d7a04
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/evidence/EXACT-ASSEMBLY.json
@@ -0,0 +1,127 @@
+{
+  "status": "PASS_ASYNC_COMPLEX_AND_CITED_BIT_EXACT_ASSEMBLY",
+  "complex_lower": "1404182247558147721001/1000000000000000000000000",
+  "complex_decimal": "0.001404182247558147721001",
+  "next_b_rejected": "702091123779073860501/500000000000000000000000",
+  "exact_moment_receipts": [
+    {
+      "endpoint": "1404182247558147721001/1000000000000000000000000",
+      "mercator": [
+        "-1747696821776778527131470543676989804226775/842498333348457493583344221469363458551160763204392890034487820288",
+        "-27963149148428456434103528698831836867628399/13479973333575319897333507543509815336818572211270286240551805124608"
+      ],
+      "base_two": [
+        "-10372108719392101048899/5000000000000000000000000000000000000000000000",
+        "-20744207438784202097681/10000000000000000000000000000000000000000000000"
+      ],
+      "accept": true
+    },
+    {
+      "endpoint": "702091123779073860501/500000000000000000000000",
+      "mercator": [
+        "29762476568545339865592670523992796846148039/26959946667150639794667015087019630673637144422540572481103610249216",
+        "29762476568545339865592670523992796846148041/26959946667150639794667015087019630673637144422540572481103610249216"
+      ],
+      "base_two": [
+        "2759878140392540072869/2500000000000000000000000000000000000000000000",
+        "11039522561570160291593/10000000000000000000000000000000000000000000000"
+      ],
+      "accept": false
+    }
+  ],
+  "bit_lower": "391360506745414227149/250000000000000000000000",
+  "bit_result_sha256": "3494ba83280cc86548fe0cc6695c50d23e6b6ffca85aeb1a33337c1196e280cb",
+  "bit_template_sha256": "e37b52e4861c39154b5891460fb45df8651c92cd68961078f8f06596f057c822",
+  "bit_prefix_bits": 2176,
+  "bit_charged_three_level_coefficient_bits": 6464,
+  "external_row_allowance": 20161,
+  "kappa": "1402213284556683/1000000000000000000",
+  "kappa_decimal": "0.001402213284556683",
+  "binding_component": "complex",
+  "strict_outer_constraints": {
+    "bit_positive": "1404182247558147709126863915678046894276218398902254229248217292657470535130791341325889066027261571626926830520888218632400465204126245176662729054086701119648357199015227335348364607921630070359984398251373535707558111628942312363985837970507601273457587974088554804785302062197912695047001/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_above_bit": "11874136084321953105723781601097745770751782707342529464869208658674110933972738428373073169479111781367599534795873754823337270945913298880351642800984772664651635392078369929640015601748626464292441888371057687636014162029492398726542412025911445195214697937802087304952999/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "complex_below_one_over32": "29845817752441852278999/1000000000000000000000000",
+    "beta_positive": "1/1000000000000000000",
+    "beta_below_one": "999999999999999999/1000000000000000000",
+    "leaf_saving_above_bit": "10469953836763805384722781601097745770751782707342529464869208658674110933972738428373073169479111781367599534795873754823337270945913298880351642800984772664651635392078369929640015601748626464292441888371057687636014162029492398726542412025911445195214697937802087304952999/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_positive": "702091123779073853159249710280875738011245283773080220347890247426481038317178378005473997882839444487574349233182537689273402081174903955930899322917105383161449545420912548025825104945587699831627591204056697493794657563097620474434807356311488272742956016536676128935063057010401542738198437802087304952999/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "q_below_internal": "1404182247558147709126863915678046894276218398902254229248217292657470535130791341325889066027261571626926830520888218632400465204126245176662729054086701119648357199015227335348364607921630070359984398251373535707558111628942312363985837970507601273457587974088554804785302062197912695047001/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
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+      "gap": "10468953836763805384722781601097745770751782707342529464869208658674110933972738428373073169479111781367599534795873754823337270945913298880351642800984772664651635392078369929640015601748626464292441888371057687636014162029492398726542412025911445195214697937802087304952999/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "328470166949627519478719010402186838373292"
+    }
+  ],
+  "complex_template_sha256": "d69ff4e565e93d2379fafc62b12ebc200486b7f701077b05d22997a445ae2a11",
+  "owner_audit_sha256": "43fa819bd814d1ae36a3c35e46f8a2e9884427927b93c79431534945bfa2420f",
+  "invoice_sha256": "b4379c3dcafdae3afa0370cfc0c1e01b30470147bf42beb16e6a836ef9870347",
+  "bit_scope": "PR493 published profile and operator reused as a pinned dependency; this verifier reprices its published profile but does not reconstruct that unchanged bit operator.",
+  "scope": "Conditional finite witness. Inherited compiler, precision/tape and analytic-transfer contracts remain assumed; changed-host operator admission recorded separately."
+}
diff --git a/research/ranksector112-async/vendor/pr522/evidence/INDEPENDENT-FINAL-REVIEW.json b/research/ranksector112-async/vendor/pr522/evidence/INDEPENDENT-FINAL-REVIEW.json
new file mode 100644
index 0000000000..b754ecc708
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/evidence/INDEPENDENT-FINAL-REVIEW.json
@@ -0,0 +1,43 @@
+{
+  "status": "PASS_INDEPENDENT_CHANGED_CONSTRUCTION_AND_COMPLETED_REPLAY_REVIEW",
+  "kappa": "1402213284556683/1000000000000000000",
+  "kappa_decimal": "0.001402213284556683",
+  "complex_lower": "1404182247558147721001/1000000000000000000000000",
+  "template_sha256": "d69ff4e565e93d2379fafc62b12ebc200486b7f701077b05d22997a445ae2a11",
+  "completed_stages": 15,
+  "columns_each_orientation": 800,
+  "kernel_negative_controls": 99,
+  "whole_family_roles": 40320,
+  "complete_invocations": 72,
+  "actual_73_column_maps": 2842,
+  "asynchronous_negative_controls": 19,
+  "strict_outer_constraints": 47,
+  "required_prefix_bits": 210,
+  "charged_prefix_bits": 512,
+  "physical_row_coefficient": 16467,
+  "normalized_word_sha256": "d966e1481e0c09e4b7a0607429411046c6b3663ee83e6b8833958a745b82e337",
+  "fresh_source_and_receipt_bindings": {
+    "RESULT.json": "b4202a5c53b933bfb82f747978dd296fad80e291a6f95ea2c233d8853995bbf0",
+    "audit/ASYNC-AUDIT.json": "88c53e113fcbb28f9335374eadb42409c5d6719a57de65d6a3061af68cb52868",
+    "audit/OWNERS-AND-PROFILE.json": "43fa819bd814d1ae36a3c35e46f8a2e9884427927b93c79431534945bfa2420f",
+    "audit/PREFIX-AND-INVOICE.json": "b4379c3dcafdae3afa0370cfc0c1e01b30470147bf42beb16e6a836ef9870347",
+    "audit/EXACT-ASSEMBLY.json": "de523955c6389eaa3b04b1c1b148cd4fbd3f571ae4c099a22229082300ffd2e5",
+    "audit/KERNEL-SCALAR.json": "b205d2df68f6bfdeb39ed713a12a10cd02a25d240ee2c68f13c123c666e39e29",
+    "base/split-centres/CONSTRUCTION.json": "c9e42e607f162c950ffd4427a7fe50fcdc12a29965f81a0f8546cdc427357404",
+    "hosted/HOSTED.json": "7fa5eb4d8cdef206d01fb308b327e6e36f2a22634c7505a69e2003a623575547"
+  },
+  "independent_work": [
+    "Reviewed invertible U*T^-1 construction and retained arbitrary-dirt storage",
+    "Recomputed all literal owner windows, distinctness, residual intervals, remainders and paid profile",
+    "Independently reinterpreted exact scalar/Horner envelopes",
+    "Checked emitted template, source, constructor and final invoice/assembly receipt bindings",
+    "Package builder differs from research builder only by documented run_portable.py subprocess launcher; actual constructor identical"
+  ],
+  "limitations": [
+    "Inherited all-size compiler, common-label, Lemma A realization, restored-row, precision/tape and analytic-transfer contracts remain conditional",
+    "PR493 bit supplier is unchanged and cited, not freshly reverified",
+    "No new Lean formalization or kernel certification",
+    "Package manifest and final CRLF staging replay are parent-owned finalization, not executed by this reviewer"
+  ],
+  "own_processes_running": 0
+}
diff --git a/research/ranksector112-async/vendor/pr522/evidence/INDEPENDENT-NOMINATION.json b/research/ranksector112-async/vendor/pr522/evidence/INDEPENDENT-NOMINATION.json
new file mode 100644
index 0000000000..30a545b25d
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/evidence/INDEPENDENT-NOMINATION.json
@@ -0,0 +1,29 @@
+{
+  "status": "PASS_INDEPENDENT_LITERAL_OWNER_AND_PROFILE_REVIEW",
+  "calls": 72,
+  "roles": 40320,
+  "remainder_profile": {
+    "3": 3044,
+    "5": 3608,
+    "7": 92,
+    "48": 796
+  },
+  "profile": {
+    "1": 178128,
+    "2": 13104,
+    "3": 40196,
+    "4": 6336,
+    "5": 21032,
+    "6": 8928,
+    "7": 164,
+    "8": 1224,
+    "48": 796
+  },
+  "deficit": 2496,
+  "source_hashes": {
+    "RANKSECTOR-PLAN.json": "9b4b8f125a19ec5741050ca62167c0a4ea2e7f80880f4635c1b6e6c99ea506e8",
+    "RANKSECTOR-OWNERS.json.gz": "5e1ac46a2390c8355ad4b05a154c8c95ed4dd47e87f620d549c5deb26bfa95f7",
+    "RANKSECTOR-SCREEN.json": "0c4ba24edb7ca709948583d8eae89010daba71ad8a5aabca486d88e97401aa9e"
+  },
+  "scope": "Exact nomination-level chronology, original child lifetimes, complete-family uniqueness, disjoint pending-coordinate offsets, source-bound widths, all remainders. Full physical maps, phases and scalar invoice remain separate checks."
+}
diff --git a/research/ranksector112-async/vendor/pr522/evidence/INDEPENDENT-PREFIX.json b/research/ranksector112-async/vendor/pr522/evidence/INDEPENDENT-PREFIX.json
new file mode 100644
index 0000000000..f163d6100e
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/evidence/INDEPENDENT-PREFIX.json
@@ -0,0 +1,15 @@
+{
+  "status": "PASS_INDEPENDENT_SCALAR_HORNER_ENVELOPE",
+  "source_sha256": "b758341ac6c0b7f44570a30f20eca841003b69db67a98a1eefa0fd0248fc480f",
+  "backward": {
+    "peak": "57889301/2",
+    "bits": 25
+  },
+  "forward": {
+    "peak": "737611",
+    "bits": 20
+  },
+  "global_required_bits": 210,
+  "charged_bits": 512,
+  "method": "Separate positive-envelope interpreter. Unsigned binary Horner accumulator never exceeds numerator times source envelope; denominator halvings do not increase it. Every scalar update, copy and clear is included; whole stream adds37inputbits,72invocations,72bridges,4primitive margin."
+}
diff --git a/research/ranksector112-async/vendor/pr522/evidence/PAIR35-COMMUTATOR-SCREEN.json b/research/ranksector112-async/vendor/pr522/evidence/PAIR35-COMMUTATOR-SCREEN.json
new file mode 100644
index 0000000000..fe51488c70
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/evidence/PAIR35-COMMUTATOR-SCREEN.json
@@ -0,0 +1 @@
+[]
diff --git a/research/ranksector112-async/vendor/pr522/evidence/PORTABLE-REPLAY.json b/research/ranksector112-async/vendor/pr522/evidence/PORTABLE-REPLAY.json
new file mode 100644
index 0000000000..cbf913479e
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/evidence/PORTABLE-REPLAY.json
@@ -0,0 +1,88 @@
+{
+  "status": "PASS_CONDITIONAL_ASYNCHRONOUS_COMPLEX_DERIVATIVE",
+  "kappa": "1402213284556683/1000000000000000000",
+  "kappa_decimal": "0.001402213284556683",
+  "complex_lower": "1404182247558147721001/1000000000000000000000000",
+  "bit_lower": "391360506745414227149/250000000000000000000000",
+  "template_sha256": "d69ff4e565e93d2379fafc62b12ebc200486b7f701077b05d22997a445ae2a11",
+  "strict_constraints": 47,
+  "scope": "New complex program independently replayed. The unchanged PR493 bit operator and inherited all-size compiler, common-label, Lemma A realization, restored-row, precision/tape and analytic-transfer contracts remain dependencies. No unconditional multiplication bound or fresh Lean certification is claimed.",
+  "stages": [
+    {
+      "stage": "partial-factory",
+      "exit": 0,
+      "seconds": 0.6090000000258442
+    },
+    {
+      "stage": "construct-kernel92",
+      "exit": 0,
+      "seconds": 2.062999999994645
+    },
+    {
+      "stage": "construct-pair35",
+      "exit": 0,
+      "seconds": 1.6559999999881256
+    },
+    {
+      "stage": "construct-ranksector",
+      "exit": 0,
+      "seconds": 1.6719999999913853
+    },
+    {
+      "stage": "kernel-scalar-controls",
+      "exit": 0,
+      "seconds": 27.90600000001723
+    },
+    {
+      "stage": "scalar",
+      "exit": 0,
+      "seconds": 2.1710000000020955
+    },
+    {
+      "stage": "emit-local",
+      "exit": 0,
+      "seconds": 1.187000000005355
+    },
+    {
+      "stage": "phases",
+      "exit": 0,
+      "seconds": 198.46899999998277
+    },
+    {
+      "stage": "adapters",
+      "exit": 0,
+      "seconds": 1.2030000000086147
+    },
+    {
+      "stage": "parent-integration",
+      "exit": 0,
+      "seconds": 1.1400000000139698
+    },
+    {
+      "stage": "parent-replay",
+      "exit": 0,
+      "seconds": 8.187999999994645
+    },
+    {
+      "stage": "emit-async",
+      "exit": 0,
+      "seconds": 4.280999999988126
+    },
+    {
+      "stage": "independent-async",
+      "exit": 0,
+      "seconds": 23.453000000008615
+    },
+    {
+      "stage": "invoice",
+      "exit": 0,
+      "seconds": 1.8280000000086147
+    },
+    {
+      "stage": "two-moments-assembly",
+      "exit": 0,
+      "seconds": 0.5779999999795109
+    }
+  ],
+  "package_manifest_sha256": "8d86cb4990686bc00ca28b7759ab29db55b81875de31f97c7246caccdc21a7eb"
+}
diff --git a/research/ranksector112-async/vendor/pr522/evidence/PREFIX-AND-INVOICE.json b/research/ranksector112-async/vendor/pr522/evidence/PREFIX-AND-INVOICE.json
new file mode 100644
index 0000000000..25d48f5a6c
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/evidence/PREFIX-AND-INVOICE.json
@@ -0,0 +1,69 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE",
+  "template_sha256": "d69ff4e565e93d2379fafc62b12ebc200486b7f701077b05d22997a445ae2a11",
+  "global_prefix_bits": 210,
+  "charged_prefix_bits": 512,
+  "complete_invocation_sweeps": 72,
+  "bridge_sweeps": 72,
+  "row_prefix_extra": 1024,
+  "local": {
+    "backward": {
+      "events": 22124,
+      "macros": 16692,
+      "real_component_primitives": 169838,
+      "prefix_l1": "57889301/2",
+      "prefix_bits": 25,
+      "coefficient_work_primitive_count": 83983,
+      "all_exact_columns": 800,
+      "all_560_dirty_helper_columns_restored": true,
+      "private_centres_and_coefficient_work_cleared": true
+    },
+    "forward": {
+      "events": 22124,
+      "macros": 16692,
+      "real_component_primitives": 169742,
+      "prefix_l1": "737611",
+      "prefix_bits": 20,
+      "coefficient_work_primitive_count": 83919,
+      "all_exact_columns": 800,
+      "all_560_dirty_helper_columns_restored": true,
+      "private_centres_and_coefficient_work_cleared": true
+    }
+  },
+  "entering_helpers": 179,
+  "entrance_rank": 197,
+  "local_adapters": 343104,
+  "local_primitive_bound": 8898174588782,
+  "wrapper_elementary_factors_charged": 3711744,
+  "compiler": 25934336,
+  "unhosted_pervertex": 1454373093983904,
+  "hosted_rebased_pervertex": 1454373093651264,
+  "conservative_pervertex_used": 1454373093983904,
+  "finite": {
+    "physical_stock_bits": 2641,
+    "router_bits": 7984,
+    "literal_bits": 35282,
+    "physical_row_coefficient": 16467,
+    "retained_row_coefficient": 20161,
+    "required_C0_bits": 200012,
+    "halving_integer_inequality": [
+      5329,
+      4608
+    ],
+    "G_exponent": 30000,
+    "E_exponent": 100000,
+    "C0_exponent": 210000
+  },
+  "strict_checks": {
+    "local_primitive_bound": true,
+    "logical": true,
+    "router": true,
+    "literal": true,
+    "mass": true,
+    "precision": true,
+    "tape": true,
+    "row": true,
+    "halving": true
+  },
+  "scope": "Exact finite recount conditional on inherited all-size compiler/precision/tape and analytic-transfer contracts. Signed accumulation uses the supplier scalar primitive convention. Async prefix counts all72individual bridges and72complete invocations;512bits are charged, and an additional2*512 enters the two-level physical row bound."
+}
diff --git a/research/ranksector112-async/vendor/pr522/evidence/RANKSECTOR-COMMUTATOR-SCREEN.json b/research/ranksector112-async/vendor/pr522/evidence/RANKSECTOR-COMMUTATOR-SCREEN.json
new file mode 100644
index 0000000000..fe51488c70
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/evidence/RANKSECTOR-COMMUTATOR-SCREEN.json
@@ -0,0 +1 @@
+[]
diff --git a/research/ranksector112-async/vendor/pr522/evidence/TRANSPORT-CONTROLS.json b/research/ranksector112-async/vendor/pr522/evidence/TRANSPORT-CONTROLS.json
new file mode 100644
index 0000000000..ac2797863a
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/evidence/TRANSPORT-CONTROLS.json
@@ -0,0 +1,17 @@
+[
+  {
+    "control": "tampered-token",
+    "exit": 1,
+    "rejected_before_output": true
+  },
+  {
+    "control": "missing-file",
+    "exit": 1,
+    "rejected_before_output": true
+  },
+  {
+    "control": "optimized-python",
+    "exit": 1,
+    "rejected_before_output": true
+  }
+]
diff --git a/research/ranksector112-async/vendor/pr522/inputs/ASYNC-6.json b/research/ranksector112-async/vendor/pr522/inputs/ASYNC-6.json
new file mode 100644
index 0000000000..328d7f7a23
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/inputs/ASYNC-6.json
@@ -0,0 +1,12807 @@
+{
+  "status": "SAME_ORDERED_WIDTHS_LITERAL_OWNER_REUSE_NOMINATION",
+  "mode": "offset6",
+  "K": 4,
+  "T": 8,
+  "M": 73,
+  "L": 9,
+  "live": 7680,
+  "deficit": 2496,
+  "profile": {
+    "1": 178128,
+    "2": 13104,
+    "3": 40196,
+    "4": 6336,
+    "5": 21032,
+    "8": 1224,
+    "6": 8928,
+    "7": 164,
+    "48": 796
+  },
+  "patterns": [
+    [
+      [
+        0,
+        0
+      ],
+      [
+        9
+      ],
+      21
+    ],
+    [
+      [
+        0,
+        0
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+        8,
+        8
+      ],
+      47
+    ],
+    [
+      [
+        0,
+        0
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+      [
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+      ],
+      52
+    ],
+    [
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+        2
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+      120
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diff --git a/research/ranksector112-async/vendor/pr522/inputs/ASYNC-OWNERS.json.gz b/research/ranksector112-async/vendor/pr522/inputs/ASYNC-OWNERS.json.gz
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new file mode 100644
index 0000000000..b32646d91c
--- /dev/null
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diff --git a/research/ranksector112-async/vendor/pr522/inputs/KERNEL92-SELECTION.json b/research/ranksector112-async/vendor/pr522/inputs/KERNEL92-SELECTION.json
new file mode 100644
index 0000000000..200b11dcbb
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/inputs/KERNEL92-SELECTION.json
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diff --git a/research/ranksector112-async/vendor/pr522/inputs/PAIR-SELECTION.json b/research/ranksector112-async/vendor/pr522/inputs/PAIR-SELECTION.json
new file mode 100644
index 0000000000..f771643bef
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/inputs/PAIR-SELECTION.json
@@ -0,0 +1,575 @@
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+}
\ No newline at end of file
diff --git a/research/ranksector112-async/vendor/pr522/inputs/PAIR-SPEC.json b/research/ranksector112-async/vendor/pr522/inputs/PAIR-SPEC.json
new file mode 100644
index 0000000000..d582f8c469
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/inputs/PAIR-SPEC.json
@@ -0,0 +1 @@
+{"0,1,2,3": [0, 0], "0,1,4,5": [0, 0], "0,1,6,7": [0, 0], "0,2,4,6": [1, 1], "0,2,5,7": [0, 0], "0,3,4,7": [1, 1], "0,3,5,6": [0, 0], "1,2,4,7": [0, 0], "1,2,5,6": [0, 0], "1,3,4,6": [0, 0], "1,3,5,7": [0, 0], "2,3,4,5": [0, 0], "2,3,6,7": [0, 0], "4,5,6,7": [0, 0]}
\ No newline at end of file
diff --git a/research/ranksector112-async/vendor/pr522/inputs/PR493-EXPECTED.json b/research/ranksector112-async/vendor/pr522/inputs/PR493-EXPECTED.json
new file mode 100644
index 0000000000..973aaf30f1
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/inputs/PR493-EXPECTED.json
@@ -0,0 +1,91 @@
+{
+ "note": "Exact values that verify.sh must reproduce. The bit c is on the 10^-24 grid of PR #472's assembly (largest grid point admitted by both PR #315 moment engines with the inherited 10^-16 bad-branch allowance; the next grid point is rejected); kappa values are on the 10^-18 grid of the six-level, 47-inequality outer assembly.",
+ "word": {
+  "R": 489,
+  "content_sha256": "88435b75b8d6e5c722eb2aa1449f3a5e8e9601a9ffe243839ce1ec932ab76547",
+  "local_histogram": {
+   "1": 1200,
+   "2": 1440,
+   "4": 180,
+   "6": 120,
+   "8": 18
+  },
+  "source_destination_gates_A": 577,
+  "sources_rewritten": 117,
+  "five_stage_payload_bits": 100
+ },
+ "eleven": {
+  "bit_lower": "391360506745414227149/250000000000000000000000",
+  "bit_lower_decimal": "0.001565442026981656908596",
+  "profile": {
+   "1": 105600,
+   "2": 130560,
+   "4": 19680,
+   "6": 14400,
+   "7": 7680,
+   "8": 1584,
+   "48": 2,
+   "56": 2628
+  },
+  "bit": {
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+   "physical": 9609,
+   "maxchild": 56,
+   "rank_mass": 745536,
+   "hosted_residuals": 43032,
+   "prefix_bits": 2119,
+   "charged_prefix_bits": 2176,
+   "coefficient_bits": 2119,
+   "three_level_coefficient_bits": 6411,
+   "charged_three_level_coefficient_bits": 6464,
+   "row_coefficient": 19431,
+   "halving_depth": 3
+  },
+  "emitted_program_sha256": "e37b52e4861c39154b5891460fb45df8651c92cd68961078f8f06596f057c822",
+  "kappa": {
+   "pr484": {
+    "kappa": "662515748707749/500000000000000000",
+    "kappa_decimal": "0.001325031497415498",
+    "binding_component": "complex",
+    "complex_lower": "663394767670133/500000000000000000",
+    "role": "primary"
+   },
+   "pr471": {
+    "kappa": "260706019542937/200000000000000000",
+    "kappa_decimal": "0.001303530097714685",
+    "binding_component": "complex",
+    "complex_lower": "1305231506267591/1000000000000000000",
+    "role": "control (complex supplier of the current whole-residual frontier)"
+   },
+   "pr458": {
+    "kappa": "323880830669511/250000000000000000",
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+  }
+ }
+}
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diff --git a/research/ranksector112-async/vendor/pr522/inputs/work/complex-network/hamming/PROTOTYPE.json b/research/ranksector112-async/vendor/pr522/inputs/work/complex-network/hamming/PROTOTYPE.json
new file mode 100644
index 0000000000..9efe30ee10
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/inputs/work/complex-network/hamming/PROTOTYPE.json
@@ -0,0 +1,21364 @@
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diff --git a/research/ranksector112-async/vendor/pr522/inputs/work/complex-nine-native/DATA-PHASES.json b/research/ranksector112-async/vendor/pr522/inputs/work/complex-nine-native/DATA-PHASES.json
new file mode 100644
index 0000000000..6f128ce2d2
--- /dev/null
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+    "reason": "P_g C_all P_g^-1 = C_all X_delta(g) exactly. Orthogonality cancels all quadratic cross terms; both sides fix the uniform vector.",
+    "mandatory": true,
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+  "global_phase_argument": "Every C_q and every linear address permutation fixes the uniform vector. Equality of the exact Z4 Fourier multiplier therefore fixes the scalar phase as well.",
+  "scope": "All compressed data boundary operators, idle children, terminal X_q and all-live cover correction. Internal arbitrary-subspace canonical labels are checked separately."
+}
\ No newline at end of file
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diff --git a/research/ranksector112-async/vendor/pr522/inputs/work/odd-stages/clifford_exact.py b/research/ranksector112-async/vendor/pr522/inputs/work/odd-stages/clifford_exact.py
new file mode 100644
index 0000000000..166841a037
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/inputs/work/odd-stages/clifford_exact.py
@@ -0,0 +1,149 @@
+"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals.
+Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d.
+The tableau is supplemented by a literal circuit, so global phases are kept.
+"""
+from dataclasses import dataclass
+
+def parity(x):return x.bit_count()&1
+def rank(rows):
+ p={}
+ for x in rows:
+  while x:
+   b=x.bit_length()-1
+   if b not in p:p[b]=x;break
+   x^=p[b]
+ return len(p)
+def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<<j for j in range(n)) for i in range(n))
+def mv(rows,x):return sum(parity(r&x)<<i for i,r in enumerate(rows))
+def inv(rows,n):
+ a=[r|(1<<(n+i)) for i,r in enumerate(rows)]
+ for j in range(n):
+  k=next(i for i in range(j,n) if a[i]>>j&1);a[j],a[k]=a[k],a[j]
+  for i in range(n):
+   if i!=j and a[i]>>j&1:a[i]^=a[j]
+ assert [r&((1<<n)-1) for r in a]==[1<<i for i in range(n)]
+ return tuple(r>>n for r in a)
+def basis_extend(cols,n):
+ out=[]
+ for x in list(cols)+[1<<i for i in range(n)]:
+  if rank(out+[x])>len(out):out.append(x)
+ assert len(out)==n
+ return tuple(out)
+def nullspace(rows,n):
+ a=list(rows);p=[];k=0
+ for j in range(n):
+  t=next((i for i in range(k,len(a)) if a[i]>>j&1),None)
+  if t is None:continue
+  a[t],a[k]=a[k],a[t]
+  for i in range(len(a)):
+   if i!=k and a[i]>>j&1:a[i]^=a[k]
+  p.append(j);k+=1
+ return tuple((1<<j)|sum(((a[i]>>j)&1)<<v for i,v in enumerate(p)) for j in range(n) if j not in p)
+def pmul(a,b):
+ x,z,p=a;y,w,q=b
+ return x^y,z^w,(p+q+2*parity(z&y))%4
+def identity(n):return tuple([(1<<i,0,0) for i in range(n)]+[(0,1<<i,0) for i in range(n)])
+def apply(T,p):
+ n=len(T)//2;x,z,ph=p;out=(0,0,ph)
+ for i in range(n):
+  if x>>i&1:out=pmul(out,T[i])
+ for i in range(n):
+  if z>>i&1:out=pmul(out,T[n+i])
+ return out
+def compose(A,B):return tuple(apply(A,p) for p in B)
+def inverse(T):
+ n=len(T)//2;cols=[x|(z<<n) for x,z,p in T];rows=transpose(cols,2*n);cols_inv=transpose(inv(rows,2*n),2*n);out=[]
+ for j,w in enumerate(cols_inv):
+  x=w&((1<<n)-1);z=w>>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4))
+ return tuple(out)
+def qvalue(Q,alpha,x,n):
+ return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4
+def mul_i(a,p):
+ x,y=a;p%=4
+ return [(x,y),(-y,x),(-x,-y),(y,-x)][p]
+@dataclass
+class Op:
+ n:int
+ tab:tuple
+ circuit:list
+ def then(self,b):
+  assert self.n==b.n
+  return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit)
+ def adjoint(self):
+  circ=[]
+  for e in reversed(self.circuit):
+   if e[0]=='P':circ.append(('P',inv(e[1],self.n)))
+   elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2])))
+   elif e[0]=='C':circ.append(('C',e[1],-e[2]))
+   elif e[0]=='phase':circ.append(('phase',(-e[1])%4))
+   else:circ.append(e)
+  return Op(self.n,inverse(self.tab),circ)
+ def zero_state(self,basis=0):
+  N=1<<self.n;vec=[(0,0)]*N;vec[basis]=(1,0);den=0
+  for e in self.circuit:
+   if e[0]=='P':
+    v=[(0,0)]*N
+    for x,a in enumerate(vec):v[mv(e[1],x)]=a
+    vec=v
+   elif e[0]=='X':vec=[vec[x^e[1]] for x in range(N)]
+   elif e[0]=='D':vec=[mul_i(a,qvalue(e[1],e[2],x,self.n)) for x,a in enumerate(vec)]
+   elif e[0]=='phase':vec=[mul_i(a,e[1]) for a in vec]
+   elif e[0]=='C':
+    q,sgn=e[1:];v=[]
+    for x,(a,b) in enumerate(vec):
+     c,d=vec[x^q]
+     # C=(1+i)I/2+(1-i)X/2; inverse conjugates both coefficients.
+     v.append((a-sgn*b+c+sgn*d,b+sgn*a+d-sgn*c))
+    vec=v;den+=1
+   else:raise AssertionError(e)
+   while den and all((a&1)==(b&1)==0 for a,b in vec):vec=[(a//2,b//2) for a,b in vec];den-=1
+  return vec,den
+def ident(n):return Op(n,identity(n),[])
+def perm(n,G):
+ cols=transpose(G,n);gi=inv(G,n)
+ return Op(n,tuple([(a,0,0) for a in cols]+[(0,a,0) for a in gi]),[('P',tuple(G))])
+def diag(n,Q,alpha=None):
+ Q=tuple(Q);assert transpose(Q,n)==Q
+ alpha=tuple(alpha) if alpha is not None else tuple((Q[i]>>i)&1 for i in range(n))
+ assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n))
+ return Op(n,tuple([(1<<i,Q[i],alpha[i]) for i in range(n)]+[(0,1<<i,0) for i in range(n)]),[('D',Q,alpha)])
+def cgate(n,q,sgn=1):
+ return Op(n,tuple([(1<<i,0,0) for i in range(n)]+[(q if q>>i&1 else 0,1<<i,(3*sgn)%4 if q>>i&1 else 0) for i in range(n)]),[('C',q,sgn)])
+def xgate(n,b):return Op(n,tuple([(1<<i,0,0) for i in range(n)]+[(0,1<<i,2*((b>>i)&1)) for i in range(n)]),[('X',b)])
+def fourier(n,axes=None):
+ out=ident(n)
+ for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<<i))
+ return out
+def hadamard(n,axes):
+ axes=list(axes);Q=tuple(1<<i if i in axes else 0 for i in range(n));S=diag(n,Q)
+ return S.then(fourier(n,axes)).then(S)
+def canonical_frame(n,U):
+ r=len(U)
+ if r==0:return ident(n)
+ if r==n:return fourier(n)
+ G=transpose(basis_extend(U,n),n);gi=inv(G,n);Q=tuple((1<<i)^sum(parity(gi_i&gi_j)<<j for j,gi_j in enumerate(transpose(gi,n))) for i,gi_i in enumerate(transpose(gi,n)))
+ K=perm(n,G).then(diag(n,Q))
+ return K.adjoint().then(fourier(n,range(r))).then(K)
+def monomial(op):
+ n=op.n;T=op.tab;assert all(x==0 and p%2==0 for x,z,p in T[n:]);G=transpose([x for x,z,p in T[:n]],n);b=mv(G,sum((p//2)<<i for i,(x,z,p) in enumerate(T[n:])))
+ gt=transpose(G,n);cols=[mv(gt,z) for x,z,p in T[:n]];Q=transpose(cols,n);alpha=[(p-2*parity(b&z))%4 for x,z,p in T[:n]]
+ out=diag(n,Q,alpha).then(perm(n,G)).then(xgate(n,b));assert out.tab==T
+ vec,den=op.zero_state();assert den==0 and all(a==(0,0) for i,a in enumerate(vec) if i!=b);phase=[(1,0),(0,1),(-1,0),(0,-1)].index(vec[b]);out=out.then(Op(n,identity(n),[('phase',phase)]));assert out.zero_state()==op.zero_state()
+ return out,dict(matrix_rows=G,offset=b,quadratic_rows=Q,linear_Z4=alpha,phase=phase)
+def lower_child(op):
+ n=op.n;Bcols=[x for x,z,p in op.tab[n:]];r=rank(Bcols)
+ if not r:
+  mon,rec=monomial(op);return dict(rank=0,left=rec,right=None),mon
+ G=transpose(basis_extend(Bcols,n),n);A=inv(G,n);PA=perm(n,A);part=op.then(PA);Bcols=[x for x,z,p in part.tab[n:]];Dcols=[z for x,z,p in part.tab[n:]]
+ picks=[];selected=[]
+ for j,x in enumerate(Bcols):
+  if rank(selected+[x])>len(selected):picks.append(j);selected.append(x)
+ assert len(picks)==r and all(x>>r==0 for x in Bcols)
+ Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<<r)-1) for j in picks],r)
+ Qsmall=tuple(sum(parity(row&col)<<j for j,col in enumerate(transpose(Bi,r))) for row in Dr);Q=Qsmall+(0,)*(n-r);DQ=diag(n,Q)
+ V=part.then(DQ).then(hadamard(n,range(r)));assert all(x==0 for x,z,p in V.tab[n:]);Vmon,Vrec=monomial(V)
+ S=diag(n,tuple(1<<i if i<r else 0 for i in range(n)))
+ left=S.adjoint().then(DQ.adjoint()).then(PA.adjoint());right=Vmon.then(S.adjoint()).then(xgate(n,(1<<r)-1))
+ lmon,lrec=monomial(left);rmon,rrec=monomial(right);compiled=rmon.then(fourier(n,range(r))).then(lmon)
+ assert compiled.tab==op.tab and compiled.zero_state()==op.zero_state()
+ return dict(rank=r,left=lrec,right=rrec),compiled
diff --git a/research/ranksector112-async/vendor/pr522/inputs/work/pr361/code/engines/base_two_moment.py b/research/ranksector112-async/vendor/pr522/inputs/work/pr361/code/engines/base_two_moment.py
new file mode 100644
index 0000000000..14a90fa0e7
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/inputs/work/pr361/code/engines/base_two_moment.py
@@ -0,0 +1,63 @@
+#!/usr/bin/env python3
+"""Maintainer arithmetic cross-check of the pinned PR39 certificate.
+
+Uses no producer/checker imports. Counts are inputs, not proved by this script.
+80-term rational logarithms and 12-term exponentials independently enclose
+the two moments. The accompanying written review addresses their realization.
+"""
+import argparse
+from fractions import Fraction as Q
+from hashlib import sha256
+import json
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parents[1]
+GRID = 10**30
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def log_unit(x):
+    require(1 <= x <= 2, "logarithm range")
+    z = (x-1)/(x+1)
+    lo = 2*sum((z**(2*j+1)/(2*j+1) for j in range(80)), Q(0))
+    return lo, lo+2*z**161/(161*(1-z*z))
+
+
+def log_bounds(x):
+    k = 0
+    while x > 2:
+        x /= 2
+        k += 1
+    lo, hi = log_unit(x)
+    l2, u2 = log_unit(Q(2))
+    lo, hi = lo+k*l2, hi+k*u2
+    # Outward rational rounding keeps later certificates compact.
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
+
+def exp_bounds(x):
+    require(0 <= x < 1, "exponential range")
+    term = total = Q(1)
+    for j in range(1, 13):
+        term *= x/j
+        total += term
+    tail = term*x/13/(1-x/14)
+    return total, total+tail
+
+
+def moment(m, W, entries, saving):
+    lo = hi = Q(0)
+    for t, count in entries:
+        t, count = int(t), int(count)
+        require(0 < t < m and count > 0, "improper child")
+        l, u = log_bounds(Q(m, t))
+        lower = exp_bounds(saving*l)[0]
+        upper = exp_bounds(saving*u)[1]
+        lo += Q(t*count, m*W)*lower
+        hi += Q(t*count, m*W)*upper
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
diff --git a/research/ranksector112-async/vendor/pr522/inputs/work/pr361/code/engines/moment.py b/research/ranksector112-async/vendor/pr522/inputs/work/pr361/code/engines/moment.py
new file mode 100644
index 0000000000..7d697cb452
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/inputs/work/pr361/code/engines/moment.py
@@ -0,0 +1,113 @@
+"""Independent prospective ordinary five-stage cost, never supplier admission.
+
+Consumes a raw one-invocation ledger made from the actual source/internal/target
+paths.  No packed profile is used as an input.  Missing physical/finite/compiler
+obligations must remain explicit in the accompanying report.
+"""
+from collections import Counter
+from decimal import Decimal, localcontext, ROUND_FLOOR
+from fractions import Fraction as F
+from functools import lru_cache
+from math import factorial
+import hashlib, json, sys
+from pathlib import Path
+
+DYAD = 1 << 224
+
+def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD)
+def ceil(x): return -floor(-x)
+
+@lru_cache(None)
+def logarithm(x):
+    """Mercator bounds after binary reduction; ln(2) via two Mercator sums.
+
+    For 1 <= y < 2, log(y) is an alternating series in z=y-1.
+    We instead reduce to 1 <= y < 3/2, and bound log(3/2) and
+    log(2) by the same alternating series at z=1/2 and z=1/3,
+    using log(2)=log(3/2)+log(4/3). All sums are exact rationals.
+    """
+    assert x >= 1
+    k = 0
+    while x >= 2: x /= 2; k += 1
+    j = int(x >= F(3, 2))
+    if j: x /= F(3, 2)
+    def mercator(y):
+        z=y-1
+        assert 0 <= z <= F(1,2)
+        # An even partial sum is below log; the next term bounds its tail.
+        t=z; s=F(0)
+        for n in range(1, 225):
+            s += (t if n & 1 else -t)/n
+            t *= z
+        return s, s+t/225
+    a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3))
+    return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f)
+
+def exponential(l,u):
+    assert 0 <= l <= u < F(1,10)
+    def poly(x):
+        s=t=F(1)
+        for j in range(1,25): t=t*x/j; s+=t
+        return s,t
+    lo,_=poly(l);hi,last=poly(u)
+    return floor(lo),ceil(hi+last*u/25/(1-u/26))
+
+def moment(H,m,W,a,bad=False):
+    lo=hi=F(0)
+    for r,n in H.items():
+        assert 0 < r < m and n > 0
+        l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u)
+        p=F(r*n,m*W);lo+=p*e;hi+=p*f
+    if bad:
+        # Existing envelope shape, only conditionally portable to the new cover.
+        l,u=logarithm(F(m));e,f=exponential(a*l,a*u)
+        p=F(32*m*sum(H.values()),10**16*W)
+        lo+=p*e;hi+=p*f
+    return floor(lo),ceil(hi)
+
+def decimal(x):
+    with localcontext() as c:
+        c.prec=70
+        return str(Decimal(x.numerator)/Decimal(x.denominator))
+
+def certify(H,m,W,bad=False):
+    with localcontext() as c:
+        c.prec=70
+        terms=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln()) for r,n in H.items()]
+        fallback=Decimal(32*m*sum(H.values()))/Decimal(10**16*W) if bad else Decimal(0)
+        lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003')
+        for _ in range(210):
+            a=(lo+hi)/2
+            if sum(p*(a*l).exp() for p,l in terms)+fallback*(a*lm).exp()<1:lo=a
+            else:hi=a
+        q=int(((lo+hi)/2*10**24).to_integral_value(rounding=ROUND_FLOOR))
+    lo=F(q,10**24);hi=lo+F(1,10**24)
+    lv=moment(H,m,W,lo,bad);hv=moment(H,m,W,hi,bad)
+    assert lv[1]<1<hv[0],(lo,hi,lv,hv)
+    k=F(694782719690783,10**18);required=k/(1-k)
+    at=moment(H,m,W,required,bad)
+    return dict(lower=decimal(lo),upper=decimal(hi),lower_endpoint_residual_upper=decimal(lv[1]-1),upper_endpoint_residual_lower=decimal(hv[0]-1),strict_rational_signs=True,moment_minus_one_at_current_k_required_rate=[decimal(x-1) for x in at],nominal_k_ceiling_interval=[decimal(lo/(1+lo)),decimal(hi/(1+hi))])
+
+def price(core,gauges,R,v,h):
+    core=Counter({int(k):n for k,n in core.items() if n})
+    gauges=Counter({int(k):n for k,n in gauges.items() if n})
+    m=5*h;W=4*v+R;ell=h*(h-2)  # p = 10 port: was the p = 12 literal 24*22
+    assert sum(r*n for r,n in core.items())==h*R+2*v*(h-1)+ell-sum(r*n for r,n in gauges.items())
+    idle=Counter({r:2*v for r in (2*h-2,h-1,2*h+2,4)})
+    ans={}
+    for name,bundled in [('separate_rank_a_corrections',False),('bundled_rank_5a_corrections',True)]:
+        H=Counter({r:5*n for r,n in core.items()});H.update(idle)
+        for a,n in gauges.items():H[5*a if bundled else a]+=n if bundled else 5*n
+        mass=sum(r*n for r,n in H.items());assert m*W-mass==4*v-5*ell
+        ans[name]=dict(histogram=dict(sorted(H.items())),calls=sum(H.values()),rank_mass=mass,deficit=m*W-mass,maxchild=max(H),root=certify(H,m,W),root_with_inherited_bad_envelope=certify(H,m,W,True))
+    return dict(status='PROSPECTIVE_COST_ONLY_NOT_PHYSICAL_OR_ASSEMBLY_ADMISSION',m=m,W=W,R=R,v=v,h=h,copy_calls_per_invocation=h,copy_rank=h-2,ell=ell,raw_core=dict(sorted(core.items())),auxiliary_entrances=dict(sorted(gauges.items())),idle_histogram=dict(sorted(idle.items())),profiles=ans,interval_method='Independent exact rational alternating Mercator log bounds (224 terms), 24-degree exponential with geometric tail, 224-bit outward dyadic rounding; Decimal only proposes endpoints.',bad_envelope_scope='10^-16 and 32*m^2 rank-one fallback calls per paid child are inherited assumptions, not a new m = 5h admission.')
+
+if __name__=='__main__':
+    path=Path(sys.argv[1]);raw=path.read_bytes();data=json.loads(raw)
+    core=data['one_stage_helper_histogram_including_copies']
+    gauges=data['auxiliary_entrance_rank_histogram']
+    result=price(core,gauges,data['physical_R'],data['v'],data['h'])
+    result['input_ledger_sha256']=hashlib.sha256(raw).hexdigest()
+    result['input_head']=data['head']
+    result['one_invocation_parts']={key:data[key] for key in ('physical_internal_excluding_center_copies','paid_center_copy_histogram','physical_source_histogram','physical_target_histogram')}
+    print(json.dumps(result,indent=2))
diff --git a/research/ranksector112-async/vendor/pr522/inputs/work/pr361/code/engines/outer.py b/research/ranksector112-async/vendor/pr522/inputs/work/pr361/code/engines/outer.py
new file mode 100644
index 0000000000..43007488ad
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/inputs/work/pr361/code/engines/outer.py
@@ -0,0 +1,58 @@
+#!/usr/bin/env python3
+"""Exact semantic assembly with the balanced prefix, for the paired-cube network.
+
+Prepared by eumemic with Anthropic Claude assistance. Apache-2.0. The 47 strict constraints, the seven margins and
+the finite bridge are unchanged from icekylinx's scripts/structured_bulk_assembly.py (PR144, adapted from Zhihao
+Chen's PR23). The prefix is the RaD project's (hipotures) balanced positional transform, reviewed in
+references/semantic-bulk/rad20/reports/review-balanced-transform.md: the prefix margin becomes 1-eps instead of
+1-eps(1+c), and eps(1+c)<1 remains a strict geometric condition (K_geometry) whose gap need not exceed kappa.
+The parameters c=q+eta/4 and eps=(1-eta)/(1+q) are those of the reviewed balanced assembly in
+research/copied-fixed/balanced_assembly.py, with its backoff h equal to eta. Nothing else differs from
+structured_bulk_assembly.assembly.
+"""
+from fractions import Fraction as Q
+
+
+def assembly(bit_saving,complex_saving,bridge,kappa,eta=Q(1,10**8),beta=Q(1,4)):
+    a,b=bit_saving,complex_saving
+    tau,sigma=1-a,1-b
+    q=a*(1-2*eta); lp=1-q; lam=(tau+lp)/2
+    c=q+eta/4; eps=(1-eta)/(1+q)
+    minimum=eps*q; r=(minimum+1-eps)/2; delta=eta/8
+    internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma)
+    margins=dict(balanced_prefix=1-eps,coordinate_movement=a,
+        compact_phase_layer=minimum,bulk_exposure=a,
+        Gaussian_arithmetic=min(1-eps-delta,r-delta),
+        scalar_work=1-eps-delta,dimension=eps)
+    slacks=dict(bit_positive=a,complex_above_bit=b-a,
+        complex_below_one_over32=Q(1,32)-b,beta_positive=beta,
+        beta_below_one=1-beta,leaf_saving_above_bit=(1-beta)*b-a,
+        q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q,
+        c_positive=c,c_below_one=1-c,q_below_reservations=c-q,
+        lambda_above_tau=lam-tau,lambda_above_sigma=lam-sigma,
+        lambda_above_internal=lam-internal,lambda_prime_above_lambda=lp-lam,
+        compact_leaf=lp-leaf,compact_reservations=lp-(1-c),
+        lambda_prime_below_one=q,epsilon_positive=eps,epsilon_below_one=1-eps,
+        guard_width=1-eps,K_geometry=1-eps*(1+c),K_dominates_log=eps*c,
+        record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=r-delta,
+        gamma_sublinear=1-eps-r,cell_above_band=eps-(1-r)/2,
+        prime_interval_packing=1-eps,alpha_positive=r,alpha_below_one=1-r,
+        alpha_below_one_fourth=Q(1,4)-r,delta_positive=delta,
+        delta_below_one_eighth=Q(1,8)-delta,short_record_fallback=eps-a,
+        small_field_exposure=1-eps-minimum,
+        artificial_boundary=8-eps+r-delta-minimum,
+        literal_scalar_guard=Q(bridge['semantic']['strict_literal_gap']),
+        row_product_gap=bridge['rows']['degree_gap'])
+    slacks.update({name+'_above_kappa':val-kappa for name,val in margins.items()})
+    assert len(slacks)==47 and len(margins)==7
+    assert all(v>0 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0}
+    assert min(margins.values())==minimum
+    assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2
+    assert 1-eps*(1+c)==eta-eps*eta/4
+    return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma,
+            eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam,
+            lambda_prime=lp,alpha_squared_power=r,delta=delta,
+            C0=bridge['semantic']['C0'],C1=1,kappa=kappa),
+        strict_constraints=slacks,margins=margins,minimum_margin=minimum,
+        absorption_gap=minimum-kappa,
+        recurrence=dict(internal=internal,leaf=leaf,reservations=1-c))
diff --git a/research/ranksector112-async/vendor/pr522/inputs/work/pr370-source/research/e8-bit/data/bit/bitE8-r865.json.gz b/research/ranksector112-async/vendor/pr522/inputs/work/pr370-source/research/e8-bit/data/bit/bitE8-r865.json.gz
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diff --git a/research/ranksector112-async/vendor/pr522/references/PR493-NOTICE.md b/research/ranksector112-async/vendor/pr522/references/PR493-NOTICE.md
new file mode 100644
index 0000000000..ac7d789262
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/references/PR493-NOTICE.md
@@ -0,0 +1,11 @@
+# Attribution for the included PR493 material
+
+Apache-2.0. Prepared by eumemic with substantial Anthropic Claude assistance.
+The only copied PR493 payload in this package is its published EXPECTED.json.
+Its R489 bit operator is cited, not vendored or freshly reconstructed here.
+
+The original complete notice is available with the pinned source:
+https://github.com/CrocSwap/integer-mult-bounds/blob/c3a9a436b84fe44fdc223a5784d84736d1c2d3c7/research/e8-bit-carrier-skeleton/NOTICE.md
+
+This attribution excerpt omits sections for code and historical receipt files
+that are not included in this package. It does not modify any upstream file.
diff --git a/research/ranksector112-async/vendor/pr522/research-notes/CORRELATED-REPAIR.md b/research/ranksector112-async/vendor/pr522/research-notes/CORRELATED-REPAIR.md
new file mode 100644
index 0000000000..52e2ab8ab3
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/research-notes/CORRELATED-REPAIR.md
@@ -0,0 +1,13 @@
+# Correlated owner repair
+
+The new source family is the OpenAI UniformKServer tree-rounding construction. TreeRounding.park keeps unassigned mass explicit, Rounded constrains both subtree totals and parked mass, and extended_star preserves old observables while coupling new choices. RoundingKernel.kernel_next and kernel_rounded state support and transition guarantees. These were read as source, not compiled or instantiated in the multiplication proof. The borrowed idea is to repair several assignments jointly while preserving exact marginals and charging parked mass; our deterministic finite repair is a separate construction, not the source randomized rounding theorem.
+
+Sufficient finite repair rule: choose a set of complete pending-child bins and remove only the helper roles assigned to them. Reassign exactly those role identities among those bins. Each role keeps its invocation, local register and width. Require the new pending interval to contain that invocation, total width in each bin to remain within its rank, and every physical family in an invocation to have at most one whole helper and no active data wire. Repack all selected supports contiguously and charge the exact leftover rank. Then the resulting map satisfies the same abstract complete-owner allocation contract. Full physical charts still have to be regenerated and independently replayed against the selected local provider before this becomes a deliverable.
+
+The executable screen enumerates simultaneous assignments of all roles of three selected bins, checks capacity, timeline and per-call collision constraints, and minimizes the complete contribution of the changed leftover ranks at the baseline exponent. No leftover rank is erased. Neutral-face moves are allowed in a separately recorded bounded screen to avoid mistaking a strict local minimum for a complete result.
+
+The first native scan examined 200,000 bin triples and 225,394,867 recursion nodes. It accepted no strictly improving repair. This is only a bounded discovery outcome. The separate aggregate capacity screen leaves about 0.044 percent supplier headroom in this fixed architecture, which directs further effort toward genuinely changed local providers. Neither screen proves optimality or supplies a new kappa claim.
+
+The separate 40-second neutral-face sweep accepted 120,911 cost-neutral moves and visited 2,135,369,213 recursive assignment nodes. Its final leftover histogram was unchanged: 3:3044, 5:3608, 7:92, 48:796. No new physical certificate was packaged from these neutral research maps.
+
+The selected improvement instead comes from the kernel lane's rank-sector factorization. Its ordered residual widths are byte-for-byte equal as integers to the pair35 list. Thus the original literal owner map is reused unchanged, with a fresh source-bound operator replay. The local profile delta is -56 rank-1 calls -56 rank-5 calls +56 rank-6 calls, preserving rank mass and improving every moment with exponent strictly between zero and one, since 6^a < 1 + 5^a. The measured complete-profile supplier root is about 0.0014041822501567602 before exact assembly. This actual gain must not be attributed to our unsuccessful correlated repair route.
diff --git a/research/ranksector112-async/vendor/pr522/research-notes/PORTABLE-REPLAY.md b/research/ranksector112-async/vendor/pr522/research-notes/PORTABLE-REPLAY.md
new file mode 100644
index 0000000000..59228e00c2
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/research-notes/PORTABLE-REPLAY.md
@@ -0,0 +1,7 @@
+# Fresh transport replay
+
+All 15 stages passed on a new copy with every recognized text source and input converted to CRLF. Nested factory subprocesses use the portable launcher so generated text is UTF-8/LF before raw source hashes are embedded. Static binary inputs are hashed byte-for-byte; generated gzip header bytes are distinguished from the canonical mathematical template hash. No Linux or Python 3.14 run is claimed from this Windows test.
+
+The manifest rejects changed tokens and missing files before output creation; optimized Python is explicitly rejected. No hidden file is required. No mathematical source changed after the complete portability replay: only evidence and this note were added, followed by manifest reconstruction and byte-exact upload reassembly.
+
+The new scalar program has a larger exact envelope than the preceding word. Its independent review gives forward 737611 and backward 57889301/2, requiring 25 local bits and 210 overall bits. This fits the retained 512-bit charge. The invoice derives its bound from the actual new scalar events, rather than copying the preceding 206-bit result. The physical row coefficient remains explicitly checked against its allowance.
diff --git a/research/ranksector112-async/vendor/pr522/research-notes/RANKSECTOR-PROOF.md b/research/ranksector112-async/vendor/pr522/research-notes/RANKSECTOR-PROOF.md
new file mode 100644
index 0000000000..e0b10841d5
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/research-notes/RANKSECTOR-PROOF.md
@@ -0,0 +1,56 @@
+# Coordinate-total reconstruction on an independent row sector
+
+## The implemented improvement
+
+The old partial-own factory has twelve retired registers in each of fourteen code blocks. Their clean source rows span only eight dimensions. It raises all twelve registers from their rank-three frames to the common rank-four block frame, reduces the twelve-by-eight row matrix, and forms four coordinate totals. The extra four raised rows are unnecessary for those outputs.
+
+The new factory chooses eight independent retired rows, changes basis on those eight registers so that the first four contain the required coordinate totals, and leaves the other four registers untouched until the ordinary cleanup. All 560 helpers remain present. No dirty register is erased, identified with another register, or treated as clean storage.
+
+This removes four intermediate climbs in each block. Each affected register previously paid a rank-one climb followed by a rank-five climb; it now pays one rank-six climb. The exact local delta is
+
+    -56 rank-one calls -56 rank-five calls +56 rank-six calls.
+
+The selected 99 kernel pivots, gauge selection and ordered whole-residual inventory are unchanged. The inventory is eighteen width-seven, 161 width-eight and 381 width-nine helpers. The new local profile is:
+
+    rank:   1     2    3   4    5    6  7   8
+    count: 2474  182  516  88  242  124  1  17.
+
+For every 0 < b < 1, strict subadditivity of x^(1-b) gives 6^(1-b) < 1 + 5^(1-b). Thus this change strictly reduces the recursive moment while preserving rank mass. Across the existing seventy-two invocations, the complete global child profile has the corresponding factor-seventy-two delta. The same whole-owner allocation can be retained because the ordered widths agree exactly. The final finite arithmetic replay also charges the actual scalar program and is the authority for the published supplier bound and kappa.
+
+## Sufficient algebraic construction
+
+Write the eight independent clean rows as an invertible matrix T in the eight source coordinates. Let L be the four-by-eight matrix of required coordinate sums. The four rows of L are independent. Extend them to an eight-row basis U, and form
+
+    M = U T^(-1).
+
+The emitted elementary operations apply M to precisely the eight selected physical registers at their admitted common block frame. Their clean output rows are M T = U, so the first four are exactly L. M is invertible on arbitrary physical register contents, and all unselected registers are literally unchanged by this stage. The inverse cleanup is reconstructed from the new actual word.
+
+Dirty-state correctness is not inferred from the clean row equation alone. The complete helper response matrix is recomputed, the actual target compensations and kernel prefix are reconstructed, and all scalar basis columns are checked in both orientations. For this frozen word, all 800 forward columns, all 800 inverse-transpose columns, and 99 independent omitted-kernel-correction controls pass. Every scalar denominator is a power of two and every scaling operation is a signed power of two, matching the existing finite scalar compiler.
+
+The constructor uses deterministic finite row reduction to select T and extend L. This is part of reconstruction, not an optimizer or an assumed gadget. The exact common-frame containment tests, final scalar identity, dirty-data compensation, dyadic compatibility and physical global replay remain explicit checks in the package.
+
+## OpenAI proof source and precise transfer
+
+The direct source is `lean/OAI/Analysis/Cotype/RankFactors.lean`, from the corpus's cotype-cotype project (catalogue item 326). In namespace `OAI.Cotype`, `exists_rank_pairing_matrix` constructs rectangular factors for an arbitrary square matrix P over a field:
+
+    I.transpose * P * J = identity_on_rank(P).
+
+Its proof selects the independent block in `Matrix.exists_rank_normal_form`. The following theorem, `rank_pairing_contract`, proves that these factors preserve the desired bilinear contraction exactly. We transferred the constructive principle: restrict to the independent sector needed by the output pairing instead of normalizing every redundant row. Here the independent sector has dimension eight, the requested total map has four rows, and the preserved ambient registers carry the unused dirty coordinates.
+
+This is a different construction from the preceding package's Newton-inspired pair-cover selection. The pair covers are fixed throughout this change. It is also not a claim that the Banach-space theorem automatically certifies our circuit. The file and its proof were inspected; the new rational circuit has separate finite checks. No fresh Lean compilation was performed in this round.
+
+The initially inspected alternative source, `Computability/FourierCircuit/DisplacementKernel.lean`, gives the exact `reconstruct` identity for an interior outer-product recurrence and its explicit boundary terms. This motivated a packet-to-total telescoping gate. All fifty-six coordinate totals were found in the admissible retired/packet row spans, but the winning construction is the independent rank sector described above, not a claim that a displacement factorization itself improved the final bound.
+
+## Bounded search and reproducibility
+
+The clean checkpoint, rowspace tests and frames are retained in `TOTALS-CHECKPOINT.json` and `TOTALS-GATE.json`. After the positive eight-row construction, one bounded native C++ pass enumerated the 4096 subsets of the twelve retired rows in each block over the prime 1000003. Within that modular gate, each block required at least eight independent rows to span the four coordinate totals, with 63 choices of eight rows. This is a bounded search record, not a global optimality theorem or an exclusion of redesigned factories.
+
+`construct_ranksector.py` contains the actual factory and its exact decoder assertions. `build_ranksector.py` reconstructs it, transfers only matching inherited scalar-event frames, rebuilds the existing 99-pivot selection, checks the dyadic contract and binds the complete normalized word. It invokes no discovery search. Text-source pins normalize only line endings to avoid platform-dependent CRLF failures. Whole-word normalization removes only the two established stale floating display annotations and an asserted redundant register-count field; mathematical operations, coefficients, frames and the rest of the word remain hash-bound.
+
+Normalized selected-word SHA-256:
+
+    d966e1481e0c09e4b7a0607429411046c6b3663ee83e6b8833958a745b82e337
+
+The local scalar receipt is `ranksector/SCALAR-AUDIT.json`; the source reconstruction receipt is `rebuilt-ranksector/CONSTRUCTION.json`. Physical owner maps, local complex phases, normalized spectators and the final two-engine arithmetic receipt are checked independently by the package replay.
+
+Inherited public mechanisms remain credited: PR507 supplies the partial-own factory; PR484 the gauge/kernel compiler; PR496 the pooled whole-owner interface; PR495/501/502 the frame retiming; and PR473 inspired the coordinated gauge reductions. The preceding package supplies the two-block pair cover and its 99-pivot selection, as well as the asynchronous controller and literal allocation. The improvement here is specifically the rank-sector coordinate-total reconstruction.
diff --git a/research/ranksector112-async/vendor/pr522/research-notes/RANKSECTOR-SOURCES.json b/research/ranksector112-async/vendor/pr522/research-notes/RANKSECTOR-SOURCES.json
new file mode 100644
index 0000000000..0e3b1d30f7
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/research-notes/RANKSECTOR-SOURCES.json
@@ -0,0 +1,25 @@
+{
+  "snapshot": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
+  "sources": [
+    {
+      "path": "lean/OAI/Analysis/Cotype/RankFactors.lean",
+      "sha256": "dca9d3a06e6b1d9fa3e53c9423bf41b6a192a9946f36284920d322c90b9bce55",
+      "declarations": [
+        "OAI.Cotype.exists_rank_pairing_matrix",
+        "OAI.Cotype.rank_pairing_contract"
+      ],
+      "role": "winning independent-sector construction",
+      "evidence": "Direct source/proof inspection, no fresh Lean compilation"
+    },
+    {
+      "path": "lean/OAI/Computability/FourierCircuit/DisplacementKernel.lean",
+      "sha256": "6663fc0dd25d18e0541f5328aead03e3bfd1c40e02fbaa7c171f8e6e35043b55",
+      "declarations": [
+        "OAI.ExactFourier.Displacement.reconstruct",
+        "OAI.ExactFourier.Displacement.kernel_eq_mul"
+      ],
+      "role": "screened telescoping source, not a separate numerical gain",
+      "evidence": "Direct source/proof inspection, no fresh Lean compilation"
+    }
+  ]
+}
diff --git a/research/ranksector112-async/vendor/pr522/research-notes/ROOT-WORD-PROOF.md b/research/ranksector112-async/vendor/pr522/research-notes/ROOT-WORD-PROOF.md
new file mode 100644
index 0000000000..a8c3ac6795
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/research-notes/ROOT-WORD-PROOF.md
@@ -0,0 +1,29 @@
+# Paid commutator rewrites of scalar words
+
+Source: the OpenAI DukePrimeDegree root-coordinate proof. RootCommutator.adjacent_root_conjugation gives an exact three-root transvection identity; EliminationChain.param_val identifies the actual ordered product, and EliminationWordEntries.word_val_eq_sum_single gives the compatible triangular special case. These sources were inspected, not newly compiled. No ergodic or limiting argument is imported into a finite algorithm.
+
+For three distinct registers a,b,c and rational q,r, replace the execution sequence
+
+    a += q*b; b += r*c
+
+by
+
+    b += r*c; a += q*b; a -= q*r*c.
+
+Substitution shows that both produce (a+q*b,b+r*c,c) from arbitrary initial values. Likewise, a+=q*b; c+=r*a equals c+=r*a; a+=q*b; c+=r*q*b. No zero-initialized helper is assumed. Dyadic coefficients remain dyadic under multiplication. The extra correction is an actual paid scalar gate.
+
+If the original first and second gates have frames F contained in G, put all three replacement gates at G only when every preceding register frame lies inside G and every subsequent register frame still contains G. Recompute the entire frame chain and actual prefix envelope. When gates lie farther apart, move the first past intervening gates only if their elementary operators commute; our structural gate checks that neither target occurs as the other's source and handles scales conservatively. Then apply the same identity and retain every correction. An exact all-input and physical replay is required before claiming any accepted word.
+
+For adjacent gates, let d_s and d_o be the dimensions of the shared and other first-gate registers beforehand; let f=dim(F), g=dim(G), and h the other register's next frame dimension. The old affected recursive costs at exponent a are
+
+    (f-d_s)^a + (g-f)^a + (f-d_o)^a + (h-f)^a,
+
+and the new costs are
+
+    (g-d_s)^a + (g-d_o)^a + (h-g)^a,
+
+omitting zero increments. Other registers' equal charges cancel. This gives a sufficient cost gate, but it is not assumed positive. A finite scan must also charge scalar precision and restoration.
+
+On the checked pair35 provider, the adjacent scan found no improving legal window. A larger native C++ scan inspected up to 128 following events, respecting exact commutation, and evaluated603 complete candidate frame profiles. None passed its floating discovery-price gate. GF(2) frame legality was exact; the discovery price used ordinary floating arithmetic and is not a rational nonexistence certificate. No changed word or kappa gain is claimed from this route. This is a bounded test of a sufficient transformation, not a universal barrier.
+
+The same native window test was then applied to the selected rank-sector provider: 547 full candidate profiles, no nominee passing the discovery cost gate. This follow-up is distinct from the 603-window pair35 screen above.
diff --git a/research/ranksector112-async/vendor/pr522/research-notes/ROOT-WORD-SOURCES.json b/research/ranksector112-async/vendor/pr522/research-notes/ROOT-WORD-SOURCES.json
new file mode 100644
index 0000000000..81d64db053
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/research-notes/ROOT-WORD-SOURCES.json
@@ -0,0 +1,23 @@
+{
+  "revision": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
+  "evidence": "source-only inspection; no fresh Lean kernel audit",
+  "sources": [
+    {
+      "path": "lean/OAI/NumberTheory/DukePrimeDegree/Geometry/RootCommutator.lean",
+      "sha256": "02e98ff42087d4b8ea7ed45338a024dd154c3aacdc585b1d6e06e137bb5e9d40"
+    },
+    {
+      "path": "lean/OAI/NumberTheory/DukePrimeDegree/Geometry/EliminationWordEntries.lean",
+      "sha256": "5d1be438e824ebc60b1845554aa07cfbd5f4a7bb1e424bcff2fe41c9bed0ba0e"
+    },
+    {
+      "path": "lean/OAI/NumberTheory/DukePrimeDegree/Geometry/EliminationChain.lean",
+      "sha256": "7c97dc807da3586b9e24b15415080cacf237754f2d3633df98cace573a756d07"
+    }
+  ],
+  "declarations": [
+    "DukePrimeDegree.adjacent_root_conjugation",
+    "DukePrimeDegree.EliminationChain.word_val_eq_sum_single",
+    "DukePrimeDegree.EliminationChain.param_val"
+  ]
+}
diff --git a/research/ranksector112-async/vendor/pr522/research-notes/ROUNDING-SOURCES.json b/research/ranksector112-async/vendor/pr522/research-notes/ROUNDING-SOURCES.json
new file mode 100644
index 0000000000..a7db843c4a
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/research-notes/ROUNDING-SOURCES.json
@@ -0,0 +1,21 @@
+{
+  "scope": "Source-only inspection; new deterministic finite algorithm, not direct Lean theorem application",
+  "sources": [
+    {
+      "path": "OAI/Combinatorics/UniformKServer/TreeRounding.lean",
+      "sha256": "ed3920ea2b28e78f7acfe3481a3f69b82015fa219308c0bf52db67d470fdc0f0"
+    },
+    {
+      "path": "OAI/Combinatorics/UniformKServer/RoundingKernel.lean",
+      "sha256": "f77f98dc12655abfb8553683c4fcc422dbefc3c69a5cafecd5baffe6529ed6d3"
+    },
+    {
+      "path": "OAI/Combinatorics/UniformKServer/BalancedStar.lean",
+      "sha256": "627e008394ef7267c3c014fdeb36984f4c4acc2f74380d044405764d89543419"
+    },
+    {
+      "path": "OAI/Combinatorics/UniformKServer/RealFlowConvex.lean",
+      "sha256": "6e0e4a8fc2eb7f1e0b67f2e4ce39f1ea2b254b47ff551665dea10f2bdd796c59"
+    }
+  ]
+}
diff --git a/research/ranksector112-async/vendor/pr522/research-notes/SWITCH-SCREEN.json b/research/ranksector112-async/vendor/pr522/research-notes/SWITCH-SCREEN.json
new file mode 100644
index 0000000000..94779eb5e5
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/research-notes/SWITCH-SCREEN.json
@@ -0,0 +1,15758 @@
+{
+  "status": "BOUNDED_SCREEN_COMPLETE_NO_GAIN",
+  "local_retimed_count": 28,
+  "local_raw_count": 28,
+  "raw_legal": 27,
+  "all_raw_legal_have_higher_moment": true,
+  "raw_profile_gates": [
+    {
+      "name": "local-00-02",
+      "status": "EXACT_RELATIONS_AND_FRAME_CHAINS_PASS",
+      "pivots": 99,
+      "profile": {
+        "1": 2194,
+        "2": 854,
+        "3": 44,
+        "4": 298,
+        "8": 17,
+        "6": 6,
+        "7": 1,
+        "5": 286
+      },
+      "widths": {
+        "8": 161,
+        "9": 381,
+        "7": 18
+      },
+      "widths_ordered": [
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+      "moment_difference_at_a_0p0014": 0.312813562133897
+    },
+    {
+      "name": "local-13-21",
+      "status": "EXACT_RELATIONS_AND_FRAME_CHAINS_PASS",
+      "pivots": 99,
+      "profile": {
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+      ],
+      "moment_difference_at_a_0p0014": 0.312813562133897
+    }
+  ],
+  "scope": "This is a bounded constructive candidate screen, not a proof that switches cannot improve the provider; no candidate passed the full improvement gate.",
+  "uniform_attempted": 9,
+  "uniform_saved_records": 8
+}
\ No newline at end of file
diff --git a/research/ranksector112-async/vendor/pr522/research-notes/SWITCH-SOURCES.json b/research/ranksector112-async/vendor/pr522/research-notes/SWITCH-SOURCES.json
new file mode 100644
index 0000000000..2b9207922a
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/research-notes/SWITCH-SOURCES.json
@@ -0,0 +1,22 @@
+{
+  "family": "Problem315 SwitchChain",
+  "sources": [
+    {
+      "path": "openai-math/lean\\OAI\\Probability\\SwitchChain\\FourVertexSwitch.lean",
+      "sha256": "07cc53158c1970dd75cbc2f7bf5d83c6ffc59e22d0484aaa6e17417e4bc818e3",
+      "scope": "Read source; no fresh Lean compilation or axiom audit."
+    },
+    {
+      "path": "openai-math/lean\\OAI\\Probability\\SwitchChain\\PairTradeSwitch.lean",
+      "sha256": "1357424dee22e34e6bdb86013a7e441854edf0d14874c04d9b993c5c6f3362a9",
+      "scope": "Read source; no fresh Lean compilation or axiom audit."
+    }
+  ],
+  "declarations": [
+    "fourVertexState_agrees_outside",
+    "switchStep_fourVertexState",
+    "PairFiber.fourVertexState_key",
+    "PairFiber.trade_exchange_eq_fourVertexState",
+    "PairFiber.switchStep_of_key_leftSet_exchange"
+  ]
+}
\ No newline at end of file
diff --git a/research/ranksector112-async/vendor/pr522/research-notes/Y-SWITCH-PROOF.md b/research/ranksector112-async/vendor/pr522/research-notes/Y-SWITCH-PROOF.md
new file mode 100644
index 0000000000..433d3f6539
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/research-notes/Y-SWITCH-PROOF.md
@@ -0,0 +1,11 @@
+# Degree-preserving Y-borrowing switches
+
+A new source family was read: OpenAI Problem315 SwitchChain, FourVertexSwitch and PairTradeSwitch. The exact source files and hashes are in OPENAI-SOURCE.json. Those Lean declarations construct a four-vertex edge switch preserving the relevant degrees and outside adjacency; PairTradeSwitch identifies the resulting fiber exchange. These sources were read, not freshly kernel-audited.
+
+The adaptation changes the selected output matching which borrows Y in each parity tetrad. It is distinct from the earlier own-snapshot pair-cover choice: the own snapshots stay fixed to pair35. The switch keeps one selected incident pair at each target. The scalar output change is compensated by the explicitly inverted two-output basis and recomputed scatter, rather than assuming graph degree preservation implies circuit equivalence. Every altered packet copy is retained, and the actual constructor checks its clean scalar identity.
+
+Sufficient transfer: choose a matching on each four-target tetrad; rebuild the selected target-pair transform, its inverse at the input, and its inverse-transformed scatter. If all elementary operations occur at common nested legal frames, every coefficient is in the accepted scalar compiler, and the complete dirty-column and physical-normalization audits pass, this constructs the same whole-cover endpoint. Degree preservation alone proves only the matching incidence invariant, not those additional facts. The implementation explicitly rebuilds the word; no existence of a missing gadget is assumed.
+
+Bounded results: 9 uniform selectors, 28 single-block switched selectors with inherited retiming, and 28 exact raw-frame rebuilds were screened. The unchanged uniform selector reproduces pair35. All 28 retimed local switches fail a real frame or centre chain. Raw rebuilding produces 27 legal relation/frame candidates and one centre-chain rejection. Every legal raw candidate has a strictly worse sampled paid moment at a=0.0014, unchanged99 entrance pivots and unchanged ordered helper widths. Hence none was nominated for expensive physical replay or numerical improvement. This does not rule out other switch schedules or a jointly reoptimized frame system.
+
+All scripts and failed witnesses are preserved in this directory. Heavy candidate selection uses the existing native C++ response-census engine; exact reconstruction uses rational arithmetic. No Lean formalization, publication, or new kappa claim is made for this lane.
diff --git a/research/ranksector112-async/vendor/pr522/research-notes/transvection-window.cpp b/research/ranksector112-async/vendor/pr522/research-notes/transvection-window.cpp
new file mode 100644
index 0000000000..95accecda3
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/research-notes/transvection-window.cpp
@@ -0,0 +1,24 @@
+#include <algorithm>
+#include <array>
+#include <cmath>
+#include <iostream>
+#include <vector>
+using namespace std;using B=array<int,9>;
+int dim(B b){int n=0;for(int x:b)n+=x!=0;return n;}
+B joinb(B a,B b){for(int x:b)for(int j=8;j>=0;j--)if(x>>j&1){if(a[j])x^=a[j];else{a[j]=x;break;}}return a;}
+bool sub(B a,B b){return dim(joinb(b,a))==dim(b);}
+struct E{int typ,t,s;B f;};
+bool commute(E a,E b){if(a.typ)return a.t!=b.t&&(b.typ||a.t!=b.s);if(b.typ)return b.t!=a.t&&b.t!=a.s;return a.t!=b.s&&b.t!=a.s;}
+double p(int n){return n?pow(double(n),1.-.001396):0.;}
+double eval(const vector<E>&es,vector<B>cur,const vector<B>&finish){double cost=0;for(auto&e:es){for(int r:{e.t,e.typ?-1:e.s})if(r>=0){if(!sub(cur[r],e.f))return 1e30;cost+=p(dim(e.f)-dim(cur[r]));cur[r]=e.f;}}for(int i=0;i<int(cur.size());i++){if(!sub(cur[i],finish[i]))return 1e30;cost+=p(dim(finish[i])-dim(cur[i]));}return cost;}
+int main(){int parts;cin>>parts;bool first=true;cout<<"[";long long tested=0;
+for(int part=0;part<parts;part++){int n,r;cin>>n>>r;vector<B>initial(r),finish(r);for(auto&v:initial)for(int&x:v)cin>>x;for(auto&v:finish)for(int&x:v)cin>>x;vector<E>es(n);for(auto&e:es){cin>>e.typ>>e.t>>e.s;for(int&x:e.f)cin>>x;}double base=eval(es,initial,finish);
+for(int i=0;i<n;i++){E e=es[i];if(e.typ)continue;
+for(int j=i+1;j<n&&j<=i+128;j++){E z=es[j];int kind=0;if(!z.typ){if(e.s==z.t&&e.t!=z.s)kind=1;else if(e.t==z.s&&e.s!=z.t)kind=2;}
+if(kind&&sub(e.f,z.f)&&dim(e.f)<dim(z.f)){
+ vector<E>a(es.begin(),es.begin()+i);a.insert(a.end(),es.begin()+i+1,es.begin()+j);a.push_back(z);E ee=e;ee.f=z.f;a.push_back(ee);E corr={0,kind==1?e.t:z.t,kind==1?z.s:e.s,z.f};a.push_back(corr);a.insert(a.end(),es.begin()+j+1,es.end());tested++;
+ double gain=base-eval(a,initial,finish);if(gain>1e-10){if(!first)cout<<",";first=false;cout<<"{\"part\":"<<part<<",\"index\":"<<i<<",\"second\":"<<j<<",\"kind\":"<<kind<<",\"gain\":"<<gain<<"}";}
+}
+if(!commute(e,z))break;
+}}
+}cout<<"]\n";cerr<<"tested "<<tested<<" actual frame-cost candidates\n";}
diff --git a/research/ranksector112-async/vendor/pr522/vendor/audit_scalar_invoice.py b/research/ranksector112-async/vendor/pr522/vendor/audit_scalar_invoice.py
new file mode 100644
index 0000000000..b03fdf510f
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/vendor/audit_scalar_invoice.py
@@ -0,0 +1,82 @@
+"""Fresh PR484 scalar/prefix lowering and finite overcharge recount. OpenAI Codex.
+Reads emitted programs, canonical word and raw routes, importing no supplier code.
+Inherited all-size compiler admissibility is a condition, not inferred here.
+"""
+from pathlib import Path
+from fractions import Fraction as F
+from collections import Counter
+import gzip,json,math,hashlib
+import sys
+O=Path(sys.argv[1]);V=Path(sys.argv[2]);HOSTED=Path(sys.argv[3])
+def read(p):return json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+w=read(V/'split-centres/CANONICAL-WORD.json.gz');p=read(V/'split-centres/LOCAL-PROGRAMS.json.gz');old=read(V/'split-centres/GLOBAL-TEMPLATE.json.gz');new=read(HOSTED/'GLOBAL-TEMPLATE.json.gz');integ=read(V/'split-centres/INTEGRATION.json');checks=read(V/'split-centres/LOCAL-CHECKS.json');prior=read(V/'split-centres/INDEPENDENT-REPLAY.json');owners=read(O/'OWNERS-AND-PROFILE.json')
+N=800;M=73;R=560;L=9;T=8;VV=120;K=4
+local={}
+for ori,evs in p.items():
+ rows={('L',i):{i:F(1)}for i in range(N)};env={('L',i):F(1)for i in range(N)};peak=F(1);real=macros=0;paid=Counter();workops=0
+ for e in evs:
+  if e[0]=='climb':paid[e[5]]+=1
+  elif e[0]=='center':paid[e[4]]+=1
+  elif e[0]=='scalar':
+   macros+=1;x=e[1];op=x[0];a=tuple(x[1]);count=0
+   if op=='clear':rows[a]={};env[a]=F(0);count=1
+   elif op=='copy':rows[a]=dict(rows[tuple(x[2])]);env[a]=env[tuple(x[2])];count=1
+   elif op=='scale':
+    q=F(x[2],x[3]);num,den=abs(q.numerator),q.denominator
+    assert num and num&(num-1)==0 and den&(den-1)==0
+    rows[a]={j:q*v for j,v in rows[a].items()};env[a]*=abs(q)
+    count=abs(num.bit_length()-den.bit_length())+int(q<0)
+   elif op=='add':
+    b=tuple(x[2]);q=F(x[3],x[4]);num,den=abs(q.numerator),q.denominator
+    assert a!=b and num>0 and den&(den-1)==0
+    # Lower actual coefficient to cleared Horner work. Every intermediate
+    # magnitude envelope is explicitly included, before denominator halvings.
+    acc=0;count=1
+    for i,ch in enumerate(bin(num)[2:]):
+     if i:acc*=2;count+=1;peak=max(peak,acc*env[b])
+     if ch=='1':acc+=1;count+=1;peak=max(peak,acc*env[b])
+    v=F(acc)
+    for i in range(den.bit_length()-1):v/=2;count+=1;peak=max(peak,v*env[b])
+    assert v==abs(q);count+=2 # signed accumulation and private work clear
+    env[a]=env.get(a,F(0))+abs(q)*env[b];rr=rows.setdefault(a,{})
+    for j,z in list(rows[b].items()):
+     value=rr.get(j,F(0))+q*z
+     if value:rr[j]=value
+     else:rr.pop(j,None)
+    workops+=count
+   else:raise AssertionError(op)
+   real+=2*count;peak=max(peak,env[a])
+ assert all(not row for reg,row in rows.items()if reg[0]=='C')
+ for i in range(N):
+  expected={i:F(1)}
+  if ori=='forward'and 120<=i<240:expected[i-120]=F(1)
+  if ori=='backward'and i<120:expected[i+120]=F(-1)
+  assert rows['L',i]==expected
+ assert peak==F(prior['local'][ori]['prefix_l1_upper']) and peak<2**192
+ assert real==checks[ori]['real_component_primitive_bound']and macros==checks[ori]['scalar_macros']
+ assert dict(paid)=={int(r):z for r,z in checks[ori]['paid_profile'].items()}
+ local[ori]=dict(events=len(evs),macros=macros,real_component_primitives=real,prefix_l1=str(peak),prefix_bits=peak.numerator.bit_length()-peak.denominator.bit_length()+1,coefficient_work_primitive_count=workops,all_exact_columns=N,all_560_dirty_helper_columns_restored=True,private_centres_and_coefficient_work_cleared=True)
+centres=len(w['centers']);widths=[9-len(w['frames'][f])for f in w['start'][240:]];enter=sum(x<9 for x in widths)
+children=sum(checks['forward']['paid_profile'].values());macros=max(x['macros']for x in local.values());compiler=64*(M+1)**3
+adapters=16*(macros+children+N+centres)+64*M
+primitive_bound=max(x['real_component_primitives']for x in local.values())+adapters*compiler
+bridges=sum(e['kind']=='bridge'for e in old['recipe']);bridgeadd=2*VV*T*bridges;shifts=K*VV*T;moves=2*K*VV*T
+oldW=old['live'];oldP=old['physical'];oldNB=(oldW-2*VV*K*T)//L
+scalar=sum(local[c['orientation']]['real_component_primitives']for c in old['calls'])
+nonlocal_items=4*VV*T*L+2*VV*T*L+2*L*T*R+sum(e['replicas']for e in old['idle_children'])+L*oldNB+bridgeadd+shifts+moves+oldW+oldP+2*L*T*enter*144
+outside=8*nonlocal_items+64*M
+pervertex=scalar+bridgeadd+shifts+moves+oldW+(72*adapters+outside)*compiler+64*oldP
+invoice=integ['finite_invoice'];assert (primitive_bound,adapters,pervertex,compiler)==(invoice['local_primitive_bound'],invoice['local_adapters'],invoice['pervertex'],invoice['compiler'])
+# Independent hosted stock rebase, retaining the larger unhosted operation
+# overcharge; only the stock and mass in the common router/literal change.
+W=new['live'];P=new['physical'];mass=owners['rank_mass'];profile=owners['paid_profile']
+assert M*W-mass==2496 and P==W+R+centres+2
+rebase=pervertex-oldP*65+P*65-oldW+W;used=max(rebase,pervertex)
+r=M//2;group=2**(r*r)
+for i in range(1,r+1):group*=2**(2*i)-1
+stock=group*P;smass=group*mass;logical=group*used+64;router=compiler*(logical+1)*(stock+1)**2
+G,E,C0=2**30000,2**100000,2**210000;B=smass+E;literal=2*G*stock**2+8*smass+4*stock+4+32*M;row=2*stock.bit_length()+9909+252;maxchild=max(map(int,profile))
+ineq=dict(local_primitive_bound=primitive_bound<2**48,logical=logical<2**6050,router=router<G,literal=literal<E,mass=B<2**100001,precision=32*M*B*B<C0,tape=2*B+18<C0,row=row<20161,halving=M*M>2*maxchild*maxchild)
+assert all(ineq.values())
+out=dict(status='PASS_INDEPENDENT_SCALAR_PREFIX_AND_HOSTED_FINITE_INVOICE',local=local,entering_helpers=enter,entrance_rank=sum(9-x for x in widths),local_adapters=adapters,local_primitive_bound=primitive_bound,wrapper_elementary_factors_charged=2*72*enter*144,compiler=compiler,unhosted_pervertex=pervertex,hosted_rebased_pervertex=rebase,conservative_pervertex_used=used,finite=dict(physical_stock_bits=stock.bit_length(),router_bits=router.bit_length(),literal_bits=literal.bit_length(),physical_row_coefficient=row,retained_row_coefficient=20161,required_C0_bits=(32*M*B*B).bit_length(),halving_integer_inequality=[M*M,2*maxchild*maxchild],G_exponent=30000,E_exponent=100000,C0_exponent=210000),strict_checks=ineq,scope='Exact finite recount conditional on inherited all-size compiler/precision/tape and analytic-transfer contracts. Signed accumulation uses the supplier scalar primitive convention.')
+(O/'PREFIX-AND-INVOICE.json').write_text(json.dumps(out,indent=2)+'\n');print(json.dumps(out,indent=2),flush=True)
diff --git a/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/adapters_gk.py b/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/adapters_gk.py
new file mode 100644
index 0000000000..252ca9393d
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/adapters_gk.py
@@ -0,0 +1,59 @@
+"""Paid residual wrappers for entering helpers (Lemma A): generation and independent decoding.  Apache-2.0.
+Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.  The wrapper construction follows PR #458
+(chafreaky): a helper that starts at frame E and ends at FULL has the physical residual S_E = T_FULL T_E^-1 (apply T_E^-1 first);
+S_E = L_E (C_[w] x I) R_E with R_E applied first; the wrappers  R_E^-1  before the whole local invocation and  L_E^-1  after its
+full-frame cleanup turn the residual into the coordinate factor C_[w] x I and restore the other 9 - w coordinates identically.
+usage: adapters_gk.py CANONICAL-WORD.json.gz RESIDUAL-ADAPTERS.json OUT-LEMMA-A.json
+Writes the recipes (generation uses clifford_exact.lower_child) and then DECODES the serialized monomials with the primitive
+constructors of clifford_exact (not lower_child) and checks, for every entrance frame, that  L_E^-1 S_E R_E^-1  has exactly the
+tableau and zero-state vector (global phase included) of  fourier(9, range(w)); mutated recipes (wrong phase, swapped sides, wrong
+translation, wrong width) must be rejected."""
+import copy, gzip, json, sys
+from pathlib import Path
+R = Path(__file__).resolve().parent.parent.parent
+sys.path.insert(0, str(R / 'split-centres-global/vendor'))
+from clifford_exact import canonical_frame, lower_child, fourier, diag, perm, xgate, Op, identity
+n = 9; FULL = tuple(1 << i for i in range(n))
+def monomial_op(rec):
+    """decode a serialized monomial (matrix rows, quadratic rows, Z4 linear part, translation, phase)"""
+    out = diag(n, tuple(rec['quadratic_rows']), tuple(rec['linear_Z4'])).then(perm(n, tuple(rec['matrix_rows']))).then(xgate(n, rec['offset']))
+    return out.then(Op(n, identity(n), [('phase', rec['phase'])]))
+def S_of(U):
+    return canonical_frame(n, tuple(U)).adjoint().then(canonical_frame(n, FULL))
+def wrapped_ok(U, rec):
+    """exactly: L^-1 S R^-1 = C_[w] x I  (apply order: R^-1, S, L^-1)"""
+    w = n - len(U); S = S_of(U); Rm = monomial_op(rec['right']); Lm = monomial_op(rec['left'])
+    net = Rm.adjoint().then(S).then(Lm.adjoint()); target = fourier(n, range(w))
+    return rec['rank'] == w and net.tab == target.tab and net.zero_state() == target.zero_state()
+def main():
+    c = json.load(gzip.open(sys.argv[1])); frames = c['frames']; v = c['v']
+    starts = sorted({c['start'][r] for r in range(2 * v, len(c['start'])) if c['start'][r] != 0})
+    recipes = {}
+    for f in starts:
+        U = frames[f]; rec, compiled = lower_child(S_of(U))
+        recipes[str(f)] = dict(frame=f, vectors=list(U), entrance_rank=len(U), rank=rec['rank'], left=rec['left'], right=rec['right'])
+    Path(sys.argv[2]).write_text(json.dumps(dict(status='RESIDUAL_ADAPTER_RECIPES', recipes=recipes), sort_keys=True, separators=(',', ':')) + '\n')
+    # ---- independent decode of the serialized file
+    data = json.loads(Path(sys.argv[2]).read_text())['recipes']
+    dot = lambda a, b: bin(a & b).count('1') & 1
+    detail = []
+    for f in starts:
+        rec = data[str(f)]; U = frames[f]
+        assert wrapped_ok(U, rec), ('wrapper product is not C_[w] x I', f)
+        detail.append(dict(frame=f, entrance_rank=len(U), residual_width=n - len(U), vectors=list(U), all_even_weight=all(bin(x).count('1') % 2 == 0 for x in U),
+                           totally_isotropic=all(dot(a, b) == 0 for a in U for b in U)))
+    controls = []
+    def reject(name, fn):
+        f = starts[0]; rec = copy.deepcopy(data[str(f)]); fn(rec)
+        if wrapped_ok(frames[f], rec): raise AssertionError('mutated wrapper accepted: ' + name)
+        controls.append(name)
+    reject('wrong global phase', lambda r: r['right'].__setitem__('phase', (r['right']['phase'] + 1) % 4))
+    reject('wrong translation', lambda r: r['left'].__setitem__('offset', r['left']['offset'] ^ 1))
+    reject('wrong quadratic form', lambda r: r['right'].__setitem__('quadratic_rows', [x ^ 2 if i == 0 else x for i, x in enumerate(r['right']['quadratic_rows'])]) if False else r['right']['linear_Z4'].__setitem__(0, (r['right']['linear_Z4'][0] + 2) % 4))
+    reject('sides swapped', lambda r: (r.__setitem__('left', r['right']), r.__setitem__('right', r['left'])))
+    reject('wrong width', lambda r: r.__setitem__('rank', r['rank'] + 1))
+    res = dict(status='PASS_RESIDUAL_WRAPPERS_ARE_EXACT', frames=len(detail), wrappers_reject=controls, all_even_weight=all(d['all_even_weight'] for d in detail),
+               all_totally_isotropic=all(d['totally_isotropic'] for d in detail), detail=detail)
+    Path(sys.argv[3]).write_text(json.dumps(res, indent=1) + '\n')
+    print('Lemma A (exact): L^-1 S_E R^-1 = C_[w] x I for', len(detail), 'entrance frames, global phase included;', len(controls), 'wrapper mutations rejected; all-even-weight:', res['all_even_weight'])
+if __name__ == '__main__': main()
diff --git a/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/audit_gk.py b/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/audit_gk.py
new file mode 100644
index 0000000000..e80ca6b8b3
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/audit_gk.py
@@ -0,0 +1,189 @@
+# GK: modified copy of PR #433's complex_audit.py (icekylinx with Codex; PR #425) by DreamingOfClouds with Claude Opus 5.5
+# (Anthropic), via Claude Code.  Every change is marked "GK:"; with a word that has no start_extra / target_levels the
+# behaviour and the written files are PR #433's.
+# Modified from PR425 by icekylinx with Codex assistance.
+"""Read-back audit, independent of the Hamming producer and its row state."""
+import copy,gzip,hashlib,importlib.util,json,math,time
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+OUT=Path('split-centres');p=OUT/'FULL-WORD.json.gz'
+word=json.load(gzip.open(p));v=120;n=240+word['report']['R'];start=time.monotonic()
+def apply(e,rows):
+    if e[0]=='scale':
+        _,t,a,b,*_=e;q=Q(a,b);assert q
+        rows[t]={j:q*x for j,x in rows[t].items()}
+    else:
+        _,t,s,a,b,*_=e;q=Q(a,b);assert t!=s
+        for j,x in list(rows[s].items()):
+            z=rows[t].get(j,Q(0))+q*x
+            if z:rows[t][j]=z
+            else:rows[t].pop(j,None)
+def ident():return [{r:Q(1)} for r in range(n)]
+def inv(e):
+    e=copy.deepcopy(e)
+    if e[0]=='add':e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    return e
+def dual(e):
+    e=inv(e)
+    if e[0]=='add':e[1],e[2]=e[2],e[1]
+    return e
+
+main=word['A']+word['cut']+word['B']
+assert all(not 120<=e[2]<240 for e in word['A']+word['B'] if e[0]=='add' and not 120<=e[1]<240)
+matrix=ident()
+for e in main:apply(e,matrix)
+print('full main columns',n,'replayed',flush=True)
+# Compute -A_Y^-1 B_S using only rows of the explicit main operator.
+dirty=[{} for r in range(n)]
+for r in range(v,2*v):dirty[r]={j:x for j,x in matrix[r].items() if j>=2*v}
+for e in word['precondition']:apply(e,dirty)
+comp=[]
+for r in range(v,2*v):
+    for j,q in sorted(dirty[r].items()):comp.append(['add',r,j,-q.numerator,q.denominator,[]])
+
+cleanup=[inv(e) for e in reversed(word['A']+word['B']) if not v<=e[1]<2*v]
+assert [e[:-1] for e in cleanup]==[e[:-1] for e in word['cleanup']]
+program=word['precondition']+comp+main+cleanup
+actual=ident()
+for e in program:apply(e,actual)
+expected=ident()
+for t in range(v):expected[v+t][t]=Q(1)
+assert actual==expected
+print('PASS exact arbitrary dirt and restored sources/helpers',flush=True)
+back=ident()
+for e in program:apply(dual(e),back)
+expected_back=ident()
+for t in range(v):expected_back[t][v+t]=Q(-1)
+assert back==expected_back
+print('PASS exact inverse-transpose on every column',flush=True)
+# Independent sparse vector controls avoid repeating a dense full replay.
+def vector(es,x):
+    x=list(map(Q,x))
+    for e in es:
+        if e[0]=='scale':x[e[1]]*=Q(e[2],e[3])
+        else:x[e[1]]+=Q(e[3],e[4])*x[e[2]]
+    return x
+sample=[((i*137+13)%101)-50 for i in range(n)]
+want=vector(program,sample)
+controls={
+    'missing_dirty_compensation':word['precondition']+main+cleanup,
+    'missing_Y_inverse_basis':comp+main+cleanup,
+    'missing_source_cleanup':word['precondition']+comp+main,
+    'wrong_dual_event_order':[dual(e) for e in reversed(program)],
+}
+for name,es in controls.items():
+    expected_sample=vector([dual(e) for e in program],sample) if name=='wrong_dual_event_order' else want
+    assert vector(es,sample)!=expected_sample,name
+
+# Orthogonal transvection and a port permutation bring the new geometry onto
+# the already fixed 120-port routing family. Every incidence is transformed.
+old=json.load(gzip.open('work/higher-stage-e8/verified/gcert1-e8-retimed.json.gz'))
+def tau(x):return x^(43 if (x&43).bit_count()%2 else 0)
+assert 43 .bit_count()%2==0
+assert set(map(tau,word['ports']))==set(old['ports'])
+mapping={i:old['ports'].index(tau(q)) for i,q in enumerate(word['ports'])}
+mapping.update({v+i:v+mapping[i] for i in range(v)})
+mapping.update({r:r for r in range(2*v,n)})
+def basis(vs):
+    b={}
+    for x in vs:
+        for k in sorted(b,reverse=True):
+            if x>>k&1:x^=b[k]
+        if x:
+            k=x.bit_length()-1
+            for j in b:
+                if b[j]>>k&1:b[j]^=x
+            b[k]=x
+    return tuple(b[k] for k in sorted(b,reverse=True))
+def perp(x):return basis([z for z in range(1,512) if not (x&z).bit_count()%2])
+full=tuple(1<<i for i in range(8,-1,-1));frames=[(),full];fi={f:i for i,f in enumerate(frames)}
+def fid(f):
+    f=basis(f)
+    if f not in fi:fi[f]=len(frames);frames.append(f)
+    return fi[f]
+def canonical(e):
+    e=copy.deepcopy(e);e[1]=mapping[e[1]]
+    if e[0]=='add':e[2]=mapping[e[2]]
+    if e[-1] is not None:e[-1]=fid([tau(x) for x in e[-1]])
+    return e
+can={key:[canonical(e) for e in word[key]] for key in ('A','B','cut','cleanup','precondition')}
+can['compensation']=[canonical(e) for e in comp]
+can['start']=[fid([q]) for q in old['ports']]+[0]*(v+word['report']['R'])
+for _r,_E in word.get('start_extra',{}).items():
+    assert 2*v<=int(_r)<2*v+word['report']['R'],('an entrance (residual wrapper, spectators, bank footprint) is defined for helper registers only',_r)   # GK
+    can['start'][int(_r)]=fid([tau(x) for x in _E])   # GK: helper entrances
+can['final']=[1]*v+[fid(perp(q)) for q in old['ports']]+[1]*word['report']['R']
+can['ports']=old['ports'];can['centers']=[mapping[r] for r in word['centers']]
+can['center_frames']=[fid([tau(x) for x in f]) for f in word['center_frames']]
+tlev={}   # GK: nonzero-frame compensation raises targets before the centre scatter
+for _t,_E in word.get('target_levels',{}).items():tlev[mapping[v+int(_t)]-v]=fid([tau(x) for x in _E])
+if tlev:can['target_levels']=tlev
+can['h']=9;can['v']=v;can['R']=word['report']['R'];can['frames']=frames
+cur=list(can['start']);paid=Counter();edges=set();incidences=0
+def climb(r,f):
+    old=cur[r]
+    assert basis(frames[old]+frames[f])==frames[f]
+    if old!=f:
+        delta=len(frames[f])-len(frames[old]);assert delta>0
+        edges.add((old,f));paid[delta]+=1;cur[r]=f
+for part in ('A','B'):
+    if part=='B':
+        assert all(cur[r]==f for r,f in zip(can['centers'],can['center_frames']))
+        assert all(cur[r]==tlev.get(r-v,0) for r in range(v,2*v))   # GK: targets sit at their level
+        for r_c,f in zip(can['centers'],can['center_frames']):
+            # GK: a centre copy descends cf -> served levels (descending chain) -> lowest served level; at the defaults the
+            # only served level is 0 and this is PR #433's single child of rank |cf|
+            served={tlev.get(e[1]-v,0) for e in can['cut'] if e[2]==r_c}
+            o=f
+            for Lv in sorted(served,key=lambda x:-len(frames[x])):
+                assert basis(frames[Lv]+frames[o])==tuple(frames[o]),('centre level outside the previous frame',r_c)
+                if Lv!=o:
+                    paid[len(frames[o])-len(frames[Lv])]+=1
+                    if not(o==f and Lv==0):edges.add((o,Lv));edges.add((Lv,o))   # (cf,0),(0,cf) are added by the phase script
+                    o=Lv
+    for e in can[part]:
+        rs=[e[1]]+([e[2]] if e[0]=='add' else [])
+        for r in rs:climb(r,e[-1]);incidences+=1
+for r,f in enumerate(can['final']):climb(r,f)
+assert dict(paid)=={int(r):x for r,x in word['report']['local_profile'].items()}
+# GK: entrances lower the helper climb by their rank; centre descents may stop above frame zero
+if not word.get('start_extra') and not word.get('target_levels'):assert sum(r*x for r,x in paid.items())==9*can['R']+240*8+72
+else:assert sum(r*x for r,x in paid.items())==sum(int(r)*x for r,x in word['report']['local_profile'].items())
+can['local_profile']=dict(sorted(paid.items()));can['edges']=sorted(edges)
+cp=OUT/'CANONICAL-WORD.json.gz';cp.write_bytes(gzip.compress(json.dumps(can,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+
+def engine(name):
+    p=Path('work/pr361/code/engines')/(name+'.py');s=importlib.util.spec_from_file_location('hamming_'+name,p)
+    m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m
+M,M2=engine('moment'),engine('base_two_moment');m,W=73,word['report'].get('live',12720)   # GK: unhosted stock of the word
+HG={int(r):z for r,z in word['report']['global_profile'].items()}
+root=M.certify(HG,m,W,True);b=Q(int(Q(root['lower'])*10**18),10**18);grid=Q(1,10**18)
+assert M.moment(HG,m,W,b,True)[1]<1<M.moment(HG,m,W,b+grid,True)[0]
+fallback=32*m*m*sum(HG.values())
+def second(a):
+    lo,hi=M2.moment(m,W,list(HG.items()),a)
+    l2,h2=M2.moment(m,W,[(1,fallback)],a)
+    return lo+l2/10**16,hi+h2/10**16
+assert second(b)[1]<1<second(b+grid)[0]
+coeff=Counter(str(Q(e[3],e[4]) if e[0]=='add' else Q(e[2],e[3])) for e in program)
+report={'status':'PASS_EXACT_SCALAR_AND_FRAME_RESEARCH_CANDIDATE_NOT_YET_ADMITTED',
+        'full_word_sha256':hashlib.sha256(p.read_bytes()).hexdigest(),
+        'canonical_word_sha256':hashlib.sha256(cp.read_bytes()).hexdigest(),
+        'live_columns_each_orientation':n,'arbitrary_helper_columns':can['R'],
+        'all_live_source_and_helper_rows_restored':True,'all_target_rows_correct':True,
+        'negative_controls_rejected':list(controls),'old_response_additions':len(comp),
+        'complete_forward_scalar_operations':len(program),'coefficient_histogram':dict(coeff),
+        'frames':len(frames),'nested_directed_edges':len(edges),'common_frame_incidences':incidences,
+        'orthogonal_transport_vector':43,'transported_ports_exactly_match_fixed_routes':True,
+        'local_profile':dict(sorted(paid.items())),
+        'prospective_complex_b':str(b),'prospective_b_float':float(b),
+        'prospective_gain_percent':float(100*(b/Q(999388595603943,10**18)-1)),
+        'two_rational_moment_engines':True,'next_b_grid_rejected':True,
+        'remaining':['new general scalar-interface proof integration','exact phase and emitted local/global program','finite invoice and outer assembly'],
+        'scope':'Substantial new scalar-network candidate. All parameter values remain prospective until the expanded scalar interface and complete phase-aware supplier are admitted.',
+        'seconds':time.monotonic()-start}
+(OUT/'SCALAR-FRAME-AUDIT.json').write_text(json.dumps(report,indent=2)+'\n')
+print('PASS prospective b',float(b),'gain',report['prospective_gain_percent'],'percent; seconds',report['seconds'],flush=True)
diff --git a/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/emit_gk.py b/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/emit_gk.py
new file mode 100644
index 0000000000..0dd1853bb5
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/emit_gk.py
@@ -0,0 +1,156 @@
+# GK: modified copy of PR #433's complex_emit.py (icekylinx with Codex assistance; PR #425) by DreamingOfClouds with Claude Opus 5.5
+# (Anthropic), via Claude Code.  Every change is marked "GK:".  On a word without start_extra / target_levels the behaviour
+# and every written file equal PR #433's (regression anchor in verify.py).
+import sys as _sys, os as _os; _sys.path.insert(0, _os.path.dirname(_os.path.abspath(__file__)))
+# Adapted from PR425 by icekylinx with Codex assistance.
+"""Emit both local programs, integrate the fixed nine-stage geometry, and bill.
+
+The expanded scalar interface is justified in PROOF.txt. This script does not
+claim a Lean proof or discharge the inherited all-size/analytic interfaces.
+"""
+import copy,gzip,hashlib,importlib.util,json,math
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+OUT=Path('split-centres');cp=OUT/'CANONICAL-WORD.json.gz'
+c=json.load(gzip.open(cp))
+frames=c['frames'];v,R,h=c['v'],c['R'],c['h'];n=2*v+R
+def digest(x):return hashlib.sha256(json.dumps(x,sort_keys=True,separators=(',',':')).encode()).hexdigest()
+def basis(vs):
+    b={}
+    for x in vs:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+def dual(e):
+    e=list(e)
+    if e[0]=='add':e[1],e[2]=e[2],e[1];e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    return e
+def scalar(e,back):
+    e=dual(e) if back else list(e)
+    if e[0]=='add':return ['add',['L',e[1]],['L',e[2]],e[3],e[4]]
+    return ['scale',['L',e[1]],e[2],e[3]]
+def primitive_bound(e):
+    if e[0] in ('clear','copy'):return 1
+    q=Q(e[3],e[4]) if e[0]=='add' else Q(e[2],e[3])
+    a,b=abs(q.numerator),q.denominator
+    assert b&(b-1)==0
+    if e[0]=='scale':
+        assert a&(a-1)==0
+        return abs(a.bit_length()-b.bit_length())+int(q<0)
+    # Exact binary Horner multiplication on a cleared private stream, repeated
+    # halving, signed accumulation into the target, then clear the private stream.
+    return 3+(a.bit_length()-1)+a.bit_count()+(b.bit_length()-1)
+
+def emit(back):
+    out=[];cur=c['start'].copy()
+    def event(e):out.append(e)
+    def scal(e,f):event(['scalar',e,f])
+    event(['phase','zero_frame_precondition'])
+    for e in c['precondition']+c['compensation']:
+        regs=[e[1]]+([e[2]] if e[0]=='add' else [])
+        assert all(c['start'][r]==0 for r in regs)
+        scal(scalar(e,back),0)
+    event(['phase','entry_adapters'])
+    # GK: a helper that starts at a nonzero entrance frame has NO entry adapter; its paid wrapper R_E^-1 (Lemma A) precedes every gate
+    # that touches it and L_E^-1 follows the full-frame cleanup.  Words without entrances emit PR #433's events.
+    entering=[r for r,f in enumerate(c['start']) if r>=2*v and f!=0]
+    for r,f in enumerate(c['start']):
+        if r in entering:event(['residual_adapter','pre',r,f])
+        else:event(['adapter','old_to_new',r,f])
+    def climb(r,f,part):
+        old=cur[r]
+        if old==f:return
+        assert basis(frames[old]+frames[f])==tuple(frames[f])
+        rank=len(frames[f])-len(frames[old]);assert rank>0
+        event(['climb',part,r,old,f,rank]);cur[r]=f
+    for part in ('A','centers','B','final'):
+        event(['phase',part])
+        if part in ('A','B'):
+            for e in c[part]:
+                regs=[e[1]]+([e[2]] if e[0]=='add' else [])
+                for r in regs:climb(r,e[-1],part)
+                scal(scalar(e,back),e[-1])
+        elif part=='centers':
+            # GK: targets sit at their nonzero-frame-compensation level (0 at the defaults); a centre copy descends
+            # cf -> served levels (descending chain) -> lowest served level and scatters into each target at its level
+            lv=lambda r:c.get('target_levels',{}).get(str(r-v),0)
+            assert all(cur[r]==lv(r) for r in range(v,2*v))
+            for k,r in enumerate(c['centers']):
+                cf=c['center_frames'][k];assert cur[r]==cf
+                terms=[e for e in c['cut'] if e[2]==r]
+                path=[cf]+sorted({lv(e[1]) for e in terms}-{cf},key=lambda x:-len(frames[x]))
+                C=['C',k]
+                if not back:
+                    scal(['clear',C],cf);scal(['copy',C,['L',r]],cf)
+                    for a in range(len(path)):
+                        if a>0:event(['center',k,path[a-1],path[a],len(frames[path[a-1]])-len(frames[path[a]])])
+                        for e in terms:
+                            if lv(e[1])==path[a]:scal(['add',['L',e[1]],C,e[3],e[4]],path[a])
+                    scal(['clear',C],path[-1])
+                else:
+                    scal(['clear',C],path[-1])
+                    for a in range(len(path)-1,-1,-1):
+                        for e in terms:
+                            if lv(e[1])==path[a]:scal(['add',C,['L',e[1]],e[3],e[4]],path[a])
+                        if a>0:event(['center',k,path[a],path[a-1],len(frames[path[a-1]])-len(frames[path[a]])])
+                    scal(['add',['L',r],C,-1,1],cf);scal(['clear',C],cf)
+        else:
+            for r,f in enumerate(c['final']):climb(r,f,part)
+    event(['phase','exit_adapters'])
+    for r,f in enumerate(c['final']):event(['adapter','new_to_old',r,f])
+    event(['phase','full_frame_cleanup'])
+    for e in c['cleanup']:
+        regs=[e[1]]+([e[2]] if e[0]=='add' else [])
+        assert all(c['final'][r]==1 for r in regs)
+        scal(scalar(e,back),1)
+    for r in entering:event(['residual_adapter','post',r,c['start'][r]])   # GK: L_E^-1 after the full-frame cleanup
+    event(['phase','done'])
+    return out
+
+def check_local(events,back):
+    # Literal scalar replay of the emitted stream, including center lifetimes.
+    state={('L',r):{r:Q(1)} for r in range(n)};live=[];paid=Counter();prims=0;macros=0
+    for e in events:
+        if e[0]=='climb':assert not live;paid[e[5]]+=1
+        elif e[0]=='center':assert live==[e[1]];paid[e[4]]+=1
+        elif e[0]=='scalar':
+            op=e[1];tag=op[0];t=tuple(op[1]);macros+=1;prims+=2*primitive_bound(op)
+            if tag=='clear':
+                state[t]={}
+                if t[0]=='C' and t[1] in live:live.remove(t[1])
+            elif tag=='copy':state[t]=dict(state.get(tuple(op[2]),{}));live.append(t[1])
+            elif tag=='scale':state[t]={j:Q(op[2],op[3])*x for j,x in state[t].items()}
+            else:
+                s=tuple(op[2]);q=Q(op[3],op[4]);row=state.setdefault(t,{})
+                if t[0]=='C' and t[1] not in live:live.append(t[1])
+                for j,x in list(state.get(s,{}).items()):
+                    z=row.get(j,Q(0))+q*x
+                    if z:row[j]=z
+                    else:row.pop(j,None)
+    assert not live and all(not row for r,row in state.items() if r[0]=='C')
+    for r in range(n):
+        expected={r:Q(1)}
+        if back and r<v:expected[v+r]=Q(-1)
+        elif not back and v<=r<2*v:expected[r-v]=Q(1)
+        assert state['L',r]==expected,('emitted column mismatch',back,r)
+    assert dict(paid)=={int(r):z for r,z in c['local_profile'].items()}
+    return {'sha256':digest(events),'events':len(events),'scalar_macros':macros,
+            'real_component_primitive_bound':prims,'paid_profile':dict(sorted(paid.items())),
+            'all_columns':n,'private_centers_cleared':True,'private_coefficient_stream_cleared_after_each_macro':True}
+
+programs={};checks={}
+for name,back in [('forward',False),('backward',True)]:
+    programs[name]=emit(back);checks[name]=check_local(programs[name],back)
+    print('PASS emitted',name,checks[name]['events'],'events',flush=True)
+
+
+(OUT/'LOCAL-PROGRAMS.json.gz').write_bytes(gzip.compress(json.dumps(programs,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+(OUT/'LOCAL-CHECKS.json').write_text(json.dumps(checks,indent=2)+'\n')
diff --git a/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/gk_common.py b/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/gk_common.py
new file mode 100644
index 0000000000..0e5fde920d
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/gk_common.py
@@ -0,0 +1,94 @@
+"""Shared helpers for the complex shared-donor-kernel / entrance-gauge word.  Apache-2.0.
+Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.
+
+A "gk word" is PR #433's FULL-WORD.json.gz with optional extension keys (absent in #433's word, so every default is
+#433's behaviour):
+  start_extra   {register: entrance frame (list of F2^9 vectors)}  helpers that start at a nonzero frame (width 9 - dim)
+  target_levels {target: frame}                                    frame a target reaches through nonzero-frame compensation
+Entrance gauges are ordinary gates at the head of A (target += c * helper at the entrance frame); kernel updates are
+ordinary gates at the head of A (donor += q * pivot at the entrance frame).
+"""
+import math
+from collections import Counter
+
+V, K, T, L, M = 120, 4, 8, 9, 73
+DATA = 2 * K * V * T          # 7680
+FULL = tuple(1 << i for i in range(8, -1, -1))
+
+
+def basis(vs):
+    b = {}
+    for x in vs:
+        for p in sorted(b, reverse=True):
+            if x >> p & 1: x ^= b[p]
+        if x:
+            p = x.bit_length() - 1
+            for q in b:
+                if b[q] >> p & 1: b[q] ^= x
+            b[p] = x
+    return tuple(b[p] for p in sorted(b, reverse=True))
+
+
+def widths_of(word):
+    """residual width of every helper: 9 - dim(entrance frame); 9 when the word has no extension"""
+    R = word['report']['R'] if 'R' not in word else word['R']
+    w = [L] * R
+    for r, E in word.get('start_extra', {}).items():
+        assert 2 * V <= int(r) < 2 * V + R
+        w[int(r) - 2 * V] = L - len(basis(E))
+    return w
+
+
+def split_pad(p):
+    """a pad of rank p is paid as nested commuting children of rank <= 51 (so that 73^2 > 2*child^2); rank 1 stays 1"""
+    if p == 0: return []
+    n = -(-p // 51); return [p // n + (1 if i < p % n else 0) for i in range(n)]
+
+
+def tile(items):
+    """Bank tiling of unhosted residuals.  items: list of (rep, helper, width); a bank has M = 73 cells.
+    * width-9 residuals (no wrapper acts on them): first fit in the given order, packed from offset 0, eight per bank, pad rank 1
+      (PR #433/#442's tiling and routes [2, slot]);
+    * ENTERING residuals (width w < 9, paid wrappers, e = 9 - w spectators): banks of their own in which every entering helper is the ONLY
+      owner of its bank family in its invocation (the one-helper rule of PR #458 extended to banks): bank j holds the j-th entering
+      helper of each replica, residuals packed from offset 0 in replica order (at most one helper per replica, hence per invocation).
+      The spectators of an entering helper are the first e cells of the bank beyond every residual cell of the bank (the pad, which no call
+      uses for a residual, is paid as before: rank 73 - sum of widths; the spectators are borrowed inside it and not deducted).
+    Returns (assign, banks, pads): assign[(rep, helper)] = (bank, offset, width, pure, spectators) with pure = the bank holds only width-9
+    residuals and spectators = () for width 9; pads = Counter of pad ranks (split into children of rank <= 51)."""
+    assign = {}; pads = Counter(); fill = []
+    for z, (rep, h, w) in enumerate(items):             # width 9: first fit, as PR #433 (all widths 9 reproduces it exactly)
+        if w != L: continue
+        for b, f in enumerate(fill):
+            if f + w <= M: break
+        else:
+            b = len(fill); fill.append(0)
+        assign[(rep, h)] = (b, fill[b], w, True, ()); fill[b] += w
+    nwide = len(fill); byrep = {}
+    for rep, h, w in items:
+        if w < L: byrep.setdefault(rep, []).append((h, w))
+    cells = [0] * max((len(v) for v in byrep.values()), default=0); emax = [0] * len(cells); place = {}
+    for rep in sorted(byrep):                           # the j-th entering helper of every replica goes to entering bank j
+        for j, (h, w) in enumerate(byrep[rep]):
+            place[(rep, h)] = (nwide + j, cells[j], w); cells[j] += w; emax[j] = max(emax[j], L - w)
+    for j in range(len(cells)): assert cells[j] + emax[j] <= M, ('entering bank without room for its spectators', j)
+    for (rep, h), (b, off, w) in place.items():
+        assign[(rep, h)] = (b, off, w, False, tuple(range(cells[b - nwide], cells[b - nwide] + L - w)))
+    fill += cells
+    for f in fill:
+        for part in split_pad(M - f): pads[part] += 1
+    return assign, len(fill), pads
+
+
+def route(off, w, pure, sp=()):
+    """owner route of a banked helper residual: PR #433's [2, slot] for width 9 (pure width-9 bank); an entering helper (w < 9) is
+    [2, offset, width, [spectator cells]] with e = 9 - w spectators"""
+    if w == L: assert pure and not sp; return [2, off // L]
+    assert not pure and len(sp) == L - w; return [2, off, w, list(sp)]
+
+
+def unhosted_stock(widths):
+    """live stock and padding histogram of the unhosted (parent) template, per stage x nine"""
+    R = len(widths)
+    _, nb, pads = tile([(rep, h, widths[h]) for rep in range(T) for h in range(R)])
+    return DATA + L * nb, Counter({r: z * L for r, z in pads.items()})
diff --git a/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/gk_word.py b/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/gk_word.py
new file mode 100644
index 0000000000..15782ba625
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/gk_word.py
@@ -0,0 +1,194 @@
+"""Apply a frozen selection (shared-donor kernel + entrance gauges) to PR #433's complex word.  Apache-2.0.
+Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.
+usage: gk_word.py BASE_FULL-WORD.json.gz SELECTION.json OUT_FULL-WORD.json.gz
+An empty selection ({}) copies the input byte for byte (regression anchor).
+
+selection = {"kernel": [{"E": [x], "donors": [h..], "pivots": [h..]}..], "gauge": {"h": [x..]}}   (h = helper index 0..R-1)
+Kernel (PR #417/#435/#434/#440): a pivot starts at E; every donor receives  donor += -q * pivot  at frame E before the main
+word, where col(pivot) = sum q_d col(d) are the exact dirty-response columns; the pivot's frame-zero compensation vanishes.
+Gauge (#401/#408-#416): the compensation  target += -C[t,h] * helper  of helper h is executed at frame E_h as the first gates
+of the main word; h starts at E_h and its targets climb to the level L_t = largest E over their entering helpers.
+The exact verification is the arbitrary-dirt replay of audit_gk.py; this module also checks the structural conditions."""
+import copy, gzip, hashlib, json, sys
+from collections import Counter, defaultdict
+from fractions import Fraction as Q
+from pathlib import Path
+sys.path.insert(0, str(Path(__file__).resolve().parent))
+from gk_common import *
+
+
+def apply_op(e, rows):
+    if e[0] == 'scale':
+        _, t, a, b, *_ = e; q = Q(a, b); rows[t] = {j: q * x for j, x in rows[t].items()}
+    else:
+        _, t, s, a, b, *_ = e; q = Q(a, b)
+        for j, x in list(rows[s].items()):
+            z = rows[t].get(j, Q(0)) + q * x
+            if z: rows[t][j] = z
+            else: rows[t].pop(j, None)
+
+
+def inverse(e, F):
+    e = copy.deepcopy(e)
+    if e[0] == 'add': e[3] *= -1
+    else: e[2], e[3] = e[3], e[2]
+    e[-1] = list(F); return e
+
+
+def responses(word):
+    """dirty-response columns col[h] = {target: coefficient} of the unmodified word (after the frame-zero preconditioner)"""
+    R = word['report']['R']; n = 2 * V + R
+    rows = [{r: Q(1)} for r in range(n)]
+    for e in word['A'] + word['cut'] + word['B']: apply_op(e, rows)
+    dirty = [{} for _ in range(n)]
+    for r in range(V, 2 * V): dirty[r] = {j: x for j, x in rows[r].items() if j >= 2 * V}
+    for e in word['precondition']: apply_op(e, dirty)
+    col = [{} for _ in range(R)]
+    for r in range(V, 2 * V):
+        for j, x in dirty[r].items(): col[j - 2 * V][r - V] = x
+    return col
+
+
+def first_frames(word):
+    first = {}
+    for seq in (word['A'], word['B']):
+        for e in seq:
+            F = basis(e[-1])
+            for r in [e[1]] + ([e[2]] if e[0] == 'add' else []):
+                if r >= 2 * V: first.setdefault(r - 2 * V, F)
+    return first
+
+
+def solve_relation(col, donors, p):
+    """exact rational c with col[p] = sum_d c_d col[d]; None if p is not in the span"""
+    ts = sorted({t for d in donors for t in col[d]} | set(col[p]))
+    idx = {t: i for i, t in enumerate(ts)}
+    Mx = [[Q(0)] * (len(donors) + 1) for _ in ts]
+    for ci, d in enumerate(donors):
+        for t, x in col[d].items(): Mx[idx[t]][ci] = x
+    for t, x in col[p].items(): Mx[idx[t]][-1] = x
+    piv = []; r = 0
+    for c in range(len(donors)):
+        pr = next((i for i in range(r, len(Mx)) if Mx[i][c]), None)
+        if pr is None: continue
+        Mx[r], Mx[pr] = Mx[pr], Mx[r]; q = Mx[r][c]; Mx[r] = [x / q for x in Mx[r]]
+        for i in range(len(Mx)):
+            if i != r and Mx[i][c]:
+                f = Mx[i][c]; Mx[i] = [a - f * b for a, b in zip(Mx[i], Mx[r])]
+        piv.append(c); r += 1
+    if any(Mx[i][-1] for i in range(r, len(Mx))): return None
+    assert r == len(donors), 'donors must have independent response columns'
+    return {donors[c]: Mx[i][-1] for i, c in enumerate(piv) if Mx[i][-1]}
+
+
+def span(U):
+    s = {0}
+    for b in U: s |= {x ^ b for x in s}
+    return s
+
+
+def perp(x): return basis([z for z in range(1, 512) if not (x & z).bit_count() % 2])
+
+
+def profile(word):
+    """local paid profile of a gk word by direct simulation of the frame chains (second implementation: audit_gk.py)"""
+    R = word['report']['R']; n = 2 * V + R; P = word['ports']
+    cur = {}
+    for r in range(n):
+        cur[r] = (P[r],) if r < V else ((basis(word['start_extra'][str(r)]) if str(r) in word.get('start_extra', {}) else ()) if r >= 2 * V else ())
+    paid = Counter()
+    def climb(r, F):
+        F = basis(F); o = cur[r]
+        assert basis(list(o) + list(F)) == F, ('frame violation', r, o, F)
+        if o != F: paid[len(F) - len(o)] += 1; cur[r] = F
+    lev = {int(t): basis(E) for t, E in word.get('target_levels', {}).items()}
+    for seq, part in ((word['A'], 'A'), (word['B'], 'B')):
+        if part == 'B':
+            for r, f in zip(word['centers'], word['center_frames']):
+                assert cur[r] == basis(f), 'centre frame'
+                served = sorted({lev.get(e[1] - V, ()) for e in word['cut'] if e[2] == r}, key=lambda E: -len(E))
+                o = basis(f)
+                for Lv in served:
+                    assert span(Lv) <= span(o), 'served levels must descend inside the centre frame'
+                    if Lv != o: paid[len(o) - len(Lv)] += 1; o = Lv
+            for t in range(V): assert cur[V + t] == lev.get(t, ()), 'target level at the centre scatter'
+        for e in seq:
+            for r in [e[1]] + ([e[2]] if e[0] == 'add' else []): climb(r, e[-1])
+    for r in range(n): climb(r, FULL if (r < V or r >= 2 * V) else perp(P[r - V]))
+    return paid
+
+
+def global_profile(local, widths):
+    """unhosted nine-stage profile: local x (stages*replicas) + the 240*8 idle children per rank + bank pads"""
+    live, pads = unhosted_stock(widths)
+    g = Counter({r: z * L * T for r, z in local.items()})
+    for r in (16, 8, 32, 8, 48, 8, 48, 32, 16): g[r] += 240 * T
+    g.update(pads)
+    return live, g
+
+
+def build(word, sel, check=True):    # check=False only for the mutation controls that must be caught by the certifying scripts
+    if not sel: return word
+    w = copy.deepcopy(word); R = w['report']['R']
+    col = responses(word); first = first_frames(word)
+    gauge = {int(h): basis(E) for h, E in sel.get('gauge', {}).items()}
+    classes = sel.get('kernel', [])
+    pivots = {p for c in classes for p in c['pivots']}; donors = {d for c in classes for d in c['donors']}
+    assert not (pivots & donors) and not (pivots | donors) & set(gauge) and len(pivots) == sum(len(c['pivots']) for c in classes)
+    # --- structural conditions -------------------------------------------------------------------------------------
+    for h, E in gauge.items():
+        assert not check or span(E) <= span(first[h]), ('gauge entrance outside the first frame', h)
+    levels = defaultdict(list)
+    for h, E in gauge.items():
+        for t in col[h]: levels[t].append(E)
+    for t, Es in levels.items():                                   # pairwise nested comps per target
+        for a in Es:
+            for b in Es: assert not check or span(a) <= span(b) or span(b) <= span(a), ('non-nested gauges at target', t)
+    lev = {t: max(Es, key=len) for t, Es in levels.items()}
+    for k, r in enumerate(w['centers']):                              # chain per centre, inside the centre frame
+        served = {lev.get(e[1] - V, ()) for e in w['cut'] if e[2] == r}
+        for a in served:
+            for b in served: assert not check or span(a) <= span(b) or span(b) <= span(a), ('centre chain', k)
+        top = max(served, key=len)
+        assert not check or span(top) <= span(basis(w['center_frames'][k])), ('level outside centre frame', k)
+    # --- gates ----------------------------------------------------------------------------------------------------------
+    gates = []
+    for h, E in sorted(gauge.items(), key=lambda kv: (len(kv[1]), kv[0])):
+        for t, x in sorted(col[h].items()):
+            c = -x; gates.append(['add', V + t, 2 * V + h, c.numerator, c.denominator, list(E)])
+    pre = []
+    start = {2 * V + h: list(E) for h, E in gauge.items()}
+    for cl in sorted(classes, key=lambda c: (len(c['E']), c['E'])):
+        E = basis(cl['E'])
+        for x in [*cl['donors'], *cl['pivots']]: assert span(E) <= span(first[x]), ('kernel entrance outside the first frame', x)
+        for p in cl['pivots']:
+            rel = solve_relation(col, cl['donors'], p)
+            assert rel is not None, ('pivot response not in the donor span', p)
+            start[2 * V + p] = list(E)
+            for d, c in rel.items():
+                q = -c; pre.append(['add', 2 * V + d, 2 * V + p, q.numerator, q.denominator, list(E)])
+    w['A'] = gates + pre + w['A']
+    w['cleanup'] = [inverse(e, FULL) for e in reversed(w['A'] + w['B']) if not V <= e[1] < 2 * V]
+    w['start_extra'] = {str(r): list(E) for r, E in sorted(start.items())}
+    w['target_levels'] = {str(t): list(E) for t, E in sorted(lev.items()) if E}
+    if not check: return w
+    prof = profile(w); widths = widths_of(w)
+    live, g = global_profile(prof, widths)
+    w['report']['local_profile'] = {str(k): z for k, z in sorted(prof.items())}
+    w['report']['global_profile'] = {str(k): z for k, z in sorted(g.items())}
+    w['report']['live'] = live
+    w['report']['entrance_rank'] = sum(L - x for x in widths); w['report']['entering_helpers'] = sum(1 for x in widths if x < L)
+    w['report']['selection_sha256'] = hashlib.sha256(json.dumps(sel, sort_keys=True).encode()).hexdigest()
+    return w
+
+
+def dump(w): return gzip.compress(json.dumps(w, sort_keys=True, separators=(',', ':')).encode(), mtime=0)
+
+
+if __name__ == '__main__':
+    src, selp, out = map(Path, sys.argv[1:4])
+    sel = json.loads(selp.read_text())
+    if not sel: out.write_bytes(src.read_bytes()); print('empty selection: copied byte for byte'); sys.exit(0)
+    word = json.load(gzip.open(src)); w = build(word, sel); out.write_bytes(dump(w))
+    print('gk word: entering helpers', w['report']['entering_helpers'], 'entrance rank', w['report']['entrance_rank'],
+          'local profile', w['report']['local_profile'], 'unhosted live', w['report']['live'])
diff --git a/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/integrate_gk.py b/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/integrate_gk.py
new file mode 100644
index 0000000000..df261063e1
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/integrate_gk.py
@@ -0,0 +1,123 @@
+# GK: modified copy of PR #433's complex_integrate.py (icekylinx with Codex assistance; PR #425) by DreamingOfClouds with Claude Opus 5.5
+# (Anthropic), via Claude Code.  Every change is marked "GK:".  On a word without start_extra / target_levels the behaviour
+# and every written file equal PR #433's (regression anchor in verify.py).
+import sys as _sys, os as _os; _sys.path.insert(0, _os.path.dirname(_os.path.abspath(__file__)))
+# Adapted from PR425 for heterogeneous centres by icekylinx, with Codex assistance.
+import copy,gzip,hashlib,importlib.util,json,math
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+OUT=Path('split-centres');cp=OUT/'CANONICAL-WORD.json.gz'
+c=json.load(gzip.open(cp));audit=json.loads((OUT/'SCALAR-FRAME-AUDIT.json').read_text())
+phase=json.loads((OUT/'CLIFFORD-REVIEW.json').read_text());sha=lambda p:hashlib.sha256(Path(p).read_bytes()).hexdigest()
+assert phase['canonical_word_sha256']==audit['canonical_word_sha256']==sha(cp)
+assert phase['all_child_equalities_include_global_phase']
+programs=json.load(gzip.open(OUT/'LOCAL-PROGRAMS.json.gz'));checks=json.loads((OUT/'LOCAL-CHECKS.json').read_text())
+frames=c['frames'];v,R,h=c['v'],c['R'],c['h'];n=2*v+R;private_centres=len(c['centers'])
+for z in checks.values():z['paid_profile']={int(r):n for r,n in z['paid_profile'].items()}
+old=Path('work/complex-nine-native');template=json.load(gzip.open(old/'GLOBAL-TEMPLATE.json.gz'))
+data_phase=json.loads((old/'DATA-PHASES.json').read_text())
+assert template['exact_data_phase_recipe_sha256']==sha(old/'DATA-PHASES.json')
+assert data_phase['status']=='PASS_EXACT_Z4_DATA_ROUTE_IDLE_AND_TERMINAL_PHASES'
+m,T,L,k=73,8,9,4
+# GK: residual widths 9 - dim(start frame); banks tile per width class (all 9: PR #433's eight residuals + one pad)
+from gk_common import tile,route
+widths=[h-len(frames[c['start'][2*v+i]]) for i in range(R)]
+assign,nb,pads=tile([(rep,i,widths[i]) for rep in range(T) for i in range(R)]);entering0=any(w_<h for w_ in widths)
+W=2*v*k*T+L*nb;physical=W+R+private_centres+2
+template['version']='hamming-mutable-basis-nine-v1';template['live']=W;template['physical']=physical
+template['local_programs']=programs;paid=Counter();assignments=set();event_count=0;scalar_primitives=0
+for call in template['calls']:
+    stage,rep,pair=call['stage'],call['replica'],call['pair'];ori=call['orientation']
+    owners=[[rep*2*k*v+(2*pair+r//v)*v+r%v,[1,stage,r%v]] for r in range(2*v)]
+    for r in range(R):
+        bank,off_,w_,pure_,sp_=assign[rep,r];owners.append([2*v*k*T+stage*nb+bank,route(off_,w_,pure_,sp_)])   # GK: [2,slot] in pure width-9 banks, [2,offset,width,spectators] for entering helpers
+        assignments.add((stage,rep,r,bank,off_))
+    assert len(owners)==n and len({(f,json.dumps(route)) for f,route in owners})==n
+    assert all(f<W for f,route in owners)   # GK: every owner lies in the live stock (none in the private namespace)
+    fam=Counter(f for f,route in owners)   # GK: an entering helper is the only owner of its bank family in the invocation (PR #458's rule, banks included); the data families are the 240 distinct active ones
+    assert all(fam[f]==1 for f,route in owners[:2*v]) and all(fam[owners[2*v+r][0]]==1 for r in range(R) if widths[r]<h),('entering helper shares its bank family',stage,rep)
+    call['owners']=owners;call['local_program_sha256']=checks[ori]['sha256']
+    for r,z in checks[ori]['paid_profile'].items():paid[r]+=z
+    event_count+=checks[ori]['events'];scalar_primitives+=checks[ori]['real_component_primitive_bound']
+assert len(assignments)==L*T*R and len(template['calls'])==72
+for item in template['idle_children']:paid[item['rank']]+=item['replicas']
+for r_,z_ in pads.items():paid[r_]+=z_*L   # GK: bank pads (rank 1 each at width 9 and 8)
+assert dict(paid)=={int(r):z for r,z in json.load(gzip.open(OUT/'FULL-WORD.json.gz'))['report']['global_profile'].items()}
+mass=sum(r*z for r,z in paid.items());assert m*W-mass==2496
+if entering0:template['route_semantics']['helper']+='; entering helpers: paid wrappers R_E^-1 before and L_E^-1 after the invocation; an entering helper is the only owner of its bank family in the invocation, route [2, offset, width, spectator cells] with the spectators the first cells of the bank beyond every residual cell'   # GK
+template['bank_padding']['families']=list(range(7680,W))
+template['cover_final_correction']['families']=[0,W]
+template['cover_final_correction']['charged_calls_per_cover']=W
+for e in template['execution_schedule']:
+    if e['kind']=='bank_padding_cover_sweep':e['families']=[7680,W]
+    elif e['kind']=='translate_every_live_family':e.update(template['cover_final_correction'])
+template['private_namespace']={'centers':[W,W+private_centres],'reserved_tableau':[W+private_centres,W+private_centres+R],
+                               'coefficient':[physical-2,physical]}
+template['exact_local_clifford_recipe_sha256']=sha(OUT/'CLIFFORD-RECIPES.json')
+if (OUT/'RESIDUAL-ADAPTERS.json').exists():template['residual_adapter_sha256']=sha(OUT/'RESIDUAL-ADAPTERS.json')   # GK: paid wrappers of entering helpers (Lemma A)
+template['expanded_scalar_interface']='See PROOF.txt: mutable source basis, frame-zero output preconditioner, explicit dirty compensator, and full-frame inverse source/helper cleanup.'
+blob=json.dumps(template,sort_keys=True,separators=(',',':')).encode()
+(OUT/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(blob,mtime=0))
+
+# Fresh finite overcharge, with the changed stock, scalar counts, coefficient
+# lowering, and private work reserve. No unchanged local invoice is assumed.
+compiler=64*(m+1)**3;macros=max(z['scalar_macros'] for z in checks.values());children=sum(checks['forward']['paid_profile'].values())
+adapters=16*(macros+children+n+private_centres)+64*m
+local_bound=max(z['real_component_primitive_bound'] for z in checks.values())+adapters*compiler
+bridges=[e for e in template['recipe'] if e['kind']=='bridge'];bridge_adds=2*v*T*len(bridges)
+terminal_shifts=k*v*T;terminal_moves=2*k*v*T
+entering=sum(1 for w_ in widths if w_<h)   # GK: entrance adapters (Lemma A): a monomial on 9 bits is at most 81+45+9=135 elementary factors (matrix, quadratic form, translation); charge 144 at entry and at exit of every entering helper in every invocation
+nonlocal_items=4*v*T*L+2*v*T*L+2*L*T*R+sum(e['replicas'] for e in template['idle_children'])+L*nb+bridge_adds+terminal_shifts+terminal_moves+W+physical+2*L*T*entering*144
+outside=8*nonlocal_items+64*m
+pervertex=scalar_primitives+bridge_adds+terminal_shifts+terminal_moves+W+(72*adapters+outside)*compiler+64*physical
+r=m//2;group=2**(r*r)*math.prod(2**(2*i)-1 for i in range(1,r+1));stock=group*physical
+smass=group*mass;logical=group*pervertex+64;router=compiler*(logical+1)*(stock+1)**2
+GG,EE,C0=1<<30000,1<<100000,1<<210000;BB=smass+EE
+literal=2*GG*stock**2+8*smass+4*stock+4+32*m
+maxchild=max(paid);depth=2;assert m**depth>2*maxchild**depth
+assert local_bound<1<<48 and logical<1<<6050 and router<GG and literal<EE and BB<1<<100001
+assert 32*m*BB*BB<C0 and 2*BB+18<C0
+row=depth*stock.bit_length()+9909+252;assert row<20161
+
+def load(name):
+    sp=importlib.util.spec_from_file_location('hamming_integrate_'+name,Path('work/pr361/code/engines')/(name+'.py'))
+    mod=importlib.util.module_from_spec(sp);sp.loader.exec_module(mod);return mod
+Outer=load('outer');b=Q(audit['prospective_complex_b']);bit=Q(json.loads(Path('BIT-PRICE.json').read_text())['lower'])
+eta=Q(1,10**12);beta=Q(1,10**9);grid=Q(1,10**18)
+s=Q(int(((1-beta)*min(b,bit)-grid)*10**18),10**18);assert s<bit
+chain=[Q(384599,10**10)];cutoffs=[]
+for _ in range(3):
+    a=chain[-1];z=(1-s)*s+s*a;gap=min(s-z,1-z-s,1-z-s*(1-a),1-s)
+    assert a<z<s<1-z and gap>0
+    bound=max(math.ceil(36/gap**2),math.ceil(2*(4+512)/gap))
+    assert bound*gap**2>=36 and bound*gap>=2*(4+512)
+    cutoffs.append(str(bound));chain.append(z)
+bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1},
+        'rows':{'degree_gap':Q(10**6)-Q(51*20161,25)}}
+q=chain[-1]*(1-2*eta);ticks=(1-eta)*q/(1+q)/grid;kap=Q((ticks.numerator-1)//ticks.denominator,10**18)
+assembly=Outer.assembly(chain[-1],b,bridge,kap,eta=eta,beta=beta)
+try:Outer.assembly(chain[-1],b,bridge,kap+grid,eta=eta,beta=beta)
+except AssertionError:pass
+else:raise AssertionError('next kappa grid accepted')
+result={'status':'PASS_NEW_STRUCTURAL_PROGRAM_AND_FINITE_ASSEMBLY_PENDING_REPLAY',
+        'canonical_word_sha256':sha(cp),'scalar_audit_sha256':sha(OUT/'SCALAR-FRAME-AUDIT.json'),
+        'exact_phase_receipt_sha256':sha(OUT/'CLIFFORD-REVIEW.json'),'global_template_sha256':hashlib.sha256(blob).hexdigest(),
+        'local_program_checks':checks,'R':R,'m':m,'live':W,'physical':physical,
+        'bank_assignments':len(assignments),'rank_mass':mass,'deficit':2496,
+        'global_profile':dict(sorted(paid.items())),'emitted_local_events_all_calls':event_count,
+        'finite_invoice':{'local_primitive_bound':local_bound,'local_adapters':adapters,
+                          'pervertex':pervertex,'physical_stock_bits':stock.bit_length(),
+                          'router_bits':router.bit_length(),'literal_bits':literal.bit_length(),
+                          'physical_row_coefficient':row,'retained_row_coefficient':20161,
+                          'compiler':compiler,'G_exponent':30000,'E_exponent':100000,'C0_exponent':210000,
+                          'required_C0_bits':(32*m*BB*BB).bit_length(),'halving_degree':depth,
+                          'halving_integer_inequality':[m**depth,2*maxchild**depth]},
+        'complex_b':str(b),'bit_c':str(bit),'prospective_kappa':str(kap),'kappa_float':float(kap),
+        'log2_kappa':math.log2(float(kap)),
+        'kappa_gain_percent':float(100*(kap/Q(998390813251625,10**18)-1)),
+        'strict_outer_constraints':{name:str(z) for name,z in assembly['strict_constraints'].items()},
+        'next_kappa_grid_rejected':True,'bootstrap_cutoffs_log2':cutoffs,
+        'scope':'New finite scalar interface with a written conjugation proof, conditional on inherited all-size compiler, precision/tape and analytic transfer. Independent emitted-program replay and fresh package replay still required before final promotion.'}
+(OUT/'INTEGRATION.json').write_text(json.dumps(result,indent=2)+'\n')
+print('PASS prospective kappa',float(kap),'gain',result['kappa_gain_percent'],'percent',flush=True)
diff --git a/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/onehost_gk.py b/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/onehost_gk.py
new file mode 100644
index 0000000000..220cc7a2f5
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/onehost_gk.py
@@ -0,0 +1,111 @@
+"""Whole-residual idle-axis hosting with at most ONE helper per physical family per invocation (the rule of PR #458), plus the exact
+host chart with explicit spectator coordinates.  Apache-2.0.  Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.
+A copy (port) of an idle child hosts a PATTERN: residuals of pairwise distinct stages inside the child's window, offsets 0, w1, w1+w2, ...
+(a residual is whole: one slot in one family).  The children of one (pair, side) have pairwise disjoint windows (checked), so the
+families they share never host two helpers of one invocation, and the integer programme needs only the distinct-stage condition.
+Chart: for the host's port q the parent's idle basis is B_q = U_q (+) I (PR #433 geometry; the construction is that of PR #458).  A hosted
+residual of width w occupies the pending vectors b_off..b_(off+w-1) of its child; the other e = 9 - w coordinates of the local nine are
+SPECTATORS: the first e basis indices of B_q not occupied by the residual, in increasing order.  The paid wrappers (adapters_gk.py) act on
+these nine coordinates and restore the spectators identically."""
+import math
+from collections import Counter
+
+H, M = 9, 73
+
+
+def cost(r, m): return r * math.log(m / r) if r else 0.0
+
+
+def patterns(rank, stages, widths):
+    out = [()]
+    ws = sorted(widths, reverse=True)
+    def rec(i, cur, tot):
+        for j in range(i, len(stages)):
+            for w in ws:
+                if tot + w <= rank:
+                    c = cur + [(stages[j], w)]; out.append(tuple(c)); rec(j + 1, c, tot + w)
+    rec(0, [], 0)
+    return out
+
+
+def solve(win, copies, avail, m, pad_value, time_limit=600):
+    """win {idx: (pair, rank, stages)}, avail {(stage, width): helpers per replica}.  Maximise saved idle cost (+ pad_value per hosted residual)."""
+    import numpy as np
+    from scipy.optimize import milp, LinearConstraint, Bounds
+    widths = sorted({w for (_, w) in avail}); var = []
+    for idx, (p, r, st) in sorted(win.items()):
+        for pat in patterns(r, sorted(st), widths): var.append((idx, pat))
+    n = len(var); c = np.zeros(n)
+    for j, (idx, pat) in enumerate(var):
+        r = win[idx][1]; c[j] = -(cost(r, m) - cost(r - sum(w for _, w in pat), m) + pad_value * len(pat))
+    rows, lo, hi = [], [], []
+    by = {}
+    for j, (idx, pat) in enumerate(var): by.setdefault(idx, []).append(j)
+    for idx, js in by.items():
+        row = np.zeros(n); row[js] = 1; rows.append(row); lo.append(copies); hi.append(copies)
+    for (s, w), a in sorted(avail.items()):
+        row = np.zeros(n)
+        for j, (idx, pat) in enumerate(var): row[j] = sum(1 for sw in pat if sw == (s, w))
+        rows.append(row); lo.append(0); hi.append(a)
+    res = milp(c, constraints=LinearConstraint(np.array(rows), lo, hi), integrality=np.ones(n), bounds=Bounds(np.zeros(n), np.full(n, np.inf)),
+               options=dict(time_limit=time_limit, disp=False))
+    assert res.x is not None, res.message
+    x = [int(round(t)) for t in res.x]
+    return [[idx, [list(sw) for sw in pat], x[j]] for j, (idx, pat) in enumerate(var) if x[j]], -res.fun
+
+
+def save(path, key, sel, val):
+    import json
+    from pathlib import Path
+    p = Path(path); d = json.loads(p.read_text()) if p.exists() else {}
+    d[key] = dict(rule='one-helper-per-family', patterns=sorted(sel), proxy_saving=val)
+    p.write_text(json.dumps(d, indent=1, sort_keys=True) + '\n')
+
+
+def load(path, key):
+    import json
+    from pathlib import Path
+    d = json.loads(Path(path).read_text())[key]; assert d['rule'] == 'one-helper-per-family'
+    return d['patterns'], d['proxy_saving']
+
+
+def check_disjoint_groups(win, pair_of, side_of):
+    """children of one (pair, side) share their physical families; their windows must be disjoint"""
+    seen = {}
+    for idx, (p, r, st) in win.items():
+        for s in st:
+            k = (pair_of[idx], side_of[idx], s); assert k not in seen, ('windows of two children of one family group overlap', idx, seen[k], k); seen[k] = idx
+
+
+def expand(win, sel, widths, V):
+    """-> slots [idx, port, off, w, s, h] (one replica), rem {(idx, port): remaining pending rank}"""
+    R = len(widths); pool = {}
+    for h in sorted(range(R)): pool.setdefault(widths[h], []).append(h)
+    pool = {(s, w): list(hs) for s in range(9) for w, hs in pool.items()}
+    slots = []; rem = {}; used = Counter()
+    for idx, pat, copies in sorted(sel, key=lambda e: (e[0], e[1])):
+        r = win[idx][1]
+        for _ in range(copies):
+            cp = used[idx]; used[idx] += 1; assert cp < V; off = 0
+            assert len({s for s, w in pat}) == len(pat)
+            for s, w in pat:
+                assert s in win[idx][2] and off + w <= r
+                slots.append([idx, cp, off, w, s, pool[s, w].pop(0)]); off += w
+            rem[idx, cp] = r - off
+    assert all(n == V for n in used.values()) and len(used) == len(win)
+    return slots, rem
+
+
+def idle_basis(q):
+    """PR #433 / #458: the parent's orthonormal idle basis U_q (+) I for port q (H = 9 local coordinates, M = 73)"""
+    z = next(i for i in range(H) if not (q >> i & 1)); a = q ^ (1 << z); order = list(range(H)); order[0], order[z] = order[z], order[0]
+    return [(1 << i) ^ (a if a >> i & 1 else 0) for i in order] + [1 << i for i in range(H, M)]
+
+
+def spectators(q, pending, off, w):
+    """indices (into B_q) of the e = 9 - w spectator coordinates of a residual at pending[off:off+w]"""
+    B = idle_basis(q); occ = [B.index(x) for x in pending[off:off + w]]
+    assert len(set(occ)) == w
+    sp = [j for j in range(M) if j not in occ][:H - w]
+    assert len(sp) == H - w
+    return sp
diff --git a/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/replay_gk.py b/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/replay_gk.py
new file mode 100644
index 0000000000..629de3b6ce
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/code/replay_gk.py
@@ -0,0 +1,280 @@
+# GK: modified copy of PR #433's complex_replay.py (icekylinx with Codex assistance; PR #425) by DreamingOfClouds with Claude Opus 5.5
+# (Anthropic), via Claude Code.  Every change is marked "GK:".  On a word without start_extra / target_levels the behaviour
+# and every written file equal PR #433's (regression anchor in verify.py).
+import sys as _sys, os as _os; _sys.path.insert(0, _os.path.dirname(_os.path.abspath(__file__)))
+# Adapted for heterogeneous centres by icekylinx with Codex assistance.
+"""Independent read-back of the serialized local/global instruction stream."""
+import copy,gzip,hashlib,importlib.util,json,math
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+OUT=Path('split-centres');P=OUT/'GLOBAL-TEMPLATE.json.gz'
+ir=json.load(gzip.open(P));c=json.load(gzip.open(OUT/'CANONICAL-WORD.json.gz'))
+integration=json.loads((OUT/'INTEGRATION.json').read_text())
+assert hashlib.sha256(gzip.decompress(P.read_bytes())).hexdigest()==integration['global_template_sha256']
+assert c['ports']==json.load(gzip.open('work/higher-stage-e8/verified/gcert1-e8-retimed.json.gz'))['ports']
+v,R,h=c['v'],c['R'],c['h'];n=2*v+R;frames=c['frames']
+from gk_common import tile   # GK
+widths=[h-len(frames[c['start'][2*v+i]]) for i in range(R)]
+assign,nb,pads=tile([(rep,i,widths[i]) for rep in range(8) for i in range(R)]);W=7680+9*nb
+levels={int(t):f for t,f in c.get('target_levels',{}).items()}
+entering=[r for r,f in enumerate(c['start']) if r>=2*v and f!=0];plain={r for r in range(n) if r not in set(entering)}   # GK
+def contains(a,b):
+    for x in a:
+        for y in b:
+            if x>>(y.bit_length()-1)&1:x^=y
+        if x:return False
+    return True
+def local(events,back):
+    rows={('L',r):{r:Q(1)} for r in range(n)}
+    norm={('L',r):Q(1) for r in range(n)};prefix=Q(1);cur=c['start'].copy();private={}
+    hist=Counter();phases=[];entry=[];exit=[];centers=[];matrix_hash=hashlib.sha256();chain={};wrappers=[]
+    allowed=['zero_frame_precondition','entry_adapters','A','centers','B','final','exit_adapters','full_frame_cleanup','done']
+    for event in events:
+        tag=event[0]
+        if tag=='phase':
+            phases.append(event[1]);assert phases==allowed[:len(phases)]
+            if event[1]=='A':assert entry==[(r,f) for r,f in enumerate(c['start']) if r in plain] and sorted(r for k_,r,f_ in wrappers if k_=='pre')==entering   # GK
+            if event[1]=='centers':assert all(cur[r]==levels.get(r-v,0) for r in range(v,2*v))   # GK
+            if event[1]=='full_frame_cleanup':assert cur==c['final'] and exit==list(enumerate(c['final']))
+            assert not private
+        elif tag=='residual_adapter':   # GK: paid wrappers of entering helpers: R_E^-1 before the invocation, L_E^-1 after the full-frame cleanup
+            _,kind,r,f=event;assert r in entering and f==c['start'][r] and kind in ('pre','post')
+            assert (kind=='pre' and phases[-1]=='entry_adapters') or (kind=='post' and phases[-1]=='full_frame_cleanup')
+            assert (kind,r) not in {(k,x) for k,x,_ in wrappers};wrappers.append((kind,r,f))
+        elif tag=='adapter':
+            assert event[3]==(c['start'] if event[1]=='old_to_new' else c['final'])[event[2]]
+            (entry if event[1]=='old_to_new' else exit).append((event[2],event[3]))
+        elif tag=='climb':
+            _,part,r,a,b,rank=event
+            assert not private and phases[-1]==part and cur[r]==a
+            assert contains(frames[a],frames[b]) and rank==len(frames[b])-len(frames[a])>0
+            hist[rank]+=1;cur[r]=b
+        elif tag=='center':
+            _,k,a,b,rank=event
+            assert phases[-1]=='centers' and private=={('C',k):a}
+            cf=c['center_frames'][k];cr=len(frames[cf])
+            # GK: stepwise descent cf -> served levels -> lowest (forward), reversed ascent (backward); each step is a nested child
+            assert contains(frames[a],frames[b]) if back else contains(frames[b],frames[a])
+            assert rank==abs(len(frames[a])-len(frames[b]))>0
+            chain.setdefault(k,[]).append((a,b))
+            private['C',k]=b;hist[rank]+=1;centers.append(k)
+        elif tag=='scalar':
+            _,e,f=event;op=e[0];target=tuple(e[1]);source=tuple(e[2]) if op in ('copy','add') else None
+            if target[0]=='C' and op=='clear':
+                assert private.get(target,f)==f
+                private.pop(target,None)
+            else:
+                for r in (target,source):
+                    if r is None:continue
+                    if r[0]=='L':assert cur[r[1]]==f,('common frame',r,cur[r[1]],f)
+                    else:
+                        if r==target and r not in private:private[r]=f
+                        assert private[r]==f
+            if op=='clear':rows[target]={};norm[target]=Q(0)
+            elif op=='copy':rows[target]=dict(rows[source]);norm[target]=norm[source]
+            elif op=='scale':
+                q=Q(e[2],e[3]);a,b=abs(q.numerator),q.denominator
+                assert a&(a-1)==0 and b&(b-1)==0
+                rows[target]={j:q*x for j,x in rows[target].items()};norm[target]*=abs(q)
+            else:
+                q=Q(e[3],e[4]);a,b=abs(q.numerator),q.denominator
+                assert source!=target and b&(b-1)==0
+                # Independent symbolic replay of the cleared coefficient work.
+                w=0
+                for bit in bin(a)[2:]:w=2*w+int(bit)
+                assert Q(w,b)*(1 if q>0 else -1)==q
+                prefix=max(prefix,Q(a)*norm[source])
+                norm[target]=norm.get(target,Q(0))+abs(q)*norm[source]
+                row=rows.setdefault(target,{})
+                for j,x in list(rows[source].items()):
+                    z=row.get(j,Q(0))+q*x
+                    if z:row[j]=z
+                    else:row.pop(j,None)
+            prefix=max(prefix,norm[target])
+        else:raise AssertionError(tag)
+    assert phases==allowed and set(centers)==set(range(len(c['centers']))) and not private
+    assert sorted(r for k,r,_ in wrappers if k=='pre')==entering and sorted(r for k,r,_ in wrappers if k=='post')==entering   # GK
+    for k,st in chain.items():   # GK: the steps of each centre chain link up and end at the centre frame
+        cf=c['center_frames'][k]
+        if back:assert st[-1][1]==cf and all(st[i][1]==st[i+1][0] for i in range(len(st)-1))
+        else:assert st[0][0]==cf and all(st[i][1]==st[i+1][0] for i in range(len(st)-1))
+    assert all(not row for reg,row in rows.items() if reg[0]=='C')
+    for r in range(n):
+        expected={r:Q(1)}
+        if back and r<v:expected[v+r]=Q(-1)
+        elif not back and v<=r<2*v:expected[r-v]=Q(1)
+        assert rows['L',r]==expected
+    # A 192-bit local payload allowance vastly dominates even coefficient work.
+    assert prefix<2**192
+    return hist,{'all_exact_columns':n,'prefix_l1_upper':str(prefix),
+                 'prefix_bits_upper':prefix.numerator.bit_length()-prefix.denominator.bit_length()+1,
+                 'charged_payload_bits':192,'private_work_erased':True}
+
+profiles={};checks={}
+for name in ('forward','backward'):
+    profiles[name],checks[name]=local(ir['local_programs'][name],name=='backward')
+    assert dict(profiles[name])=={int(r):z for r,z in c['local_profile'].items()}
+    print('independent emitted replay PASS',name,flush=True)
+controls=[]
+for name,mut in [
+    ('wrong_scale',lambda es:next(e for e in es if e[0]=='scalar' and e[1][0]=='scale')[1].__setitem__(2,3)),
+    ('missing_center',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='center'))),
+    ('wrong_common_frame',lambda es:next(e for e in es if e[0]=='scalar' and e[2]!=0).__setitem__(2,0)),
+    ('wrong_child_rank',lambda es:next(e for e in es if e[0]=='climb').__setitem__(5,99)),
+]+([
+    ('missing_pre_wrapper',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='pre'))),
+    ('missing_post_wrapper',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='post'))),
+    ('wrapper_with_wrong_frame',lambda es:next(e for e in es if e[0]=='residual_adapter').__setitem__(3,0)),
+    ('wrapper_in_wrong_phase',lambda es:es.insert(es.index(['phase','A']),es.pop(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='post')))),
+    ('wrapper_on_a_data_register',lambda es:next(e for e in es if e[0]=='residual_adapter').__setitem__(2,3)),
+    ('wrapper_on_a_target_register',lambda es:next(e for e in es if e[0]=='residual_adapter').__setitem__(2,v+3)),
+    ('wrapper_on_a_centre_register',lambda es:next(e for e in es if e[0]=='residual_adapter').__setitem__(2,['C',0])),
+] if entering else [])+([
+    ('centre_step_not_nested',lambda es:next(e for e in es if e[0]=='center').__setitem__(3,next(f for f in range(len(frames)) if not contains(frames[f],frames[next(e for e in es if e[0]=='center')[2]]) and not contains(frames[next(e for e in es if e[0]=='center')[2]],frames[f])))),
+    ('centre_descent_step_skipped',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='center' and e[3]!=0))),
+] if levels else []):
+    es=copy.deepcopy(ir['local_programs']['forward']);mut(es)
+    try:local(es,False)
+    except (AssertionError,KeyError):controls.append(name)
+    else:raise AssertionError('mutation accepted: '+name)
+
+def residual_cells(route):
+    """cells of a bank family occupied by a helper residual (independent of tile): a width-9 slot or [offset, offset + width)"""
+    return set(range(route[1]*9,route[1]*9+9)) if len(route)==2 else set(range(route[1],route[1]+route[2]))
+def bank_rule(owners,occ,sole=True):
+    """GK: the one-helper rule of PR #458 on EVERY register class of one invocation (owners: 240 active data owners, then the 560 helpers).
+    data class (family < 7680): only the active wires, each the sole owner of its family; bank class (7680 <= family < W): helpers only; an ENTERING
+    helper (width < 9) is the sole owner of its bank family, its route is [2, offset, width, spectators] with the spectators the first
+    cells of the bank beyond every residual cell of it (occ[family] = those cells, over all invocations); width-9 helpers share a pure bank in
+    disjoint 9-cell slots (no wrapper acts on them); nobody owns a family of the private namespace (family >= W).  sole=False skips only the
+    sole-owner assertion (used by a control to show that the footprints themselves are fine)."""
+    fam=Counter(f for f,_ in owners);foot={}
+    for i,(f,route) in enumerate(owners):
+        assert f<W,('owner in the private namespace',f)
+        if f<7680:
+            assert i<240 and route[0]==1 and fam[f]==1,('data class: only the active wires, each alone on its family',i,f)
+        else:
+            assert i>=240 and route[0]==2,('bank class: helpers only',i,f);w=widths[i-240]
+            if w==9: assert len(route)==2,('width-9 helper in a pure bank',i)
+            else:
+                if sole: assert fam[f]==1,('entering helper shares its bank family in one invocation',i,f)
+                assert len(route)==4 and route[2]==w and len(set(route[3]))==9-w==len(route[3]),('entering helper without a spectator record',i)
+                assert route[3]==list(range(len(occ[f]),len(occ[f])+9-w)) and len(occ[f])+9-w<=73,('spectators are not the first cells beyond the residuals',i,f)
+            cells=residual_cells(route)|(set(route[3]) if len(route)==4 else set())
+            assert len(cells)==9 and not cells&foot.setdefault(f,set()),('footprints overlap on a bank family',i,f);foot[f]|=cells
+def global_check(t):
+    assert t['live']==W and t['physical']==W+R+len(c['centers'])+2   # GK
+    occ={}
+    for call in t['calls']:
+        for fam,route in call['owners'][240:]:occ.setdefault(fam,set()).update(residual_cells(route))
+    assert all(cs==set(range(len(cs))) for cs in occ.values()),'bank residuals are packed from cell 0'
+    # Eight data-wire scalar columns, independently recomposed.
+    matrix=[[int(i==j) for j in range(8)] for i in range(8)]
+    for e in t['recipe']:
+        if e['kind']=='local':
+            a=2*e['pair'];b=a+1;dst,src,q=(a,b,-1) if e['reverse'] else (b,a,1)
+            matrix[dst]=[x+q*y for x,y in zip(matrix[dst],matrix[src])]
+        elif e['kind']=='bridge':
+            i,j,q=e['dst'],e['src'],e['coefficient']
+            matrix[2*i]=[x+q*y for x,y in zip(matrix[2*i],matrix[2*j])]
+            matrix[2*j+1]=[x-q*y for x,y in zip(matrix[2*j+1],matrix[2*i+1])]
+        else:
+            assert e['kind']=='terminal';old=copy.deepcopy(matrix)
+            for i in range(4):matrix[2*i]=old[2*i+1];matrix[2*i+1]=[-x for x in old[2*i]]
+    assert matrix==[[int(i==j) for j in range(8)] for i in range(8)]
+    seen=set();hist=Counter();pairs={e['stage']:e for e in t['recipe'] if e['kind']=='local'}
+    for call in t['calls']:
+        stage,rep,pair=call['stage'],call['replica'],call['pair']
+        assert (stage,rep) not in seen;seen.add((stage,rep))
+        assert pair==pairs[stage]['pair']
+        assert call['orientation']==('backward' if pairs[stage]['reverse'] else 'forward')
+        assert len(call['owners'])==800
+        for r,(fam,route) in enumerate(call['owners']):
+            if r<240:assert fam==rep*960+(2*pair+r//120)*120+r%120 and route==[1,stage,r%120]
+            else:
+                bk,off_,w_,pure_,sp_=assign[rep,r-240];assert fam==7680+stage*nb+bk and route==([2,off_//9] if (w_==9 and pure_) else [2,off_,w_,list(sp_)])   # GK
+        assert len(set((f,json.dumps(r)) for f,r in call['owners']))==800
+        bank_rule(call['owners'],occ)   # GK: the rule on every register class, stated independently of tile()
+        for r,z in profiles[call['orientation']].items():hist[r]+=z
+    assert seen=={(s,r) for s in range(9) for r in range(8)}
+    for child in t['idle_children']:hist[child['rank']]+=child['replicas']
+    assert t['bank_padding']=={'families':list(range(7680,W)),'axis':72,'child_rank':1}
+    for r_,z_ in pads.items():hist[r_]+=z_*9   # GK
+    assert t['cover_final_correction']['families']==[0,W]
+    assert t['cover_final_correction']['charged_calls_per_cover']==W
+    assert t['execution_schedule'][-1]=={'kind':'translate_every_live_family',**{k:v for k,v in t['cover_final_correction'].items() if k!='kind'}}
+    assert 73*W-sum(r*z for r,z in hist.items())==2496
+    return hist
+H=global_check(ir)
+# Derivative repair: select two genuine width-9 owners; a fixed route may already match.
+pure_alias=[r for r in range(240,800) if widths[r-240]==9 and len(ir['calls'][0]['owners'][r][1])==2]
+assert len(pure_alias)>=2
+alias_src,alias_dst=pure_alias[:2]
+assert ir['calls'][0]['owners'][alias_src]!=ir['calls'][0]['owners'][alias_dst]
+def alias_owner(owners):
+    owners[alias_dst]=copy.deepcopy(owners[alias_src])
+for name,mut in [('missing_padding',lambda t:t['bank_padding']['families'].pop()),
+                 ('aliased_owner',lambda t:alias_owner(t['calls'][0]['owners'])),
+                 ('missing_cover_phase',lambda t:t['cover_final_correction'].__setitem__('charged_calls_per_cover',0))]:
+    t=copy.deepcopy(ir);mut(t)
+    assert t!=ir,('vacuous global mutation',name)
+    try:global_check(t)
+    except (AssertionError,KeyError):controls.append(name)
+    else:raise AssertionError('global mutation accepted: '+name)
+# GK: controls of the rule itself, one per register class, run on bank_rule (not on the equality with tile()); only for words with entering
+# helpers (the anchor's INDEPENDENT-REPLAY.json must stay byte-identical to PR #433's)
+occ_all={}
+for call in ir['calls']:
+    for fam_,route_ in call['owners'][240:]:occ_all.setdefault(fam_,set()).update(residual_cells(route_))
+def rule_control(name,mut,must):
+    o=copy.deepcopy(ir['calls'][0]['owners']);mut(o)
+    try:bank_rule(o,occ_all)
+    except AssertionError as e:
+        assert must in str(e),(name,str(e));controls.append(name)
+    else:raise AssertionError('rule mutation accepted: '+name)
+bank_rule(ir['calls'][0]['owners'],occ_all)
+rule_control('same_width_pure_helper_alias',alias_owner,'footprints overlap')
+ent=[r for r in range(240,800) if widths[r-240]<9]
+if entering:
+    a_,b_=ent[0],ent[1]
+    def to_one_bank(o):   # bank class: b joins a's bank family at the next free cells, with a spectator of its own
+        fa=o[a_][0];free=len(occ_all[fa]);o[b_]=[fa,[2,free,widths[b_-240],[free+widths[b_-240]]]]
+    rule_control('two_entering_helpers_on_one_bank_family',to_one_bank,'shares its bank family')
+    rule_control('bank_spectator_is_a_residual_cell',lambda o:o[a_][1].__setitem__(3,[o[a_][1][1]]+o[a_][1][3][1:]),'first cells beyond')
+    rule_control('bank_spectator_shifted',lambda o:o[a_][1].__setitem__(3,[x+1 for x in o[a_][1][3]]),'first cells beyond')
+    rule_control('bank_spectator_record_dropped',lambda o:o[a_].__setitem__(1,o[a_][1][:3]),'without a spectator record')
+    rule_control('bank_spectator_count_wrong',lambda o:o[a_][1].__setitem__(3,o[a_][1][3]*2),'without a spectator record')
+    rule_control('second_owner_on_an_active_data_family',lambda o:o.__setitem__(241,[o[0][0],[1,0,0]]),'data class')
+    rule_control('helper_owner_on_an_active_data_family',lambda o:o.__setitem__(250,[o[3][0],[2,0]]),'data class')
+    rule_control('active_wire_on_a_bank_family',lambda o:o.__setitem__(5,[7680,[1,0,5]]),'bank class')
+    C_=len(c['centers'])
+    rule_control('owner_in_the_private_namespace_centres',lambda o:o.__setitem__(300,[W+3,[2,0]]),'private namespace')
+    rule_control('owner_in_the_private_namespace_reserved_tableau',lambda o:o.__setitem__(300,[W+C_+5,[2,0]]),'private namespace')
+    rule_control('owner_in_the_private_namespace_coefficient',lambda o:o.__setitem__(300,[W+C_+R+1,[2,0]]),'private namespace')
+    t=copy.deepcopy(ir);t['calls'][0]['owners'][0][0]+=960   # copies: an active owner of replica 0's invocation on a family of replica 1
+    try:global_check(t)
+    except (AssertionError,KeyError):controls.append('active_owner_on_the_family_of_another_replica')
+    else:raise AssertionError('global mutation accepted: active_owner_on_the_family_of_another_replica')
+assert dict(H)=={int(r):z for r,z in integration['global_profile'].items()}
+
+def load(name):
+    sp=importlib.util.spec_from_file_location('replay_hamming_'+name,Path('work/pr361/code/engines')/(name+'.py'))
+    m=importlib.util.module_from_spec(sp);sp.loader.exec_module(m);return m
+M,B=load('moment'),load('base_two_moment');b=Q(integration['complex_b']);grid=Q(1,10**18)
+assert M.moment(H,73,W,b,True)[1]<1<M.moment(H,73,W,b+grid,True)[0]
+def other(a):
+    lo,hi=B.moment(73,W,list(H.items()),a)
+    l2,h2=B.moment(73,W,[(1,32*73**2*sum(H.values()))],a)
+    return lo+l2/10**16,hi+h2/10**16
+assert other(b)[1]<1<other(b+grid)[0]
+result={'status':'PASS_INDEPENDENT_NEW_STRUCTURAL_IR_REPLAY',
+        'template_sha256':integration['global_template_sha256'],'local':checks,
+        'mutation_controls_rejected':controls,'all_eight_global_scalar_columns':True,
+        'bank_owners_and_padding_exact':True,'paid_profile':dict(sorted(H.items())),
+        'two_rational_moment_engines':True,'complex_b':str(b),
+        'next_b_grid_rejected':True,
+        'scope':'Independent finite replay; retains the written generic scalar-interface lemma and inherited all-size/analytic assumptions.'}
+(OUT/'INDEPENDENT-REPLAY.json').write_text(json.dumps(result,indent=2)+'\n')
+print('PASS independent local/global replay and two exact moments',flush=True)
diff --git a/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/data/selections/gauge80-kernel42.json b/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/data/selections/gauge80-kernel42.json
new file mode 100644
index 0000000000..cf624433f0
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/vendor/complex/e8-complex-gauge-kernel/data/selections/gauge80-kernel42.json
@@ -0,0 +1,470 @@
+{
+ "gauge": {
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+   510
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+  "135": [
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+  "540": [
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+   24
+  ],
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+ },
+ "kernel": [
+  {
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+   ],
+   "pivots": [
+    390,
+    391,
+    418,
+    419
+   ]
+  },
+  {
+   "E": [
+    390
+   ],
+   "donors": [
+    324,
+    325,
+    328,
+    329,
+    380,
+    384,
+    440,
+    444
+   ],
+   "pivots": [
+    381,
+    385,
+    441,
+    445,
+    498,
+    499,
+    500,
+    501
+   ]
+  },
+  {
+   "E": [
+    6
+   ],
+   "donors": [
+    128,
+    129
+   ],
+   "pivots": [
+    156,
+    157
+   ]
+  },
+  {
+   "E": [
+    414
+   ],
+   "donors": [
+    218,
+    219,
+    302,
+    303
+   ],
+   "pivots": [
+    358,
+    359,
+    386,
+    387
+   ]
+  },
+  {
+   "E": [
+    384
+   ],
+   "donors": [
+    162,
+    163,
+    240,
+    241,
+    300,
+    352,
+    353,
+    356,
+    360,
+    361,
+    412,
+    416,
+    417,
+    438,
+    442
+   ],
+   "pivots": [
+    301,
+    357,
+    413,
+    436,
+    437,
+    439,
+    443,
+    496,
+    497,
+    502,
+    503
+   ]
+  },
+  {
+   "E": [
+    126
+   ],
+   "donors": [
+    160,
+    161
+   ],
+   "pivots": [
+    242,
+    243
+   ]
+  },
+  {
+   "E": [
+    102
+   ],
+   "donors": [
+    188,
+    189
+   ],
+   "pivots": [
+    244,
+    245
+   ]
+  },
+  {
+   "E": [
+    30
+   ],
+   "donors": [
+    132,
+    133
+   ],
+   "pivots": [
+    268,
+    269
+   ]
+  },
+  {
+   "E": [
+    96
+   ],
+   "donors": [
+    186,
+    187
+   ],
+   "pivots": [
+    216,
+    217
+   ]
+  },
+  {
+   "E": [
+    120
+   ],
+   "donors": [
+    158,
+    159
+   ],
+   "pivots": [
+    214,
+    215
+   ]
+  },
+  {
+   "E": [
+    480
+   ],
+   "donors": [
+    272,
+    273,
+    298
+   ],
+   "pivots": [
+    299
+   ]
+  },
+  {
+   "E": [
+    24
+   ],
+   "donors": [
+    130,
+    131
+   ],
+   "pivots": [
+    212,
+    213
+   ]
+  }
+ ]
+}
\ No newline at end of file
diff --git a/research/ranksector112-async/vendor/pr522/vendor/complex/split-centres-global/code/complex_phases_full.py b/research/ranksector112-async/vendor/pr522/vendor/complex/split-centres-global/code/complex_phases_full.py
new file mode 100644
index 0000000000..b5a5bd64b4
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/vendor/complex/split-centres-global/code/complex_phases_full.py
@@ -0,0 +1,39 @@
+# Adapted from PR425 for heterogeneous centres by icekylinx with Codex assistance.
+"""Exact phase-aware lowering of every used edge of the new structural word."""
+import gzip,hashlib,json,sys,time
+from collections import Counter
+from pathlib import Path
+sys.path.insert(0,str(Path('work/odd-stages').resolve()))
+from clifford_exact import *
+
+OUT=Path('split-centres');P=OUT/'CANONICAL-WORD.json.gz'
+c=json.load(gzip.open(P));n=c['h'];frames=c['frames'];start=time.monotonic();ops=[]
+for U in frames:
+    op=canonical_frame(n,U)
+    L=[u|(u<<n) for u in U]+[v<<n for v in nullspace(U,n)]
+    pre=[x|(z<<n) for x,z,p in inverse(op.tab)[n:]]
+    assert rank(L)==n and rank(L+pre)==n
+    assert rank([x for x,z,p in op.tab[n:]])==len(U)
+    ops.append(op)
+edges=set(map(tuple,c['edges']))|{(a,b) for f in c['center_frames'] for a,b in ((f,0),(0,f))};recipes=[];hist=Counter()
+for i,(a,b) in enumerate(sorted(edges)):
+    op=ops[a].adjoint().then(ops[b]);rec,compiled=lower_child(op)
+    assert rec['rank']==abs(len(frames[a])-len(frames[b]))
+    hist[rec['rank']]+=1;recipes.append({'old':a,'new':b,**rec})
+    if i%200==0:print('exact phase edges',i,'/',len(edges),'seconds',time.monotonic()-start,flush=True)
+adapters=[];F=fourier(n)
+for i,q in enumerate(c['ports']):
+    for role,old,f in [('source',cgate(n,q),c['start'][i]),
+                       ('target',cgate(n,q).adjoint().then(F),c['final'][c['v']+i])]:
+        rec,compiled=lower_child(old.adjoint().then(ops[f]));assert rec['rank']==0
+        adapters.append({'port':i,'role':role,'frame':f,**rec})
+raw=json.dumps({'children':recipes,'endpoint_adapters':adapters},sort_keys=True,separators=(',',':')).encode()
+(OUT/'CLIFFORD-RECIPES.json').write_bytes(raw)
+result={'status':'PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES',
+        'canonical_word_sha256':hashlib.sha256(P.read_bytes()).hexdigest(),
+        'frames':len(frames),'directed_edges':len(edges),'ranks':dict(hist),
+        'endpoint_adapters':len(adapters),'all_child_equalities_include_global_phase':True,
+        'recipe_sha256':hashlib.sha256(raw).hexdigest(),'seconds':time.monotonic()-start,
+        'scope':'Every local frame and center transition. Expanded scalar-interface integration and global emitted program are separate obligations.'}
+(OUT/'CLIFFORD-REVIEW.json').write_text(json.dumps(result,indent=2)+'\n')
+print('PASS exact local phases',result['seconds'],'seconds',flush=True)
diff --git a/research/ranksector112-async/vendor/pr522/vendor/complex/split-centres-global/vendor/clifford_exact.py b/research/ranksector112-async/vendor/pr522/vendor/complex/split-centres-global/vendor/clifford_exact.py
new file mode 100644
index 0000000000..166841a037
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/vendor/complex/split-centres-global/vendor/clifford_exact.py
@@ -0,0 +1,149 @@
+"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals.
+Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d.
+The tableau is supplemented by a literal circuit, so global phases are kept.
+"""
+from dataclasses import dataclass
+
+def parity(x):return x.bit_count()&1
+def rank(rows):
+ p={}
+ for x in rows:
+  while x:
+   b=x.bit_length()-1
+   if b not in p:p[b]=x;break
+   x^=p[b]
+ return len(p)
+def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<<j for j in range(n)) for i in range(n))
+def mv(rows,x):return sum(parity(r&x)<<i for i,r in enumerate(rows))
+def inv(rows,n):
+ a=[r|(1<<(n+i)) for i,r in enumerate(rows)]
+ for j in range(n):
+  k=next(i for i in range(j,n) if a[i]>>j&1);a[j],a[k]=a[k],a[j]
+  for i in range(n):
+   if i!=j and a[i]>>j&1:a[i]^=a[j]
+ assert [r&((1<<n)-1) for r in a]==[1<<i for i in range(n)]
+ return tuple(r>>n for r in a)
+def basis_extend(cols,n):
+ out=[]
+ for x in list(cols)+[1<<i for i in range(n)]:
+  if rank(out+[x])>len(out):out.append(x)
+ assert len(out)==n
+ return tuple(out)
+def nullspace(rows,n):
+ a=list(rows);p=[];k=0
+ for j in range(n):
+  t=next((i for i in range(k,len(a)) if a[i]>>j&1),None)
+  if t is None:continue
+  a[t],a[k]=a[k],a[t]
+  for i in range(len(a)):
+   if i!=k and a[i]>>j&1:a[i]^=a[k]
+  p.append(j);k+=1
+ return tuple((1<<j)|sum(((a[i]>>j)&1)<<v for i,v in enumerate(p)) for j in range(n) if j not in p)
+def pmul(a,b):
+ x,z,p=a;y,w,q=b
+ return x^y,z^w,(p+q+2*parity(z&y))%4
+def identity(n):return tuple([(1<<i,0,0) for i in range(n)]+[(0,1<<i,0) for i in range(n)])
+def apply(T,p):
+ n=len(T)//2;x,z,ph=p;out=(0,0,ph)
+ for i in range(n):
+  if x>>i&1:out=pmul(out,T[i])
+ for i in range(n):
+  if z>>i&1:out=pmul(out,T[n+i])
+ return out
+def compose(A,B):return tuple(apply(A,p) for p in B)
+def inverse(T):
+ n=len(T)//2;cols=[x|(z<<n) for x,z,p in T];rows=transpose(cols,2*n);cols_inv=transpose(inv(rows,2*n),2*n);out=[]
+ for j,w in enumerate(cols_inv):
+  x=w&((1<<n)-1);z=w>>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4))
+ return tuple(out)
+def qvalue(Q,alpha,x,n):
+ return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4
+def mul_i(a,p):
+ x,y=a;p%=4
+ return [(x,y),(-y,x),(-x,-y),(y,-x)][p]
+@dataclass
+class Op:
+ n:int
+ tab:tuple
+ circuit:list
+ def then(self,b):
+  assert self.n==b.n
+  return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit)
+ def adjoint(self):
+  circ=[]
+  for e in reversed(self.circuit):
+   if e[0]=='P':circ.append(('P',inv(e[1],self.n)))
+   elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2])))
+   elif e[0]=='C':circ.append(('C',e[1],-e[2]))
+   elif e[0]=='phase':circ.append(('phase',(-e[1])%4))
+   else:circ.append(e)
+  return Op(self.n,inverse(self.tab),circ)
+ def zero_state(self,basis=0):
+  N=1<<self.n;vec=[(0,0)]*N;vec[basis]=(1,0);den=0
+  for e in self.circuit:
+   if e[0]=='P':
+    v=[(0,0)]*N
+    for x,a in enumerate(vec):v[mv(e[1],x)]=a
+    vec=v
+   elif e[0]=='X':vec=[vec[x^e[1]] for x in range(N)]
+   elif e[0]=='D':vec=[mul_i(a,qvalue(e[1],e[2],x,self.n)) for x,a in enumerate(vec)]
+   elif e[0]=='phase':vec=[mul_i(a,e[1]) for a in vec]
+   elif e[0]=='C':
+    q,sgn=e[1:];v=[]
+    for x,(a,b) in enumerate(vec):
+     c,d=vec[x^q]
+     # C=(1+i)I/2+(1-i)X/2; inverse conjugates both coefficients.
+     v.append((a-sgn*b+c+sgn*d,b+sgn*a+d-sgn*c))
+    vec=v;den+=1
+   else:raise AssertionError(e)
+   while den and all((a&1)==(b&1)==0 for a,b in vec):vec=[(a//2,b//2) for a,b in vec];den-=1
+  return vec,den
+def ident(n):return Op(n,identity(n),[])
+def perm(n,G):
+ cols=transpose(G,n);gi=inv(G,n)
+ return Op(n,tuple([(a,0,0) for a in cols]+[(0,a,0) for a in gi]),[('P',tuple(G))])
+def diag(n,Q,alpha=None):
+ Q=tuple(Q);assert transpose(Q,n)==Q
+ alpha=tuple(alpha) if alpha is not None else tuple((Q[i]>>i)&1 for i in range(n))
+ assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n))
+ return Op(n,tuple([(1<<i,Q[i],alpha[i]) for i in range(n)]+[(0,1<<i,0) for i in range(n)]),[('D',Q,alpha)])
+def cgate(n,q,sgn=1):
+ return Op(n,tuple([(1<<i,0,0) for i in range(n)]+[(q if q>>i&1 else 0,1<<i,(3*sgn)%4 if q>>i&1 else 0) for i in range(n)]),[('C',q,sgn)])
+def xgate(n,b):return Op(n,tuple([(1<<i,0,0) for i in range(n)]+[(0,1<<i,2*((b>>i)&1)) for i in range(n)]),[('X',b)])
+def fourier(n,axes=None):
+ out=ident(n)
+ for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<<i))
+ return out
+def hadamard(n,axes):
+ axes=list(axes);Q=tuple(1<<i if i in axes else 0 for i in range(n));S=diag(n,Q)
+ return S.then(fourier(n,axes)).then(S)
+def canonical_frame(n,U):
+ r=len(U)
+ if r==0:return ident(n)
+ if r==n:return fourier(n)
+ G=transpose(basis_extend(U,n),n);gi=inv(G,n);Q=tuple((1<<i)^sum(parity(gi_i&gi_j)<<j for j,gi_j in enumerate(transpose(gi,n))) for i,gi_i in enumerate(transpose(gi,n)))
+ K=perm(n,G).then(diag(n,Q))
+ return K.adjoint().then(fourier(n,range(r))).then(K)
+def monomial(op):
+ n=op.n;T=op.tab;assert all(x==0 and p%2==0 for x,z,p in T[n:]);G=transpose([x for x,z,p in T[:n]],n);b=mv(G,sum((p//2)<<i for i,(x,z,p) in enumerate(T[n:])))
+ gt=transpose(G,n);cols=[mv(gt,z) for x,z,p in T[:n]];Q=transpose(cols,n);alpha=[(p-2*parity(b&z))%4 for x,z,p in T[:n]]
+ out=diag(n,Q,alpha).then(perm(n,G)).then(xgate(n,b));assert out.tab==T
+ vec,den=op.zero_state();assert den==0 and all(a==(0,0) for i,a in enumerate(vec) if i!=b);phase=[(1,0),(0,1),(-1,0),(0,-1)].index(vec[b]);out=out.then(Op(n,identity(n),[('phase',phase)]));assert out.zero_state()==op.zero_state()
+ return out,dict(matrix_rows=G,offset=b,quadratic_rows=Q,linear_Z4=alpha,phase=phase)
+def lower_child(op):
+ n=op.n;Bcols=[x for x,z,p in op.tab[n:]];r=rank(Bcols)
+ if not r:
+  mon,rec=monomial(op);return dict(rank=0,left=rec,right=None),mon
+ G=transpose(basis_extend(Bcols,n),n);A=inv(G,n);PA=perm(n,A);part=op.then(PA);Bcols=[x for x,z,p in part.tab[n:]];Dcols=[z for x,z,p in part.tab[n:]]
+ picks=[];selected=[]
+ for j,x in enumerate(Bcols):
+  if rank(selected+[x])>len(selected):picks.append(j);selected.append(x)
+ assert len(picks)==r and all(x>>r==0 for x in Bcols)
+ Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<<r)-1) for j in picks],r)
+ Qsmall=tuple(sum(parity(row&col)<<j for j,col in enumerate(transpose(Bi,r))) for row in Dr);Q=Qsmall+(0,)*(n-r);DQ=diag(n,Q)
+ V=part.then(DQ).then(hadamard(n,range(r)));assert all(x==0 for x,z,p in V.tab[n:]);Vmon,Vrec=monomial(V)
+ S=diag(n,tuple(1<<i if i<r else 0 for i in range(n)))
+ left=S.adjoint().then(DQ.adjoint()).then(PA.adjoint());right=Vmon.then(S.adjoint()).then(xgate(n,(1<<r)-1))
+ lmon,lrec=monomial(left);rmon,rrec=monomial(right);compiled=rmon.then(fourier(n,range(r))).then(lmon)
+ assert compiled.tab==op.tab and compiled.zero_state()==op.zero_state()
+ return dict(rank=r,left=lrec,right=rrec),compiled
diff --git a/research/ranksector112-async/vendor/pr522/verify.py b/research/ranksector112-async/vendor/pr522/verify.py
new file mode 100644
index 0000000000..8b9e7ca399
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/verify.py
@@ -0,0 +1,64 @@
+"""Offline, stdlib-only reconstruction of the asynchronous complex derivative.
+The unchanged PR493 bit operator is a cited dependency, not freshly verified here.
+"""
+from pathlib import Path
+import argparse,hashlib,json,os,shutil,subprocess,sys,time,gzip
+if not __debug__:raise RuntimeError('Assertions must remain enabled; do not use -O or PYTHONOPTIMIZE.')
+sys.dont_write_bytecode=True
+if hasattr(sys,'set_int_max_str_digits'):sys.set_int_max_str_digits(0)
+P=Path(__file__).resolve().parent
+a=argparse.ArgumentParser();a.add_argument('--work',type=Path,required=True);args=a.parse_args()
+W=args.work.resolve();assert P not in W.parents and W!=P,'Output must be outside this package.';assert not W.exists(),'Choose a new output directory; existing outputs are preserved.'
+mf=P/'MANIFEST.json'
+if mf.exists():
+ manifest=json.loads(mf.read_text());assert manifest['format']=='sha256-lf-text-v1'
+ for n,entry in manifest['files'].items():
+  data=(P/n).read_bytes()
+  assert entry['mode'] in ['raw','lf-text'],n
+  if entry['mode']=='lf-text':data=data.replace(b'\r\n',b'\n')
+  assert hashlib.sha256(data).hexdigest()==entry['sha256'],n
+W.mkdir(parents=True);V=W/'base';V.mkdir();shutil.copytree(P/'inputs/work',V/'work')
+# Canonicalize generated copies, never edit immutable checked-out inputs.
+for f in (V/'work').rglob('*'):
+ if f.is_file() and f.suffix in {'.json','.txt','.md','.py','.sh'}:
+  f.write_bytes(f.read_text(encoding='utf-8').encode('utf-8'))
+(V/'ASYNC-6.json').write_bytes((P/'inputs/ASYNC-6.json').read_text(encoding='utf-8').encode('utf-8'))
+bit=json.loads((P/'inputs/PR493-EXPECTED.json').read_text())['eleven']
+(V/'BIT-PRICE.json').write_text(json.dumps({'lower':bit['bit_lower'],'scope':'PR493 cited published supplier'}))
+C=P/'vendor/complex';G=C/'e8-complex-gauge-kernel';A=W/'audit';A.mkdir();H=W/'hosted'
+env=dict(os.environ,PYTHONUTF8='1',PYTHONDONTWRITEBYTECODE='1',PYTHONINTMAXSTRDIGITS='0',TEMP=str(W),TMP=str(W))
+env.pop('PYTHONOPTIMIZE',None)
+steps=[]
+def run(name,script,*argv):
+ start=time.monotonic();print('RUN',name,flush=True)
+ with (W/(name+'.log')).open('w',encoding='utf-8') as log:
+  result=subprocess.run([sys.executable,'-B',str(P/'code/run_portable.py'),str(script),*map(str,argv)],cwd=V,env=env,stdout=log,stderr=subprocess.STDOUT)
+ steps.append({'stage':name,'exit':result.returncode,'seconds':time.monotonic()-start})
+ (W/'STEPS.json').write_text(json.dumps(steps,indent=2)+'\n')
+ if result.returncode:
+  print((W/(name+'.log')).read_text()[-5000:]);raise SystemExit(result.returncode)
+ print('PASS',name,flush=True)
+run('partial-factory',P/'code/construct_partial.py',V/'work/complex-network/hamming',V/'partial-base')
+run('construct-kernel92',P/'code/build_kernel92.py',G/'code',V/'partial-base/FULL-WORD.json.gz',P/'inputs/KERNEL84-SELECTION.json',P/'inputs/RETIME-FRAMES.json.gz',P/'inputs/KERNEL92-SELECTION.json',V/'reference-kernel92')
+run('construct-pair35',P/'code/build_pair35.py',P/'code/construct_partial.py',V/'work/complex-network/hamming',G/'code',V/'partial-base/FULL-WORD.json.gz',V/'reference-kernel92/RETIMED-BASE.json.gz',P/'inputs/PAIR-SPEC.json',P/'inputs/PAIR-SELECTION.json',V/'reference-pair35')
+run('construct-ranksector',P/'code/build_ranksector.py',V/'work/complex-network/hamming',G/'code',V/'reference-pair35/factory/FULL-WORD.json.gz',V/'reference-pair35/RETIMED-BASE.json.gz',P/'inputs/PAIR-SPEC.json',P/'inputs/PAIR-SELECTION.json',V/'split-centres')
+run('kernel-scalar-controls',P/'code/audit_kernel_scalar.py',V/'split-centres/FULL-WORD.json.gz',V/'split-centres/SELECTION.json',A/'KERNEL-SCALAR.json')
+run('scalar',G/'code/audit_gk.py')
+run('emit-local',G/'code/emit_gk.py')
+run('phases',C/'split-centres-global/code/complex_phases_full.py')
+run('adapters',G/'code/adapters_gk.py',V/'split-centres/CANONICAL-WORD.json.gz',V/'split-centres/RESIDUAL-ADAPTERS.json',V/'LEMMA-A.json')
+run('parent-integration',G/'code/integrate_gk.py')
+run('parent-replay',G/'code/replay_gk.py')
+run('emit-async',P/'code/emit_async.py',G,V,P/'inputs/ASYNC-OWNERS.json.gz',V/'ASYNC-6.json',H)
+run('independent-async',P/'code/audit_async.py',V,H,A/'ASYNC-AUDIT.json')
+run('invoice',P/'code/audit_async_invoice.py',A,V,H)
+run('two-moments-assembly',P/'code/assemble.py',A,V,H,P/'inputs/PR493-EXPECTED.json')
+x=json.loads((A/'EXACT-ASSEMBLY.json').read_text());audit=json.loads((A/'ASYNC-AUDIT.json').read_text())
+assert all(z['exit']==0 for z in steps)
+result={'status':'PASS_CONDITIONAL_ASYNCHRONOUS_COMPLEX_DERIVATIVE','kappa':x['kappa'],'kappa_decimal':x['kappa_decimal'],'complex_lower':x['complex_lower'],'bit_lower':x['bit_lower'],'template_sha256':x['complex_template_sha256'],'strict_constraints':len(x['strict_outer_constraints']),'scope':'New complex program independently replayed. The unchanged PR493 bit operator and inherited all-size compiler, common-label, Lemma A realization, restored-row, precision/tape and analytic-transfer contracts remain dependencies. No unconditional multiplication bound or fresh Lean certification is claimed.','stages':steps,'package_manifest_sha256':hashlib.sha256(mf.read_bytes()).hexdigest() if mf.exists() else None}
+expected=P/'EXPECTED.json'
+if expected.exists():
+ e=json.loads(expected.read_text())
+ for key in ['kappa','complex_lower','bit_lower','template_sha256']:assert result[key]==e[key],key
+(W/'RESULT.json').write_text(json.dumps(result,indent=2)+'\n')
+print(result['status'],'kappa',result['kappa_decimal'],flush=True)
diff --git a/research/ranksector112-async/vendor/pr522/verify.sh b/research/ranksector112-async/vendor/pr522/verify.sh
new file mode 100644
index 0000000000..275570d71e
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr522/verify.sh
@@ -0,0 +1,10 @@
+#!/usr/bin/env bash
+set -euo pipefail
+here="$(cd -- "$(dirname -- "$0")" && pwd)"
+if [ "$#" -eq 0 ]; then
+  out="$(mktemp -d)/run"
+  echo "Output: $out"
+  exec python3 -B "$here/verify.py" --work "$out"
+else
+  exec python3 -B "$here/verify.py" "$@"
+fi
diff --git a/research/ranksector112-async/vendor/pr523/ADAPTATIONS.json b/research/ranksector112-async/vendor/pr523/ADAPTATIONS.json
new file mode 100644
index 0000000000..e5f1cd3cf4
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/ADAPTATIONS.json
@@ -0,0 +1,35 @@
+{
+  "emit_local112.py": {
+    "upstream": "vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/emit_gk.py",
+    "sha256": "4e415bff1d9f154496ed38e6889929b600aa0f3d583a375e8ca257ad8f51fa23",
+    "edits": [
+      "OUT = Path(sys.argv[1]); all emitter and local replay code unchanged"
+    ]
+  },
+  "phases_local112.py": {
+    "upstream": "vendor/pr514/vendor/complex/split-centres-global/code/complex_phases_full.py",
+    "sha256": "0f2795aaffafe0c64d77f3748ef2109a3c42c58da867e4cf269a0a8cb6109466",
+    "edits": [
+      "OUT and Clifford module paths from command-line arguments; all exact phase code unchanged"
+    ]
+  },
+  "audit_local112.py": {
+    "upstream": "vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/replay_gk.py",
+    "sha256": "2f064890bdde1eb9ea2c9a339e8ae9713dcffe0274be4b1ef6208ad2b7ba5a2a",
+    "edits": [
+      "Retain exact contains(), local(), both-orientation loop and all 13 local controls unchanged; replace global-template loader with LOCAL-PROGRAMS and emit local-only receipt"
+    ]
+  },
+  "global_serialization": {
+    "files": [
+      "code/restrict_global.py",
+      "code/audit_global_restriction.py",
+      "code/emit_async.py"
+    ],
+    "edits": [
+      "Bind the two generated-gzip provenance fields by decompressed content, with separate raw receipt bindings preserved.",
+      "Normalize only LF/CRLF for the nominated plan digest embedded in the template."
+    ],
+    "mathematical_changes": false
+  }
+}
diff --git a/research/ranksector112-async/vendor/pr523/EXPECTED.json b/research/ranksector112-async/vendor/pr523/EXPECTED.json
new file mode 100644
index 0000000000..4ff80054c8
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/EXPECTED.json
@@ -0,0 +1,26 @@
+{
+  "kappa": "182243220215421/125000000000000000",
+  "kappa_decimal": "0.001457945761723368",
+  "complex_lower": "1460074471110324279467/1000000000000000000000000",
+  "complex_decimal": "0.001460074471110324279467",
+  "bit_lower": "391360506745414227149/250000000000000000000000",
+  "complex_template_sha256": "2ae6ac3aff97a861d037ee51d6dcdd7bfe79ecbb0d8f1e186754428abc997a99",
+  "global_profile": {
+    "1": 182232,
+    "2": 11520,
+    "3": 41514,
+    "4": 6336,
+    "5": 24726,
+    "6": 4896,
+    "7": 132,
+    "8": 72,
+    "48": 230
+  },
+  "live": 7168,
+  "physical": 7738,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "strict_constraints": 47,
+  "whole_owner_roles": 40320,
+  "scope": "Conditional witness with the same inherited interfaces as PR514; unchanged PR493 bit operator remains a cited dependency."
+}
diff --git a/research/ranksector112-async/vendor/pr523/LICENSE b/research/ranksector112-async/vendor/pr523/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
+
+      "License" shall mean the terms and conditions for use, reproduction,
+      and distribution as defined by Sections 1 through 9 of this document.
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+      outstanding shares, or (iii) beneficial ownership of such entity.
+
+      "You" (or "Your") shall mean an individual or Legal Entity
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+
+      "Work" shall mean the work of authorship, whether in Source or
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+      "Derivative Works" shall mean any work, whether in Source or Object
+      form, that is based on (or derived from) the Work and for which the
+      editorial revisions, annotations, elaborations, or other modifications
+      represent, as a whole, an original work of authorship. For the purposes
+      of this License, Derivative Works shall not include works that remain
+      separable from, or merely link (or bind by name) to the interfaces of,
+      the Work and Derivative Works thereof.
+
+      "Contribution" shall mean any work of authorship, including
+      the original version of the Work and any modifications or additions
+      to that Work or Derivative Works thereof, that is intentionally
+      submitted to Licensor for inclusion in the Work by the copyright owner
+      or by an individual or Legal Entity authorized to submit on behalf of
+      the copyright owner. For the purposes of this definition, "submitted"
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+      to the Licensor or its representatives, including but not limited to
+      communication on electronic mailing lists, source code control systems,
+      and issue tracking systems that are managed by, or on behalf of, the
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+      designated in writing by the copyright owner as "Not a Contribution."
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+      on behalf of whom a Contribution has been received by Licensor and
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+   2. Grant of Copyright License. Subject to the terms and conditions of
+      this License, each Contributor hereby grants to You a perpetual,
+      worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+      copyright license to reproduce, prepare Derivative Works of,
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+      Work and such Derivative Works in Source or Object form.
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+   3. Grant of Patent License. Subject to the terms and conditions of
+      this License, each Contributor hereby grants to You a perpetual,
+      worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+      (except as stated in this section) patent license to make, have made,
+      use, offer to sell, sell, import, and otherwise transfer the Work,
+      where such license applies only to those patent claims licensable
+      by such Contributor that are necessarily infringed by their
+      Contribution(s) alone or by combination of their Contribution(s)
+      with the Work to which such Contribution(s) was submitted. If You
+      institute patent litigation against any entity (including a
+      cross-claim or counterclaim in a lawsuit) alleging that the Work
+      or a Contribution incorporated within the Work constitutes direct
+      or contributory patent infringement, then any patent licenses
+      granted to You under this License for that Work shall terminate
+      as of the date such litigation is filed.
+
+   4. Redistribution. You may reproduce and distribute copies of the
+      Work or Derivative Works thereof in any medium, with or without
+      modifications, and in Source or Object form, provided that You
+      meet the following conditions:
+
+      (a) You must give any other recipients of the Work or
+          Derivative Works a copy of this License; and
+
+      (b) You must cause any modified files to carry prominent notices
+          stating that You changed the files; and
+
+      (c) You must retain, in the Source form of any Derivative Works
+          that You distribute, all copyright, patent, trademark, and
+          attribution notices from the Source form of the Work,
+          excluding those notices that do not pertain to any part of
+          the Derivative Works; and
+
+      (d) If the Work includes a "NOTICE" text file as part of its
+          distribution, then any Derivative Works that You distribute must
+          include a readable copy of the attribution notices contained
+          within such NOTICE file, excluding those notices that do not
+          pertain to any part of the Derivative Works, in at least one
+          of the following places: within a NOTICE text file distributed
+          as part of the Derivative Works; within the Source form or
+          documentation, if provided along with the Derivative Works; or,
+          within a display generated by the Derivative Works, if and
+          wherever such third-party notices normally appear. The contents
+          of the NOTICE file are for informational purposes only and
+          do not modify the License. You may add Your own attribution
+          notices within Derivative Works that You distribute, alongside
+          or as an addendum to the NOTICE text from the Work, provided
+          that such additional attribution notices cannot be construed
+          as modifying the License.
+
+      You may add Your own copyright statement to Your modifications and
+      may provide additional or different license terms and conditions
+      for use, reproduction, or distribution of Your modifications, or
+      for any such Derivative Works as a whole, provided Your use,
+      reproduction, and distribution of the Work otherwise complies with
+      the conditions stated in this License.
+
+   5. Submission of Contributions. Unless You explicitly state otherwise,
+      any Contribution intentionally submitted for inclusion in the Work
+      by You to the Licensor shall be under the terms and conditions of
+      this License, without any additional terms or conditions.
+      Notwithstanding the above, nothing herein shall supersede or modify
+      the terms of any separate license agreement you may have executed
+      with Licensor regarding such Contributions.
+
+   6. Trademarks. This License does not grant permission to use the trade
+      names, trademarks, service marks, or product names of the Licensor,
+      except as required for reasonable and customary use in describing the
+      origin of the Work and reproducing the content of the NOTICE file.
+
+   7. Disclaimer of Warranty. Unless required by applicable law or
+      agreed to in writing, Licensor provides the Work (and each
+      Contributor provides its Contributions) on an "AS IS" BASIS,
+      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
+      implied, including, without limitation, any warranties or conditions
+      of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A
+      PARTICULAR PURPOSE. You are solely responsible for determining the
+      appropriateness of using or redistributing the Work and assume any
+      risks associated with Your exercise of permissions under this License.
+
+   8. Limitation of Liability. In no event and under no legal theory,
+      whether in tort (including negligence), contract, or otherwise,
+      unless required by applicable law (such as deliberate and grossly
+      negligent acts) or agreed to in writing, shall any Contributor be
+      liable to You for damages, including any direct, indirect, special,
+      incidental, or consequential damages of any character arising as a
+      result of this License or out of the use or inability to use the
+      Work (including but not limited to damages for loss of goodwill,
+      work stoppage, computer failure or malfunction, or any and all
+      other commercial damages or losses), even if such Contributor
+      has been advised of the possibility of such damages.
+
+   9. Accepting Warranty or Additional Liability. While redistributing
+      the Work or Derivative Works thereof, You may choose to offer,
+      and charge a fee for, acceptance of support, warranty, indemnity,
+      or other liability obligations and/or rights consistent with this
+      License. However, in accepting such obligations, You may act only
+      on Your own behalf and on Your sole responsibility, not on behalf
+      of any other Contributor, and only if You agree to indemnify,
+      defend, and hold each Contributor harmless for any liability
+      incurred by, or claims asserted against, such Contributor by reason
+      of your accepting any such warranty or additional liability.
+
+   END OF TERMS AND CONDITIONS
+
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+
+      To apply the Apache License to your work, attach the following
+      boilerplate notice, with the fields enclosed by brackets "[]"
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+      file or class name and description of purpose be included on the
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+
+   Copyright [yyyy] [name of copyright owner]
+
+   Licensed under the Apache License, Version 2.0 (the "License");
+   you may not use this file except in compliance with the License.
+   You may obtain a copy of the License at
+
+       http://www.apache.org/licenses/LICENSE-2.0
+
+   Unless required by applicable law or agreed to in writing, software
+   distributed under the License is distributed on an "AS IS" BASIS,
+   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+   See the License for the specific language governing permissions and
+   limitations under the License.
diff --git a/research/ranksector112-async/vendor/pr523/LOCAL-VALIDATION.json b/research/ranksector112-async/vendor/pr523/LOCAL-VALIDATION.json
new file mode 100644
index 0000000000..323fddc72b
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/LOCAL-VALIDATION.json
@@ -0,0 +1,149 @@
+{
+  "status": "PASS_LOCAL_RECONSTRUCTION_AND_PACKAGING_EQUIVALENCE",
+  "python": "3.14.8 (main, Oct  2 2026, 10:23:31) [GCC 16.2.1 20260810]",
+  "platform": "Linux",
+  "original_archive_sha256": "79b52493ed518e2263033a353b458e92b25f69fe9b819fb11bcbdac2a4409d23",
+  "reconstruction": {
+    "status": "PASS_CONDITIONAL_PUNCTURED112_GLOBAL_KAPPA",
+    "kappa": "182243220215421/125000000000000000",
+    "kappa_decimal": "0.001457945761723368",
+    "complex_lower": "1460074471110324279467/1000000000000000000000000",
+    "bit_lower": "391360506745414227149/250000000000000000000000",
+    "template_sha256": "2ae6ac3aff97a861d037ee51d6dcdd7bfe79ecbb0d8f1e186754428abc997a99",
+    "live": 7168,
+    "physical": 7738,
+    "deficit": 2560,
+    "global_profile": {
+      "1": 182232,
+      "2": 11520,
+      "3": 41514,
+      "4": 6336,
+      "5": 24726,
+      "6": 4896,
+      "7": 132,
+      "8": 72,
+      "48": 230
+    },
+    "strict_constraints": 47,
+    "improvement_over_pinned514": "66422302131539/1391523459591829",
+    "whole_owner_roles": 40320,
+    "all_own_stages": 14,
+    "pinned_predecessor_stages": 13,
+    "package_manifest_sha256": "ad811117f072d8e274fc24a65f7c361480bdf9ff415c4391bb1ce5210efb3309",
+    "seconds": 487.4682761729928,
+    "steps": [
+      {
+        "stage": "01-pinned514-full-replay",
+        "exit": 0,
+        "seconds": 252.5638241529814
+      },
+      {
+        "stage": "02-restrict-local",
+        "exit": 0,
+        "seconds": 0.3044327960233204
+      },
+      {
+        "stage": "03-exact-word-transport",
+        "exit": 0,
+        "seconds": 0.33720749500207603
+      },
+      {
+        "stage": "04-emit-local",
+        "exit": 0,
+        "seconds": 0.9979033580166288
+      },
+      {
+        "stage": "05-independent-local",
+        "exit": 0,
+        "seconds": 4.314806153997779
+      },
+      {
+        "stage": "06-exact-local-phases",
+        "exit": 0,
+        "seconds": 184.75575182097964
+      },
+      {
+        "stage": "07-residual-wrappers",
+        "exit": 0,
+        "seconds": 0.9754966790205799
+      },
+      {
+        "stage": "08-restrict-global-data",
+        "exit": 0,
+        "seconds": 1.896387071989011
+      },
+      {
+        "stage": "09-independent-global-restriction",
+        "exit": 0,
+        "seconds": 8.02704970096238
+      },
+      {
+        "stage": "10-emit-whole-owners",
+        "exit": 0,
+        "seconds": 4.4006109239999205
+      },
+      {
+        "stage": "11-independent-hosted-program",
+        "exit": 0,
+        "seconds": 21.840246197010856
+      },
+      {
+        "stage": "12-independent-raw-reconstruction",
+        "exit": 0,
+        "seconds": 4.635197088995483
+      },
+      {
+        "stage": "13-scalar-prefix-and-finite-invoice",
+        "exit": 0,
+        "seconds": 1.8959346679621376
+      },
+      {
+        "stage": "14-two-moments-and-global-assembly",
+        "exit": 0,
+        "seconds": 0.5078898860374466
+      }
+    ],
+    "scope": "Finite complex restriction, exact local phases, whole physical owners, complete fee inventory, two rational moments and 47 outer inequalities checked. The unchanged PR493 bit operator, all-size compiler, common-label/mutable-basis realization, normalized Lemma A, restored-row, precision/tape and analytic-transfer contracts remain dependencies. No unconditional theorem or new Lean certification."
+  },
+  "packaging": {
+    "executable_python_asts_unchanged": true,
+    "mathematical_inputs_unchanged": true,
+    "changed_files": [
+      "NOTICE.md",
+      "PORTABILITY.md",
+      "PROOF.md",
+      "README.md",
+      "SOURCES.json",
+      "verify.py",
+      "code/audit_112_independent.py",
+      "code/audit_local112.py",
+      "code/audit_port112_transport.py",
+      "code/build_port112.py",
+      "proof/GLOBAL-RESTRICTION.md",
+      "proof/INDEPENDENT-REVIEW.md",
+      "proof/LOCAL-RESTRICTION.md"
+    ],
+    "excluded_optional_files": [
+      "RESEARCH.md",
+      "discovery/"
+    ],
+    "changes": "Attribution, Markdown math delimiters, documentation, source credit correction for Dugongue PR505, and manifest refresh. Original Pro artifacts remain archived."
+  },
+  "historical_ci_fix": {
+    "checks": [
+      "joint_dual_compose.py: PASS",
+      "test_joint_reclaim.py: 16 tests PASS"
+    ],
+    "source_changes": [
+      "Makefile pin",
+      "README.md pin"
+    ],
+    "derived_certificate_changes": [
+      "source_manifest_sha256",
+      "certificate_sha256"
+    ],
+    "mathematical_certificate_unchanged": true,
+    "historical_full_replay_rerun": false
+  },
+  "ci": "Python 3.11 and 3.14 workflow added; remote results pending."
+}
diff --git a/research/ranksector112-async/vendor/pr523/MANIFEST.json b/research/ranksector112-async/vendor/pr523/MANIFEST.json
new file mode 100644
index 0000000000..ed2501db2e
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/MANIFEST.json
@@ -0,0 +1,501 @@
+{
+  "format": "sha256-lf-text-v1",
+  "files": {
+    "ADAPTATIONS.json": {
+      "mode": "lf-text",
+      "sha256": "87d40442fe987e641d697d7c0ba9e1e44f840291980b1dbd2560950447713b90"
+    },
+    "EXPECTED.json": {
+      "mode": "lf-text",
+      "sha256": "80bf7af2b7918e2b4acf3b8e6dcc6ebeeca03335d40a26d39f9c62223101dd6e"
+    },
+    "LICENSE": {
+      "mode": "lf-text",
+      "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4"
+    },
+    "NOTICE.md": {
+      "mode": "lf-text",
+      "sha256": "18d13f5af8df2b29e2c8111a79312b4cc406663b9e124b3e42e424be83a8c7f0"
+    },
+    "PORTABILITY.md": {
+      "mode": "lf-text",
+      "sha256": "f0b521f80df85bfe3b73af0ed9c599b3b79ca6489c9fce14bd3de40303494bf6"
+    },
+    "PROOF.md": {
+      "mode": "lf-text",
+      "sha256": "8c574d618ee00dae772af0f97c4e216ec10f071d2eef2c7de472a00f0a9f5fd2"
+    },
+    "README.md": {
+      "mode": "lf-text",
+      "sha256": "099b1115a721b1218e97ab591f2c41e271b7bdd457bba423ef509a53823d9d0d"
+    },
+    "REPRODUCTION.json": {
+      "mode": "lf-text",
+      "sha256": "232f42f96c4a5f7f7719d20034add8287fe121bfa33e62954bf8b2c95a5fb6b0"
+    },
+    "SOURCES.json": {
+      "mode": "lf-text",
+      "sha256": "0bfce40d86c849f18e8872ee9e8462b0a69a34ed04e01e942a6614645f686f4b"
+    },
+    "code/assemble.py": {
+      "mode": "lf-text",
+      "sha256": "71b4cbbbc5acdfe06ac67879cf54ea761e29e52143af1cd8410ad672a5cc190b"
+    },
+    "code/audit_112_independent.py": {
+      "mode": "lf-text",
+      "sha256": "00a1bba7f42cffc1d12aa31d7c4c445681e3abaea933bdf8c9126d405d1fb7f6"
+    },
+    "code/audit_async.py": {
+      "mode": "lf-text",
+      "sha256": "e17ad47bf9dd7ef7491b32f810007ee27183688d9bb588c17683e1927d336dcb"
+    },
+    "code/audit_async_invoice.py": {
+      "mode": "lf-text",
+      "sha256": "b58586a2d7173db083682e239b8ce9173172f506479e18250fd8bd73b175a9ce"
+    },
+    "code/audit_global_restriction.py": {
+      "mode": "lf-text",
+      "sha256": "332731ea8ea75e82c5c4d52bc6a321adf3f499e1549d52928b11991857ddcf25"
+    },
+    "code/audit_local112.py": {
+      "mode": "lf-text",
+      "sha256": "62ffe854885457bf82b6c7f43526dc5902a9739721aaccdedfe6f5848feb8448"
+    },
+    "code/audit_port112_transport.py": {
+      "mode": "lf-text",
+      "sha256": "82c66ad6803d4356cac1472b7a8535826f95aba4fbc408d2f05d3a2b038fb97a"
+    },
+    "code/build_port112.py": {
+      "mode": "lf-text",
+      "sha256": "0f13f01092b4c4494b86575a602b49f9ff02b6754de08d477fa5cc298326d290"
+    },
+    "code/emit_async.py": {
+      "mode": "lf-text",
+      "sha256": "cdf9a59786b4d24ca25b9c671a9e35a13ef5d438e51ffc4de4bcb3e9001ef1af"
+    },
+    "code/emit_local112.py": {
+      "mode": "lf-text",
+      "sha256": "eefc76e0bee003015fe21ac685c2cce658033d5444add404d2d509c7d6f39bac"
+    },
+    "code/phases_local112.py": {
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+      "sha256": "f027a9273bcf4e0971258c160b7d3b3c196366b32a529cff6e6a0e666b03826b"
+    },
+    "vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/integrate_gk.py": {
+      "mode": "lf-text",
+      "sha256": "2e807893180a3716b36a81f1a7d933bd55f2299489b6f236ba5c644d87739209"
+    },
+    "vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/onehost_gk.py": {
+      "mode": "lf-text",
+      "sha256": "416b318c1b6b8c7b72e24713b1b18d8772ec368e042a321b4418c63a74711590"
+    },
+    "vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/replay_gk.py": {
+      "mode": "lf-text",
+      "sha256": "2f064890bdde1eb9ea2c9a339e8ae9713dcffe0274be4b1ef6208ad2b7ba5a2a"
+    },
+    "vendor/pr514/vendor/complex/e8-complex-gauge-kernel/data/selections/gauge80-kernel42.json": {
+      "mode": "lf-text",
+      "sha256": "436e4acadee227dbfcb66386c9ccaa38e68054e8ed4870bb174eeb41363375bb"
+    },
+    "vendor/pr514/vendor/complex/split-centres-global/code/complex_phases_full.py": {
+      "mode": "lf-text",
+      "sha256": "0f2795aaffafe0c64d77f3748ef2109a3c42c58da867e4cf269a0a8cb6109466"
+    },
+    "vendor/pr514/vendor/complex/split-centres-global/vendor/clifford_exact.py": {
+      "mode": "lf-text",
+      "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962"
+    },
+    "vendor/pr514/verify.py": {
+      "mode": "lf-text",
+      "sha256": "ae9b5763e656696add6d106fe70d90facb5d2700fb8e66e4eea678c46b1d5720"
+    },
+    "vendor/pr514/verify.sh": {
+      "mode": "lf-text",
+      "sha256": "2b1b51f757d8ddf81941c8c96007a2256336856c2e017bcf6c3a37576c82bc8b"
+    },
+    "verify.py": {
+      "mode": "lf-text",
+      "sha256": "6678465d71c8cc0028e4434c1fa24f221f7cf8ca6dc4b52bc99c37c643de9707"
+    },
+    "LOCAL-VALIDATION.json": {
+      "mode": "lf-text",
+      "sha256": "bbe8070d65ae5b8a9a264e070ee849de595e36e7a390a11b980ee13802fe734d"
+    }
+  }
+}
diff --git a/research/ranksector112-async/vendor/pr523/NOTICE.md b/research/ranksector112-async/vendor/pr523/NOTICE.md
new file mode 100644
index 0000000000..5725e0f953
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/NOTICE.md
@@ -0,0 +1,51 @@
+# Attribution and scope of the increment
+
+Prepared for icekylinx with GPT-6 Astra assistance. Apache-2.0;
+see LICENSE. Local review and submission packaging used OpenAI Codex.
+Copyright 2026 icekylinx. Original author and assistance notices in retained and adapted
+source are preserved. This note supplements, and does not replace,
+`vendor/pr514/NOTICE.md` and its nested source notices.
+
+## New work in this package
+
+The new contribution is the exact puncture of eight isolated coordinate-port
+summands, the explicit retained-port transport and global data restriction,
+a newly discovered full whole-owner allocation for the smaller family stock,
+the independently written raw restriction/chart/window/owner audit, and the
+complete new finite invoice and exact global kappa assembly. The proof and
+reproduction runner combine those ingredients without adding nominal gains.
+
+## Substantial inherited contributions
+
+- PR514 (Dugongue): combined 92-pivot word, coordinated entrance gauges,
+  literal asynchronous whole-owner methodology, verifier and offline package.
+- PR507 (eumemic): partial-own factory, 84-pivot reference and the
+  pinned retiming map, inherited through PR514.
+- PR484 (DreamingOfClouds) and PR496 (eumemic): gauge/kernel construction,
+  normalized residual wrappers, whole-owner parent and invoice ancestry.
+- PR493 (eumemic): unchanged R489 bit operator and its cited endpoint.
+- PR495, PR501 and PR502: body retiming and its integrations; PR473:
+  single-gauge inspiration; PR505 (Dugongue) and PR506: asynchronous scheduling lineage
+  and related composition/portability feedback.
+- PR458: whole-owner spectator wrappers. PR433, PR425 and PR370: geometry,
+  scalar and phase compilation. PR361 and PR315: exact moments and outer
+  arithmetic. Other response-kernel/gauge ancestors are retained in the
+  original notices and SOURCES.json.
+
+Specific adapted source files retain their existing author headers.
+`ADAPTATIONS.json` records the source hashes for the CLI-only local emitter
+and phase adaptations and the extracted unchanged local audit routines.
+
+## Comparisons and exclusions
+
+PR518 is a newer numerical comparison; none of its additional pair choices,
+99-pivot word or owner transport is copied. PR510's higher bit rate is also
+not used. PR517's smaller asynchronous witness and packing ceiling are public
+context, not dependencies. PR520's open allocator and delivery map were seen
+only in the final comparison refresh; its code was not adopted. PR516 and PR519 are formalization context, not new
+Lean certifications claimed here. The disputed split-residual interfaces of
+PR494/499 are not used. Failed cyclic-packet and E7 experiments contribute no
+numerical saving.
+
+Credits identify ingredients and provenance, not independent additive gains
+or a claim that every inherited interface has been freshly verified.
diff --git a/research/ranksector112-async/vendor/pr523/PORTABILITY.md b/research/ranksector112-async/vendor/pr523/PORTABILITY.md
new file mode 100644
index 0000000000..2cf5f20566
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/PORTABILITY.md
@@ -0,0 +1,54 @@
+# Serialization and execution scope
+
+The clean reconstruction was executed with CPython 3.12.14 on Linux, using
+only the Python standard library. Python 3.11 or later is the source-level
+requirement. That receipt describes the original Pro execution. Local submission validation
+is recorded separately in `LOCAL-VALIDATION.json`. The checks below address specific identified serialization
+dependencies; they are not a claim of exhaustive platform testing.
+
+## Text files
+
+Manifest entries marked `lf-text` normalize only CRLF to LF. The inherited
+runner materializes its plain-text working inputs with LF endings and runs
+its retained scripts with UTF-8/LF output. The new scripts use that same
+portable launcher.
+
+The 112-port emitter normalizes LF/CRLF when binding the nominated plan. This
+is necessary because that plan digest is embedded in the canonical global
+template. No other character or JSON token is discarded by that binding.
+The fixed owner-map gzip input is binary and is validated without text
+normalization.
+
+## Generated gzip files
+
+The official Python gzip documentation records changes to the generated
+gzip OS byte and default compression level:
+https://docs.python.org/3/library/gzip.html#gzip.compress
+
+The two new generated-gzip provenance fields embedded in the template are
+explicitly named `parent_global_template_content_sha256` and
+`canonical_word_content_sha256`. They hash the exact decompressed bytes,
+which contain the canonical JSON instructions. Container headers and
+compression levels do not change the mathematical object.
+
+Raw file hashes remain in auxiliary receipts and are compared against the
+files generated by that same run. The predecessor's expected template already
+uses semantic event lists and plain JSON recipe hashes; it has no regenerated
+raw-gzip binding embedded in the fixed expected template. Its immutable
+binary input owner map remains bound byte-for-byte.
+
+The final whole-owner template hash is likewise the SHA256 of its decompressed
+canonical content. The serialization correction changes the template's
+provenance metadata and therefore its identifier, but no instruction, frame,
+owner, paid child, exact moment or kappa changes.
+
+## Runtime requirements
+
+Keep Python assertions enabled. The main runner refuses `-O`, older Python,
+an existing output directory, or a changed/missing manifest input before
+starting reconstruction. The output directory can be anywhere outside this
+package and the command can be launched from any working directory.
+
+No network or optimizer is needed for replay. Timing fields and raw compressed
+file bytes can differ between environments, while the canonical mathematical
+content, exact rates and final expected template remain the comparison targets.
diff --git a/research/ranksector112-async/vendor/pr523/PROOF.md b/research/ranksector112-async/vendor/pr523/PROOF.md
new file mode 100644
index 0000000000..5ce78e57cb
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/PROOF.md
@@ -0,0 +1,199 @@
+# Conditional construction argument
+
+The exact finite result is
+`kappa = 182243220215421/125000000000000000`.
+This note explains how the changed finite ingredients satisfy the same
+interfaces used by pinned PR514. It does not prove the inherited all-size or
+analytic interfaces. Full credits are in `NOTICE.md` and `SOURCES.json`.
+
+## Proposition 1: exact direct-sum restriction
+
+Let P be the original normalized scalar operator after arranging its eight coordinate
+source/target pairs separately from the other registers. The old Hamming
+scalar word, its canonical transport and the new word are supplied explicitly.
+Comparison of A, B, precondition, compensation, cut and cleanup shows that
+the deleted registers have exactly eight occurrences: unit shears on their
+own source/target pairs. Hence
+
+$$
+P=\left(\bigoplus_{i=1}^8 J_i\right)\oplus P_{112},
+\qquad J_i(x_i,y_i)=(x_i,y_i+x_i).
+$$
+
+The old identity on all arbitrary data and helper columns implies that
+P112 is the required 112-data-port shear and restores every helper in this
+normalized scalar interface. Physically, a complete invocation leaves the
+declared residual transform on a helper's owner and restores its spectator
+coordinates, as specified in Proposition 3. The
+separate exact transport and emitted-program replays verify this conclusion
+directly in both orientations. They also verify the actual frame at each
+operand, nested recursive steps, cleared private work, and ordered wrappers.
+
+No retained frame, coefficient, scalar gate or helper entrance is modified.
+The exact local Clifford and residual-wrapper checks therefore realize the
+same conditional operator interface on the retained registers. The new local
+cost is obtained by deleting precisely sixteen rank-8 and eight rank-1
+children. Its rank mass is 6706 and its center-rank sum is 64.
+See `proof/LOCAL-RESTRICTION.md` for indices, coefficients and source checks.
+
+## Proposition 2: retained global data controller
+
+The old controller's data families are indexed by replica, one of four pairs,
+side, and port. Keep precisely the 112 canonical ports selected in Proposition
+1, and reindex each data-family component by the same order-preserving map.
+Each full local invocation is replaced by P112 in the appropriate orientation.
+Every data chart, bridge, idle axis, stage translation and terminal correction
+for a retained port is exactly the corresponding old object.
+
+The local source/target basis operations may mix the code ports inside a
+complete invocation. Proposition 1 is why that fact is harmless: no removed
+coordinate register participates, and the complete endpoint is the required
+portwise data shear. The outer controller is restricted only at complete
+invocation boundaries. The proof does not assume that every individual
+factory instruction is portwise independent.
+
+The independent restriction audit compares all retained recipe objects,
+reconstructs every actual 73-dimensional orthogonal basis, and verifies the
+complete per-replica event order and terminal correction. This establishes the
+data-controller induction, subject to the same inherited local operator and
+cover interfaces. See `proof/GLOBAL-RESTRICTION.md`.
+
+## Proposition 3: whole physical owners implement every residual
+
+Order the 72 complete invocations lexicographically by
+`(7*stage + 6*replica, stage, replica)`. This preserves every replica's original
+controller order. The literal assignment lists all 72*560 helper uses.
+
+For each use, the independent audit establishes:
+
+1. The owner is an actual retained data family and is idle throughout that
+   complete invocation, taking account of every bridge touch.
+2. The family's pending child contains the assigned residual factors, as
+   actual vectors in its orthogonal port basis.
+3. Residual and spectator coordinates extend to a full orthogonal 73-column
+   chart. The existing normalized wrappers act identically on the spectators.
+4. All 560 helper families are distinct and avoid all 224 active data families
+   of that invocation. Its full 784-owner map is injective.
+5. Assigned factors in each pending child are disjoint, and every unassigned
+   factor is covered by its explicit paid remainder before the family's next
+   touch.
+
+The complete local interface accepts arbitrary helper dirt and restores its
+spectators. Induction over the actual event schedule therefore substitutes
+each invocation's specified residual for a factor of its owner's original
+pending child. The product of all such factors and the paid complement is
+exactly that child. No residual has more than one owner, and no gate crosses
+an unfinished local invocation.
+
+Consequently the final hosted template has the same required retained data
+endpoint as Proposition 2. Its full private namespace is disjoint from its
+7168 data families. Its physical stock is 7738. Intermediate legacy bank
+display metadata is inactive: the final template's bank family list is empty.
+
+## Proposition 4: exact complete recursive invoice
+
+Literal replay gives local profile
+
+$$
+H_{\mathrm{loc}}=\{1:2531,2:160,3:530,4:88,5:298,6:68,7:1,8:1\}.
+$$
+
+Subtracting the verified assigned pending axes from the original idle children
+gives the remainder profile
+
+$$
+H_{\mathrm{rem}}=\{3:3354,5:3270,7:60,48:230\}.
+$$
+
+There are exactly 72 complete invocations, so
+
+$$
+H=72H_{\mathrm{loc}}+H_{\mathrm{rem}}
+=\{1:182232,2:11520,3:41514,4:6336,5:24726,6:4896,
+7:132,8:72,48:230\}.
+$$
+
+Direct integer summation gives
+
+$$
+\sum_r rH[r]=520704=73\cdot7168-2560.
+$$
+
+This agrees with the independent geometry identity
+`D = 8*((9-1)*112 - 9*64) = 2560`.
+The maximum child rank is 48; `73^2 > 2*48^2` verifies the retained halving
+condition. The exact finite invoice charges all local scalar primitives,
+wrappers, physical routing, terminal correction and private work. Its global
+prefix is bounded by 206 bits while retaining a 512-bit allowance, including
+72 complete local cover sweeps and 72 individual bridge sweeps.
+
+These facts are independently checked from the final program and actual
+owner footprints, not inferred from the nominal optimization objective.
+The objective and its solver gap have no proof role.
+
+## Proposition 5: complex moment and global assembly
+
+For the fully paid H above, m=73 and W=7168, the inherited complex moment
+including its exceptional-class envelope is
+
+$$
+F(a)=\sum_r\frac{rH[r]}{mW}\left(\frac mr\right)^a
+ +\frac{32m\sum_r H[r]}{10^{16}W}m^a.
+$$
+
+The Mercator and independent base-two implementations produce enclosing
+rational intervals at both neighboring endpoints. Both establish
+
+$$
+F(b)<1<F(b+10^{-24}),\qquad
+b=\frac{1460074471110324279467}{10^{24}}.
+$$
+
+The same two engines reprice the pinned PR493 bit histogram at
+
+$$
+c=\frac{391360506745414227149}{250000000000000000000000}.
+$$
+
+Its unchanged physical operator remains a cited dependency. Set
+`eta=beta=10^-18` and
+`s=min(c,(1-beta)*b)-10^-24`. Starting at the inherited certified seed
+`a0=384599/10^10`, six steps use
+
+$$
+a_{j+1}=(1-s)s+s a_j.
+$$
+
+Every step's strict gap and sufficient finite cutoff are recorded exactly.
+Then `q=a6*(1-2*eta)` and the selected kappa is the largest multiple of
+`10^-18` strictly below `(1-eta)*q/(1+q)` for this assembly. The inherited
+outer engine checks all 47 strict rational inequalities, including row,
+literal scalar, precision and exposed-work constraints. All pass at
+
+$$
+\kappa=\frac{182243220215421}{125000000000000000}.
+$$
+
+The next grid point and invalid eta/beta controls fail. The exact proof
+objects are `evidence/EXACT-ASSEMBLY.json` and its reconstructed counterpart
+under the requested work directory.
+
+## Conditional conclusion and comparison
+
+Under the same all-size compiler, common-label/mutable-basis, normalized
+Lemma A, restored-row, precision/tape and analytic-transfer contracts as
+PR514, Propositions 1-5 give the claimed global exponent saving in the
+inherited integer-multiplication framework. No stronger interface is introduced
+by the puncture or the whole-owner allocation.
+
+The exact improvement relative to pinned PR514 is
+
+$$
+\frac{\kappa}{0.001391523459591829}-1
+=\frac{66422302131539}{1391523459591829}
+\approx0.0477335122693673.
+$$
+
+The newer comparison PR518 gives `0.001393662920776407`; the same new witness
+exceeds it by approximately 4.6125099541 percent. Neither comparison means
+that runtime at a practical input size improves by that percentage.
diff --git a/research/ranksector112-async/vendor/pr523/README.md b/research/ranksector112-async/vendor/pr523/README.md
new file mode 100644
index 0000000000..a8383f3147
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/README.md
@@ -0,0 +1,271 @@
+# Puncturing eight isolated ports: a larger global kappa
+
+Contributed by **icekylinx**, with GPT-6 Astra assistance; reviewed and packaged with OpenAI Codex. This is an incremental
+research package over pinned PR514, with its complete offline dependencies.
+
+## Result
+
+The new checked **conditional global** exponent saving is
+
+$$
+\boxed{\kappa=\frac{182243220215421}{125000000000000000}
+             =0.001457945761723368.}
+$$
+
+Under the inherited integer-multiplication framework this is the parameter in
+$T(n)=O(n(\log n)^{1-\kappa})$. It is a finite conditional witness, with the
+scope described below. Percentages compare exponent savings, not measured
+runtime.
+
+| Quantity | Pinned PR514 | This construction |
+| --- | ---: | ---: |
+| Global kappa | 0.001391523459591829 | **0.001457945761723368** |
+| Complex rate b | 0.001393462495344162153490 | **0.001460074471110324279467** |
+| Bit rate c, cited PR493 | 0.001565442026981656908596 | same |
+| Local ports v | 120 | **112** |
+| Ambient local dimension h | 9 | 9 |
+| Helpers R | 560 | 560 |
+| Sum of retained-center ranks | 72 | **64** |
+| Local child rank mass | 6842 | **6706** |
+| Global ambient dimension m | 73 | 73 |
+| Data/live families W | 7680 | **7168** |
+| Physical families | 8258 | **7738** |
+| Global rank deficit | 2496 | **2560** |
+
+This is **4.7733512269% above PR514**, an absolute kappa increase of
+`66422302131539/1000000000000000000`.
+
+During the final public comparison, PR518 appeared with kappa
+`0.001393662920776407`. The present result is **4.6125099541% above that
+newer comparable claimed witness**. PR518 is a comparison, not a code or proof
+dependency; its extra seven pivots were not adopted. The public snapshot was
+checked through PR520 at 2026-10-12 00:09 UTC. PR520 supplies an open allocator
+and a delivery map, with no higher global kappa reported. See `SOURCES.json`
+and `evidence/PUBLIC-SNAPSHOT.json` for the comparison and immutable pins.
+
+The new contribution is the **exact removal of eight isolated data-port
+summands, followed by a complete new physical owner allocation and global
+recount**. The scalar factory, 92-pivot kernel, entrance gauges, and existing
+body retiming are retained from the attributed predecessor. No headline gains
+are added together.
+
+## Reproduce from an empty output directory
+
+Python **3.11 or later**, standard library only, with assertions enabled:
+
+```bash
+python -B verify.py --work /absolute/path/to/a-new-output-directory
+```
+
+The directory must not already exist and must be outside this package.
+There are no network, optimizer, NumPy, SciPy, C++ or Lean dependencies for
+verification. The literal owner assignment is an input which every checker
+validates; verification does not rerun the optimization used to discover it.
+The two exact Clifford passes are the longest steps, so allow several minutes.
+
+The runner first executes the full thirteen-stage pinned PR514 reconstruction.
+It then builds the 112-port restriction, reconstructs local instructions,
+checks both orientations and phases, rebuilds the restricted data controller,
+emits actual whole owners, independently recounts all costs, and runs two
+rational moment engines and all 47 strict outer inequalities. Fourteen
+top-level stages, including the nested predecessor replay, must pass.
+
+The final output is `RESULT.json`; all exact numerical inequalities and
+bootstrap parameters appear in `audit/EXACT-ASSEMBLY.json`. Per-stage logs and
+`STEPS.json` identify any failure. Every input is hashed by `MANIFEST.json`.
+Only LF/CRLF normalization is permitted for manifest text entries. Generated
+timing receipts can vary in their `seconds` fields; the canonical recipes,
+global template, paid histogram and exact rates are deterministic. Generated
+gzip provenance inside the template binds decompressed content; its container
+header and compression level are not mathematical inputs. The nominated-plan
+binding normalizes LF/CRLF before hashing. `PORTABILITY.md` records the scope.
+
+The original Pro clean replay passed all stages in about 651 seconds. `REPRODUCTION.json`, `evidence/COLD-REPLAY.json` and
+`evidence/COLD-STEPS.json` record that run. Every published numerical and
+physical certificate under `evidence/` is from that completed reconstruction.
+`LOCAL-VALIDATION.json` records the separate submission validation.
+
+## Structural argument
+
+### 1. A direct-sum component can be removed exactly
+
+The old 120-port Hamming construction consists of eight coordinate lines and
+112 code lines. In the literal PR514 word the coordinate source/target pairs
+occur only in eight additions `y_i += x_i`. They never occur in the factory
+body, target preconditioner, dirty-helper compensation, or full-frame cleanup.
+
+`code/build_port112.py` checks every occurrence before deleting any register.
+It rejects any removed-register operation other than the exact specified unit
+shear. The full word is therefore the direct sum of these eight elementary
+shears and the word on the remaining 112 ports and all 560 dirty helpers.
+The retained normalized scalar operator is exactly
+
+$$
+ (x,s,y)\longmapsto(x,s,y+x),\qquad x,y\in K^{112},\ s\in K^{560}.
+$$
+
+All helper identities, coefficients, frames, donor relations, and entrance
+gauges stay the same. The original orthogonal transvection maps the removed
+ports to canonical indices `0,13,22,35,40,51,54,119`; all global data layers
+use precisely the complementary set, in its original order.
+
+Each removed pair eliminates two rank-8 children and one rank-1 center
+descent. The actual local cost is thus the old profile minus sixteen rank-8
+and eight rank-1 children:
+
+```text
+{1:2531, 2:160, 3:530, 4:88, 5:298, 6:68, 7:1, 8:1}
+```
+
+Its rank mass is 6706. The 560 helper residuals still have widths
+`{7:18, 8:154, 9:388}`. At nine stages and eight replicas,
+
+$$
+W=8\cdot8\cdot112=7168,\qquad
+D=8\bigl(8\cdot112-9\cdot64\bigr)=2560.
+$$
+
+These identities motivate the construction; they do not by themselves certify
+a globally usable supplier. The following placement and recount are essential.
+
+### 2. Every helper receives a complete legal physical owner
+
+The controller uses 72 complete invocations, ordered by
+`(7*stage + 6*replica, stage, replica)`. Every replica keeps its original event
+order. The new `inputs/OWNERS112.json.gz` supplies all **40,320** helper uses.
+
+The changed global template gives every helper one whole physical family.
+Within each invocation the 560 helper owners are distinct and avoid its
+224 active data families, so all **784 owners are different**. Helpers are
+never split among several registers.
+
+Owner windows are reconstructed from the actual controller, including bridge
+touches. Residual factors fit in actual pending axes; spectator coordinates
+are explicit and restored by the same normalized wrappers used in PR514.
+There are **3214 distinct actual orthogonal 73-column charts** and **349200
+covered pending axes**. Every uncovered pending factor remains a paid child.
+The literal remainder histogram is
+
+```text
+{3:3354, 5:3270, 7:60, 48:230}
+```
+
+Adding it to 72 copies of the local profile yields the complete global invoice:
+
+| Recursive rank r | Paid count H[r] |
+| ---: | ---: |
+| 1 | 182232 |
+| 2 | 11520 |
+| 3 | 41514 |
+| 4 | 6336 |
+| 5 | 24726 |
+| 6 | 4896 |
+| 7 | 132 |
+| 8 | 72 |
+| 48 | 230 |
+
+Its mass is **520704**, and
+
+$$
+73\cdot7168-520704=2560,\qquad 73^2=5329>2\cdot48^2=4608.
+$$
+
+The physical stock is `7168 + 8 + 560 + 2 = 7738`, including private center,
+reserved-tableau and coefficient work. The final construction has zero
+unhosted helper banks.
+
+### 3. The global number comes from the fully paid supplier
+
+Both independent rational moment implementations accept
+
+```text
+b = 1460074471110324279467 / 1000000000000000000000000
+```
+
+and reject `b + 10^-24`, including the retained exceptional-class fallback
+term. The unchanged cited PR493 bit profile is repriced by both engines at
+its published endpoint. The complex supplier remains the binding component.
+
+Six exact bootstrap stages and all **47 strict outer inequalities** then
+admit the stated global kappa. The adjacent `10^-18` kappa grid point and
+the invalid parameter controls `zero_eta`, `zero_beta`, `unit_beta` are
+rejected. This is an adjacent-grid check for this selected assembly, not an
+optimality claim over all constructions or parameters.
+
+The finite scalar and routing invoice is rebuilt for the new physical program:
+
+| Check | Required | Retained allowance |
+| --- | ---: | ---: |
+| Global coefficient prefix, bits | 206 | 512 |
+| Physical row coefficient | 16467 | 20161 |
+| Router bound, bits | 7984 | exponent 30000 |
+| Literal overhead, bits | 35282 | exponent 100000 |
+| C0 bound, bits | 200012 | exponent 210000 |
+
+All nine finite invoice checks pass. Constants and exact rational margins are
+preserved in the evidence rather than being inferred from a local percentage.
+
+## Independent validation and evidence
+
+The new source has two complementary global audits. The adapted physical
+checker verifies the emitted complete template. A separately written raw
+checker imports neither an emitter nor a hosting checker and does not read
+the nominated profile or nominated windows. It independently infers the port
+restriction, replays the two local programs over `Fraction`, rebuilds real
+charts and actual idle windows, validates all literal owners, and derives the
+same full histogram. `verify.py` requires their results to agree.
+
+The local replay checks every one of 784 arbitrary data/helper columns in both
+orientations, each containing 25,242 events. Thirteen local mutation controls
+are rejected. The exact local Clifford pass checks 968 frames, 2943 directed
+edges (a conservative superset of those used), and 224 port endpoint adapters, with global
+phases included. The edge recipe histogram is not used as the paid invoice.
+All twelve entrance-frame wrapper recipes are decoded independently, and five
+corrupted wrappers are rejected. The new global restriction audit rejects 13
+controls; the final owner/controller audit rejects 19 controls.
+
+The global data recipes are selected unchanged from the pinned predecessor:
+their actual vectors, stage and idle translations, and terminal corrections
+are compared exactly. The inherited data-phase derivation is not claimed as a
+new analytic or Lean proof. See `proof/GLOBAL-RESTRICTION.md` for this boundary.
+
+Useful files:
+
+- `EXPECTED.json`: concise exact expected result and structural counts.
+- `evidence/EXACT-ASSEMBLY.json`: both moments, bootstrap and 47 strict margins.
+- `evidence/INDEPENDENT112-RAW-AUDIT.json`: independently reconstructed operator,
+  charts, chronology, owners and paid profile.
+- `evidence/ASYNC-AUDIT.json`, `evidence/PREFIX-AND-INVOICE.json`: complete
+  physical template audit and finite invoice.
+- `evidence/hosted/GLOBAL-TEMPLATE.json.gz`: actual complete hosted template.
+- `evidence/local/`: local words, emitted programs, phase and wrapper evidence.
+- `PROOF.md`, `proof/`: conditional argument and detailed restriction reviews.
+
+## Scope and direct credits
+
+This is a **new checked finite conditional construction**. It retains the
+all-size compiler, common-label/mutable-basis realization, normalized Lemma A,
+restored-row, precision/tape and analytic-transfer interfaces. The restriction
+does not strengthen or prove these interfaces. No unconditional multiplication
+theorem, fresh Lean certification, universal optimum, or practical speedup is
+claimed. The unchanged PR493 bit operator is a cited dependency; this package
+reprices its histogram rather than reconstructing that operator.
+
+[PR514](https://github.com/CrocSwap/integer-mult-bounds/pull/514) supplies the
+pinned combined word, 92-pivot kernel and asynchronous construction.
+[PR507](https://github.com/CrocSwap/integer-mult-bounds/pull/507) supplies the
+partial-own factory and retiming reference;
+[PR484](https://github.com/CrocSwap/integer-mult-bounds/pull/484) and
+[PR496](https://github.com/CrocSwap/integer-mult-bounds/pull/496) supply the
+gauge/kernel, wrapper, whole-owner and invoice ancestry.
+[PR493](https://github.com/CrocSwap/integer-mult-bounds/pull/493) supplies the
+unchanged bit operator. The original notices preserve the other substantial
+geometry, compiler, retiming, wrapper and arithmetic contributions.
+`NOTICE.md`, `SOURCES.json` and the untouched `vendor/pr514/` notices distinguish
+new work, inherited ingredients, comparisons and excluded interfaces.
+
+The restricted intermediate parent is used as a data/controller scaffold.
+Its legacy bank-padding display is not a proof of an executable bank program;
+the final template has no bank families, and its complete costs are audited
+from its actual whole owners and remainders. This is explained in the global
+restriction proof. The final witness uses no disputed split-residual interface.
diff --git a/research/ranksector112-async/vendor/pr523/REPRODUCTION.json b/research/ranksector112-async/vendor/pr523/REPRODUCTION.json
new file mode 100644
index 0000000000..03062aa830
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/REPRODUCTION.json
@@ -0,0 +1,17 @@
+{
+  "status": "PASS_COMPLETE_COLD_RECONSTRUCTION",
+  "command": "python -B verify.py --work /absolute/path/to/a-new-output-directory",
+  "launch_directory": "/tmp",
+  "python": "3.12.14 (main, Aug 25 2026, 14:00:49) [Clang 22.1.3 ]",
+  "platform": "linux",
+  "zlib_runtime": "1.3.2",
+  "top_level_stages": 14,
+  "nested_predecessor_stages": 13,
+  "seconds": 650.614535019,
+  "kappa": "182243220215421/125000000000000000",
+  "complex_template_sha256": "2ae6ac3aff97a861d037ee51d6dcdd7bfe79ecbb0d8f1e186754428abc997a99",
+  "serialization_fix_preserved_all_executable_template_fields": true,
+  "current_primary_evidence": "evidence/COLD-REPLAY.json",
+  "all_math_code_and_inputs_present": true,
+  "scope": "The complete code pipeline and newly generated artifacts passed. Documentation, optional discovery sources, and this receipt are finalized after the numerical replay. No other OS or Python version was executed."
+}
diff --git a/research/ranksector112-async/vendor/pr523/SOURCES.json b/research/ranksector112-async/vendor/pr523/SOURCES.json
new file mode 100644
index 0000000000..385a202fbc
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/SOURCES.json
@@ -0,0 +1,118 @@
+{
+  "prepared_at_utc": "2026-10-12T00:00:25Z",
+  "repository": "https://github.com/CrocSwap/integer-mult-bounds",
+  "new_contribution": "Exact 112-port direct-sum restriction, new complete physical whole-owner allocation, independent raw geometric/chronological audit and exact global assembly.",
+  "baseline": {
+    "pr": 514,
+    "author": "Dugongue",
+    "head_repository": "Dugongue/integer-mult-bounds",
+    "head": "246bfacd4cb4072836ae3147099f548bb728229f",
+    "source_path": "research/partial-kernel92-async",
+    "local_path": "vendor/pr514",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/514",
+    "kappa": "1391523459591829/1000000000000000000",
+    "manifest_sha256": "4e6ffc149df6515f330d984e99b86e7d1deef01ed2bbac24bba3f19708f36c02"
+  },
+  "pinned_bit_supplier": {
+    "pr": 493,
+    "author": "eumemic",
+    "head": "c3a9a436b84fe44fdc223a5784d84736d1c2d3c7",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/493",
+    "scope": "Published profile repriced; unchanged operator cited, not freshly rebuilt."
+  },
+  "comparison_only": [
+    {
+      "pr": 518,
+      "author": "Dugongue",
+      "head": "e0a071dce251eeca96d446f73147048cfebbd5c7",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/518",
+      "kappa": "1393662920776407/1000000000000000000",
+      "created_at": "2026-10-11T23:50:50Z",
+      "role": "Newer comparable numerical report observed during packaging; no added pair choices, 99-pivot word, or owner transport copied."
+    },
+    {
+      "pr": 519,
+      "head": "ffd3c48a80ba8b579dc300e785e387fe8acddfef",
+      "role": "Automatic-width binary counting formalization; public context only."
+    },
+    {
+      "pr": 517,
+      "head": "65518fcff5a7bd490365273ae5469a82aac14853",
+      "kappa": "0.001389125582984265",
+      "role": "Smaller asynchronous result and fixed-word packing ceiling; no code adopted."
+    },
+    {
+      "pr": 516,
+      "head": "1c6b6ff9366a94e1f86a6c5d661a7df75c6ff814",
+      "role": "Lemma A Lean realization, updated during work; formal context only, not recompiled or used as a newly discharged interface.",
+      "first_observed_head": "871b1c51e53918c5e6c945dfe8ef45546c17da56"
+    },
+    {
+      "pr": 510,
+      "head": "64edee18af02aab0c1696b677a0287dd0146381b",
+      "role": "Larger nonbinding bit rate; not adopted."
+    },
+    {
+      "pr": 520,
+      "head": "6077fa76950facbce11ec2f04dfbc93493114a44",
+      "author": "higherbeing",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/520",
+      "role": "Open asynchronous allocator and delivery map. Viewed only during the final comparison refresh; no code or claimed gain adopted. No larger global kappa stated."
+    }
+  ],
+  "retained_ancestry": [
+    {
+      "pr": 496,
+      "head": "00cf70efd6a8637531deafef698157ca83e249ee",
+      "role": "whole-owner parent, invoice and assembly ancestry"
+    },
+    {
+      "pr": 484,
+      "head": "035845ce95f31d0a2dcfb42b8c8e13411271fa5f",
+      "role": "PR496 pinned gauge80-kernel42 parent, not newer moving head"
+    },
+    {
+      "pr": 493,
+      "head": "c3a9a436b84fe44fdc223a5784d84736d1c2d3c7",
+      "role": "unchanged cited R489 bit supplier"
+    },
+    {
+      "pr": 502,
+      "head": "4d30b8322184598e65e90a92389e17e1baedd9eb",
+      "role": "retiming transfer constructor and PR495 schedule fixture"
+    },
+    {
+      "pr": 501,
+      "head": "1dc056496fdbbc74073ed26d948a2dc235dbf356",
+      "role": "parallel retiming integration; credited, no duplicated gain"
+    },
+    {
+      "pr": 473,
+      "head": "628b454d3df00367d2d4f78de7d4eb9cbcbd47ca",
+      "role": "single-helper gauge withdrawal inspiration"
+    },
+    {
+      "pr": 507,
+      "head": "8d4444cf8a16d500cbb94add6e4fa8bcfb9c7d5e",
+      "role": "partial-own factory, 84-pivot reference and retiming map"
+    },
+    {
+      "pr": 505,
+      "head": "4ee769c8e28837482272b5f4742497da8e2fc9d4",
+      "role": "Complete-invocation asynchronous scheduling",
+      "author": "Dugongue"
+    },
+    {
+      "pr": 506,
+      "head": "a4948baee6c7ea35323db74ff636620c6af2925a",
+      "role": "public asynchronous retiming comparison and portability feedback"
+    }
+  ],
+  "original_additional_credits_file": "vendor/pr514/NOTICE.md",
+  "excluded_interfaces": {
+    "494": "Disputed residual splitting is not used.",
+    "499": "Larger claimed number using the disputed split-residual interface is not a proof ingredient."
+  },
+  "last_public_comparison_utc": "2026-10-12T00:09:14Z",
+  "public_snapshot": "evidence/PUBLIC-SNAPSHOT.json"
+}
diff --git a/research/ranksector112-async/vendor/pr523/code/assemble.py b/research/ranksector112-async/vendor/pr523/code/assemble.py
new file mode 100644
index 0000000000..a234aecb14
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/code/assemble.py
@@ -0,0 +1,42 @@
+"""Two exact moment engines and strict outer composition of a new PR484 rehosting
+with the unchanged published PR493 bit supplier. Prepared by OpenAI Codex; arithmetic
+engines are pinned inherited PR361/Mercator and independent base-two code.
+Usage: assemble_candidate.py AUDIT_OUT PARENT_VARIANT HOSTED BIT_RESULT
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+import json,gzip,sys,hashlib,importlib.util
+O,V,H,B=map(Path,sys.argv[1:5]);sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+def load(n):
+ p=V/'work/pr361/code/engines'/(n+'.py');s=importlib.util.spec_from_file_location('candidate_'+n,p);m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m
+M,Other,Outer=[load(n)for n in ['moment','base_two_moment','outer']]
+owner=json.loads((O/'OWNERS-AND-PROFILE.json').read_text());inv=json.loads((O/'PREFIX-AND-INVOICE.json').read_text());host=json.loads((H/'HOSTED.json').read_text());bit=json.loads(B.read_text())["eleven"];P={int(r):n for r,n in owner['paid_profile'].items()};m,W=73,owner['live'];assert m*W-sum(r*n for r,n in P.items())==2560
+rc=M.certify(P,m,W,True);b=Q(rc['lower']);bp=Q(rc['upper']);assert bp-b==Q(1,10**24)
+fallback=32*m*m*sum(P.values());receipts=[]
+for z,accept in[(b,True),(bp,False)]:
+ ml,mh=M.moment(P,m,W,z,True);a,c=Other.moment(m,W,list(P.items()),z);d,e=Other.moment(m,W,[(1,fallback)],z);a+=d/10**16;c+=e/10**16
+ assert (mh<1 and c<1)if accept else(ml>1 and a>1)
+ receipts.append(dict(endpoint=str(z),mercator=[str(ml-1),str(mh-1)],base_two=[str(a-1),str(c-1)],accept=accept))
+# Reprice the cited unchanged bit histogram, clearly separate from bit operator verification.
+bitP={int(r):n for r,n in bit['profile'].items()};bitc=Q(bit['bit_lower']);bitnext=bitc+Q(1,10**24)
+for zz,accepted in [(bitc,True),(bitnext,False)]:
+ bl,bh=M.moment(bitP,78,9600,zz,True)
+ ol,oh=Other.moment(78,9600,list(bitP.items()),zz)
+ fl,fh=Other.moment(78,9600,[(1,32*78*78*sum(bitP.values()))],zz)
+ assert (bh<1 and oh+fh/10**16<1) if accepted else (bl>1 and ol+fl/10**16>1)
+c=Q(bit['bit_lower']);eta=beta=Q(1,10**18);grid=Q(1,10**18);s=min(c,(1-beta)*b)-Q(1,10**24)
+assert 0<s<c and s<(1-beta)*b
+coeff=int(bit['bit']['charged_three_level_coefficient_bits']);row=max(20161,int(bit['bit']['row_coefficient']),inv['finite']['physical_row_coefficient']);chain=[Q(384599,10**10)];cuts=[]
+def ceil(x):return -(-x.numerator//x.denominator)
+for i in range(6):
+ old=chain[-1];a=(1-s)*s+s*old;gap=min(s-a,1-a-s,1-a-s*(1-old),1-s);assert old<a<s<1-a and gap>0
+ cut=max(ceil(36/gap**2),ceil(2*(4+coeff)/gap));assert cut*gap**2>=36 and cut*gap>=2*(4+coeff);cuts.append(dict(gap=str(gap),cutoff_log2=str(cut)));chain.append(a)
+q=chain[-1]*(1-2*eta);margin=(1-eta)*q/(1+q);ticks=margin/grid;kap=grid*((ticks.numerator-1)//ticks.denominator)
+bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1},'rows':{'degree_gap':Q(10**6)-Q(51*row,25)}}
+a=Outer.assembly(chain[-1],b,bridge,kap,eta=eta,beta=beta);assert len(a['strict_constraints'])==47 and all(x>0 for x in a['strict_constraints'].values());controls=[]
+for name,k,e,be in [('next_grid',kap+grid,eta,beta),('zero_eta',kap,Q(0),beta),('zero_beta',kap,eta,Q(0)),('unit_beta',kap,eta,Q(1))]:
+ try:Outer.assembly(chain[-1],b,bridge,k,eta=e,beta=be)
+ except AssertionError:controls.append(name)
+ else:raise AssertionError(name)
+res=dict(status='PASS_ASYNC_COMPLEX_AND_CITED_BIT_EXACT_ASSEMBLY',complex_lower=str(b),complex_decimal=rc['lower'],next_b_rejected=str(bp),exact_moment_receipts=receipts,bit_lower=str(c),bit_result_sha256=sha(B),bit_template_sha256=bit['emitted_program_sha256'],bit_prefix_bits=bit['bit']['charged_prefix_bits'],bit_charged_three_level_coefficient_bits=coeff,external_row_allowance=row,kappa=str(kap),kappa_decimal=f'{float(kap):.18f}',binding_component='bit'if c<(1-beta)*b else'complex',strict_outer_constraints={k:str(v)for k,v in a['strict_constraints'].items()},outer_controls=controls,bootstrap=cuts,complex_template_sha256=host['template_sha256'],owner_audit_sha256=sha(O/'OWNERS-AND-PROFILE.json'),invoice_sha256=sha(O/'PREFIX-AND-INVOICE.json'),bit_scope='PR493 published profile and operator reused as a pinned dependency; this verifier reprices its published profile but does not reconstruct that unchanged bit operator.',scope='Conditional finite witness. Inherited compiler, precision/tape and analytic-transfer contracts remain assumed; changed-host operator admission recorded separately.')
+(O/'EXACT-ASSEMBLY.json').write_text(json.dumps(res,indent=2)+'\n');print(res['status'],'b',res['complex_decimal'],'kappa',res['kappa_decimal'],flush=True)
diff --git a/research/ranksector112-async/vendor/pr523/code/audit_112_independent.py b/research/ranksector112-async/vendor/pr523/code/audit_112_independent.py
new file mode 100644
index 0000000000..96897ec72d
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/code/audit_112_independent.py
@@ -0,0 +1,280 @@
+"""Independent raw-artifact audit of the 112-port restriction and whole owners.
+Prepared for icekylinx with GPT-6 Astra assistance.
+
+Does not import an emitter, hosting optimizer, nominated profile, nominated
+windows, or the adapted PR514 checker.  Inputs are the original checked local
+and global artifacts, the new literal local word/program, and 40,320 owners.
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+from collections import Counter, defaultdict
+from functools import lru_cache
+import argparse, gzip, hashlib, json, time
+
+ap=argparse.ArgumentParser()
+ap.add_argument('--original-base',type=Path,required=True)
+ap.add_argument('--local',type=Path,required=True)
+ap.add_argument('--owners',type=Path,required=True)
+ap.add_argument('--out',type=Path,required=True)
+a=ap.parse_args(); start_time=time.monotonic()
+
+def read(p):
+    data=p.read_bytes()
+    return json.loads(gzip.decompress(data) if p.suffix=='.gz' else data)
+def digest(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+def out(name,z):(a.out/name).write_text(json.dumps(z,indent=2,sort_keys=True)+'\n')
+a.out.mkdir(parents=True,exist_ok=True)
+old=read(a.original_base/'split-centres/CANONICAL-WORD.json.gz')
+new=read(a.local/'CANONICAL-WORD.json.gz')
+programs=read(a.local/'LOCAL-PROGRAMS.json.gz')
+parent=read(a.original_base/'split-centres/GLOBAL-TEMPLATE.json.gz')
+phase=read(a.original_base/'work/complex-nine-native/DATA-PHASES.json')
+roles=read(a.owners)
+V=new['v'];R=new['R'];N=2*V+R;H=new['h'];M=parent['m'];T=8
+assert (old['v'],V,R,H,M)==(120,112,560,9,73)
+
+# Infer the restriction from actual labels, not its producer's mapping file.
+assert len(set(new['ports']))==V and set(new['ports'])<set(old['ports'])
+kept=[i for i,q in enumerate(old['ports']) if q in set(new['ports'])]
+assert [old['ports'][i] for i in kept]==new['ports']
+rmp={oldi:newi for newi,oldi in enumerate(kept)}
+rmp.update({120+oldi:V+newi for newi,oldi in enumerate(kept)})
+rmp.update({240+h:2*V+h for h in range(R)})
+removed=set(range(240+R))-set(rmp)
+assert len(removed)==16 and new['frames']==old['frames']
+removed_ops=Counter()
+for name in ('A','B','precondition','compensation','cut','cleanup'):
+    result=[]
+    for event in old[name]:
+        rs=event[1:3] if event[0]=='add' else event[1:2]
+        if any(r in removed for r in rs):
+            assert name=='cut' and event[0]=='add'
+            assert event[1]==120+event[2] and event[3:5]==[1,1]
+            removed_ops[name]+=1
+            continue
+        z=event.copy();z[1]=rmp[z[1]]
+        if z[0]=='add':z[2]=rmp[z[2]]
+        result.append(z)
+    assert result==new[name],('not a literal restriction',name)
+assert removed_ops=={'cut':8}
+for name in ('start','final'):
+    assert new[name]==[old[name][r] for r in sorted(rmp,key=rmp.get)]
+assert new['centers']==[rmp[r] for r in old['centers'] if r in rmp]
+assert new['center_frames']==[f for r,f in zip(old['centers'],old['center_frames']) if r in rmp]
+assert new['target_levels']=={str(rmp[120+int(t)]-V):f for t,f in old.get('target_levels',{}).items()}
+frames=new['frames']
+
+@lru_cache(None)
+def subspace(i):
+    s={0}
+    for x in frames[i]:s|={y^x for y in s}
+    assert len(s)==1<<len(frames[i])
+    return frozenset(s)
+
+# Replay each literal local instruction, including all independent dirt columns.
+# Recursive events contribute one child only after their actual endpoint frames
+# have been checked. Scalar events are replayed as exact rational sparse rows.
+local_results={}
+for orientation,events in programs.items():
+    state={('L',r):{r:Q(1)} for r in range(N)}
+    cur={('L',r):new['start'][r] for r in range(N)}
+    private=set(); profile=Counter(); current_phase=None; macros=0
+    entries={r for r in range(2*V,N) if new['start'][r]!=0}
+    adapters_seen=set();residual_seen=set();last_scalar=-1;first_post=None
+    for event_index,event in enumerate(events):
+        tag=event[0]
+        if tag=='phase':current_phase=event[1];continue
+        if tag=='climb':
+            _,part,r,fr,to,rank=event
+            assert current_phase==part and cur['L',r]==fr
+            assert subspace(fr)<subspace(to) and rank==len(frames[to])-len(frames[fr])
+            cur['L',r]=to;profile[rank]+=1
+        elif tag=='center':
+            _,k,fr,to,rank=event;reg=('C',k)
+            assert current_phase=='centers' and reg in private and cur[reg]==fr
+            assert subspace(fr)<subspace(to) or subspace(to)<subspace(fr)
+            assert rank==abs(len(frames[to])-len(frames[fr]))
+            cur[reg]=to;profile[rank]+=1
+        elif tag=='adapter':
+            _,kind,r,f=event
+            assert (kind,r) not in adapters_seen;adapters_seen.add((kind,r))
+            if kind=='old_to_new':
+                assert current_phase=='entry_adapters' and r not in entries and f==new['start'][r]
+            else:
+                assert kind=='new_to_old' and current_phase=='exit_adapters' and f==new['final'][r]
+        elif tag=='residual_adapter':
+            _,kind,r,f=event
+            assert r in entries and f==new['start'][r] and (kind,r) not in residual_seen
+            residual_seen.add((kind,r))
+            if kind=='pre':assert current_phase=='entry_adapters'
+            else:
+                assert kind=='post' and current_phase=='full_frame_cleanup'
+                if first_post is None:first_post=event_index
+        elif tag=='scalar':
+            _,e,f=event;op=e[0];t=tuple(e[1]);macros+=1;last_scalar=event_index
+            if op in ('clear','copy'):
+                if op=='clear':
+                    if t in private:assert cur[t]==f;private.remove(t)
+                    state[t]={};cur[t]=f
+                else:
+                    source=tuple(e[2]);assert cur[source]==f
+                    assert not state.get(t,{}) and t not in private
+                    state[t]=state[source].copy();cur[t]=f;private.add(t)
+            else:
+                if t[0]=='C' and t not in private:
+                    assert not state.get(t,{})
+                    private.add(t);cur[t]=f
+                assert cur[t]==f,(orientation,current_phase,'target-frame',t,cur[t],f)
+                if op=='scale':
+                    q=Q(e[2],e[3]);assert q
+                    state[t]={j:q*x for j,x in state[t].items()}
+                else:
+                    assert op=='add';s=tuple(e[2]);assert t!=s and cur[s]==f
+                    q=Q(e[3],e[4]);row=state[t]
+                    for j,x in tuple(state[s].items()):
+                        z=row.get(j,Q(0))+q*x
+                        if z:row[j]=z
+                        else:row.pop(j,None)
+        else:raise AssertionError(('unknown local event',tag))
+    assert not private and all(not row for reg,row in state.items() if reg[0]=='C')
+    assert adapters_seen=={('old_to_new',r) for r in range(N) if r not in entries}|{('new_to_old',r) for r in range(N)}
+    assert residual_seen=={(kind,r) for kind in ('pre','post') for r in entries}
+    assert first_post is not None and first_post>last_scalar
+    for r in range(N):
+        desired={r:Q(1)}
+        if orientation=='forward' and V<=r<2*V:desired[r-V]=Q(1)
+        if orientation=='backward' and r<V:desired[V+r]=Q(-1)
+        assert state['L',r]==desired,(orientation,r)
+        assert cur['L',r]==new['final'][r]
+    local_results[orientation]={'events':len(events),'scalar_macros':macros,'columns':N,'profile':dict(sorted(profile.items()))}
+assert set(local_results)=={'forward','backward'}
+local=Counter(local_results['forward']['profile'])
+assert local==Counter(local_results['backward']['profile'])
+assert local==Counter({int(r):n for r,n in new['local_profile'].items()})
+widths=[H-len(frames[new['start'][2*V+h]]) for h in range(R)]
+assert Counter(widths)=={7:18,8:154,9:388}
+old_adapters=read(a.original_base/'split-centres/RESIDUAL-ADAPTERS.json')['recipes']
+new_adapters=read(a.local/'RESIDUAL-ADAPTERS.json')['recipes']
+for f in {new['start'][2*V+h] for h,w in enumerate(widths) if w<H}:
+    assert new_adapters[str(f)]==old_adapters[str(f)]
+
+# Derive the complete invocation order directly from its controller formula.
+order=sorted(((s,rep) for s in range(9) for rep in range(T)),key=lambda z:(7*z[0]+6*z[1],z[0],z[1]))
+pos_call={}; timeline=[]; blocks={};s=None
+for event in parent['execution_schedule']:
+    if event['kind'] in ('bank_padding_cover_sweep','translate_every_live_family'):continue
+    if event['kind']=='local_cover_sweep':s=event['stage'];blocks[s]=[]
+    assert s is not None;blocks[s].append(event)
+for tm,(stage,rep) in enumerate(order):
+    for e in blocks[stage]:
+        if e['kind']=='local_cover_sweep':pos_call[stage,rep]=len(timeline)
+        timeline.append((rep,e))
+assert len(pos_call)==72
+stage_pairs={e['stage']:e['pair'] for e in parent['recipe'] if e['kind']=='local'}
+child_rank={}
+for child in parent['idle_children']:
+    i=child['child'];r=child['rank']
+    assert i not in child_rank or child_rank[i]==r
+    child_rank[i]=r
+child_pair={};child_side={};windows={};last_touch={}
+for pos,(rep,e) in enumerate(timeline):
+    kind=e['kind']
+    if kind=='local_cover_sweep':last_touch[rep,stage_pairs[e['stage']]]=pos
+    elif kind=='bridge':
+        last_touch[rep,e['src']]=pos;last_touch[rep,e['dst']]=pos
+    elif kind=='idle_cover_sweep':
+        pair=e['pair']
+        for side,i in enumerate(e['child_indices']):
+            if i in child_rank:
+                child_pair[i]=pair;child_side[i]=side
+                windows[rep,i]=(last_touch.get((rep,pair),-1),pos)
+assert len(windows)==T*len(child_rank)
+
+# Construct the actual orthogonal port charts by a transvection. Each chosen
+# pending vector is checked as a vector, not merely a nominal offset.
+phase_by_q={z['q']:z for z in phase['recipes']}
+assert len(phase_by_q)==120
+charts=[];idle_vectors={}
+for port,q in enumerate(new['ports']):
+    z=next(i for i in range(H) if not(q>>i)&1)
+    a0=q^(1<<z);assert a0.bit_count()%2==0
+    local_order=[z]+[i for i in range(H) if i!=z]
+    # Only q needs to be first. Match the inherited chart's remaining order
+    # by swapping z with 0, which is part of the fixed chart convention.
+    local_order=list(range(H));local_order[0],local_order[z]=local_order[z],local_order[0]
+    B=[(1<<i)^(a0 if (a0>>i)&1 else 0) for i in local_order]+[1<<i for i in range(H,M)]
+    assert B[0]==q and len(set(B))==M
+    assert all(((x&y).bit_count()&1)==int(i==j) for i,x in enumerate(B) for j,y in enumerate(B))
+    charts.append(B)
+    pr=phase_by_q[q]
+    for i,rank in child_rank.items():
+        axes=pr['idle_children'][i]['orthogonal_axes']
+        assert len(axes)==rank==pr['idle_children'][i]['rank'] and all(x in B for x in axes)
+        assert len(set(axes))==rank
+        idle_vectors[port,i]=axes
+
+# Every complete invocation contains all active data owners and exactly one
+# assigned whole physical owner for every helper. Check full-family exclusion.
+by_call=defaultdict(list);used=defaultdict(set);role_ids=set();family_roles=Counter();chart_hashes=set()
+for role in roles:
+    s,rep,h=role['stage'],role['replica'],role['helper']
+    assert (s,rep,h) not in role_ids;role_ids.add((s,rep,h))
+    assert 0<=h<R and role['time']==order.index((s,rep))
+    fam=role['family'];orep,remainder=divmod(fam,8*V)
+    pairside,port=divmod(remainder,V);pair,side=divmod(pairside,2)
+    assert 0<=orep<T and role['owner_replica']==orep and role['port']==port
+    assert role['copy']==orep*V+port
+    i=role['child'];off=role['offset'];width=role['width']
+    assert pair==child_pair[i] and side==child_side[i]
+    assert width==widths[h] and 0<=off and off+width<=child_rank[i]
+    lo,hi=windows[orep,i];assert lo<pos_call[s,rep]<hi
+    occupied=set(range(off,off+width));key=(orep,i,port)
+    assert not used[key]&occupied
+    used[key]|=occupied;family_roles[fam]+=1;by_call[s,rep].append(fam)
+    B=charts[port];actual=idle_vectors[port,i][off:off+width]
+    assert len(actual)==width
+    first=[B.index(x) for x in actual]
+    spectators=[j for j in range(M) if j not in first][:H-width]
+    orderB=first+spectators+[j for j in range(M) if j not in first+spectators]
+    assert len(orderB)==len(set(orderB))==M and len(first+spectators)==H
+    sigma=[B[j] for j in orderB]
+    assert sigma[:width]==actual
+    # All pairwise products inherit the already checked orthonormal basis.
+    assert len(set(sigma))==M and set(sigma)==set(B)
+    chart_hashes.add(hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest())
+assert role_ids=={(s,rep,h) for s in range(9) for rep in range(T) for h in range(R)}
+for (s,rep),helpers in by_call.items():
+    active={rep*(8*V)+(2*stage_pairs[s]+side)*V+p for side in (0,1) for p in range(V)}
+    assert len(active)==2*V and len(helpers)==R and len(set(helpers))==R
+    assert not active&set(helpers)
+    assert len(active|set(helpers))==N
+
+# Recount every paid child from the literal local programs and the unused
+# source idle axes. Never consume a nominated histogram or residual count.
+paid=Counter({r:n*len(order) for r,n in local.items()});remainders=Counter();covered=0
+for orep in range(T):
+    for port in range(V):
+        for i,rank in child_rank.items():
+            cells=used[orep,i,port]
+            assert cells==set(range(len(cells)))
+            covered+=len(cells);left=rank-len(cells)
+            assert left>=0
+            if left:paid[left]+=1;remainders[left]+=1
+stock=T*8*V;mass=sum(r*n for r,n in paid.items());deficit=M*stock-mass
+assert covered==len(order)*sum(widths)
+assert deficit==T*((9-1)*V-9*sum(len(frames[f]) for f in new['center_frames']))
+assert M*M>2*max(paid)**2
+result={
+ 'status':'PASS_INDEPENDENT_RAW_112_RESTRICTION_LOCAL_COLUMNS_CHARTS_WINDOWS_OWNERS_AND_PROFILE',
+ 'inputs':{str(p):digest(p) for p in [a.original_base/'split-centres/CANONICAL-WORD.json.gz',a.original_base/'split-centres/GLOBAL-TEMPLATE.json.gz',a.original_base/'work/complex-nine-native/DATA-PHASES.json',a.local/'CANONICAL-WORD.json.gz',a.local/'LOCAL-PROGRAMS.json.gz',a.local/'RESIDUAL-ADAPTERS.json',a.owners]},
+ 'local':local_results,'deleted_scalar_operations':dict(removed_ops),'deleted_canonical_ports':sorted(set(range(120))-set(kept)),
+ 'v':V,'helpers':R,'live':stock,'physical':stock+len(new['centers'])+R+2,
+ 'deficit':deficit,'rank_mass':mass,'paid_profile':dict(sorted(paid.items())),
+ 'residual_widths':dict(Counter(widths)),'whole_owner_roles':len(roles),'invocations':len(order),
+ 'all_owners_per_call_distinct':N,'pending_axes_covered':covered,'idle_remainders':dict(sorted(remainders.items())),
+ 'actual_orthogonal_charts':len(chart_hashes),'same_local_frames_and_residual_wrappers_as_PR514':True,
+ 'no_nominated_profile_or_windows_used':True,'no_emitter_or_hosting_checker_imported':True,
+ 'seconds':time.monotonic()-start_time,
+ 'scope':'Independent finite restriction, all rational scalar columns, nested local frames, fixed whole-owner schedule, actual port charts and paid histogram. The inherited all-size/compiler, common-label realization, precision/tape and analytic transfer interfaces remain conditions.'}
+out('INDEPENDENT112-RAW-AUDIT.json',result)
+print(json.dumps(result,indent=2))
diff --git a/research/ranksector112-async/vendor/pr523/code/audit_async.py b/research/ranksector112-async/vendor/pr523/code/audit_async.py
new file mode 100644
index 0000000000..9f6322ce0e
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/code/audit_async.py
@@ -0,0 +1,149 @@
+"""OpenAI Codex independent serialized ASYNCHRONOUS controller/spectator audit.
+Imports no emitter, optimizer, expander, edge-coloring, or source hosting code.
+CLI: VERIFIED_VARIANT POOLED_HOSTED OUT.json
+The local provider is read from VERIFIED_VARIANT, never from a baseline width histogram.
+"""
+import sys,json,gzip,hashlib,copy
+from pathlib import Path
+from collections import Counter,defaultdict
+BASE,OUT,REPORT=map(lambda p:Path(p).resolve(),sys.argv[1:4]);read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+parent=read(BASE/'split-centres/GLOBAL-TEMPLATE.json.gz');canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz');checks=read(BASE/'split-centres/LOCAL-CHECKS.json');ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json');ct=read(OUT/'GLOBAL-TEMPLATE.json.gz');summary=read(OUT/'HOSTED.json');V=canon['v'];R=canon['R'];N=2*V+R;CENTRES=len(canon['centers']);assert V==112 and canon['h']==9; width=[9-len(canon['frames'][canon['start'][2*V+h]])for h in range(R)];prank={e['child']:e['rank']for e in parent['idle_children']};M=73;T=8;DATA=8*T*V;PHYSICAL=DATA+CENTRES+R+2;CALLS=72;HOSTED=CALLS*R
+
+def orthobasis(port):
+ q=canon['ports'][port];z=next(i for i in range(9)if(q>>i)&1==0);a=q^(1<<z);order=list(range(9));order[z],order[0]=order[0],order[z]
+ b=[(1<<i)^(a if a>>i&1 else 0)for i in order]+[1<<i for i in range(9,73)]
+ assert len(b)==73 and all((x&y).bit_count()%2==int(i==j)for i,x in enumerate(b)for j,y in enumerate(b));return b
+bases=[orthobasis(p)for p in range(V)]
+# Bind the selected provider's actual normalization recipes, including newly
+# selected entrance frames; a baseline recipe registry cannot silently survive.
+required_artifacts={'split-centres/CANONICAL-WORD.json.gz','split-centres/LOCAL-PROGRAMS.json.gz','split-centres/LOCAL-CHECKS.json','split-centres/RESIDUAL-ADAPTERS.json','work/complex-nine-native/DATA-PHASES.json'}
+assert required_artifacts <= set(summary['source_artifacts'])
+adapter_path=BASE/'split-centres/RESIDUAL-ADAPTERS.json'
+assert hashlib.sha256(adapter_path.read_bytes()).hexdigest()==parent['residual_adapter_sha256']
+adapters=read(adapter_path)['recipes']
+for h,w in enumerate(width):
+ if w<9:
+  f=canon['start'][(2*V)+h];a=adapters[str(f)]
+  assert a['frame']==f and a['vectors']==canon['frames'][f] and a['rank']==w and a['entrance_rank']==9-w
+
+def audit(t):
+ assert(t['live'],t['physical'])==(DATA,PHYSICAL)
+ assert t['local_programs']==parent['local_programs']and t['recipe']==parent['recipe']and 'each local invocation completes before the next' in t['loop_order'].lower()
+ assert len(t['calls'])==72 and t['hosting']['max_helpers_per_physical_family_per_call']==1 and t['hosting']['banks']==[0]*9
+ for key in('exact_data_phase_recipe_sha256','exact_local_clifford_recipe_sha256','residual_adapter_sha256','adapter_policy'):assert t[key]==parent[key]
+ # Independently project the literal schedule onto every data replica.
+ src=parent['execution_schedule'];assert t['async_schedule']['source_schedule']==src
+ assert t['async_schedule']['source_call_order']==[[c['stage'],c['replica']]for c in parent['calls']]
+ order=[(c['stage'],c['replica'])for c in t['calls']]
+ assert [list(x)for x in order]==t['async_schedule']['order'] and len(set(order))==72
+ all_local=[];perrep={r:[]for r in range(8)};globals_=[]
+ for e in t['execution_schedule']:
+  j=e['source_event'];old=copy.deepcopy(src[j])
+  if 'replica'in e:
+   r=e['replica'];assert 0<=r<8 and j<30;perrep[r].append(j)
+   expected=old|dict(source_event=j,replica=r,replicas=[r],time=e['time'])
+   assert e==expected
+   assert 0<=e['time']<72 and order[e['time']][1]==r
+   if e['kind']=='local_cover_sweep':
+    assert order[e['time']]==(e['stage'],r);all_local.append((e['stage'],r,e['time']))
+  else:
+   globals_.append(j);expected=old|dict(source_event=j)
+   if e['kind']=='bank_padding_cover_sweep':expected['families']=[DATA,DATA]
+   if e['kind']=='translate_every_live_family':expected.update(families=[0,DATA],charged_calls_per_cover=DATA)
+   assert e==expected
+ assert all(v==list(range(30))for v in perrep.values()) and globals_==[30,31]
+ assert all_local==[(st,r,i)for i,(st,r)in enumerate(order)]
+ assert all('replica'in e for e in t['execution_schedule'][:-2])
+ assert [e['source_event']for e in t['execution_schedule'][-2:]]==[30,31]
+ # Local cover calls are indivisible; a block then runs the source events
+ # up to that replica's next local invocation.
+ block=-1
+ for e in t['execution_schedule'][:-2]:
+  if e['kind']=='local_cover_sweep':block+=1
+  assert e['time']==block
+ assert t['bank_padding']==dict(parent['bank_padding'],families=[])
+ assert t['cover_final_correction']==dict(parent['cover_final_correction'],families=[0,DATA],charged_calls_per_cover=DATA)
+ assert t['private_namespace']=={'centers':[DATA,DATA+CENTRES],'reserved_tableau':[DATA+CENTRES,DATA+CENTRES+R],'coefficient':[DATA+CENTRES+R,PHYSICAL]}
+ # Actual physical touch intervals include every individual bridge.
+ pairs={};sides={};windows={};last={};callpos={};stagepair={e['stage']:e['pair']for e in parent['recipe']if e['kind']=='local'}
+ for pos,e in enumerate(t['execution_schedule']):
+  if 'replica'not in e:continue
+  rep=e['replica']
+  if e['kind']=='local_cover_sweep':
+   pair=stagepair[e['stage']];callpos[e['stage'],rep]=pos;last[rep,pair]=pos
+  elif e['kind']=='bridge':last[rep,e['src']]=last[rep,e['dst']]=pos
+  elif e['kind']=='idle_cover_sweep':
+   for side,i in enumerate(e['child_indices']):
+    if i not in prank:continue
+    pairs[i]=e['pair'];sides[i]=side;windows[rep,i]=(last.get((rep,e['pair']),-1),pos)
+ used=defaultdict(set);roles={};paid=Counter();sigmas={};digest=hashlib.sha256();entering=0;cross=0;touches=defaultdict(list)
+ for call in t['calls']:
+  old=next(z for z in parent['calls']if(z['stage'],z['replica'])==(call['stage'],call['replica']))
+  assert {k:v for k,v in call.items()if k not in('owners','time')}=={k:v for k,v in old.items()if k!='owners'}
+  s,rep,pair=call['stage'],call['replica'],call['pair'];assert call['time']==t['async_schedule']['order'].index([s,rep]);own=call['owners'];assert len(own)==N and len({f for f,rt in own})==N and all(0<=f<DATA for f,rt in own)
+  assert own[:(2*V)]==old['owners'][:(2*V)]
+  for h,(family,route)in enumerate(own[(2*V):]):
+   w=width[h];typ,i,off=route[:3];ownerrep,sub=divmod(family,(8*V));fampair,sub=divmod(sub,(2*V));side,port=divmod(sub,V)
+   assert windows[ownerrep,i][0]<callpos[s,rep]<windows[ownerrep,i][1] and fampair==pairs[i] and side==sides[i] and 0<=off and off+w<=prank[i]
+   B=bases[port];pend=[int(x)for x in ph['recipes'][port]['idle_children'][i]['orthogonal_axes']];assert len(pend)==prank[i]
+   occ=[B.index(v)for v in pend[off:off+w]];sp=[j for j in range(M)if j not in occ][:9-w]
+   assert route==([3,i,off]if w==9 else[4,i,off,w,sp]);assert len(set(occ+sp))==9
+   order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert sorted(order)==list(range(M));sigma=[B[j]for j in order]
+   assert sigma[:w]==pend[off:off+w]and sigma[w:9]==[B[j]for j in sp]
+   sh=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sh]=sigma;digest.update(json.dumps([s,rep,h,family,sh],separators=(',',':')).encode()+b'\n')
+   key=(i,ownerrep,port);cells=set(range(off,off+w));assert not used[key]&cells;used[key]|=cells
+   role=(s,rep,h);assert role not in roles;roles[role]=dict(stage=s,replica=rep,helper=h,family=family,owner_replica=ownerrep,child=i,copy=ownerrep*V+port,port=port,offset=off,width=w)
+   touches[family].append((s,rep,h));entering+=w<9;cross+=rep!=ownerrep
+  for r,n in checks[call['orientation']]['paid_profile'].items():paid[int(r)]+=n
+ assert set(roles)=={(s,rep,h)for s in range(9)for rep in range(8)for h in range(R)}
+ # The frozen pooled metadata must bind the actual serialized owner maps.
+ assert len(t['hosting']['pooled_slots'])==HOSTED
+ for z in t['hosting']['pooled_slots']:
+  key=(z['stage'],z['replica'],z['helper']);assert key in roles
+  assert {k:z[k]for k in roles[key]}==roles[key]
+ assert len({(z['stage'],z['replica'],z['helper'])for z in t['hosting']['pooled_slots']})==HOSTED
+ rem={};wanted=[]
+ for old in parent['idle_children']:
+  i,port=old['child'],old['port']
+  for rep in range(T):
+   u=used[i,rep,port];assert u==set(range(len(u)));r=old['rank']-len(u)
+   if r:
+    f=rep*(8*V)+(2*pairs[i]+sides[i])*V+port;wanted.append(dict(child=i,port=port,replica=rep,replicas=1,family=f,rank=r,hosted=len(u),pending_offset=len(u)));paid[r]+=1
+ assert t['idle_children']==wanted
+ mass=sum(r*n for r,n in paid.items());assert73=73*DATA-mass;assert assert73==2560 and 73**2>2*max(paid)**2
+ return dict(profile=dict(sorted(paid.items())),mass=mass,hosted=HOSTED,entering=entering,cross_replica=cross,sigma_digest=digest.hexdigest(),sigmas=sigmas,idle_remainders=len(wanted),busy_family_checks=len(roles),invocations=72)
+
+r=audit(ct);raw=gzip.decompress((OUT/'GLOBAL-TEMPLATE.json.gz').read_bytes());assert hashlib.sha256(raw).hexdigest()==summary['template_sha256'];assert r['profile']=={int(k):v for k,v in summary['global_profile'].items()};assert r['sigmas']==read(OUT/'ACTUAL-SIGMAS.json.gz');assert r['sigma_digest']==summary['sigma_stream_sha256']
+assert all(hashlib.sha256((BASE/name).read_bytes()).hexdigest()==value for name,value in summary['source_artifacts'].items())
+controls=[]
+def reject(name,mut):
+ q=copy.deepcopy(ct);mut(q)
+ try:audit(q)
+ except(AssertionError,KeyError,IndexError,ValueError,TypeError):controls.append(name)
+ else:raise AssertionError('ACCEPTED '+name)
+reject('wrong call time',lambda q:q['calls'][0].__setitem__('time',71))
+enter=lambda q:next(o for c in q['calls']for o in c['owners'][(2*V):]if o[1][0]==4)
+reject('alias two whole owners',lambda q:q['calls'][0]['owners'].__setitem__((2*V+1),q['calls'][0]['owners'][(2*V)]))
+reject('helper on active data family',lambda q:q['calls'][0]['owners'][(2*V)].__setitem__(0,q['calls'][0]['owners'][0][0]))
+reject('owner in private namespace',lambda q:q['calls'][0]['owners'][(2*V)].__setitem__(0,DATA))
+reject('unbound change of owner replica',lambda q:q['calls'][0]['owners'][(2*V)].__setitem__(0,(q['calls'][0]['owners'][(2*V)][0]+(8*V))%DATA))
+reject('omit complete invocation',lambda q:q['calls'].pop())
+reject('reorder invocation replicas',lambda q:q['calls'].__setitem__(0,q['calls'][1]))
+reject('interleave local invocations',lambda q:q.__setitem__('loop_order','interleaved local instructions'))
+reject('change local instruction stream',lambda q:q['local_programs']['forward'].pop())
+reject('wrong residual width',lambda q:enter(q)[1].__setitem__(3,enter(q)[1][3]-1))
+reject('wrong spectator coordinate',lambda q:enter(q)[1][4].__setitem__(0,72))
+reject('omit spectator route',lambda q:enter(q).__setitem__(1,enter(q)[1][:3]))
+reject('overlap residual footprint',lambda q:q['calls'][0]['owners'][(2*V)][1].__setitem__(2,100))
+reject('omit idle remainder',lambda q:q['idle_children'].pop())
+reject('underpay idle remainder',lambda q:q['idle_children'][0].__setitem__('rank',0))
+reject('omit bridge touch',lambda q:q['execution_schedule'].pop(next(i for i,e in enumerate(q['execution_schedule'])if e['kind']=='bridge')))
+reject('remove one-owner rule',lambda q:q['hosting'].pop('max_helpers_per_physical_family_per_call'))
+reject('duplicate frozen role',lambda q:q['hosting']['pooled_slots'].__setitem__(1,q['hosting']['pooled_slots'][0]))
+reject('understate physical reserve',lambda q:q.__setitem__('physical',PHYSICAL-1))
+report=dict(status='PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS',template_sha256=summary['template_sha256'],complex_template_sha256=summary['template_sha256'],complex_live=DATA,complex_profile=r['profile'],complex_hosted_residuals=HOSTED,physical=PHYSICAL,rank_mass=r['mass'],deficit=2560,entering_helper_roles=r['entering'],cross_replica_helper_roles=r['cross_replica'],one_owner_per_complete_invocation=True,helper_busy_family_window_checks=r['busy_family_checks'],complete_invocations=r['invocations'],actual_orthogonal_73column_maps=len(r['sigmas']),actual_sigma_stream_sha256=r['sigma_digest'],all_actual_residual_and_spectator_charts=True,idle_remainders=r['idle_remainders'],mutations_rejected=controls,widths=dict(sorted(Counter(width).items())),scope='Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses unchanged source local program and normalized residual-wrapper identities; all-size compilation and complete coefficient invoice are separate inherited obligations.')
+REPORT.write_text(json.dumps(report,indent=2)+'\n');print(json.dumps(report,indent=2))
+
+owners=dict(status='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE',template_sha256=summary['template_sha256'],paid_profile=r['profile'],live=DATA,physical=PHYSICAL,rank_mass=r['mass'],deficit=2560,hosted_residuals=HOSTED,banked_residuals=0,all_784_owners_per_call_distinct=True,actual_helper_owner_charts=HOSTED,actual_73column_sigmas=len(r['sigmas']),cross_replica_helper_roles=r['cross_replica'],explicit_idle_remainder_children=r['idle_remainders'],source_idle_children_charged=sum(x['replicas']for x in parent['idle_children']),source_artifacts=summary['source_artifacts'],controller_audit_sha256=hashlib.sha256(REPORT.read_bytes()).hexdigest())
+(REPORT.parent/'OWNERS-AND-PROFILE.json').write_text(json.dumps(owners,indent=2)+'\n')
+
diff --git a/research/ranksector112-async/vendor/pr523/code/audit_async_invoice.py b/research/ranksector112-async/vendor/pr523/code/audit_async_invoice.py
new file mode 100644
index 0000000000..9a2b15f35a
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/code/audit_async_invoice.py
@@ -0,0 +1,100 @@
+"""Async PR484 scalar/prefix lowering and finite overcharge recount. OpenAI Codex.
+Reads emitted programs, canonical word and raw routes, importing no supplier code.
+Inherited all-size compiler admissibility is a condition, not inferred here.
+"""
+from pathlib import Path
+from fractions import Fraction as F
+from collections import Counter
+import gzip,json,math,hashlib
+import sys
+O=Path(sys.argv[1]);V=Path(sys.argv[2]);HOSTED=Path(sys.argv[3])
+def read(p):return json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+w=read(V/'split-centres/CANONICAL-WORD.json.gz');p=read(V/'split-centres/LOCAL-PROGRAMS.json.gz');old=read(V/'split-centres/GLOBAL-TEMPLATE.json.gz');new=read(HOSTED/'GLOBAL-TEMPLATE.json.gz');integ=read(V/'split-centres/INTEGRATION.json');checks=read(V/'split-centres/LOCAL-CHECKS.json');prior=read(V/'split-centres/INDEPENDENT-REPLAY.json');owners=read(O/'OWNERS-AND-PROFILE.json')
+VV=w['v'];R=w['R'];N=2*VV+R;M=73;L=9;T=8;K=4
+assert VV==112 and w['h']==9
+PAYLOAD=512
+control=read(O/'ASYNC-AUDIT.json')
+raw=gzip.decompress((HOSTED/'GLOBAL-TEMPLATE.json.gz').read_bytes());th=hashlib.sha256(raw).hexdigest()
+assert th==control['complex_template_sha256']==owners['template_sha256']
+assert control['one_owner_per_complete_invocation'] and control['complete_invocations']==72
+assert new['local_programs']==old['local_programs'] and new['recipe']==old['recipe']
+assert Counter(c['orientation']for c in new['calls'])==Counter(c['orientation']for c in old['calls'])
+local={}
+for ori,evs in p.items():
+ rows={('L',i):{i:F(1)}for i in range(N)};env={('L',i):F(1)for i in range(N)};peak=F(1);real=macros=0;paid=Counter();workops=0
+ for e in evs:
+  if e[0]=='climb':paid[e[5]]+=1
+  elif e[0]=='center':paid[e[4]]+=1
+  elif e[0]=='scalar':
+   macros+=1;x=e[1];op=x[0];a=tuple(x[1]);count=0
+   if op=='clear':rows[a]={};env[a]=F(0);count=1
+   elif op=='copy':rows[a]=dict(rows[tuple(x[2])]);env[a]=env[tuple(x[2])];count=1
+   elif op=='scale':
+    q=F(x[2],x[3]);num,den=abs(q.numerator),q.denominator
+    assert num and num&(num-1)==0 and den&(den-1)==0
+    rows[a]={j:q*v for j,v in rows[a].items()};env[a]*=abs(q)
+    count=abs(num.bit_length()-den.bit_length())+int(q<0)
+   elif op=='add':
+    b=tuple(x[2]);q=F(x[3],x[4]);num,den=abs(q.numerator),q.denominator
+    assert a!=b and num>0 and den&(den-1)==0
+    # Lower actual coefficient to cleared Horner work. Every intermediate
+    # magnitude envelope is explicitly included, before denominator halvings.
+    acc=0;count=1
+    for i,ch in enumerate(bin(num)[2:]):
+     if i:acc*=2;count+=1;peak=max(peak,acc*env[b])
+     if ch=='1':acc+=1;count+=1;peak=max(peak,acc*env[b])
+    v=F(acc)
+    for i in range(den.bit_length()-1):v/=2;count+=1;peak=max(peak,v*env[b])
+    assert v==abs(q);count+=2 # signed accumulation and private work clear
+    env[a]=env.get(a,F(0))+abs(q)*env[b];rr=rows.setdefault(a,{})
+    for j,z in list(rows[b].items()):
+     value=rr.get(j,F(0))+q*z
+     if value:rr[j]=value
+     else:rr.pop(j,None)
+    workops+=count
+   else:raise AssertionError(op)
+   real+=2*count;peak=max(peak,env[a])
+ assert all(not row for reg,row in rows.items()if reg[0]=='C')
+ for i in range(N):
+  expected={i:F(1)}
+  if ori=='forward'and VV<=i<(2*VV):expected[i-VV]=F(1)
+  if ori=='backward'and i<VV:expected[i+VV]=F(-1)
+  assert rows['L',i]==expected
+ assert peak==F(prior['local'][ori]['prefix_l1_upper']) and peak<2**192
+ assert real==checks[ori]['real_component_primitive_bound']and macros==checks[ori]['scalar_macros']
+ assert dict(paid)=={int(r):z for r,z in checks[ori]['paid_profile'].items()}
+ local[ori]=dict(events=len(evs),macros=macros,real_component_primitives=real,prefix_l1=str(peak),prefix_bits=peak.numerator.bit_length()-peak.denominator.bit_length()+1,coefficient_work_primitive_count=workops,all_exact_columns=N,all_560_dirty_helper_columns_restored=True,private_centres_and_coefficient_work_cleared=True)
+centres=len(w['centers']);widths=[9-len(w['frames'][f])for f in w['start'][(2*VV):]];enter=sum(x<9 for x in widths)
+children=sum(checks['forward']['paid_profile'].values());macros=max(x['macros']for x in local.values());compiler=64*(M+1)**3
+adapters=16*(macros+children+N+centres)+64*M
+primitive_bound=max(x['real_component_primitives']for x in local.values())+adapters*compiler
+bridges=sum(e['kind']=='bridge'for e in old['recipe']);bridgeadd=2*VV*T*bridges;assert sum(e['kind']=='bridge'for e in new['execution_schedule'])==T*bridges
+shifts=K*VV*T;moves=2*K*VV*T
+oldW=old['live'];oldP=old['physical'];oldNB=(oldW-2*VV*K*T)//L
+scalar=sum(local[c['orientation']]['real_component_primitives']for c in old['calls'])
+nonlocal_items=4*VV*T*L+2*VV*T*L+2*L*T*R+sum(e['replicas']for e in old['idle_children'])+L*oldNB+bridgeadd+shifts+moves+oldW+oldP+2*L*T*enter*144
+outside=8*nonlocal_items+64*M
+pervertex=scalar+bridgeadd+shifts+moves+oldW+(72*adapters+outside)*compiler+64*oldP
+invoice=integ['finite_invoice'];assert (primitive_bound,adapters,pervertex,compiler)==(invoice['local_primitive_bound'],invoice['local_adapters'],invoice['pervertex'],invoice['compiler'])
+# Independent hosted stock rebase, retaining the larger unhosted operation
+# overcharge; only the stock and mass in the common router/literal change.
+W=new['live'];P=new['physical'];mass=owners['rank_mass'];profile=owners['paid_profile']
+assert M*W-mass==2560 and P==W+R+centres+2
+rebase=pervertex-oldP*65+P*65-oldW+W;used=max(rebase,pervertex)
+r=M//2;group=2**(r*r)
+for i in range(1,r+1):group*=2**(2*i)-1
+stock=group*P;smass=group*mass;logical=group*used+64;router=compiler*(logical+1)*(stock+1)**2
+G,E,C0=2**30000,2**100000,2**210000;B=smass+E;literal=2*G*stock**2+8*smass+4*stock+4+32*M;row=2*stock.bit_length()+9909+252+2*PAYLOAD;maxchild=max(map(int,profile))
+ineq=dict(local_primitive_bound=primitive_bound<2**48,logical=logical<2**6050,router=router<G,literal=literal<E,mass=B<2**100001,precision=32*M*B*B<C0,tape=2*B+18<C0,row=row<20161,halving=M*M>2*maxchild*maxchild)
+assert all(ineq.values())
+localbits=max(x['prefix_bits']for x in local.values());input_l2_bits=(M+1)//2
+bridge_sweeps=sum(e['kind']=='bridge'for e in new['execution_schedule'])
+required_prefix=localbits+input_l2_bits+len(new['calls'])+bridge_sweeps+4
+assert localbits==21 and bridge_sweeps==72 and required_prefix==206 and required_prefix<PAYLOAD
+assert owners['explicit_idle_remainder_children']<=owners['source_idle_children_charged']
+assert new['physical']<=old['physical'] and new['live']<=old['live'] and not new['bank_padding']['families']
+out=dict(status='PASS_INDEPENDENT_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE',template_sha256=th,global_prefix_bits=required_prefix,charged_prefix_bits=PAYLOAD,complete_invocation_sweeps=72,bridge_sweeps=bridge_sweeps,row_prefix_extra=2*PAYLOAD,local=local,entering_helpers=enter,entrance_rank=sum(9-x for x in widths),local_adapters=adapters,local_primitive_bound=primitive_bound,wrapper_elementary_factors_charged=2*72*enter*144,compiler=compiler,unhosted_pervertex=pervertex,hosted_rebased_pervertex=rebase,conservative_pervertex_used=used,finite=dict(physical_stock_bits=stock.bit_length(),router_bits=router.bit_length(),literal_bits=literal.bit_length(),physical_row_coefficient=row,retained_row_coefficient=20161,required_C0_bits=(32*M*B*B).bit_length(),halving_integer_inequality=[M*M,2*maxchild*maxchild],G_exponent=30000,E_exponent=100000,C0_exponent=210000),strict_checks=ineq,scope='Exact finite recount conditional on inherited all-size compiler/precision/tape and analytic-transfer contracts. Signed accumulation uses the supplier scalar primitive convention. Async prefix counts all72individual bridges and72complete invocations;512bits are charged, and an additional2*512 enters the two-level physical row bound.')
+(O/'PREFIX-AND-INVOICE.json').write_text(json.dumps(out,indent=2)+'\n');print(json.dumps(out,indent=2),flush=True)
+
+prefix=dict(status='PASS_ASYNC_GLOBAL_PREFIX',template_sha256=th,global_prefix_bits=required_prefix,retained_payload_bits=PAYLOAD,complete_invocation_cover_sweeps=len(new['calls']),bridge_factor_two_sweeps=bridge_sweeps,local_scalar_coefficient_work_prefix_bits=localbits,stream_input_sup_to_l2_bits=input_l2_bits,primitive_arithmetic_margin_bits=4,controller_audit_sha256=hashlib.sha256((O/'ASYNC-AUDIT.json').read_bytes()).hexdigest(),proof=f'Each complete normalized invocation has unitary helper endpoints and a data shear with at most two unitary summands. Distinct full orthogonal owner charts act by right-translation bijections on the retained cover group. Thus the maximum full-stream L2 norm grows by at most2per complete local cover sweep and individual bridge. All72local sweeps and72individual bridge sweeps are counted. Unit-modulus phases, idle children, terminal translations and normalized spectator endpoints are unitary. The independently replayed scalar/Horner envelope costs {localbits} bits, initial sup-to-L2 conversion {input_l2_bits} bits, primitive margin 4 bits: total {required_prefix} < {PAYLOAD}. All-size child/compiler and precision/tape interfaces remain inherited.')
+(O/'GLOBAL-PREFIX.json').write_text(json.dumps(prefix,indent=2)+'\n')
diff --git a/research/ranksector112-async/vendor/pr523/code/audit_global_restriction.py b/research/ranksector112-async/vendor/pr523/code/audit_global_restriction.py
new file mode 100644
index 0000000000..9c7aecc82d
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/code/audit_global_restriction.py
@@ -0,0 +1,297 @@
+"""Independently check the 112-port global data restriction of PR514.
+
+Uses only the serialized old/new artifacts and the Python standard library.
+Imports neither the restriction emitter nor the local/global emitters.
+Usage: python audit_global_restriction.py OLD_BASE NEW_BASE REPORT.json
+
+The verified object here is the restricted data/controller interface.  The
+final complete whole-owner placement and its finite invoice are separate
+audits.  In particular, no execution of the parent's obsolete rank-one-only
+bank-padding display field is asserted here.
+"""
+from pathlib import Path
+from collections import Counter
+import argparse
+import copy
+import gzip
+import hashlib
+import json
+import sys
+
+
+def need(condition, message):
+    if not condition:
+        raise AssertionError(message)
+
+
+def read(path):
+    data = path.read_bytes()
+    return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data)
+
+
+def filehash(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def objhash(value):
+    return hashlib.sha256(json.dumps(value, sort_keys=True,
+                                    separators=(',', ':')).encode()).hexdigest()
+
+
+parser = argparse.ArgumentParser(description=__doc__,
+                                 formatter_class=argparse.RawDescriptionHelpFormatter)
+parser.add_argument('old_base', type=Path, help='Replayed pinned PR514 base directory')
+parser.add_argument('new_base', type=Path, help='Restricted 112-port base directory')
+parser.add_argument('report', type=Path, help='Destination JSON audit receipt')
+args = parser.parse_args()
+if sys.version_info < (3, 10):
+    parser.error('Python 3.10 or later is required for exact integer bit_count')
+OLD, NEW, REPORT = (p.resolve() for p in (args.old_base, args.new_base, args.report))
+OS, NS = OLD / 'split-centres', NEW / 'split-centres'
+old = read(OS / 'GLOBAL-TEMPLATE.json.gz')
+oldcan = read(OS / 'CANONICAL-WORD.json.gz')
+oldphase = read(OLD / 'work/complex-nine-native/DATA-PHASES.json')
+can = read(NS / 'CANONICAL-WORD.json.gz')
+checks = read(NS / 'LOCAL-CHECKS.json')
+programs = read(NS / 'LOCAL-PROGRAMS.json.gz')
+local_replay = read(NS / 'INDEPENDENT-REPLAY.json')
+local_phase = read(NS / 'CLIFFORD-REVIEW.json')
+restriction = read(NS / 'RESTRICTION.json')
+transport = read(NS / 'TRANSPORT.json')
+state = dict(template=read(NS / 'GLOBAL-TEMPLATE.json.gz'),
+             phase=read(NEW / 'work/complex-nine-native/DATA-PHASES.json'),
+             mapping=read(NS / 'PORT-MAPPING.json'),
+             invoice=read(NS / 'INTEGRATION.json'))
+
+bindings = {
+    'canonical': filehash(NS / 'CANONICAL-WORD.json.gz'),
+    'canonical_content': hashlib.sha256(gzip.decompress((NS / 'CANONICAL-WORD.json.gz').read_bytes())).hexdigest(),
+    'programs': filehash(NS / 'LOCAL-PROGRAMS.json.gz'),
+    'local_phase': filehash(NS / 'CLIFFORD-RECIPES.json'),
+    'adapters': filehash(NS / 'RESIDUAL-ADAPTERS.json'),
+    'old_template': filehash(OS / 'GLOBAL-TEMPLATE.json.gz'),
+    'old_template_content': hashlib.sha256(gzip.decompress((OS / 'GLOBAL-TEMPLATE.json.gz').read_bytes())).hexdigest(),
+    'old_phase': filehash(OLD / 'work/complex-nine-native/DATA-PHASES.json'),
+    'phase': filehash(NEW / 'work/complex-nine-native/DATA-PHASES.json'),
+}
+need(local_replay['canonical_word_sha256'] == local_phase['canonical_word_sha256']
+     == transport['canonical_sha256'] == bindings['canonical'],
+     'Local independent receipts must bind this canonical word')
+need(local_replay['local_programs_sha256'] == bindings['programs'],
+     'Local replay must bind this expanded program')
+need(local_phase['recipe_sha256'] == bindings['local_phase']
+     and local_phase['all_child_equalities_include_global_phase'],
+     'Local phase receipt must include the scalar phase')
+need(transport['independently_recomputed_helper_compensations_match'] == 12094,
+     'Arbitrary helper dirt transport was not independently certified')
+for orientation, program in programs.items():
+    need(objhash(program) == checks[orientation]['sha256'], 'Local program hash')
+    need(local_replay['local'][orientation]['all_exact_columns'] == 784
+         and local_replay['local'][orientation]['private_work_erased'],
+         'Local replay must cover all data/helper columns and cleanup')
+    need(local_replay['paid_profiles'][orientation]
+         == checks[orientation]['paid_profile'], 'Local paid profiles')
+
+
+def audit(s):
+    t, ph, mp, inv = (s[k] for k in ('template', 'phase', 'mapping', 'invoice'))
+    nto = mp['new_to_old']
+    omitted = [i for i in range(120) if i not in nto]
+    need(len(nto) == len(set(nto)) == 112 and nto == sorted(nto), 'Port injection')
+    need(omitted == [0, 13, 22, 35, 40, 51, 54, 119], 'Exactly the eight axis ports')
+    need(omitted == restriction['removed_canonical_source_indices'], 'Local/global selection')
+    need({str(p): i for i, p in enumerate(nto)} == mp['old_to_new'], 'Inverse port map')
+    otn = {p: i for i, p in enumerate(nto)}
+    need((can['h'], can['v'], can['R'], len(can['centers'])) == (9, 112, 560, 8),
+         'Local dimensions and private center count')
+    need(can['ports'] == [oldcan['ports'][p] for p in nto], 'Actual binary port labels')
+    need(can['frames'] == oldcan['frames']
+         and can['start'][224:] == oldcan['start'][240:]
+         and can['final'][224:] == oldcan['final'][240:], 'Helper frames unchanged')
+    need(t['m'] == 73 and (t['live'], t['physical']) == (12208, 12778),
+         'Live and private stock')
+    need(t['private_namespace'] == dict(centers=[12208, 12216],
+                                      reserved_tableau=[12216, 12776],
+                                      coefficient=[12776, 12778]), 'Private ranges')
+    need(t['local_programs'] == programs, 'Use the new verified local program')
+    for key in ('recipe', 'loop_order', 'cover', 'adapter_policy', 'route_semantics',
+                'expanded_scalar_interface'):
+        need(t[key] == old[key], 'Inherited controller field ' + key)
+    need('each local invocation completes before the next' in t['loop_order'].lower(),
+         'Complete invocations must remain indivisible')
+    need(t['exact_data_phase_recipe_sha256'] == bindings['phase']
+         and t['exact_local_clifford_recipe_sha256'] == bindings['local_phase']
+         and t['residual_adapter_sha256'] == bindings['adapters'], 'Global recipe hashes')
+    provenance = t['port_restriction']
+    need(provenance['new_to_old'] == nto
+         and provenance['parent_global_template_content_sha256'] == bindings['old_template_content']
+         and provenance['parent_data_phase_sha256'] == bindings['old_phase']
+         and provenance['canonical_word_content_sha256'] == bindings['canonical_content'], 'Provenance')
+
+    # The old polynomial verification applies to each selected literal recipe.
+    # This comparison includes every axis, every Z4 translation, and the
+    # terminal correction; it is stronger than comparing only rank histograms.
+    need(ph['m'] == 73 and ph['ports'] == 112 and len(ph['recipes']) == 112,
+         'Data phase dimensions')
+    for key in ('status', 'cover_correction', 'global_phase_argument'):
+        need(ph[key] == oldphase[key], 'Inherited phase statement ' + key)
+    need(ph['source_parent_sha256'] == bindings['old_phase'], 'Parent phase provenance')
+    for p, op in enumerate(nto):
+        got = copy.deepcopy(ph['recipes'][p])
+        need(got['port'] == p and got['q'] == can['ports'][p], 'Phase port labels')
+        got['port'] = op
+        need(got == oldphase['recipes'][op], 'Exact per-port phase recipe restriction')
+        q = can['ports'][p]
+        z = next(i for i in range(9) if not ((q >> i) & 1))
+        a = q ^ (1 << z)
+        order = list(range(9))
+        order[0], order[z] = order[z], order[0]
+        basis = [(1 << i) ^ (a if (a >> i) & 1 else 0) for i in order]
+        basis += [1 << i for i in range(9, 73)]
+        need(all(((x & y).bit_count() & 1) == (i == j)
+                 for i, x in enumerate(basis) for j, y in enumerate(basis)),
+             'Orthogonal 73-dimensional port chart')
+        for child in got['idle_children']:
+            axes = child['orthogonal_axes']
+            need(len(axes) == len(set(axes)) == child['rank']
+                 and set(axes) <= set(basis), 'Literal idle child axes')
+    need(ph['terminal_omission_controls_rejected'] == 112, 'Terminal control count')
+
+    # The source event list acts separately at every port after a complete
+    # verified local invocation.  Preserve all events and all replica order.
+    schedule = copy.deepcopy(old['execution_schedule'])
+    correction = dict(old['cover_final_correction'], families=[0, 12208],
+                      charged_calls_per_cover=12208)
+    for event in schedule:
+        if event['kind'] == 'bank_padding_cover_sweep':
+            event['families'] = [7168, 12208]
+        elif event['kind'] == 'translate_every_live_family':
+            event.update(correction)
+    need(t['execution_schedule'] == schedule and t['cover_final_correction'] == correction,
+         'Exact inherited event order and terminal cover correction')
+    want_idle = []
+    for child in old['idle_children']:
+        if child['port'] in otn:
+            want_idle.append(dict(child, port=otn[child['port']]))
+    need(t['idle_children'] == want_idle and len(want_idle) == 2016,
+         'Every selected idle child with unchanged multiplicity')
+    need(t['bank_padding'] == dict(old['bank_padding'], families=list(range(7168, 12208))),
+         'Inherited bank metadata and exact renumbering')
+
+    need(len(t['calls']) == len(old['calls']) == 72, 'Number of complete invocations')
+    need([(c['stage'], c['replica']) for c in t['calls']]
+         == [(s, r) for s in range(9) for r in range(8)], 'Invocation order')
+    bank_cells = {}
+    paid = Counter()
+    helper_roles = 0
+    data_roles = 0
+    for call, parent in zip(t['calls'], old['calls']):
+        for key in ('orientation', 'stage', 'replica', 'pair', 'window'):
+            need(call[key] == parent[key], 'Inherited call ' + key)
+        need(call['local_program_sha256'] == checks[call['orientation']]['sha256'],
+             'Call-local word binding')
+        owners = call['owners']
+        need(len(owners) == 784, 'Local owner count')
+        rep, pair, stage = (call[k] for k in ('replica', 'pair', 'stage'))
+        for side in range(2):
+            for p, op in enumerate(nto):
+                need(owners[112 * side + p]
+                     == [896 * rep + 112 * (2 * pair + side) + p, [1, stage, p]],
+                     'Literal new data family')
+                need(parent['owners'][120 * side + op]
+                     == [960 * rep + 120 * (2 * pair + side) + op, [1, stage, op]],
+                     'Literal source data family')
+                data_roles += 1
+        multiplicities = Counter(f for f, route in owners)
+        for h, (family, route) in enumerate(owners[224:]):
+            oldfamily, oldroute = parent['owners'][240 + h]
+            need(family == oldfamily - 512 and route == oldroute, 'Helper bank route unchanged')
+            need(7168 <= family < 12208, 'Bank owner stock bounds')
+            width = 9 - len(can['frames'][can['start'][224 + h]])
+            need(route[0] == 2, 'Bank routing kind')
+            if width < 9:
+                need(multiplicities[family] == 1, 'Entering helper has one whole owner')
+                need(len(route) == 4 and route[2] == width
+                     and len(route[3]) == 9 - width, 'Entering width and spectators')
+            off = 9 * route[1] if len(route) == 2 else route[1]
+            cells = set(range(off, off + width))
+            need(0 <= off and off + width <= 73, 'Bank residual interval')
+            previous = bank_cells.setdefault(family, set())
+            need(not previous & cells, 'Disjoint bank residual intervals')
+            previous.update(cells)
+            helper_roles += 1
+        paid.update({int(r): n for r, n in checks[call['orientation']]['paid_profile'].items()})
+    need(helper_roles == 40320 and data_roles == 16128, 'All literal owner roles')
+    need(set(bank_cells) == set(range(7168, 12208)), 'Every retained bank accounted for')
+    pads = Counter()
+    for cells in bank_cells.values():
+        need(cells == set(range(len(cells))), 'Bank used cells form the literal prefix')
+        leftover = 73 - len(cells)
+        need(0 < leftover <= 51, 'One legal complementary bank child suffices')
+        pads[leftover] += 1
+    need(pads == Counter({1: 3492, 9: 1386, 17: 162}), 'Actual bank remainder spectrum')
+    paid.update(pads)
+    for child in t['idle_children']:
+        need(child['rank'] == ph['recipes'][child['port']]['idle_children'][child['child']]['rank'],
+             'Paid idle rank equals literal phase recipe')
+        paid[child['rank']] += child['replicas']
+    mass = sum(r * n for r, n in paid.items())
+    need(mass == 888624 and 73 * 12208 - mass == 2560, 'Unhosted rank-mass identity')
+    need(inv['live'] == 12208 and inv['physical'] == 12778
+         and inv['rank_mass'] == mass and inv['deficit'] == 2560,
+         'Invoice stock and rank mass')
+    need(inv['global_profile'] == {str(r): n for r, n in paid.items()}
+         and inv['bank_remainder_profile'] == {str(r): n for r, n in pads.items()},
+         'Invoice must use literal remainders, not obsolete bank display rank')
+    return dict(retained_ports=112, deleted_canonical_ports=omitted, data_owner_roles=data_roles,
+                helper_owner_roles=helper_roles, complete_invocations=72,
+                exact_port_phase_recipes=112, exact_stage_alignments=1008,
+                exact_idle_axis_recipes=2240, paid_idle_children=2016,
+                replicated_paid_idle_children=sum(x['replicas'] for x in want_idle),
+                bank_families=5040, bank_remainder_profile=dict(sorted(pads.items())),
+                unhosted_paid_profile=dict(sorted(paid.items())),
+                unhosted_rank_mass=mass, unhosted_live=12208, unhosted_physical=12778,
+                deficit=2560)
+
+
+result = audit(state)
+need(objhash(state['template']) == state['invoice']['global_template_sha256'],
+     'Invoice template content hash')
+controls = []
+
+
+def reject(name, mutation):
+    changed = copy.deepcopy(state)
+    mutation(changed)
+    try:
+        audit(changed)
+    except (AssertionError, KeyError, IndexError, ValueError, TypeError):
+        controls.append(name)
+    else:
+        raise AssertionError('Accepted negative control: ' + name)
+
+
+reject('duplicate selected port', lambda s: s['mapping']['new_to_old'].__setitem__(0, 2))
+reject('wrong phase port label', lambda s: s['phase']['recipes'][0].__setitem__('q', 1))
+reject('wrong inherited idle axis', lambda s: s['phase']['recipes'][0]['idle_children'][0]['orthogonal_axes'].__setitem__(0, 1))
+reject('missing terminal port correction', lambda s: s['phase']['recipes'][0].__setitem__('terminal_Y_translation', 0))
+reject('wrong data owner family', lambda s: s['template']['calls'][0]['owners'][0].__setitem__(0, 1))
+reject('wrong canonical data route', lambda s: s['template']['calls'][0]['owners'][0][1].__setitem__(2, 1))
+reject('stale local program hash', lambda s: s['template']['calls'][0].__setitem__('local_program_sha256', 'old'))
+reject('changed entering bank owner', lambda s: s['template']['calls'][0]['owners'][224].__setitem__(0, 7168))
+reject('missing complete invocation', lambda s: s['template']['calls'].pop())
+reject('missing paid idle child', lambda s: s['template']['idle_children'].pop())
+reject('missing cover correction', lambda s: s['template']['execution_schedule'].pop())
+reject('understated private reserve', lambda s: s['template'].__setitem__('physical', 12777))
+reject('unpaid bank remainder', lambda s: s['invoice']['global_profile'].__setitem__('17', 0))
+
+report = dict(status='PASS_INDEPENDENT_GLOBAL_DATA_PORT_RESTRICTION',
+              **result, source_bindings=bindings, negative_controls_rejected=controls,
+              local_scalar_replay_receipt_sha256=filehash(NS / 'INDEPENDENT-REPLAY.json'),
+              local_phase_receipt_sha256=filehash(NS / 'CLIFFORD-REVIEW.json'),
+              template_content_sha256=objhash(state['template']),
+              scope='Exact restriction of all inherited global data routes, phase recipes, complete-call order, idle axes and terminal corrections. Local arbitrary-dirt identities are supplied by the newly hash-bound independent local replay. Actual bank remainders are recounted for the conservative parent invoice. Final whole-owner placement, executable global program, finite compilation and outer exponent require their separate fresh audits.')
+REPORT.parent.mkdir(parents=True, exist_ok=True)
+REPORT.write_text(json.dumps(report, indent=2) + '\n')
+print(json.dumps({k: report[k] for k in ('status', 'retained_ports', 'data_owner_roles',
+      'helper_owner_roles', 'unhosted_rank_mass', 'deficit', 'negative_controls_rejected')}, indent=2))
diff --git a/research/ranksector112-async/vendor/pr523/code/audit_local112.py b/research/ranksector112-async/vendor/pr523/code/audit_local112.py
new file mode 100644
index 0000000000..034677e03b
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/code/audit_local112.py
@@ -0,0 +1,144 @@
+# Local-only extraction of the attributed PR514 / PR433 independent replay.
+# Prepared for icekylinx with GPT-6 Astra assistance. Apache-2.0.
+# The complete local checker and its negative controls are retained verbatim.
+# Global hosting is verified separately for the changed 112-port geometry.
+import copy,gzip,hashlib,json,sys
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+OUT=Path(sys.argv[1])
+c=json.load(gzip.open(OUT/'CANONICAL-WORD.json.gz'))
+ir={'local_programs':json.load(gzip.open(OUT/'LOCAL-PROGRAMS.json.gz'))}
+v,R,h=c['v'],c['R'],c['h'];n=2*v+R;frames=c['frames']
+levels={int(t):f for t,f in c.get('target_levels',{}).items()}
+entering=[r for r,f in enumerate(c['start']) if r>=2*v and f!=0]
+plain={r for r in range(n) if r not in set(entering)}
+def contains(a,b):
+    for x in a:
+        for y in b:
+            if x>>(y.bit_length()-1)&1:x^=y
+        if x:return False
+    return True
+def local(events,back):
+    rows={('L',r):{r:Q(1)} for r in range(n)}
+    norm={('L',r):Q(1) for r in range(n)};prefix=Q(1);cur=c['start'].copy();private={}
+    hist=Counter();phases=[];entry=[];exit=[];centers=[];matrix_hash=hashlib.sha256();chain={};wrappers=[]
+    allowed=['zero_frame_precondition','entry_adapters','A','centers','B','final','exit_adapters','full_frame_cleanup','done']
+    for event in events:
+        tag=event[0]
+        if tag=='phase':
+            phases.append(event[1]);assert phases==allowed[:len(phases)]
+            if event[1]=='A':assert entry==[(r,f) for r,f in enumerate(c['start']) if r in plain] and sorted(r for k_,r,f_ in wrappers if k_=='pre')==entering   # GK
+            if event[1]=='centers':assert all(cur[r]==levels.get(r-v,0) for r in range(v,2*v))   # GK
+            if event[1]=='full_frame_cleanup':assert cur==c['final'] and exit==list(enumerate(c['final']))
+            assert not private
+        elif tag=='residual_adapter':   # GK: paid wrappers of entering helpers: R_E^-1 before the invocation, L_E^-1 after the full-frame cleanup
+            _,kind,r,f=event;assert r in entering and f==c['start'][r] and kind in ('pre','post')
+            assert (kind=='pre' and phases[-1]=='entry_adapters') or (kind=='post' and phases[-1]=='full_frame_cleanup')
+            assert (kind,r) not in {(k,x) for k,x,_ in wrappers};wrappers.append((kind,r,f))
+        elif tag=='adapter':
+            assert event[3]==(c['start'] if event[1]=='old_to_new' else c['final'])[event[2]]
+            (entry if event[1]=='old_to_new' else exit).append((event[2],event[3]))
+        elif tag=='climb':
+            _,part,r,a,b,rank=event
+            assert not private and phases[-1]==part and cur[r]==a
+            assert contains(frames[a],frames[b]) and rank==len(frames[b])-len(frames[a])>0
+            hist[rank]+=1;cur[r]=b
+        elif tag=='center':
+            _,k,a,b,rank=event
+            assert phases[-1]=='centers' and private=={('C',k):a}
+            cf=c['center_frames'][k];cr=len(frames[cf])
+            # GK: stepwise descent cf -> served levels -> lowest (forward), reversed ascent (backward); each step is a nested child
+            assert contains(frames[a],frames[b]) if back else contains(frames[b],frames[a])
+            assert rank==abs(len(frames[a])-len(frames[b]))>0
+            chain.setdefault(k,[]).append((a,b))
+            private['C',k]=b;hist[rank]+=1;centers.append(k)
+        elif tag=='scalar':
+            _,e,f=event;op=e[0];target=tuple(e[1]);source=tuple(e[2]) if op in ('copy','add') else None
+            if target[0]=='C' and op=='clear':
+                assert private.get(target,f)==f
+                private.pop(target,None)
+            else:
+                for r in (target,source):
+                    if r is None:continue
+                    if r[0]=='L':assert cur[r[1]]==f,('common frame',r,cur[r[1]],f)
+                    else:
+                        if r==target and r not in private:private[r]=f
+                        assert private[r]==f
+            if op=='clear':rows[target]={};norm[target]=Q(0)
+            elif op=='copy':rows[target]=dict(rows[source]);norm[target]=norm[source]
+            elif op=='scale':
+                q=Q(e[2],e[3]);a,b=abs(q.numerator),q.denominator
+                assert a&(a-1)==0 and b&(b-1)==0
+                rows[target]={j:q*x for j,x in rows[target].items()};norm[target]*=abs(q)
+            else:
+                q=Q(e[3],e[4]);a,b=abs(q.numerator),q.denominator
+                assert source!=target and b&(b-1)==0
+                # Independent symbolic replay of the cleared coefficient work.
+                w=0
+                for bit in bin(a)[2:]:w=2*w+int(bit)
+                assert Q(w,b)*(1 if q>0 else -1)==q
+                prefix=max(prefix,Q(a)*norm[source])
+                norm[target]=norm.get(target,Q(0))+abs(q)*norm[source]
+                row=rows.setdefault(target,{})
+                for j,x in list(rows[source].items()):
+                    z=row.get(j,Q(0))+q*x
+                    if z:row[j]=z
+                    else:row.pop(j,None)
+            prefix=max(prefix,norm[target])
+        else:raise AssertionError(tag)
+    assert phases==allowed and set(centers)==set(range(len(c['centers']))) and not private
+    assert sorted(r for k,r,_ in wrappers if k=='pre')==entering and sorted(r for k,r,_ in wrappers if k=='post')==entering   # GK
+    for k,st in chain.items():   # GK: the steps of each centre chain link up and end at the centre frame
+        cf=c['center_frames'][k]
+        if back:assert st[-1][1]==cf and all(st[i][1]==st[i+1][0] for i in range(len(st)-1))
+        else:assert st[0][0]==cf and all(st[i][1]==st[i+1][0] for i in range(len(st)-1))
+    assert all(not row for reg,row in rows.items() if reg[0]=='C')
+    for r in range(n):
+        expected={r:Q(1)}
+        if back and r<v:expected[v+r]=Q(-1)
+        elif not back and v<=r<2*v:expected[r-v]=Q(1)
+        assert rows['L',r]==expected
+    # A 192-bit local payload allowance vastly dominates even coefficient work.
+    assert prefix<2**192
+    return hist,{'all_exact_columns':n,'prefix_l1_upper':str(prefix),
+                 'prefix_bits_upper':prefix.numerator.bit_length()-prefix.denominator.bit_length()+1,
+                 'charged_payload_bits':192,'private_work_erased':True}
+
+profiles={};checks={}
+for name in ('forward','backward'):
+    profiles[name],checks[name]=local(ir['local_programs'][name],name=='backward')
+    assert dict(profiles[name])=={int(r):z for r,z in c['local_profile'].items()}
+    print('independent emitted replay PASS',name,flush=True)
+controls=[]
+for name,mut in [
+    ('wrong_scale',lambda es:next(e for e in es if e[0]=='scalar' and e[1][0]=='scale')[1].__setitem__(2,3)),
+    ('missing_center',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='center'))),
+    ('wrong_common_frame',lambda es:next(e for e in es if e[0]=='scalar' and e[2]!=0).__setitem__(2,0)),
+    ('wrong_child_rank',lambda es:next(e for e in es if e[0]=='climb').__setitem__(5,99)),
+]+([
+    ('missing_pre_wrapper',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='pre'))),
+    ('missing_post_wrapper',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='post'))),
+    ('wrapper_with_wrong_frame',lambda es:next(e for e in es if e[0]=='residual_adapter').__setitem__(3,0)),
+    ('wrapper_in_wrong_phase',lambda es:es.insert(es.index(['phase','A']),es.pop(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='post')))),
+    ('wrapper_on_a_data_register',lambda es:next(e for e in es if e[0]=='residual_adapter').__setitem__(2,3)),
+    ('wrapper_on_a_target_register',lambda es:next(e for e in es if e[0]=='residual_adapter').__setitem__(2,v+3)),
+    ('wrapper_on_a_centre_register',lambda es:next(e for e in es if e[0]=='residual_adapter').__setitem__(2,['C',0])),
+] if entering else [])+([
+    ('centre_step_not_nested',lambda es:next(e for e in es if e[0]=='center').__setitem__(3,next(f for f in range(len(frames)) if not contains(frames[f],frames[next(e for e in es if e[0]=='center')[2]]) and not contains(frames[next(e for e in es if e[0]=='center')[2]],frames[f])))),
+    ('centre_descent_step_skipped',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='center' and e[3]!=0))),
+] if levels else []):
+    es=copy.deepcopy(ir['local_programs']['forward']);mut(es)
+    try:local(es,False)
+    except (AssertionError,KeyError):controls.append(name)
+    else:raise AssertionError('mutation accepted: '+name)
+
+
+result={'status':'PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY',
+'canonical_word_sha256':hashlib.sha256((OUT/'CANONICAL-WORD.json.gz').read_bytes()).hexdigest(),
+'local_programs_sha256':hashlib.sha256((OUT/'LOCAL-PROGRAMS.json.gz').read_bytes()).hexdigest(),
+'v':v,'helpers':R,'local':checks,'paid_profiles':{name:dict(H) for name,H in profiles.items()},
+'entering_helpers':len(entering),'negative_controls_rejected':controls,
+'scope':'Literal forward and inverse-transpose replay on every arbitrary data/helper column, physical frame incidence, ordered paid wrappers, cleared private work and prefix coefficients. Global hosting and outer exponent are separate.'}
+(OUT/'INDEPENDENT-LOCAL-REPLAY.json').write_text(json.dumps(result,indent=2)+'\n')
+print(result['status'],len(controls),'controls rejected',flush=True)
diff --git a/research/ranksector112-async/vendor/pr523/code/audit_port112_transport.py b/research/ranksector112-async/vendor/pr523/code/audit_port112_transport.py
new file mode 100644
index 0000000000..92a677ab9f
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/code/audit_port112_transport.py
@@ -0,0 +1,108 @@
+"""Independently match the restricted Hamming and canonical scalar words.
+Prepared for icekylinx with GPT-6 Astra assistance. Apache-2.0.
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+import copy, gzip, hashlib, json, sys
+
+out = Path(sys.argv[1])
+w = json.load(gzip.open(out / 'FULL-WORD.json.gz'))
+c = json.load(gzip.open(out / 'CANONICAL-WORD.json.gz'))
+v, R = c['v'], c['R']
+assert v == len(w['ports']) == 112 and R == w['report']['R']
+n = 2 * v + R
+
+
+def basis(vs):
+    b = {}
+    for x in vs:
+        for k in sorted(b, reverse=True):
+            if x >> k & 1:
+                x ^= b[k]
+        if x:
+            k = x.bit_length() - 1
+            for j in b:
+                if b[j] >> k & 1:
+                    b[j] ^= x
+            b[k] = x
+    return tuple(b[k] for k in sorted(b, reverse=True))
+
+
+def tau(x):
+    return x ^ (43 if (x & 43).bit_count() % 2 else 0)
+
+
+assert 43 .bit_count() % 2 == 0
+assert set(map(tau, w['ports'])) == set(c['ports'])
+mp = {i: c['ports'].index(tau(p)) for i, p in enumerate(w['ports'])}
+mp.update({v + i: v + mp[i] for i in range(v)})
+mp.update({2 * v + h: 2 * v + h for h in range(R)})
+fi = {basis(f): i for i, f in enumerate(c['frames'])}
+
+
+def frame(F):
+    return fi[basis(tau(x) for x in F)]
+
+
+def event(e):
+    e = copy.deepcopy(e)
+    e[1] = mp[e[1]]
+    if e[0] == 'add':
+        e[2] = mp[e[2]]
+    if e[-1] is not None:
+        e[-1] = frame(e[-1])
+    return e
+
+
+for seq in ['A', 'B', 'cut', 'cleanup', 'precondition']:
+    assert [event(e) for e in w[seq]] == c[seq], seq
+assert [mp[r] for r in w['centers']] == c['centers']
+assert [frame(F) for F in w['center_frames']] == c['center_frames']
+assert {str(mp[v + int(t)] - v): frame(F) for t, F in w['target_levels'].items()} == c['target_levels']
+for r in range(n):
+    expected = frame([w['ports'][r]]) if r < v else frame(w.get('start_extra', {}).get(str(r), []))
+    assert c['start'][mp[r]] == expected
+
+
+def apply(e, rows):
+    if e[0] == 'scale':
+        _, t, a, b, *_ = e
+        rows[t] = {j: Q(a, b) * x for j, x in rows[t].items()}
+        return
+    _, t, s, a, b, *_ = e
+    q = Q(a, b)
+    for j, x in list(rows[s].items()):
+        z = rows[t].get(j, Q(0)) + q * x
+        if z:
+            rows[t][j] = z
+        else:
+            rows[t].pop(j, None)
+
+
+mx = [{i: Q(1)} for i in range(n)]
+for e in w['A'] + w['cut'] + w['B']:
+    apply(e, mx)
+dirty = [{} for _ in range(n)]
+for t in range(v, 2 * v):
+    dirty[t] = {r: x for r, x in mx[t].items() if r >= 2 * v}
+for e in w['precondition']:
+    apply(e, dirty)
+comp = []
+for t in range(v, 2 * v):
+    for r, x in sorted(dirty[t].items()):
+        assert str(r) not in w['start_extra'], ('illegal frame-zero compensation of entering helper', r)
+        comp.append(['add', t, r, -x.numerator, x.denominator, []])
+assert [event(e) for e in comp] == c['compensation']
+
+report = {
+    'status': 'PASS_EXACT_112_PORT_WORD_TRANSPORT',
+    'word_sha256': hashlib.sha256((out / 'FULL-WORD.json.gz').read_bytes()).hexdigest(),
+    'canonical_sha256': hashlib.sha256((out / 'CANONICAL-WORD.json.gz').read_bytes()).hexdigest(),
+    'hamming_to_canonical_source_map': {i: mp[i] for i in range(v)},
+    'all_main_cleanup_precondition_center_and_entrance_frames_match': True,
+    'independently_recomputed_helper_compensations_match': len(comp),
+    'columns_in_recomputed_raw_main': n,
+    'scope': 'Exact transport of the whole raw word to the canonical word, including recomputed arbitrary-dirt compensation. Canonical emitted replay supplies both orientation identities.',
+}
+(out / 'TRANSPORT.json').write_text(json.dumps(report, indent=2) + '\n')
+print(report['status'], len(comp), 'compensations', flush=True)
diff --git a/research/ranksector112-async/vendor/pr523/code/build_port112.py b/research/ranksector112-async/vendor/pr523/code/build_port112.py
new file mode 100644
index 0000000000..93b3b0af67
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/code/build_port112.py
@@ -0,0 +1,128 @@
+"""Delete the eight isolated coordinate ports from the PR514 local supplier.
+
+Prepared for icekylinx with GPT-6 Astra assistance.  Apache-2.0.
+This is an exact restriction of the attributed PR507/PR514 scalar construction;
+helper identities, entrance gauges, kernel relations, and gate frames survive.
+No hosting or global-exponent claim is made by this local transformation.
+"""
+from pathlib import Path
+from collections import Counter
+import copy, gzip, hashlib, json, sys
+
+
+def read(p):
+    return json.loads(gzip.decompress(p.read_bytes()) if p.suffix == '.gz' else p.read_bytes())
+
+
+def dump(p, obj):
+    raw = json.dumps(obj, sort_keys=True, separators=(',', ':')).encode()
+    p.write_bytes(gzip.compress(raw, mtime=0) if p.suffix == '.gz' else raw)
+
+
+src, out = map(Path, sys.argv[1:3])
+out.mkdir(parents=True, exist_ok=False)
+w = read(src / 'FULL-WORD.json.gz')
+c = read(src / 'CANONICAL-WORD.json.gz')
+old_v, new_v = 120, 112
+R = w['report']['R']
+axes = [i for i, row in enumerate(w['root_lines']) if sum(x != 0 for x in row) == 1]
+assert axes == list(range(8))
+assert w['centers'][8:] == axes
+assert list(map(len, w['center_frames'])) == [8] * 8 + [1] * 8
+assert len(w['ports']) == old_v and c['v'] == old_v and c['R'] == R
+
+
+def restriction(old, removed, canonical=False):
+    """Reject any purportedly deleted data register used by a body gate."""
+    keep = [i for i in range(old_v) if i not in removed]
+    rank = {s: i for i, s in enumerate(keep)}
+    mp = dict(rank)
+    mp.update({old_v + s: new_v + i for s, i in rank.items()})
+    mp.update({2 * old_v + h: 2 * new_v + h for h in range(R)})
+    deleted = set(removed) | {old_v + i for i in removed}
+    z = copy.deepcopy(old)
+    deleted_events = Counter()
+    for seq in ['A', 'B', 'cleanup', 'precondition', 'cut'] + (['compensation'] if canonical else []):
+        events = []
+        for e in old[seq]:
+            regs = [e[1]] + ([e[2]] if e[0] == 'add' else [])
+            if deleted.intersection(regs):
+                assert seq == 'cut' and e[0] == 'add'
+                assert e[1] - old_v == e[2] and e[2] in removed
+                assert e[3:5] == [1, 1]
+                deleted_events[seq] += 1
+                continue
+            a = copy.deepcopy(e)
+            a[1] = mp[a[1]]
+            if a[0] == 'add':
+                a[2] = mp[a[2]]
+            events.append(a)
+        z[seq] = events
+    assert deleted_events == {'cut': 8}
+    ci = [j for j, r in enumerate(old['centers']) if r not in deleted]
+    assert len(ci) == 8
+    z['centers'] = [mp[old['centers'][j]] for j in ci]
+    z['center_frames'] = [old['center_frames'][j] for j in ci]
+    z['ports'] = [old['ports'][s] for s in keep]
+    z['target_levels'] = {str(rank[int(t)]): E for t, E in old.get('target_levels', {}).items() if int(t) not in removed}
+    assert len(z['target_levels']) == len(old.get('target_levels', {}))
+    if canonical:
+        z['v'] = new_v
+        z['start'] = [old['start'][r] for r in sorted(mp, key=mp.get)]
+        z['final'] = [old['final'][r] for r in sorted(mp, key=mp.get)]
+        z['local_profile'] = dict(Counter({int(r): n for r, n in old['local_profile'].items()}) - Counter({1: 8, 8: 16}))
+    else:
+        z['root_lines'] = [old['root_lines'][s] for s in keep]
+        z['scatter'] = [[old['scatter'][s][j] for j in ci] for s in keep]
+        z['start_extra'] = {str(mp[int(r)]): E for r, E in old.get('start_extra', {}).items()}
+        H = Counter({int(r): n for r, n in old['report']['local_profile'].items()})
+        H.subtract({1: 8, 8: 16})
+        assert all(n > 0 for n in H.values())
+        z['report'] = {
+            'status': 'EXACT_PORT_RESTRICTION_PENDING_LOCAL_REPLAY',
+            'h': 9, 'v': new_v, 'R': R, 'cst': 64,
+            'm': 73, 'local_profile': dict(sorted(H.items())),
+            'centre_ranks': [8] * 8,
+            'entering_helpers': len(z['start_extra']),
+            'entrance_rank': sum(len(E) for E in z['start_extra'].values()),
+            'source_columns_exact': new_v,
+            'borrowed_output_pairs': old['report']['borrowed_output_pairs'],
+            'selection_sha256': old['report']['selection_sha256'],
+            'inherited_helper_indices': True,
+            'scalar_operations_A': len(z['A']), 'scalar_operations_B': len(z['B']),
+        }
+    return z, mp, sorted(removed), deleted_events
+
+
+new_w, wm, _, we = restriction(w, set(axes))
+tau = lambda x: x ^ (43 if (x & 43).bit_count() % 2 else 0)
+assert {tau(p) for p in w['ports']} == set(c['ports'])
+canonical_removed = {c['ports'].index(tau(w['ports'][i])) for i in axes}
+new_c, cm, _, ce = restriction(c, canonical_removed, True)
+assert {tau(p) for p in new_w['ports']} == set(new_c['ports'])
+dump(out / 'FULL-WORD.json.gz', new_w)
+dump(out / 'CANONICAL-WORD.json.gz', new_c)
+port_mapping = {
+    'old_to_new': {i: cm[i] for i in range(old_v) if i in cm},
+    'new_to_old': sorted(i for i in range(old_v) if i in cm),
+    'old_to_new_hamming': {i: wm[i] for i in range(old_v) if i in wm},
+    'tau_hamming_axes_to_old_canonical': [c['ports'].index(tau(w['ports'][i])) for i in axes],
+}
+assert len(port_mapping['new_to_old']) == new_v
+assert all(port_mapping['old_to_new'][old] == new for new, old in enumerate(port_mapping['new_to_old']))
+(out / 'PORT-MAPPING.json').write_text(json.dumps(port_mapping, indent=2) + '\n')
+receipt = {
+    'status': 'PASS_EXACT_LOCAL_PORT_RESTRICTION',
+    'source_files': {p.name: hashlib.sha256(p.read_bytes()).hexdigest() for p in (src / 'FULL-WORD.json.gz', src / 'CANONICAL-WORD.json.gz')},
+    'removed_hamming_source_indices': axes,
+    'removed_canonical_source_indices': sorted(canonical_removed),
+    'full_register_map': wm, 'canonical_register_map': cm,
+    'only_deleted_explicit_operations': dict(we),
+    'preserved_helper_indices': list(range(R)),
+    'before': {'v': old_v, 'R': R, 'cst': 72, 'local_profile': c['local_profile']},
+    'after': {'v': new_v, 'R': R, 'cst': 64, 'local_profile': new_c['local_profile']},
+    'saved_local_children': {1: 8, 8: 16},
+    'scope': 'Exact restriction of all scalar body, compensation, cleanup, and frame labels. Global hosting and outer exponent require fresh certificates.',
+}
+dump(out / 'RESTRICTION.json', receipt)
+print(json.dumps({k: receipt[k] for k in ['status', 'removed_canonical_source_indices', 'before', 'after']}, indent=2))
diff --git a/research/ranksector112-async/vendor/pr523/code/emit_async.py b/research/ranksector112-async/vendor/pr523/code/emit_async.py
new file mode 100644
index 0000000000..54cbad05e3
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/code/emit_async.py
@@ -0,0 +1,90 @@
+"""Punctured 112-port whole-owner derivative, adapted for icekylinx with GPT-6 Astra.
+Based on PR514 and its credited PR484/507 lineage.
+CLI: SOURCE484_PACKAGE VERIFIED_VARIANT ASYNC-OWNERS.json.gz ASYNC-PLAN.json OUT
+No optimizer or unpublished word builder runs. The frozen map explicitly names
+one whole helper per family per complete invocation, plus borrowed spectators.
+"""
+import sys,json,gzip,hashlib,copy
+from pathlib import Path
+from collections import Counter,defaultdict
+SOURCE,BASE,MAP,PLAN,OUT=map(lambda p:Path(p).resolve(),sys.argv[1:6]);assert not OUT.exists();OUT.mkdir(parents=True)
+sys.path.insert(0,str(SOURCE/'code'));import onehost_gk as OH
+read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+plan=read(PLAN);call_order=[tuple(x)for x in plan['order']];assert len(call_order)==len(set(call_order))==72;at={x:i for i,x in enumerate(call_order)}
+parent=read(BASE/'split-centres/GLOBAL-TEMPLATE.json.gz');t=copy.deepcopy(parent);canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz');checks=read(BASE/'split-centres/LOCAL-CHECKS.json');ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json');roles=read(MAP);T=8;V=112;M=73;R=560;DATA=8*T*V
+assert(len(roles),len(canon['start']),len(ph['recipes']))==(72*R,2*V+R,V)
+widths=[9-len(canon['frames'][canon['start'][(2*V)+h]])for h in range(R)];assert widths==plan['baseline_widths'], 'source-bound selected provider widths'
+rank={z['child']:z['rank']for z in parent['idle_children']};side={};pairs={}
+for e in parent['execution_schedule']:
+ if e['kind']=='idle_cover_sweep':
+  for sd,ch in enumerate(e['child_indices']):side[ch]=sd;pairs[ch]=e['pair']
+bycall=defaultdict(dict);used=defaultdict(set);sigmas={};digest=hashlib.sha256();entering=0
+for z in roles:
+ s,rep,h=z['stage'],z['replica'],z['helper'];i,cp,off,w,f=z['child'],z['copy'],z['offset'],z['width'],z['family'];orp,port=divmod(cp,V)
+ assert 0<=s<9 and 0<=rep<T and 0<=h<R and w==widths[h] and 0<=orp<T
+ assert f==orp*(8*V)+(2*pairs[i]+side[i])*V+port
+ assert(h not in bycall[s,rep])and off>=0 and off+w<=rank[i]
+ assert z['time']==at[s,rep] and z['time'] in plan['windows'][f'{orp},{i}'][1]
+ B=OH.idle_basis(canon['ports'][port]);pending=list(map(int,ph['recipes'][port]['idle_children'][i]['orthogonal_axes']));assert len(pending)==rank[i]
+ occ=[B.index(v)for v in pending[off:off+w]];sp=OH.spectators(canon['ports'][port],pending,off,w)if w<9 else[]
+ order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert len(order)==len(set(order))==M
+ sigma=[B[j]for j in order];sigmahash=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sigmahash]=sigma
+ route=[4,i,off,w,sp]if w<9 else[3,i,off];bycall[s,rep][h]=[f,route];entering+=w<9
+ cells=set(range(off,off+w));assert not used[i,orp,port]&cells;used[i,orp,port]|=cells
+ digest.update(json.dumps([s,rep,h,f,sigmahash],separators=(',',':')).encode()+b'\n')
+for c in t['calls']:
+ k=(c['stage'],c['replica']);assert set(bycall[k])==set(range(R))
+ c['owners']=c['owners'][:(2*V)]+[bycall[k][h]for h in range(R)];assert len({f for f,r in c['owners']})==2*V+R and all(f<DATA for f,r in c['owners'])
+newidle=[];paid=Counter()
+for c in t['calls']:
+ for r,n in checks[c['orientation']]['paid_profile'].items():paid[int(r)]+=n
+for old in parent['idle_children']:
+ i,port=old['child'],old['port']
+ for rep in range(T):
+  u=used[i,rep,port];assert u==set(range(len(u)));left=old['rank']-len(u)
+  if left:
+   f=rep*(8*V)+(2*pairs[i]+side[i])*V+port;newidle.append(dict(child=i,port=port,replica=rep,replicas=1,family=f,rank=left,hosted=len(u),pending_offset=len(u)));paid[left]+=1
+assert M*DATA-sum(r*n for r,n in paid.items())==2560
+C=len(canon['centers']);physical=DATA+C+R+2
+assert parent['physical']-parent['live']==C+R+2
+# Local circuits, exact phase recipes, normalized wrappers and data routes stay
+# byte-identical; only full-family helper placement and idle remainders change.
+t.update(version='punctured112-asynchronous-whole-owner-v1',live=DATA,physical=physical,idle_children=newidle,private_namespace={'centers':[DATA,DATA+C],'reserved_tableau':[DATA+C,DATA+C+R],'coefficient':[physical-2,physical]})
+t['hosting']=dict(rule='one-helper-per-physical-family-per-complete-invocation',max_helpers_per_physical_family_per_call=1,scope='asynchronously interleaved data replicas; each whole helper occurs once per(stage,invocation replica)',pooled_slots=roles,banks=[0]*9,owner_map_sha256=hashlib.sha256(MAP.read_bytes()).hexdigest(),idle_remainder_semantics='Each idle_children item acts once, on its explicit replica/family, at pending_offset with the stated rank; replicas=1.')
+t['route_semantics']['helper']='Whole physical family may belong to another replica; actual orthogonal port basis followed by residual/spectator coordinate permutation. Entering helpers have paid wrappers around the complete invocation; at most one helper and no active data wire uses that family in that invocation. Route[4,child,offset,width,spectators], width9 route[3,child,offset].'
+t['bank_padding']['families']=[];t['cover_final_correction']['families']=[0,DATA];t['cover_final_correction']['charged_calls_per_cover']=DATA
+for e in t['execution_schedule']:
+ if e['kind']=='bank_padding_cover_sweep':e['families']=[DATA,DATA]
+ elif e['kind']=='translate_every_live_family':e.update(t['cover_final_correction'])
+# Expand the retained controller into one-replica blocks; each block consists
+# of its full local cover sweep and every following replica-local event before
+# its next local sweep. Final whole-stock correction remains after all replicas.
+blocks={};globals_=[];st=None
+for ei,e in enumerate(parent['execution_schedule']):
+ if e['kind']in('bank_padding_cover_sweep','translate_every_live_family'):
+  globals_.append((ei,e));continue
+ if e['kind']=='local_cover_sweep':st=e['stage'];blocks[st]=[]
+ assert st is not None
+ blocks[st].append((ei,e))
+new_schedule=[]
+for tm,(s,rep)in enumerate(call_order):
+ for ei,e in blocks[s]:
+  ne=copy.deepcopy(e);ne.update(replica=rep,replicas=[rep],source_event=ei,time=tm)
+  new_schedule.append(ne)
+for ei,e in globals_:
+ ne=copy.deepcopy(e);ne['source_event']=ei
+ if e['kind']=='bank_padding_cover_sweep':ne['families']=[DATA,DATA]
+ else:ne.update(t['cover_final_correction'])
+ new_schedule.append(ne)
+t['execution_schedule']=new_schedule
+cmap={(c['stage'],c['replica']):c for c in t['calls']}
+t['calls']=[dict(cmap[s,rep],time=tm)for tm,(s,rep)in enumerate(call_order)]
+t['loop_order']='Follow the explicit asynchronous execution_schedule. Each local invocation completes before the next, including its entire cover sweep and normalization wrappers. Per-replica source event order is preserved; each idle remainder executes before that replica next touches its family.'
+t['async_schedule']=dict(order=[list(x)for x in call_order],source_plan_sha256=hashlib.sha256(PLAN.read_bytes().replace(b'\r\n',b'\n')).hexdigest(),source_schedule=parent['execution_schedule'],source_call_order=[[c['stage'],c['replica']]for c in parent['calls']],scope='Only independent replica controllers are interleaved. Owner windows are measured on the owner replica timeline; no within-cover or within-invocation interleaving.')
+assert dict(sorted(paid.items()))=={int(k):v for k,v in plan['profile'].items()}
+assert M*M>2*max(paid)**2
+
+assert t['local_programs']==parent['local_programs']
+raw=json.dumps(t,sort_keys=True,separators=(',',':')).encode();(OUT/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+res=dict(status='EMITTED_ASYNCHRONOUS_WHOLE_OWNER_COMPLEX_TEMPLATE',template_sha256=hashlib.sha256(raw).hexdigest(),parent_template_sha256=hashlib.sha256(gzip.decompress((BASE/'split-centres/GLOBAL-TEMPLATE.json.gz').read_bytes())).hexdigest(),live=DATA,physical=physical,global_profile=dict(sorted(paid.items())),rank_mass=sum(r*n for r,n in paid.items()),deficit=2560,maxchild=max(paid),hosted_residuals=len(roles),banks_per_stage=[0]*9,entering_helper_roles=entering,unique_actual_73column_sigmas=len(sigmas),sigma_stream_sha256=digest.hexdigest(),cross_replica_helper_roles=sum(z['replica']!=z['owner_replica']for z in roles),asynchronous_order_sha256=hashlib.sha256(json.dumps(call_order,separators=(',',':')).encode()).hexdigest(),source_artifacts={p.relative_to(BASE).as_posix():hashlib.sha256(p.read_bytes()).hexdigest()for p in [BASE/'split-centres/CANONICAL-WORD.json.gz',BASE/'split-centres/LOCAL-PROGRAMS.json.gz',BASE/'split-centres/LOCAL-CHECKS.json',BASE/'split-centres/RESIDUAL-ADAPTERS.json',BASE/'work/complex-nine-native/DATA-PHASES.json']},scope='New emitted complete-invocation placement; independent controller/spectator/normalization and complete finite invoice admission required.')
+(OUT/'HOSTED.json').write_text(json.dumps(res,indent=2)+'\n');(OUT/'ACTUAL-SIGMAS.json.gz').write_bytes(gzip.compress(json.dumps(sigmas,separators=(',',':')).encode(),mtime=0));print(json.dumps(res,indent=2))
diff --git a/research/ranksector112-async/vendor/pr523/code/emit_local112.py b/research/ranksector112-async/vendor/pr523/code/emit_local112.py
new file mode 100644
index 0000000000..a54170b002
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/code/emit_local112.py
@@ -0,0 +1,156 @@
+# GK: modified copy of PR #433's complex_emit.py (icekylinx with Codex assistance; PR #425) by DreamingOfClouds with Claude Opus 5.5
+# (Anthropic), via Claude Code.  Every change is marked "GK:".  On a word without start_extra / target_levels the behaviour
+# and every written file equal PR #433's (regression anchor in verify.py).
+import sys as _sys, os as _os; _sys.path.insert(0, _os.path.dirname(_os.path.abspath(__file__)))
+# Adapted from PR425 by icekylinx with Codex assistance.
+"""Emit both local programs, integrate the fixed nine-stage geometry, and bill.
+
+The expanded scalar interface is justified in PROOF.txt. This script does not
+claim a Lean proof or discharge the inherited all-size/analytic interfaces.
+"""
+import copy,gzip,hashlib,importlib.util,json,math
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+OUT=Path(_sys.argv[1]);cp=OUT/'CANONICAL-WORD.json.gz'
+c=json.load(gzip.open(cp))
+frames=c['frames'];v,R,h=c['v'],c['R'],c['h'];n=2*v+R
+def digest(x):return hashlib.sha256(json.dumps(x,sort_keys=True,separators=(',',':')).encode()).hexdigest()
+def basis(vs):
+    b={}
+    for x in vs:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+def dual(e):
+    e=list(e)
+    if e[0]=='add':e[1],e[2]=e[2],e[1];e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    return e
+def scalar(e,back):
+    e=dual(e) if back else list(e)
+    if e[0]=='add':return ['add',['L',e[1]],['L',e[2]],e[3],e[4]]
+    return ['scale',['L',e[1]],e[2],e[3]]
+def primitive_bound(e):
+    if e[0] in ('clear','copy'):return 1
+    q=Q(e[3],e[4]) if e[0]=='add' else Q(e[2],e[3])
+    a,b=abs(q.numerator),q.denominator
+    assert b&(b-1)==0
+    if e[0]=='scale':
+        assert a&(a-1)==0
+        return abs(a.bit_length()-b.bit_length())+int(q<0)
+    # Exact binary Horner multiplication on a cleared private stream, repeated
+    # halving, signed accumulation into the target, then clear the private stream.
+    return 3+(a.bit_length()-1)+a.bit_count()+(b.bit_length()-1)
+
+def emit(back):
+    out=[];cur=c['start'].copy()
+    def event(e):out.append(e)
+    def scal(e,f):event(['scalar',e,f])
+    event(['phase','zero_frame_precondition'])
+    for e in c['precondition']+c['compensation']:
+        regs=[e[1]]+([e[2]] if e[0]=='add' else [])
+        assert all(c['start'][r]==0 for r in regs)
+        scal(scalar(e,back),0)
+    event(['phase','entry_adapters'])
+    # GK: a helper that starts at a nonzero entrance frame has NO entry adapter; its paid wrapper R_E^-1 (Lemma A) precedes every gate
+    # that touches it and L_E^-1 follows the full-frame cleanup.  Words without entrances emit PR #433's events.
+    entering=[r for r,f in enumerate(c['start']) if r>=2*v and f!=0]
+    for r,f in enumerate(c['start']):
+        if r in entering:event(['residual_adapter','pre',r,f])
+        else:event(['adapter','old_to_new',r,f])
+    def climb(r,f,part):
+        old=cur[r]
+        if old==f:return
+        assert basis(frames[old]+frames[f])==tuple(frames[f])
+        rank=len(frames[f])-len(frames[old]);assert rank>0
+        event(['climb',part,r,old,f,rank]);cur[r]=f
+    for part in ('A','centers','B','final'):
+        event(['phase',part])
+        if part in ('A','B'):
+            for e in c[part]:
+                regs=[e[1]]+([e[2]] if e[0]=='add' else [])
+                for r in regs:climb(r,e[-1],part)
+                scal(scalar(e,back),e[-1])
+        elif part=='centers':
+            # GK: targets sit at their nonzero-frame-compensation level (0 at the defaults); a centre copy descends
+            # cf -> served levels (descending chain) -> lowest served level and scatters into each target at its level
+            lv=lambda r:c.get('target_levels',{}).get(str(r-v),0)
+            assert all(cur[r]==lv(r) for r in range(v,2*v))
+            for k,r in enumerate(c['centers']):
+                cf=c['center_frames'][k];assert cur[r]==cf
+                terms=[e for e in c['cut'] if e[2]==r]
+                path=[cf]+sorted({lv(e[1]) for e in terms}-{cf},key=lambda x:-len(frames[x]))
+                C=['C',k]
+                if not back:
+                    scal(['clear',C],cf);scal(['copy',C,['L',r]],cf)
+                    for a in range(len(path)):
+                        if a>0:event(['center',k,path[a-1],path[a],len(frames[path[a-1]])-len(frames[path[a]])])
+                        for e in terms:
+                            if lv(e[1])==path[a]:scal(['add',['L',e[1]],C,e[3],e[4]],path[a])
+                    scal(['clear',C],path[-1])
+                else:
+                    scal(['clear',C],path[-1])
+                    for a in range(len(path)-1,-1,-1):
+                        for e in terms:
+                            if lv(e[1])==path[a]:scal(['add',C,['L',e[1]],e[3],e[4]],path[a])
+                        if a>0:event(['center',k,path[a],path[a-1],len(frames[path[a-1]])-len(frames[path[a]])])
+                    scal(['add',['L',r],C,-1,1],cf);scal(['clear',C],cf)
+        else:
+            for r,f in enumerate(c['final']):climb(r,f,part)
+    event(['phase','exit_adapters'])
+    for r,f in enumerate(c['final']):event(['adapter','new_to_old',r,f])
+    event(['phase','full_frame_cleanup'])
+    for e in c['cleanup']:
+        regs=[e[1]]+([e[2]] if e[0]=='add' else [])
+        assert all(c['final'][r]==1 for r in regs)
+        scal(scalar(e,back),1)
+    for r in entering:event(['residual_adapter','post',r,c['start'][r]])   # GK: L_E^-1 after the full-frame cleanup
+    event(['phase','done'])
+    return out
+
+def check_local(events,back):
+    # Literal scalar replay of the emitted stream, including center lifetimes.
+    state={('L',r):{r:Q(1)} for r in range(n)};live=[];paid=Counter();prims=0;macros=0
+    for e in events:
+        if e[0]=='climb':assert not live;paid[e[5]]+=1
+        elif e[0]=='center':assert live==[e[1]];paid[e[4]]+=1
+        elif e[0]=='scalar':
+            op=e[1];tag=op[0];t=tuple(op[1]);macros+=1;prims+=2*primitive_bound(op)
+            if tag=='clear':
+                state[t]={}
+                if t[0]=='C' and t[1] in live:live.remove(t[1])
+            elif tag=='copy':state[t]=dict(state.get(tuple(op[2]),{}));live.append(t[1])
+            elif tag=='scale':state[t]={j:Q(op[2],op[3])*x for j,x in state[t].items()}
+            else:
+                s=tuple(op[2]);q=Q(op[3],op[4]);row=state.setdefault(t,{})
+                if t[0]=='C' and t[1] not in live:live.append(t[1])
+                for j,x in list(state.get(s,{}).items()):
+                    z=row.get(j,Q(0))+q*x
+                    if z:row[j]=z
+                    else:row.pop(j,None)
+    assert not live and all(not row for r,row in state.items() if r[0]=='C')
+    for r in range(n):
+        expected={r:Q(1)}
+        if back and r<v:expected[v+r]=Q(-1)
+        elif not back and v<=r<2*v:expected[r-v]=Q(1)
+        assert state['L',r]==expected,('emitted column mismatch',back,r)
+    assert dict(paid)=={int(r):z for r,z in c['local_profile'].items()}
+    return {'sha256':digest(events),'events':len(events),'scalar_macros':macros,
+            'real_component_primitive_bound':prims,'paid_profile':dict(sorted(paid.items())),
+            'all_columns':n,'private_centers_cleared':True,'private_coefficient_stream_cleared_after_each_macro':True}
+
+programs={};checks={}
+for name,back in [('forward',False),('backward',True)]:
+    programs[name]=emit(back);checks[name]=check_local(programs[name],back)
+    print('PASS emitted',name,checks[name]['events'],'events',flush=True)
+
+
+(OUT/'LOCAL-PROGRAMS.json.gz').write_bytes(gzip.compress(json.dumps(programs,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+(OUT/'LOCAL-CHECKS.json').write_text(json.dumps(checks,indent=2)+'\n')
diff --git a/research/ranksector112-async/vendor/pr523/code/phases_local112.py b/research/ranksector112-async/vendor/pr523/code/phases_local112.py
new file mode 100644
index 0000000000..d68f097d5d
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/code/phases_local112.py
@@ -0,0 +1,39 @@
+# Adapted from PR425 for heterogeneous centres by icekylinx with Codex assistance.
+"""Exact phase-aware lowering of every used edge of the new structural word."""
+import gzip,hashlib,json,sys,time
+from collections import Counter
+from pathlib import Path
+sys.path.insert(0,str(Path(sys.argv[2]).resolve()))
+from clifford_exact import *
+
+OUT=Path(sys.argv[1]);P=OUT/'CANONICAL-WORD.json.gz'
+c=json.load(gzip.open(P));n=c['h'];frames=c['frames'];start=time.monotonic();ops=[]
+for U in frames:
+    op=canonical_frame(n,U)
+    L=[u|(u<<n) for u in U]+[v<<n for v in nullspace(U,n)]
+    pre=[x|(z<<n) for x,z,p in inverse(op.tab)[n:]]
+    assert rank(L)==n and rank(L+pre)==n
+    assert rank([x for x,z,p in op.tab[n:]])==len(U)
+    ops.append(op)
+edges=set(map(tuple,c['edges']))|{(a,b) for f in c['center_frames'] for a,b in ((f,0),(0,f))};recipes=[];hist=Counter()
+for i,(a,b) in enumerate(sorted(edges)):
+    op=ops[a].adjoint().then(ops[b]);rec,compiled=lower_child(op)
+    assert rec['rank']==abs(len(frames[a])-len(frames[b]))
+    hist[rec['rank']]+=1;recipes.append({'old':a,'new':b,**rec})
+    if i%200==0:print('exact phase edges',i,'/',len(edges),'seconds',time.monotonic()-start,flush=True)
+adapters=[];F=fourier(n)
+for i,q in enumerate(c['ports']):
+    for role,old,f in [('source',cgate(n,q),c['start'][i]),
+                       ('target',cgate(n,q).adjoint().then(F),c['final'][c['v']+i])]:
+        rec,compiled=lower_child(old.adjoint().then(ops[f]));assert rec['rank']==0
+        adapters.append({'port':i,'role':role,'frame':f,**rec})
+raw=json.dumps({'children':recipes,'endpoint_adapters':adapters},sort_keys=True,separators=(',',':')).encode()
+(OUT/'CLIFFORD-RECIPES.json').write_bytes(raw)
+result={'status':'PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES',
+        'canonical_word_sha256':hashlib.sha256(P.read_bytes()).hexdigest(),
+        'frames':len(frames),'directed_edges':len(edges),'ranks':dict(hist),
+        'endpoint_adapters':len(adapters),'all_child_equalities_include_global_phase':True,
+        'recipe_sha256':hashlib.sha256(raw).hexdigest(),'seconds':time.monotonic()-start,
+        'scope':'Every local frame and center transition. Expanded scalar-interface integration and global emitted program are separate obligations.'}
+(OUT/'CLIFFORD-REVIEW.json').write_text(json.dumps(result,indent=2)+'\n')
+print('PASS exact local phases',result['seconds'],'seconds',flush=True)
diff --git a/research/ranksector112-async/vendor/pr523/code/restrict_global.py b/research/ranksector112-async/vendor/pr523/code/restrict_global.py
new file mode 100644
index 0000000000..5365b5cc80
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/code/restrict_global.py
@@ -0,0 +1,173 @@
+"""Restrict PR514's unhosted nine-stage template to its 112 code ports.
+
+This script constructs only the restricted parent. It does not claim that its
+old bank placement is the final whole-owner placement. All final hosted costs
+must be recounted from the separately emitted complete program.
+
+Usage: python restrict_global.py PARENT_BASE LOCAL112 NEW_BASE
+"""
+from pathlib import Path
+from collections import Counter
+import argparse,copy,gzip,hashlib,json,math,shutil,sys
+
+parser=argparse.ArgumentParser(description=__doc__,formatter_class=argparse.RawDescriptionHelpFormatter)
+parser.add_argument('parent_base',type=Path,help='Replayed pinned PR514 base directory')
+parser.add_argument('local112',type=Path,help='Fully verified 112-port local artifact directory')
+parser.add_argument('new_base',type=Path,help='New output base directory; must not exist')
+args=parser.parse_args()
+PARENT,LOCAL,OUT=(p.resolve()for p in(args.parent_base,args.local112,args.new_base))
+if not __debug__:raise RuntimeError('Assertions must be enabled')
+if OUT.exists():parser.error('Output directory already exists: '+str(OUT))
+def read(p):return json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+def gzip_content_sha(p):return hashlib.sha256(gzip.decompress(p.read_bytes())).hexdigest()
+def dump(p,x):
+    p.parent.mkdir(parents=True,exist_ok=True)
+    raw=json.dumps(x,sort_keys=True,separators=(',',':')).encode()
+    p.write_bytes(gzip.compress(raw,mtime=0)if p.suffix=='.gz'else raw+b'\n')
+    return hashlib.sha256(raw).hexdigest()
+
+S=PARENT/'split-centres';D=OUT/'split-centres'
+old=read(S/'GLOBAL-TEMPLATE.json.gz');can0=read(S/'CANONICAL-WORD.json.gz')
+can=read(LOCAL/'CANONICAL-WORD.json.gz');checks=read(LOCAL/'LOCAL-CHECKS.json')
+programs=read(LOCAL/'LOCAL-PROGRAMS.json.gz');mapping=read(LOCAL/'PORT-MAPPING.json')
+new_to_old=mapping['new_to_old'];old_to_new={v:i for i,v in enumerate(new_to_old)}
+assert len(new_to_old)==len(old_to_new)==112 and new_to_old==sorted(new_to_old)
+assert can['v']==112 and can['h']==9 and can['R']==560
+assert can['ports']==[can0['ports'][i]for i in new_to_old]
+assert can['frames']==can0['frames'] and len(can['centers'])==8
+assert can['start'][224:]==can0['start'][240:]
+assert can['final'][224:]==can0['final'][240:]
+assert old['live']==12720 and old['physical']==13298
+M,K,T,L,V,R=73,4,8,9,112,560
+DATA=2*K*T*V;W=old['live']-(7680-DATA);PHYSICAL=W+R+8+2
+assert (DATA,W,PHYSICAL)==(7168,12208,12778)
+
+def family(f):
+    if f>=7680:
+        assert f<old['live'];return f-512
+    comp,port=divmod(f,120);assert port in old_to_new
+    return comp*112+old_to_new[port]
+
+# The local proof artifacts are copied without modification. Global metadata
+# must bind their new actual hashes, never the parent phase/word hashes.
+names=['CANONICAL-WORD.json.gz','FULL-WORD.json.gz','LOCAL-PROGRAMS.json.gz',
+       'LOCAL-CHECKS.json','RESIDUAL-ADAPTERS.json','LEMMA-A.json',
+       'RESTRICTION.json','PORT-MAPPING.json','INDEPENDENT-LOCAL-REPLAY.json',
+       'CLIFFORD-RECIPES.json','CLIFFORD-REVIEW.json','TRANSPORT.json']
+for name in names:assert (LOCAL/name).is_file(),LOCAL/name
+D.mkdir(parents=True)
+for name in names:shutil.copyfile(LOCAL/name,D/name)
+shutil.copyfile(LOCAL/'INDEPENDENT-LOCAL-REPLAY.json',D/'INDEPENDENT-REPLAY.json')
+
+ph0=read(PARENT/'work/complex-nine-native/DATA-PHASES.json')
+ph=copy.deepcopy(ph0);ph['ports']=112
+ph['recipes']=[copy.deepcopy(ph0['recipes'][i])for i in new_to_old]
+for i,z in enumerate(ph['recipes']):
+    assert z['port']==new_to_old[i] and z['q']==can['ports'][i]
+    z['port']=i
+ph['nonzero_stage_alignment_translations']=sum(bool(v)for z in ph['recipes']for e in z['stage_alignment']for v in e.values())
+ph['terminal_omission_controls_rejected']=112
+ph['inherited_parent_exact_phase_polynomial_evaluations']=ph.pop('exact_phase_polynomial_evaluations')
+ph['restriction_method']='Each complete recipe is unchanged except its port index; the retained parent polynomial checks establish every selected equality.'
+ph['source_parent_sha256']=sha(PARENT/'work/complex-nine-native/DATA-PHASES.json')
+dump(OUT/'work/complex-nine-native/DATA-PHASES.json',ph)
+for name in ['moment.py','base_two_moment.py','outer.py']:
+    dest=OUT/'work/pr361/code/engines'/name;dest.parent.mkdir(parents=True,exist_ok=True)
+    shutil.copyfile(PARENT/'work/pr361/code/engines'/name,dest)
+
+t=copy.deepcopy(old);t['version']='hamming112-restricted-nine-stage-parent-v1'
+t['local_programs']=programs;t['live']=W;t['physical']=PHYSICAL
+t['private_namespace']={'centers':[W,W+8],'reserved_tableau':[W+8,W+8+R],
+                        'coefficient':[PHYSICAL-2,PHYSICAL]}
+for c in t['calls']:
+    oldowners=c['owners'];newowners=[]
+    for side in range(2):
+        for np,op in enumerate(new_to_old):
+            f,route=oldowners[side*120+op]
+            assert route==[1,c['stage'],op]
+            newowners.append([family(f),[1,c['stage'],np]])
+    newowners += [[family(f),copy.deepcopy(route)]for f,route in oldowners[240:]]
+    assert len(newowners)==784
+    c['owners']=newowners;c['local_program_sha256']=checks[c['orientation']]['sha256']
+t['idle_children']=[dict(e,port=old_to_new[e['port']])for e in old['idle_children']if e['port']in old_to_new]
+assert len(t['idle_children'])==18*112
+t['bank_padding']['families']=[family(f)for f in old['bank_padding']['families']]
+assert t['bank_padding']['families']==list(range(DATA,W))
+t['cover_final_correction'].update(families=[0,W],charged_calls_per_cover=W)
+for e in t['execution_schedule']:
+    if e['kind']=='bank_padding_cover_sweep':e['families']=[DATA,W]
+    elif e['kind']=='translate_every_live_family':e.update(t['cover_final_correction'])
+t['exact_data_phase_recipe_sha256']=sha(OUT/'work/complex-nine-native/DATA-PHASES.json')
+t['exact_local_clifford_recipe_sha256']=sha(D/'CLIFFORD-RECIPES.json')
+t['residual_adapter_sha256']=sha(D/'RESIDUAL-ADAPTERS.json')
+t['port_restriction']={'parent_global_template_content_sha256':gzip_content_sha(S/'GLOBAL-TEMPLATE.json.gz'),
+                       'parent_data_phase_sha256':sha(PARENT/'work/complex-nine-native/DATA-PHASES.json'),
+                       'new_to_old':new_to_old,
+                       'canonical_word_content_sha256':gzip_content_sha(D/'CANONICAL-WORD.json.gz'),
+                       'proof':'The nine-stage data route and idle recipes are a portwise direct sum after each verified complete invocation. Restrict every such sum to the selected 112 ports.'}
+template_hash=dump(D/'GLOBAL-TEMPLATE.json.gz',t)
+
+# Derive the unchanged bank remainder profile from literal old bank footprints,
+# independently of the old global histogram. A width-nine bank route is a slot
+# index; an entering route states its residual offset and width explicitly.
+foot={};bybank=Counter()
+for c in t['calls']:
+    for h,(f,rt)in enumerate(c['owners'][224:]):
+        width=9-len(can['frames'][can['start'][224+h]])
+        assert rt[0]==2
+        off=9*rt[1]if len(rt)==2 else rt[1]
+        if len(rt)>2:assert rt[2]==width
+        cells=set(range(off,off+width));assert not foot.setdefault(f,set())&cells
+        foot[f]|=cells
+assert set(foot)==set(range(DATA,W))
+pad=Counter()
+for f,cells in foot.items():
+    assert cells==set(range(len(cells)))
+    left=M-len(cells);parts=-(-left//51)
+    for i in range(parts):pad[left//parts+(i<left%parts)]+=1
+paid=Counter(pad)
+for c in t['calls']:
+    for r,n in checks[c['orientation']]['paid_profile'].items():paid[int(r)]+=n
+for e in t['idle_children']:paid[e['rank']]+=e['replicas']
+mass=sum(r*n for r,n in paid.items())
+assert M*W-mass==2560 and max(paid)==48
+
+# Fresh deterministic finite invoice using the inherited formula and enlarged
+# constant allowances. This does not reuse the old numerical kappa receipt.
+compiler=64*(M+1)**3;macros=max(z['scalar_macros']for z in checks.values())
+children=sum(checks['forward']['paid_profile'].values());N=224+R;C=8
+adapters=16*(macros+children+N+C)+64*M
+local_bound=max(z['real_component_primitive_bound']for z in checks.values())+adapters*compiler
+bridges=sum(e['kind']=='bridge'for e in t['recipe']);bridgeadd=2*V*T*bridges
+shifts=K*V*T;moves=2*K*V*T;NB=(W-DATA)//L
+widths=[9-len(can['frames'][f])for f in can['start'][224:]];enter=sum(w<9 for w in widths)
+scalar=sum(checks[c['orientation']]['real_component_primitive_bound']for c in t['calls'])
+nonlocal_items=4*V*T*L+2*V*T*L+2*L*T*R+sum(e['replicas']for e in t['idle_children'])+L*NB+bridgeadd+shifts+moves+W+PHYSICAL+2*L*T*enter*144
+outside=8*nonlocal_items+64*M
+pervertex=scalar+bridgeadd+shifts+moves+W+(72*adapters+outside)*compiler+64*PHYSICAL
+r=M//2;group=2**(r*r)*math.prod(2**(2*i)-1 for i in range(1,r+1))
+stock=group*PHYSICAL;smass=group*mass;logical=group*pervertex+64
+router=compiler*(logical+1)*(stock+1)**2
+G,E,C0=2**30000,2**100000,2**210000;B=smass+E
+literal=2*G*stock**2+8*smass+4*stock+4+32*M;depth=2
+row=depth*stock.bit_length()+9909+252
+assert local_bound<2**48 and logical<2**6050 and router<G and literal<E and B<2**100001
+assert 32*M*B*B<C0 and 2*B+18<C0 and row<20161 and M*M>2*max(paid)**2
+finite=dict(local_primitive_bound=local_bound,local_adapters=adapters,pervertex=pervertex,
+            physical_stock_bits=stock.bit_length(),router_bits=router.bit_length(),literal_bits=literal.bit_length(),
+            physical_row_coefficient=row,retained_row_coefficient=20161,compiler=compiler,
+            G_exponent=30000,E_exponent=100000,C0_exponent=210000,required_C0_bits=(32*M*B*B).bit_length(),
+            halving_degree=depth,halving_integer_inequality=[M*M,2*max(paid)**2])
+integ=dict(status='PASS_RESTRICTED_PARENT_TEMPLATE_AND_FRESH_FINITE_INVOICE',
+           canonical_word_sha256=sha(D/'CANONICAL-WORD.json.gz'),
+           exact_phase_receipt_sha256=sha(D/'CLIFFORD-REVIEW.json'),
+           global_template_sha256=template_hash,local_program_checks=checks,
+           R=R,v=V,m=M,live=W,physical=PHYSICAL,bank_assignments=L*T*R,
+           rank_mass=mass,deficit=2560,global_profile=dict(sorted(paid.items())),
+           bank_remainder_profile=dict(sorted(pad.items())),
+           emitted_local_events_all_calls=sum(checks[c['orientation']]['events']for c in t['calls']),
+           finite_invoice=finite,
+           scope='112-port unhosted parent with exact inherited data-chart restriction, new local program, and fresh finite invoice. Final whole-owner hosting and global kappa require the separate final audits.')
+dump(D/'INTEGRATION.json',integ)
+print(json.dumps({k:integ[k]for k in ['status','live','physical','rank_mass','deficit','global_profile']}),flush=True)
diff --git a/research/ranksector112-async/vendor/pr523/evidence/ASYNC-AUDIT.json b/research/ranksector112-async/vendor/pr523/evidence/ASYNC-AUDIT.json
new file mode 100644
index 0000000000..524c184858
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/evidence/ASYNC-AUDIT.json
@@ -0,0 +1,57 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS",
+  "template_sha256": "2ae6ac3aff97a861d037ee51d6dcdd7bfe79ecbb0d8f1e186754428abc997a99",
+  "complex_template_sha256": "2ae6ac3aff97a861d037ee51d6dcdd7bfe79ecbb0d8f1e186754428abc997a99",
+  "complex_live": 7168,
+  "complex_profile": {
+    "1": 182232,
+    "2": 11520,
+    "3": 41514,
+    "4": 6336,
+    "5": 24726,
+    "6": 4896,
+    "7": 132,
+    "8": 72,
+    "48": 230
+  },
+  "complex_hosted_residuals": 40320,
+  "physical": 7738,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "entering_helper_roles": 12384,
+  "cross_replica_helper_roles": 31430,
+  "one_owner_per_complete_invocation": true,
+  "helper_busy_family_window_checks": 40320,
+  "complete_invocations": 72,
+  "actual_orthogonal_73column_maps": 3214,
+  "actual_sigma_stream_sha256": "4cc12e28b22cb3d081a49fdc66dc8eda3b09eade298d0a2ddb0ba7ace33e7c17",
+  "all_actual_residual_and_spectator_charts": true,
+  "idle_remainders": 6914,
+  "mutations_rejected": [
+    "wrong call time",
+    "alias two whole owners",
+    "helper on active data family",
+    "owner in private namespace",
+    "unbound change of owner replica",
+    "omit complete invocation",
+    "reorder invocation replicas",
+    "interleave local invocations",
+    "change local instruction stream",
+    "wrong residual width",
+    "wrong spectator coordinate",
+    "omit spectator route",
+    "overlap residual footprint",
+    "omit idle remainder",
+    "underpay idle remainder",
+    "omit bridge touch",
+    "remove one-owner rule",
+    "duplicate frozen role",
+    "understate physical reserve"
+  ],
+  "widths": {
+    "7": 18,
+    "8": 154,
+    "9": 388
+  },
+  "scope": "Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses unchanged source local program and normalized residual-wrapper identities; all-size compilation and complete coefficient invoice are separate inherited obligations."
+}
diff --git a/research/ranksector112-async/vendor/pr523/evidence/COLD-REPLAY.json b/research/ranksector112-async/vendor/pr523/evidence/COLD-REPLAY.json
new file mode 100644
index 0000000000..596b326393
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/evidence/COLD-REPLAY.json
@@ -0,0 +1,102 @@
+{
+  "status": "PASS_CONDITIONAL_PUNCTURED112_GLOBAL_KAPPA",
+  "kappa": "182243220215421/125000000000000000",
+  "kappa_decimal": "0.001457945761723368",
+  "complex_lower": "1460074471110324279467/1000000000000000000000000",
+  "bit_lower": "391360506745414227149/250000000000000000000000",
+  "template_sha256": "2ae6ac3aff97a861d037ee51d6dcdd7bfe79ecbb0d8f1e186754428abc997a99",
+  "live": 7168,
+  "physical": 7738,
+  "deficit": 2560,
+  "global_profile": {
+    "1": 182232,
+    "2": 11520,
+    "3": 41514,
+    "4": 6336,
+    "5": 24726,
+    "6": 4896,
+    "7": 132,
+    "8": 72,
+    "48": 230
+  },
+  "strict_constraints": 47,
+  "improvement_over_pinned514": "66422302131539/1391523459591829",
+  "whole_owner_roles": 40320,
+  "all_own_stages": 14,
+  "pinned_predecessor_stages": 13,
+  "package_manifest_sha256": "a3b474f4b13db9b60e8a537720d64d50ecb42cfa88bd2a4c4984502bd1ec9e29",
+  "seconds": 650.614535019,
+  "steps": [
+    {
+      "stage": "01-pinned514-full-replay",
+      "exit": 0,
+      "seconds": 308.23951412299994
+    },
+    {
+      "stage": "02-restrict-local",
+      "exit": 0,
+      "seconds": 0.46915773900036584
+    },
+    {
+      "stage": "03-exact-word-transport",
+      "exit": 0,
+      "seconds": 0.4654135139999198
+    },
+    {
+      "stage": "04-emit-local",
+      "exit": 0,
+      "seconds": 1.5499576659995
+    },
+    {
+      "stage": "05-independent-local",
+      "exit": 0,
+      "seconds": 6.888225505999799
+    },
+    {
+      "stage": "06-exact-local-phases",
+      "exit": 0,
+      "seconds": 253.77691531000073
+    },
+    {
+      "stage": "07-residual-wrappers",
+      "exit": 0,
+      "seconds": 1.1274162619993149
+    },
+    {
+      "stage": "08-restrict-global-data",
+      "exit": 0,
+      "seconds": 3.223902376999831
+    },
+    {
+      "stage": "09-independent-global-restriction",
+      "exit": 0,
+      "seconds": 25.15944645200034
+    },
+    {
+      "stage": "10-emit-whole-owners",
+      "exit": 0,
+      "seconds": 12.609149544000502
+    },
+    {
+      "stage": "11-independent-hosted-program",
+      "exit": 0,
+      "seconds": 28.938579032000234
+    },
+    {
+      "stage": "12-independent-raw-reconstruction",
+      "exit": 0,
+      "seconds": 4.184479100999852
+    },
+    {
+      "stage": "13-scalar-prefix-and-finite-invoice",
+      "exit": 0,
+      "seconds": 3.3250559179996344
+    },
+    {
+      "stage": "14-two-moments-and-global-assembly",
+      "exit": 0,
+      "seconds": 0.6149898540006689
+    }
+  ],
+  "scope": "Finite complex restriction, exact local phases, whole physical owners, complete fee inventory, two rational moments and 47 outer inequalities checked. The unchanged PR493 bit operator, all-size compiler, common-label/mutable-basis realization, normalized Lemma A, restored-row, precision/tape and analytic-transfer contracts remain dependencies. No unconditional theorem or new Lean certification."
+}
diff --git a/research/ranksector112-async/vendor/pr523/evidence/COLD-STEPS.json b/research/ranksector112-async/vendor/pr523/evidence/COLD-STEPS.json
new file mode 100644
index 0000000000..06158446fb
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/evidence/COLD-STEPS.json
@@ -0,0 +1,72 @@
+[
+  {
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diff --git a/research/ranksector112-async/vendor/pr523/evidence/EXACT-ASSEMBLY.json b/research/ranksector112-async/vendor/pr523/evidence/EXACT-ASSEMBLY.json
new file mode 100644
index 0000000000..9fb041e0ca
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/evidence/EXACT-ASSEMBLY.json
@@ -0,0 +1,127 @@
+{
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+    "literal_scalar_guard": "1",
+    "row_product_gap": "23971789/25",
+    "balanced_prefix_above_kappa": "92246408469147011239995100660913306150873242790256977912565024048129773623297513605472970972801708347158668835098052545570768135287063899970196692087298726418459854378659946446411147755475154198447712860399189827308320031206673267194095449989383722565261902237953807482943011644424449859734117511281912899420183/62591254654444395266332041868923298557223381214115254081749259193277313649822372638541342068239951388860424688753593580979829497221515632869451517714027592314113851268624277564601334504368884635884089303303541241608356516625640659768857737016944853812392465638942920265468213476819170274654781518440878361668059625000000000000000",
+    "coordinate_movement_above_kappa": "2128709386956264232818844993425444039737115830916196067621324098850789293204864859174670425631951485144360908761198647560677361772523206345638147986523438512896593961487910647145257825129995439719368506919856613143003024090269528009798319298200054299046861683124356089509352472973106655523/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "compact_phase_layer_above_kappa": "237241230517620927789304470335920060749198892609133790646526118838819679787801127735453031236494055666385953170755671716727509104524386136805961394986169072834768024880285351054478506008850156500508988456765188685599708116648260859401901703779510950022955492792087097739798385340842236680634687942728276302016987/500730037235555162130656334951386388457787049712922032653994073546218509198578981108330736545919611110883397510028748647838635977772125062955612141712220738512910810148994220516810676034951077087072714426428329932866852133005125278150861896135558830499139725111543362123745707814553362197238252147527026893344477000000000000000000",
+    "bulk_exposure_above_kappa": "2128709386956264232818844993425444039737115830916196067621324098850789293204864859174670425631951485144360908761198647560677361772523206345638147986523438512896593961487910647145257825129995439719368506919856613143003024090269528009798319298200054299046861683124356089509352472973106655523/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "Gaussian_arithmetic_above_kappa": "3400119955847632908706404767541519651366952290011836423134191171349212965898145965208616459529711278663737817896131619677335980769511464283314527585026014798216876629489265469986260076175654483265290050933406499283398221332201462709667799318642764091681063117671326868289624206170397980036792259984407291096169327/4005840297884441297045250679611091107662296397703376261231952588369748073588631848866645892367356888887067180080229989182709087822177000503644897133697765908103286481191953764134485408279608616696581715411426639462934817064041002225206895169084470643993117800892346896989965662516426897577906017180216215146755816000000000000000000",
+    "scalar_work_above_kappa": "1080608020957970711445806021469413041039620097772704910750033493106817400538492377928387881142677944621454281587249322853738104936119992907027395230374979550453703974017048470410700556063091758322716181727823963802973125972844392764454249380636999882735524403623500063356921407485722285765149053714903079733909447/801168059576888259409050135922218221532459279540675252246390517673949614717726369773329178473471377777413436016045997836541817564435400100728979426739553181620657296238390752826897081655921723339316343082285327892586963412808200445041379033816894128798623560178469379397993132503285379515581203436043243029351163200000000000000000",
+    "dimension_above_kappa": "62408745345555604700914366600223712682771719446798052069123983596979664262742651409588431555057562216612546284048114766178839337876536912701316617573036307656082840818674448853858519874291061810527058452171612956839356343773549167539462294189728413381702984350440802299793688761134637208288230125983571498066057886281912899420183/62591254654444395266332041868923298557223381214115254081749259193277313649822372638541342068239951388860424688753593580979829497221515632869451517714027592314113851268624277564601334504368884635884089303303541241608356516625640659768857737016944853812392465638942920265468213476819170274654781518440878361668059625000000000000000"
+  },
+  "outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "bootstrap": [
+    {
+      "gap": "2075663143036637204008408653986961694186478842322488381925399820553912717804089/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "8355813792788"
+    },
+    {
+      "gap": "3030622765772411436900523474021300228359755425189617249465270724422472474738110705865561428897057428268737178608659437/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "3919572826901661842"
+    },
+    {
+      "gap": "4424934931870061803669044137802018342147158524915509194840440434477125988777972046430097488312327714658507510192070279292067232589866810673072335046185119921/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "1838606211958328912746291"
+    },
+    {
+      "gap": "6460734530347779280311149316655829396498459592041574785874437539110613736142108265564259801969169751943731487488257863001793816383325705103313301057701131550853150228037617642318777686618687037893/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "862459495445565344684730601667"
+    },
+    {
+      "gap": "9433153552381743151173633161030060023191882844100141330278019267148073594773463793482321191527942827331826376606513012648567287386372737639010129995680646533249459268816822024931911054024404098080010475033049332838595295363882249156969/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "404565358501615803245782312051230751"
+    },
+    {
+      "gap": "13773106683896250276493262884169083803932378675901149210706795135140825329574368048514855639091238801352439322638227476793654361852013476561487103406038512089352854742174870004560280631493080143386856996975909730471990201680701799945700953138316875643910490647527026893344477/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "189774859183368162401945302169887625384021"
+    }
+  ],
+  "complex_template_sha256": "2ae6ac3aff97a861d037ee51d6dcdd7bfe79ecbb0d8f1e186754428abc997a99",
+  "owner_audit_sha256": "59d9cf4ecbff3e40e74547e34b158cdc7e93d4c4bef02d73a95b81f0283087ca",
+  "invoice_sha256": "bb43ef04791037a37d2596c395e81191991fde6581326118995cf4318ee472a3",
+  "bit_scope": "PR493 published profile and operator reused as a pinned dependency; this verifier reprices its published profile but does not reconstruct that unchanged bit operator.",
+  "scope": "Conditional finite witness. Inherited compiler, precision/tape and analytic-transfer contracts remain assumed; changed-host operator admission recorded separately."
+}
diff --git a/research/ranksector112-async/vendor/pr523/evidence/GLOBAL-PREFIX.json b/research/ranksector112-async/vendor/pr523/evidence/GLOBAL-PREFIX.json
new file mode 100644
index 0000000000..a7709b46a2
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/evidence/GLOBAL-PREFIX.json
@@ -0,0 +1,13 @@
+{
+  "status": "PASS_ASYNC_GLOBAL_PREFIX",
+  "template_sha256": "2ae6ac3aff97a861d037ee51d6dcdd7bfe79ecbb0d8f1e186754428abc997a99",
+  "global_prefix_bits": 206,
+  "retained_payload_bits": 512,
+  "complete_invocation_cover_sweeps": 72,
+  "bridge_factor_two_sweeps": 72,
+  "local_scalar_coefficient_work_prefix_bits": 21,
+  "stream_input_sup_to_l2_bits": 37,
+  "primitive_arithmetic_margin_bits": 4,
+  "controller_audit_sha256": "325a8cc71afaf715f49b4145f2ab096aae1f107374e1bd8fc705d8a28ac2d8a0",
+  "proof": "Each complete normalized invocation has unitary helper endpoints and a data shear with at most two unitary summands. Distinct full orthogonal owner charts act by right-translation bijections on the retained cover group. Thus the maximum full-stream L2 norm grows by at most2per complete local cover sweep and individual bridge. All72local sweeps and72individual bridge sweeps are counted. Unit-modulus phases, idle children, terminal translations and normalized spectator endpoints are unitary. The independently replayed scalar/Horner envelope costs 21 bits, initial sup-to-L2 conversion 37 bits, primitive margin 4 bits: total 206 < 512. All-size child/compiler and precision/tape interfaces remain inherited."
+}
diff --git a/research/ranksector112-async/vendor/pr523/evidence/GLOBAL-RESTRICTION-AUDIT.json b/research/ranksector112-async/vendor/pr523/evidence/GLOBAL-RESTRICTION-AUDIT.json
new file mode 100644
index 0000000000..a823ab728f
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/evidence/GLOBAL-RESTRICTION-AUDIT.json
@@ -0,0 +1,77 @@
+{
+  "status": "PASS_INDEPENDENT_GLOBAL_DATA_PORT_RESTRICTION",
+  "retained_ports": 112,
+  "deleted_canonical_ports": [
+    0,
+    13,
+    22,
+    35,
+    40,
+    51,
+    54,
+    119
+  ],
+  "data_owner_roles": 16128,
+  "helper_owner_roles": 40320,
+  "complete_invocations": 72,
+  "exact_port_phase_recipes": 112,
+  "exact_stage_alignments": 1008,
+  "exact_idle_axis_recipes": 2240,
+  "paid_idle_children": 2016,
+  "replicated_paid_idle_children": 16128,
+  "bank_families": 5040,
+  "bank_remainder_profile": {
+    "1": 3492,
+    "9": 1386,
+    "17": 162
+  },
+  "unhosted_paid_profile": {
+    "1": 185724,
+    "2": 11520,
+    "3": 38160,
+    "4": 6336,
+    "5": 21456,
+    "6": 4896,
+    "7": 72,
+    "8": 5448,
+    "9": 1386,
+    "16": 3584,
+    "17": 162,
+    "32": 3584,
+    "48": 3584
+  },
+  "unhosted_rank_mass": 888624,
+  "unhosted_live": 12208,
+  "unhosted_physical": 12778,
+  "deficit": 2560,
+  "source_bindings": {
+    "canonical": "addf598581d2a20e13d0c18110607515ad90b06125616a2349e53a47bb5b6c80",
+    "canonical_content": "5226194a7beae50e9c43009df698959d596fdfb081346f32428aee798bdc1851",
+    "programs": "41a434cc1aa1bed3d3fcecea5c87f091c65a4937c6b2a31470e903e37f4578f0",
+    "local_phase": "1f37afd5a9e14b113ba56e0ac8a5200a6b41c695d2cd308dc0fd6ec46a4c73d2",
+    "adapters": "0e19e861b824ae229be801b98a64b4dd476618adf57c582782fcec0c97ada147",
+    "old_template": "496ea63118d50cec30670bf806f518861646e7f1c0ca11083b94812af0ff86b0",
+    "old_template_content": "3f17cc2d187a394e38680f9221a1ffa2bcfbc80fb096f9a37d60bc76dcde9ba2",
+    "old_phase": "f621f6d4296cb215f334830356c5f79fe10d6d04d15b3ccda76ba0885ab67d0a",
+    "phase": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa"
+  },
+  "negative_controls_rejected": [
+    "duplicate selected port",
+    "wrong phase port label",
+    "wrong inherited idle axis",
+    "missing terminal port correction",
+    "wrong data owner family",
+    "wrong canonical data route",
+    "stale local program hash",
+    "changed entering bank owner",
+    "missing complete invocation",
+    "missing paid idle child",
+    "missing cover correction",
+    "understated private reserve",
+    "unpaid bank remainder"
+  ],
+  "local_scalar_replay_receipt_sha256": "e34ab1154656d082db4ccb8dbbdf8e2bca0903a56d8bad4ffa5ede35a2c80df5",
+  "local_phase_receipt_sha256": "468a5df1937e82a0b8e8c1c2540e18480f354154325353c5596c68e7435c89c2",
+  "template_content_sha256": "7e8299995f7a86e558f9074e86b7138f5cc32a60df90be652570f3c4bfb94285",
+  "scope": "Exact restriction of all inherited global data routes, phase recipes, complete-call order, idle axes and terminal corrections. Local arbitrary-dirt identities are supplied by the newly hash-bound independent local replay. Actual bank remainders are recounted for the conservative parent invoice. Final whole-owner placement, executable global program, finite compilation and outer exponent require their separate fresh audits."
+}
diff --git a/research/ranksector112-async/vendor/pr523/evidence/INDEPENDENT112-RAW-AUDIT.json b/research/ranksector112-async/vendor/pr523/evidence/INDEPENDENT112-RAW-AUDIT.json
new file mode 100644
index 0000000000..2d44190ccd
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/evidence/INDEPENDENT112-RAW-AUDIT.json
@@ -0,0 +1,95 @@
+{
+  "actual_orthogonal_charts": 3214,
+  "all_owners_per_call_distinct": 784,
+  "deficit": 2560,
+  "deleted_canonical_ports": [
+    0,
+    13,
+    22,
+    35,
+    40,
+    51,
+    54,
+    119
+  ],
+  "deleted_scalar_operations": {
+    "cut": 8
+  },
+  "helpers": 560,
+  "idle_remainders": {
+    "3": 3354,
+    "5": 3270,
+    "7": 60,
+    "48": 230
+  },
+  "inputs": {
+    "/workspace/scratch/34fc7703659c/cold112-release/baseline514/base/split-centres/CANONICAL-WORD.json.gz": "4f17487004ca3add38993e742fa2146013ba5d1d66f8a868fe2fecaddcb908b5",
+    "/workspace/scratch/34fc7703659c/cold112-release/baseline514/base/split-centres/GLOBAL-TEMPLATE.json.gz": "496ea63118d50cec30670bf806f518861646e7f1c0ca11083b94812af0ff86b0",
+    "/workspace/scratch/34fc7703659c/cold112-release/baseline514/base/work/complex-nine-native/DATA-PHASES.json": "f621f6d4296cb215f334830356c5f79fe10d6d04d15b3ccda76ba0885ab67d0a",
+    "/workspace/scratch/34fc7703659c/cold112-release/local112/CANONICAL-WORD.json.gz": "addf598581d2a20e13d0c18110607515ad90b06125616a2349e53a47bb5b6c80",
+    "/workspace/scratch/34fc7703659c/cold112-release/local112/LOCAL-PROGRAMS.json.gz": "41a434cc1aa1bed3d3fcecea5c87f091c65a4937c6b2a31470e903e37f4578f0",
+    "/workspace/scratch/34fc7703659c/cold112-release/local112/RESIDUAL-ADAPTERS.json": "0e19e861b824ae229be801b98a64b4dd476618adf57c582782fcec0c97ada147",
+    "/workspace/scratch/34fc7703659c/deliverable/integer_mult_round19_punctured112/inputs/OWNERS112.json.gz": "2bf969a881171dfd1e7357c8e097f134fbfe5080102b8670f54f4a27ae024fe8"
+  },
+  "invocations": 72,
+  "live": 7168,
+  "local": {
+    "backward": {
+      "columns": 784,
+      "events": 25242,
+      "profile": {
+        "1": 2531,
+        "2": 160,
+        "3": 530,
+        "4": 88,
+        "5": 298,
+        "6": 68,
+        "7": 1,
+        "8": 1
+      },
+      "scalar_macros": 19816
+    },
+    "forward": {
+      "columns": 784,
+      "events": 25242,
+      "profile": {
+        "1": 2531,
+        "2": 160,
+        "3": 530,
+        "4": 88,
+        "5": 298,
+        "6": 68,
+        "7": 1,
+        "8": 1
+      },
+      "scalar_macros": 19816
+    }
+  },
+  "no_emitter_or_hosting_checker_imported": true,
+  "no_nominated_profile_or_windows_used": true,
+  "paid_profile": {
+    "1": 182232,
+    "2": 11520,
+    "3": 41514,
+    "4": 6336,
+    "5": 24726,
+    "6": 4896,
+    "7": 132,
+    "8": 72,
+    "48": 230
+  },
+  "pending_axes_covered": 349200,
+  "physical": 7738,
+  "rank_mass": 520704,
+  "residual_widths": {
+    "7": 18,
+    "8": 154,
+    "9": 388
+  },
+  "same_local_frames_and_residual_wrappers_as_PR514": true,
+  "scope": "Independent finite restriction, all rational scalar columns, nested local frames, fixed whole-owner schedule, actual port charts and paid histogram. The inherited all-size/compiler, common-label realization, precision/tape and analytic transfer interfaces remain conditions.",
+  "seconds": 3.9092095610003526,
+  "status": "PASS_INDEPENDENT_RAW_112_RESTRICTION_LOCAL_COLUMNS_CHARTS_WINDOWS_OWNERS_AND_PROFILE",
+  "v": 112,
+  "whole_owner_roles": 40320
+}
diff --git a/research/ranksector112-async/vendor/pr523/evidence/OWNERS-AND-PROFILE.json b/research/ranksector112-async/vendor/pr523/evidence/OWNERS-AND-PROFILE.json
new file mode 100644
index 0000000000..d84692e11e
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/evidence/OWNERS-AND-PROFILE.json
@@ -0,0 +1,35 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE",
+  "template_sha256": "2ae6ac3aff97a861d037ee51d6dcdd7bfe79ecbb0d8f1e186754428abc997a99",
+  "paid_profile": {
+    "1": 182232,
+    "2": 11520,
+    "3": 41514,
+    "4": 6336,
+    "5": 24726,
+    "6": 4896,
+    "7": 132,
+    "8": 72,
+    "48": 230
+  },
+  "live": 7168,
+  "physical": 7738,
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "hosted_residuals": 40320,
+  "banked_residuals": 0,
+  "all_784_owners_per_call_distinct": true,
+  "actual_helper_owner_charts": 40320,
+  "actual_73column_sigmas": 3214,
+  "cross_replica_helper_roles": 31430,
+  "explicit_idle_remainder_children": 6914,
+  "source_idle_children_charged": 16128,
+  "source_artifacts": {
+    "split-centres/CANONICAL-WORD.json.gz": "addf598581d2a20e13d0c18110607515ad90b06125616a2349e53a47bb5b6c80",
+    "split-centres/LOCAL-PROGRAMS.json.gz": "41a434cc1aa1bed3d3fcecea5c87f091c65a4937c6b2a31470e903e37f4578f0",
+    "split-centres/LOCAL-CHECKS.json": "ead7163869ecb9fc276f477c0ec0ed85dc74d7901ce04f91213bcf7ee1f20382",
+    "split-centres/RESIDUAL-ADAPTERS.json": "0e19e861b824ae229be801b98a64b4dd476618adf57c582782fcec0c97ada147",
+    "work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa"
+  },
+  "controller_audit_sha256": "325a8cc71afaf715f49b4145f2ab096aae1f107374e1bd8fc705d8a28ac2d8a0"
+}
diff --git a/research/ranksector112-async/vendor/pr523/evidence/PREDECESSOR-REPLAY.json b/research/ranksector112-async/vendor/pr523/evidence/PREDECESSOR-REPLAY.json
new file mode 100644
index 0000000000..6ee4ed0391
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/evidence/PREDECESSOR-REPLAY.json
@@ -0,0 +1,78 @@
+{
+  "status": "PASS_CONDITIONAL_ASYNCHRONOUS_COMPLEX_DERIVATIVE",
+  "kappa": "1391523459591829/1000000000000000000",
+  "kappa_decimal": "0.001391523459591829",
+  "complex_lower": "139346249534416215349/100000000000000000000000",
+  "bit_lower": "391360506745414227149/250000000000000000000000",
+  "template_sha256": "77767f67ed17413161d82f2a407e69b3beefef3fc44bfe582fb403bdc1705bd8",
+  "strict_constraints": 47,
+  "scope": "New complex program independently replayed. The unchanged PR493 bit operator and inherited all-size compiler, common-label, Lemma A realization, restored-row, precision/tape and analytic-transfer contracts remain dependencies. No unconditional multiplication bound or fresh Lean certification is claimed.",
+  "stages": [
+    {
+      "stage": "partial-factory",
+      "exit": 0,
+      "seconds": 0.49569224400056555
+    },
+    {
+      "stage": "construct-kernel92",
+      "exit": 0,
+      "seconds": 2.051531082999645
+    },
+    {
+      "stage": "kernel-scalar-controls",
+      "exit": 0,
+      "seconds": 20.970359359000213
+    },
+    {
+      "stage": "scalar",
+      "exit": 0,
+      "seconds": 2.5955701240000053
+    },
+    {
+      "stage": "emit-local",
+      "exit": 0,
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diff --git a/research/ranksector112-async/vendor/pr523/evidence/PREFIX-AND-INVOICE.json b/research/ranksector112-async/vendor/pr523/evidence/PREFIX-AND-INVOICE.json
new file mode 100644
index 0000000000..50b017a164
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/evidence/PREFIX-AND-INVOICE.json
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+{
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+    "literal": true,
+    "mass": true,
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+    "tape": true,
+    "row": true,
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+  "scope": "Exact finite recount conditional on inherited all-size compiler/precision/tape and analytic-transfer contracts. Signed accumulation uses the supplier scalar primitive convention. Async prefix counts all72individual bridges and72complete invocations;512bits are charged, and an additional2*512 enters the two-level physical row bound."
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diff --git a/research/ranksector112-async/vendor/pr523/evidence/PUBLIC-SNAPSHOT.json b/research/ranksector112-async/vendor/pr523/evidence/PUBLIC-SNAPSHOT.json
new file mode 100644
index 0000000000..e028d81e1a
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/evidence/PUBLIC-SNAPSHOT.json
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+{
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+  "source": "https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls?state=open&sort=created&direction=desc&per_page=10",
+  "scope": "Metadata and descriptions inspected for current comparison; no new code adopted during this refresh.",
+  "pulls": [
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+      "title": "Open asynchronous whole-owner allocator and a delivery-layer map of the complex word",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/520",
+      "author": "higherbeing",
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+      "updated_at": "2026-10-11T23:57:03Z"
+    },
+    {
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+      "title": "[Lean] Add automatic-width binary counting",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/519",
+      "author": "jamesyc",
+      "head": "ffd3c48a80ba8b579dc300e785e387fe8acddfef",
+      "created_at": "2026-10-11T23:51:04Z",
+      "updated_at": "2026-10-11T23:51:04Z"
+    },
+    {
+      "number": 518,
+      "title": "Conditional kappa 0.001393662920776407: blockwise pair exposure, 99 pivots and whole-owner allocation",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/518",
+      "author": "Dugongue",
+      "head": "e0a071dce251eeca96d446f73147048cfebbd5c7",
+      "created_at": "2026-10-11T23:50:50Z",
+      "updated_at": "2026-10-11T23:50:50Z"
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+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/517",
+      "author": "chafreaky",
+      "head": "65518fcff5a7bd490365273ae5469a82aac14853",
+      "created_at": "2026-10-11T23:44:12Z",
+      "updated_at": "2026-10-11T23:44:12Z"
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+    {
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+      "title": "Lemma A of #484: the realization of paid wrappers and spectators, proved in Lean 4",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/516",
+      "author": "DreamingOfClouds",
+      "head": "1c6b6ff9366a94e1f86a6c5d661a7df75c6ff814",
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+      "updated_at": "2026-10-11T23:58:28Z"
+    },
+    {
+      "number": 515,
+      "title": "Bit word R685 (R687 lineage): L-copy inline + Bcw copy deletions, c = 1.323554·10⁻³ (+0.62% over #504's R687)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/515",
+      "author": "DreamingOfClouds",
+      "head": "6590606e733768f6a7004b3f55ae35f988ba515f",
+      "created_at": "2026-10-11T23:35:02Z",
+      "updated_at": "2026-10-11T23:35:02Z"
+    },
+    {
+      "number": 514,
+      "title": "Conditional kappa 0.001391523459591829: partial-own factory, 92 pivots and asynchronous whole owners",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/514",
+      "author": "Dugongue",
+      "head": "246bfacd4cb4072836ae3147099f548bb728229f",
+      "created_at": "2026-10-11T23:22:36Z",
+      "updated_at": "2026-10-11T23:22:36Z"
+    },
+    {
+      "number": 513,
+      "title": "[Lean] Add sequential completed-bank source bindings",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/513",
+      "author": "jamesyc",
+      "head": "005dd3f4e3cba8d1761abc4ab391aaf6d14d6f73",
+      "created_at": "2026-10-11T23:10:56Z",
+      "updated_at": "2026-10-11T23:10:56Z"
+    },
+    {
+      "number": 512,
+      "title": "Conditional κ = 0.001388049083313897: fresh partial-own asynchronous whole-owner certificate",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/512",
+      "author": "chafreaky",
+      "head": "73d367fe754cf5921cd954221133b20ac752f932",
+      "created_at": "2026-10-11T23:05:48Z",
+      "updated_at": "2026-10-11T23:05:48Z"
+    },
+    {
+      "number": 511,
+      "title": "[Lean] Add checked binary count dispatcher",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/511",
+      "author": "jamesyc",
+      "head": "9a20ad04be54b1c0fa26bd4ceb689f9ea220eab5",
+      "created_at": "2026-10-11T23:03:41Z",
+      "updated_at": "2026-10-11T23:47:23Z"
+    }
+  ],
+  "comparable_numerical_frontier": {
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+  "latest_pr520": "Open allocator and delivery map; reproduces older endpoint and states an unsolved direction, with no higher global kappa reported."
+}
diff --git a/research/ranksector112-async/vendor/pr523/evidence/SERIALIZATION-CHECKS.json b/research/ranksector112-async/vendor/pr523/evidence/SERIALIZATION-CHECKS.json
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index 0000000000..304b3e07cf
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+++ b/research/ranksector112-async/vendor/pr523/evidence/SERIALIZATION-CHECKS.json
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+}
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diff --git a/research/ranksector112-async/vendor/pr523/evidence/hosted/HOSTED.json b/research/ranksector112-async/vendor/pr523/evidence/hosted/HOSTED.json
new file mode 100644
index 0000000000..67f324bec6
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/evidence/hosted/HOSTED.json
@@ -0,0 +1,46 @@
+{
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+  "template_sha256": "2ae6ac3aff97a861d037ee51d6dcdd7bfe79ecbb0d8f1e186754428abc997a99",
+  "parent_template_sha256": "7e8299995f7a86e558f9074e86b7138f5cc32a60df90be652570f3c4bfb94285",
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+  "physical": 7738,
+  "global_profile": {
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+    "2": 11520,
+    "3": 41514,
+    "4": 6336,
+    "5": 24726,
+    "6": 4896,
+    "7": 132,
+    "8": 72,
+    "48": 230
+  },
+  "rank_mass": 520704,
+  "deficit": 2560,
+  "maxchild": 48,
+  "hosted_residuals": 40320,
+  "banks_per_stage": [
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+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
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+  "entering_helper_roles": 12384,
+  "unique_actual_73column_sigmas": 3214,
+  "sigma_stream_sha256": "4cc12e28b22cb3d081a49fdc66dc8eda3b09eade298d0a2ddb0ba7ace33e7c17",
+  "cross_replica_helper_roles": 31430,
+  "asynchronous_order_sha256": "2acd6b2004be3d3ef6645f3c968feb22b5167c400bb49eb446821e5cb7af6eee",
+  "source_artifacts": {
+    "split-centres/CANONICAL-WORD.json.gz": "addf598581d2a20e13d0c18110607515ad90b06125616a2349e53a47bb5b6c80",
+    "split-centres/LOCAL-PROGRAMS.json.gz": "41a434cc1aa1bed3d3fcecea5c87f091c65a4937c6b2a31470e903e37f4578f0",
+    "split-centres/LOCAL-CHECKS.json": "ead7163869ecb9fc276f477c0ec0ed85dc74d7901ce04f91213bcf7ee1f20382",
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+  },
+  "scope": "New emitted complete-invocation placement; independent controller/spectator/normalization and complete finite invoice admission required."
+}
diff --git a/research/ranksector112-async/vendor/pr523/evidence/local/CANONICAL-WORD.json.gz b/research/ranksector112-async/vendor/pr523/evidence/local/CANONICAL-WORD.json.gz
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diff --git a/research/ranksector112-async/vendor/pr523/evidence/local/CLIFFORD-RECIPES.json b/research/ranksector112-async/vendor/pr523/evidence/local/CLIFFORD-RECIPES.json
new file mode 100644
index 0000000000..0422ae288a
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/evidence/local/CLIFFORD-RECIPES.json
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diff --git a/research/ranksector112-async/vendor/pr523/evidence/local/CLIFFORD-REVIEW.json b/research/ranksector112-async/vendor/pr523/evidence/local/CLIFFORD-REVIEW.json
new file mode 100644
index 0000000000..ad33b2911c
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/evidence/local/CLIFFORD-REVIEW.json
@@ -0,0 +1,21 @@
+{
+  "status": "PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES",
+  "canonical_word_sha256": "addf598581d2a20e13d0c18110607515ad90b06125616a2349e53a47bb5b6c80",
+  "frames": 968,
+  "directed_edges": 2943,
+  "ranks": {
+    "1": 1871,
+    "2": 154,
+    "3": 530,
+    "8": 24,
+    "6": 74,
+    "7": 2,
+    "5": 200,
+    "4": 88
+  },
+  "endpoint_adapters": 224,
+  "all_child_equalities_include_global_phase": true,
+  "recipe_sha256": "1f37afd5a9e14b113ba56e0ac8a5200a6b41c695d2cd308dc0fd6ec46a4c73d2",
+  "seconds": 253.65679077099958,
+  "scope": "Every local frame and center transition. Expanded scalar-interface integration and global emitted program are separate obligations."
+}
diff --git a/research/ranksector112-async/vendor/pr523/evidence/local/FULL-WORD.json.gz b/research/ranksector112-async/vendor/pr523/evidence/local/FULL-WORD.json.gz
new file mode 100644
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diff --git a/research/ranksector112-async/vendor/pr523/evidence/local/INDEPENDENT-LOCAL-REPLAY.json b/research/ranksector112-async/vendor/pr523/evidence/local/INDEPENDENT-LOCAL-REPLAY.json
new file mode 100644
index 0000000000..9bd4dcea28
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/evidence/local/INDEPENDENT-LOCAL-REPLAY.json
@@ -0,0 +1,62 @@
+{
+  "status": "PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY",
+  "canonical_word_sha256": "addf598581d2a20e13d0c18110607515ad90b06125616a2349e53a47bb5b6c80",
+  "local_programs_sha256": "41a434cc1aa1bed3d3fcecea5c87f091c65a4937c6b2a31470e903e37f4578f0",
+  "v": 112,
+  "helpers": 560,
+  "local": {
+    "forward": {
+      "all_exact_columns": 784,
+      "prefix_l1_upper": "57339",
+      "prefix_bits_upper": 16,
+      "charged_payload_bits": 192,
+      "private_work_erased": true
+    },
+    "backward": {
+      "all_exact_columns": 784,
+      "prefix_l1_upper": "1048913",
+      "prefix_bits_upper": 21,
+      "charged_payload_bits": 192,
+      "private_work_erased": true
+    }
+  },
+  "paid_profiles": {
+    "forward": {
+      "1": 2531,
+      "2": 160,
+      "3": 530,
+      "4": 88,
+      "5": 298,
+      "8": 1,
+      "6": 68,
+      "7": 1
+    },
+    "backward": {
+      "1": 2531,
+      "2": 160,
+      "3": 530,
+      "4": 88,
+      "5": 298,
+      "8": 1,
+      "6": 68,
+      "7": 1
+    }
+  },
+  "entering_helpers": 172,
+  "negative_controls_rejected": [
+    "wrong_scale",
+    "missing_center",
+    "wrong_common_frame",
+    "wrong_child_rank",
+    "missing_pre_wrapper",
+    "missing_post_wrapper",
+    "wrapper_with_wrong_frame",
+    "wrapper_in_wrong_phase",
+    "wrapper_on_a_data_register",
+    "wrapper_on_a_target_register",
+    "wrapper_on_a_centre_register",
+    "centre_step_not_nested",
+    "centre_descent_step_skipped"
+  ],
+  "scope": "Literal forward and inverse-transpose replay on every arbitrary data/helper column, physical frame incidence, ordered paid wrappers, cleared private work and prefix coefficients. Global hosting and outer exponent are separate."
+}
diff --git a/research/ranksector112-async/vendor/pr523/evidence/local/LEMMA-A.json b/research/ranksector112-async/vendor/pr523/evidence/local/LEMMA-A.json
new file mode 100644
index 0000000000..71339b732f
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/evidence/local/LEMMA-A.json
@@ -0,0 +1,136 @@
+{
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+ "frames": 12,
+ "wrappers_reject": [
+  "wrong global phase",
+  "wrong translation",
+  "wrong quadratic form",
+  "sides swapped",
+  "wrong width"
+ ],
+ "all_even_weight": true,
+ "all_totally_isotropic": true,
+ "detail": [
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+   "entrance_rank": 1,
+   "residual_width": 8,
+   "vectors": [
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+   ],
+   "all_even_weight": true,
+   "totally_isotropic": true
+  },
+  {
+   "frame": 3,
+   "entrance_rank": 1,
+   "residual_width": 8,
+   "vectors": [
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+   ],
+   "all_even_weight": true,
+   "totally_isotropic": true
+  },
+  {
+   "frame": 4,
+   "entrance_rank": 2,
+   "residual_width": 7,
+   "vectors": [
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+    102
+   ],
+   "all_even_weight": true,
+   "totally_isotropic": true
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+   "entrance_rank": 1,
+   "residual_width": 8,
+   "vectors": [
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+   "totally_isotropic": true
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+   "entrance_rank": 1,
+   "residual_width": 8,
+   "vectors": [
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+   "all_even_weight": true,
+   "totally_isotropic": true
+  },
+  {
+   "frame": 12,
+   "entrance_rank": 1,
+   "residual_width": 8,
+   "vectors": [
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+   ],
+   "all_even_weight": true,
+   "totally_isotropic": true
+  },
+  {
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+   "entrance_rank": 1,
+   "residual_width": 8,
+   "vectors": [
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+   "all_even_weight": true,
+   "totally_isotropic": true
+  }
+ ]
+}
diff --git a/research/ranksector112-async/vendor/pr523/evidence/local/LOCAL-CHECKS.json b/research/ranksector112-async/vendor/pr523/evidence/local/LOCAL-CHECKS.json
new file mode 100644
index 0000000000..61b7804deb
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/evidence/local/LOCAL-CHECKS.json
@@ -0,0 +1,40 @@
+{
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+    "scalar_macros": 19816,
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+    "all_columns": 784,
+    "private_centers_cleared": true,
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+}
diff --git a/research/ranksector112-async/vendor/pr523/evidence/local/LOCAL-PROGRAMS.json.gz b/research/ranksector112-async/vendor/pr523/evidence/local/LOCAL-PROGRAMS.json.gz
new file mode 100644
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index 0000000000..ee680ded63
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new file mode 100644
index 0000000000..8fa9ad8c02
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new file mode 100644
index 0000000000..3ee0f695e6
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+  "all_main_cleanup_precondition_center_and_entrance_frames_match": true,
+  "independently_recomputed_helper_compensations_match": 12094,
+  "columns_in_recomputed_raw_main": 784,
+  "scope": "Exact transport of the whole raw word to the canonical word, including recomputed arbitrary-dirt compensation. Canonical emitted replay supplies both orientation identities."
+}
diff --git a/research/ranksector112-async/vendor/pr523/inputs/ASYNC112-PLAN.json b/research/ranksector112-async/vendor/pr523/inputs/ASYNC112-PLAN.json
new file mode 100644
index 0000000000..c41b49444a
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/inputs/ASYNC112-PLAN.json
@@ -0,0 +1,12226 @@
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diff --git a/research/ranksector112-async/vendor/pr523/proof/GLOBAL-RESTRICTION.md b/research/ranksector112-async/vendor/pr523/proof/GLOBAL-RESTRICTION.md
new file mode 100644
index 0000000000..d2d5a0293a
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/proof/GLOBAL-RESTRICTION.md
@@ -0,0 +1,125 @@
+# Restricting the global controller to 112 Hamming ports
+
+This note proves the global data interface used by the new whole-owner
+construction. It is a restriction of the verified PR514 interface with a newly
+verified local provider. It does not infer a new global exponent from a local
+rank profile alone.
+
+## The selected coordinates
+
+The original Hamming description has eight coordinate-root ports and 112 code
+ports. In the canonical binary labels the eight deleted indices are
+
+`0, 13, 22, 35, 40, 51, 54, 119`.
+
+`PORT-MAPPING.json` gives the increasing injection from the 112 new indices to
+the 120 old canonical indices. The new binary port labels are exactly the
+selected old labels. The local ambient dimension remains nine, and all 560
+helper frames and all helper entrance and final frames remain unchanged. There
+are eight private centers instead of sixteen.
+
+The local restriction is not justified by deleting arbitrary internal wires.
+`RESTRICTION.json` binds the exact raw and canonical register restrictions;
+`TRANSPORT.json` checks the complete transport, including all 12,094 nonzero
+arbitrary-helper-dirt compensations. The new independent expanded-program
+replay checks all 784 data and helper columns in both orientations, all frame
+incidences, the ordered residual wrappers and private erasure. Its final
+normalized data action is diagonal in the retained port index, with the same
+forward and backward shear identities as the old provider. The new exact
+Clifford recipes include scalar phase for every local frame transition and
+endpoint adapter.
+
+## Why the global data construction restricts
+
+At the boundary of a complete local invocation, the inherited controller is a
+direct sum over the port index. Its nonlocal operations—the paired bridges,
+idle children, stage alignments, terminal translations, signed exchange and
+cover correction—also preserve that port index. The controller never
+interleaves two local invocations. Consequently the subspace containing all
+replicas and pair positions of any selected set of ports is invariant under
+each complete step of the controller. Restricting to the 112 selected ports
+therefore retains the inherited controller identity on this invariant
+subspace.
+
+This statement concerns complete, normalized local invocations. The mutable
+basis and the dirty-helper cancellation inside an invocation can mix ports;
+their legality is supplied by the new local proof and replay. No assumption
+that the individual internal scalar gates are portwise is used.
+
+For a retained port, the nine stage recipes in `DATA-PHASES.json` are copied
+exactly from its old canonical port. Only the display index `port` changes.
+Every binary label `q`, every actual orthogonal axis, every entry and exit
+translation, every idle translation and the literal terminal translation is
+unchanged. Thus the parent's exact phase-polynomial equalities apply verbatim
+to each selected recipe. The inherited number of polynomial evaluations is
+explicitly marked as inherited; it is not reported as a new numerical run.
+The independent restriction audit additionally reconstructs all 112 actual
+orthogonal 73-coordinate bases and checks the literal idle axes against them.
+
+The data family renumbering is explicit. An old family
+
+`replica * 960 + (2 * pair + side) * 120 + old_port`
+
+becomes
+
+`replica * 896 + (2 * pair + side) * 112 + new_port`.
+
+All 16,128 data-owner roles in the 72 calls satisfy this formula. Each call
+uses the newly verified local-program hash. All 2,016 nonzero idle-child
+records are the selected old records with unchanged ranks and eightfold
+replication. The full source-event order, paired bridges, terminal operations
+and cover correction are preserved.
+
+## Helpers, stock and the conservative parent invoice
+
+Before final hosting, the 5,040 old bank families are retained and shifted
+down by 512 family indices. All 40,320 helper roles preserve their old route,
+width, residual interval and spectator coordinates. Every entering helper
+still has one whole bank owner during its complete invocation. The restricted
+parent has 7,168 data families and 5,040 banks, for 12,208 live families. Its
+private intervals reserve eight centers, 560 tableau streams and two
+coefficient streams, giving 12,778 physical families.
+
+The old parent contains a legacy bank-padding display field mentioning only
+axis 72 and rank one. The actual entering-bank remainders also include rank
+nine and rank seventeen. This field is not used as evidence for an executable
+bank-padding implementation. The restriction audit reconstructs every bank
+footprint from the serialized owners. Their complementary ranks are exactly
+
+| Rank | Number of bank remainders |
+| ---: | ---: |
+| 1 | 3,492 |
+| 9 | 1,386 |
+| 17 | 162 |
+
+The fresh conservative invoice uses these actual ranks, together with all 72
+new local profiles and all selected idle children. Its total child rank mass
+is 888,624, so
+
+$$
+73\cdot12,208-888,624=2,560.
+$$
+
+The deterministic finite-operation allowance is recomputed with the new
+counts. It keeps the inherited compiler factor `64 * 74**3`, the same
+orthogonal-cover formula and the same large finite constants. The separate
+whole-owner constructor removes every bank family and replaces pending data
+children by actual helper routes and complementary remainders. Its serialized
+chronology, physical owner uniqueness, phase maps, paid profile and finite
+invoice must pass the final independent audits. No whole-owner exponent or
+execution claim is made merely from this restricted parent.
+
+## Independent verification
+
+`audit_global_restriction.py` imports only the Python standard library. It
+reads the old and new serialized artifacts, without importing the restriction
+emitter, local emitter or hosting optimizer. It binds the new local scalar and
+phase certificates by hash, checks every retained phase recipe and owner
+record, verifies all private ranges, reconstructs the actual bank remainders,
+and independently recounts the parent rank mass. Negative controls cover port
+selection, binary labels, idle axes, terminal corrections, data families,
+canonical routes, local hashes, helper owners, omitted invocations and idle
+children, the cover correction, private reserve and unpaid bank remainders.
+
+The result is `GLOBAL-RESTRICTION-AUDIT.json`. The final global kappa receipt is
+a separate artifact of the complete new whole-owner program.
diff --git a/research/ranksector112-async/vendor/pr523/proof/INDEPENDENT-REVIEW.md b/research/ranksector112-async/vendor/pr523/proof/INDEPENDENT-REVIEW.md
new file mode 100644
index 0000000000..1a708d59b8
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/proof/INDEPENDENT-REVIEW.md
@@ -0,0 +1,120 @@
+# Independent review of the 112-port construction
+
+Prepared for icekylinx with GPT-6 Astra assistance. The finite constructions
+and conditional interfaces of PR514 and its credited ancestors are retained.
+
+## Finding
+
+The puncture is a valid restriction of the literal local word. Its new whole
+physical owners are valid in the unchanged asynchronous controller. A separate
+checker, which imports neither an emitter nor a hosting checker and does not
+read the nominated histogram or nominated idle windows, reconstructs the
+following complete paid histogram:
+
+| Rank | Count |
+| ---: | ---: |
+| 1 | 182232 |
+| 2 | 11520 |
+| 3 | 41514 |
+| 4 | 6336 |
+| 5 | 24726 |
+| 6 | 4896 |
+| 7 | 132 |
+| 8 | 72 |
+| 48 | 230 |
+
+The live stock is 7168, the physical stock is 7738, the rank mass is 520704,
+and the rank deficit is 2560. The exact moment and outer assembly should take
+this reconstructed histogram as their supplier input.
+
+## Why restriction preserves the local contract
+
+The checker infers the retained set directly from the old and new binary port
+labels. It does not trust the transformation's mapping receipt. The eight
+removed old canonical indices are 0, 13, 22, 35, 40, 51, 54, and 119.
+
+It compares every operation of A, B, the target preconditioner, dirty
+compensation, the center cut, and full-frame cleanup under the resulting
+register map. Exactly eight operations disappear: each is a unit coordinate
+shear from a removed source into its own removed target. No other operation
+reads or writes any removed register. The scalar word therefore splits as
+the direct sum of those eight independent shears and the retained word.
+
+The retained word is independently replayed over exact rational numbers in
+both orientations. Each orientation has 25242 literal events and 19816 scalar
+macros. All 784 independent input columns have the required shear endpoint;
+all source and helper rows return, and every private center is cleared.
+The checker also follows each actual frame label and nested recursive
+transition. It checks all entry and exit adapters and the placement of every
+residual wrapper around the complete invocation.
+
+Every retained frame is literally unchanged. Every residual-wrapper recipe
+used by the 112-port word equals its corresponding recipe in the original
+checked word. The wrapper is an identity on its declared spectator factor
+and a normalized residual transform on the same local coordinates as before.
+Neither statement depends on the presence of the eight discarded source and
+target rows. The puncture introduces no stronger Lemma A or common-label
+assumption: it instantiates the same interfaces on fewer data rows, using
+the same local frames, scalar coefficients, and normalized wrappers.
+
+## Why the global restriction is compatible with hosting
+
+For each retained port, the four-pair data controller uses precisely its
+original port chart. The independent checker constructs the 73-dimensional
+orthogonal basis directly as a binary transvection of the standard basis and
+checks its Gram matrix. The retained port labels are a subset of the original
+labels, so their controller phase recipes and endpoint translations retain
+their original meaning.
+
+The order of the 72 complete invocations is independently reconstructed as
+the increasing order of `(7*stage + 6*replica, stage, replica)`. The checker
+expands the original controller events and measures each pending interval
+between the previous actual local or bridge touch and the pending child.
+This includes individual bridge touches rather than using stage endpoints as
+a proxy for liveness.
+
+All 40320 helper assignments lie strictly inside their owners' resulting idle
+intervals. In each invocation, the 560 helper families are distinct and avoid
+all 224 active data families. Thus all 784 owners of that invocation are
+different. Each assigned residual occupies its prescribed actual pending
+vectors. Its spectator coordinates lie outside that residual, and the full
+73-vector chart is a permutation of the verified orthogonal basis. The
+assignments use 3214 distinct actual charts.
+
+The occupied pending vectors are pairwise disjoint within each owner interval.
+They cover 349200 axes in total. The remaining original pending factors have
+the exact histogram `{3:3354, 5:3270, 7:60, 48:230}`. Adding these literal
+remainders to 72 copies of the independently counted local profile gives the
+global histogram above. No residual is split between physical owners.
+
+Induction over the controller events now uses the retained complete-invocation
+contract: each invocation performs its data shear on arbitrary dirt, restores
+the borrowed spectators, and leaves its stated residual on each idle owner.
+The assigned factors and paid complement exactly complete the original
+pending child before that family is touched again. The per-port controller
+therefore retains its original endpoint on every surviving data family.
+
+## Scope of the conclusion
+
+This establishes the finite local restriction, owner chronology, concrete
+charts, restored spectators, and complete recursive rank profile. Exact
+Clifford phases, the finite scalar and routing invoice, and rational moment
+and outer inequalities are also required in the assembled deliverable; this
+review is an additional independent check of the changed finite ingredients.
+
+The all-size compilation, common-label realization, precision and tape, and
+analytic transfer conditions inherited from the source framework remain
+conditions. Restricting the finite word does not prove those interfaces.
+
+The approximately 4.77 percent global-kappa improvement certified by the
+completed exact assembly is a structural advance for this round: both the
+data-family count and the deficit change. The exact certified kappa, rather
+than this rounded comparison, is the authoritative numerical conclusion.
+
+## Reproduction
+
+`audit_112_independent.py` accepts the original verified base directory, the
+new local-artifact directory, the literal `OWNERS112.json.gz`, and an output
+directory. Its `INDEPENDENT112-RAW-AUDIT.json` records input hashes and the
+reconstructed results. It reads no optimization output except the literal
+physical assignments that it verifies.
diff --git a/research/ranksector112-async/vendor/pr523/proof/LOCAL-RESTRICTION.md b/research/ranksector112-async/vendor/pr523/proof/LOCAL-RESTRICTION.md
new file mode 100644
index 0000000000..e55608520a
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/proof/LOCAL-RESTRICTION.md
@@ -0,0 +1,111 @@
+# Removing the isolated coordinate ports
+
+Prepared for icekylinx with GPT-6 Astra assistance. The Hamming packet factory,
+mutable source and target bases, source restoration, entrance gauges, and exact
+kernel selection are inherited from the attributed PR507/PR514 construction.
+
+## Exact restriction
+
+In the Hamming ordering of the 120 E8 root lines, sources 0 through 7 are the
+coordinate lines. Their only scalar occurrences in the complete PR514 word are
+the eight retained-center additions `y_i += x_i`. In particular, none occurs in
+`A`, `B`, the target preconditioner, the full-frame cleanup, or the helper dirt
+compensation. The other 112 source lines are the eight sign classes on each of
+the fourteen weight-four Hamming blocks.
+
+`build_port112.py` checks these statements against both the original Hamming
+word and the independently produced canonical word before removing anything.
+It refuses a word if a deleted register occurs in any other operation, or if a
+deleted center addition has any coefficient or destination other than the
+specified identity addition.
+
+Consequently the complete scalar operator, after grouping the coordinate
+registers separately, is a direct sum of the eight elementary coordinate
+shears and the operator on the 112 code lines and all 560 helpers. Restricting
+to the second summand gives exactly
+
+$$
+ (x,s,y)\longmapsto(x,s,y+x),\qquad x,y\in K^{112},\ s\in K^{560}.
+$$
+
+This holds on arbitrary data and arbitrary helper dirt. Its inverse transpose
+is the corresponding reverse shear. The restriction changes no scalar
+coefficient, no frame, no helper identity, no helper entrance, no kernel donor
+relation, and no source or target basis operation. All retained-register maps
+are explicit in `evidence/local/RESTRICTION.json` and
+`evidence/local/PORT-MAPPING.json` in the package, and under `local112/`
+in a fresh replay output directory.
+
+## Canonical routing indices
+
+The original orthogonal transvection is
+$\tau(p)=p+\langle p,43\rangle43$. The eight Hamming coordinate lines map,
+in their original order, to canonical indices
+
+$$
+ 35,0,13,54,40,119,22,51.
+$$
+
+The new canonical word retains the other old canonical indices in increasing
+order. The 112-port binary geometry still has ambient dimension 9. The
+transvection, common-frame incidences, Clifford frames, and all residual
+wrappers are unchanged on the retained registers. A global template must
+restrict every data-family layer to this same subset; reusing a 120-port
+owner schedule without a new hosting certificate is not authorized by this
+local argument.
+
+## Exact local cost
+
+Each removed source has one unused line-to-full transition of rank 8. Each
+removed target has one zero-to-hyperplane transition of rank 8. Each removed
+retained center descends from its line with rank 1. Thus the local saving is
+exactly sixteen rank-8 children and eight rank-1 children. The retained center
+rank sum changes from 72 to 64.
+
+| Recursive rank | PR514 local count | 112-port local count |
+|---:|---:|---:|
+| 1 | 2539 | 2531 |
+| 2 | 160 | 160 |
+| 3 | 530 | 530 |
+| 4 | 88 | 88 |
+| 5 | 298 | 298 |
+| 6 | 68 | 68 |
+| 7 | 1 | 1 |
+| 8 | 17 | 1 |
+
+The new rank mass is 6706. It equals the unchanged helper residual mass 4850,
+plus $224\cdot8=1792$ data transitions, plus the 64 retained-center ranks.
+The helper widths remain 18 of width 7, 154 of width 8, and 388 of width 9.
+
+For the existing nine-stage controller, the formal deficit per replica is
+
+$$
+ (9-1)v-9\,\mathrm{cst}.
+$$
+
+It changes from 312 to 320. With eight replicas the value changes from 2496
+to 2560. The data stock changes from 7680 to 7168. These identities alone do
+not price the new whole-residual-hosted supplier: its physical assignments,
+unused remainders, finite invoice, and rational moment must be rebuilt.
+
+## Independent checks
+
+The retained PR514 emitter is used with only its output-directory argument
+adapted. It emits 25,242 instructions in each orientation. A separate reader
+retains the complete local replay and its controls from the PR514 independent
+audit. It checks all 784 scalar columns in both orientations, exact common
+frames, the literal paid child profile, the location and order of every
+residual wrapper, and cleared private centers and coefficient work. Thirteen
+negative controls are rejected.
+
+The residual-wrapper checker is run without code changes on the new
+canonical word. It verifies all twelve entrance-frame recipes, including
+their global phases, and rejects five corrupted wrappers. The exact Clifford
+phase checker is retained with only its input and module-directory arguments
+adapted. `ADAPTATIONS.json` records the precise source hashes and edits.
+
+The global argument retains the same all-size/compiler, target-label,
+mutable-basis, physical-hosting, finite-precision, and analytic interfaces as
+the source construction. This restriction introduces no new algebraic
+interface. A certified global kappa is a separate output of the new global
+owner schedule and moment/outer assembly.
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/EXPECTED.json b/research/ranksector112-async/vendor/pr523/vendor/pr514/EXPECTED.json
new file mode 100644
index 0000000000..ddf88093f5
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/EXPECTED.json
@@ -0,0 +1,8 @@
+{
+  "kappa": "1391523459591829/1000000000000000000",
+  "kappa_decimal": "0.001391523459591829",
+  "complex_lower": "139346249534416215349/100000000000000000000000",
+  "bit_lower": "391360506745414227149/250000000000000000000000",
+  "template_sha256": "77767f67ed17413161d82f2a407e69b3beefef3fc44bfe582fb403bdc1705bd8",
+  "strict_constraints": 47
+}
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/LICENSE b/research/ranksector112-async/vendor/pr523/vendor/pr514/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
+
+      "License" shall mean the terms and conditions for use, reproduction,
+      and distribution as defined by Sections 1 through 9 of this document.
+
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diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/MANIFEST.json b/research/ranksector112-async/vendor/pr523/vendor/pr514/MANIFEST.json
new file mode 100644
index 0000000000..77aa9de44b
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/MANIFEST.json
@@ -0,0 +1,277 @@
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+      "mode": "lf-text",
+      "sha256": "0f2795aaffafe0c64d77f3748ef2109a3c42c58da867e4cf269a0a8cb6109466"
+    },
+    "vendor/complex/split-centres-global/vendor/clifford_exact.py": {
+      "mode": "lf-text",
+      "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962"
+    },
+    "verify.py": {
+      "mode": "lf-text",
+      "sha256": "ae9b5763e656696add6d106fe70d90facb5d2700fb8e66e4eea678c46b1d5720"
+    },
+    "verify.sh": {
+      "mode": "lf-text",
+      "sha256": "2b1b51f757d8ddf81941c8c96007a2256336856c2e017bcf6c3a37576c82bc8b"
+    },
+    "evidence/PORTABLE-REPLAY.json": {
+      "mode": "lf-text",
+      "sha256": "d307e5f71b148454c5be5575d0f93650fa494fd307564cd679b47892bf39e958"
+    },
+    "evidence/TRANSPORT-CONTROLS.json": {
+      "mode": "lf-text",
+      "sha256": "af70924e999305938a693718e34b1f3a4e7199e4050bde193a416426df755bae"
+    },
+    "research-notes/REPLAY-REPAIRS.md": {
+      "mode": "lf-text",
+      "sha256": "0ad48be86ec6c5b3617b3ef9e728587c57f549aac9826041665d0d04c21c561c"
+    }
+  }
+}
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/NOTICE.md b/research/ranksector112-async/vendor/pr523/vendor/pr514/NOTICE.md
new file mode 100644
index 0000000000..1a413bfa41
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/NOTICE.md
@@ -0,0 +1,9 @@
+# Scoped attribution
+
+Prepared with OpenAI Codex assistance. Apache-2.0; see LICENSE. Original authorship notices in included vendor code are retained.
+
+PR507 directly supplies the partial-own factory, 84-pivot reference and its retiming map. PR484 supplies the gauge/kernel construction and wrappers; PR496 supplies whole-owner pooling and invoice ancestry. PR493 supplies the unchanged cited bit operator. PR495 supplies body-frame retiming, with PR501 and PR502 integrating it. PR473's single-gauge proposal inspired our coordinated four-gauge collapse; its updated schedule was also considered. PR505 contains our prior asynchronous complete-invocation scheduling. PR506 supplies a related public comparison and portability feedback. PR477's experiment log informed bounded route selection.
+
+Earlier retained ancestry includes PR433/425/370 for geometry and the scalar/phase compiler, PR458 for whole-owner spectator wrappers, PR361/315 for exact moments and outer arithmetic, and PR434/417/435/440/401/408/416 for response-kernel and gauge methods. SOURCES.json separates direct ingredients, ancestry, comparisons and excluded interfaces; credits do not mean their gains were added independently.
+
+Our contribution here is the actual combined reconstructed 92-pivot word and literal whole-owner allocation, with complete fresh checks of the changed complex program. OpenAI math, the Problem 1.8 implementation and the installed machine compiler sources informed the documented research adaptations. No fresh Lean certification is claimed.
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/PORTABILITY.md b/research/ranksector112-async/vendor/pr523/vendor/pr514/PORTABILITY.md
new file mode 100644
index 0000000000..c5c9dd7743
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/PORTABILITY.md
@@ -0,0 +1,11 @@
+# Portable replay and browser uploads
+
+No hidden file is required. MANIFEST.json binds every included file except itself. Each entry declares either exact raw-byte hashing (gzip and other binary inputs) or SHA-256 after converting CRLF to LF (recognized text files). This accepts only the platform newline distinction; it does not ignore whitespace, JSON values, source code or any other content. An omitted file or changed token still fails.
+
+verify.py copies static work inputs into its new output directory, canonicalizes recognized text there, and creates an LF copy of the frozen asynchronous plan. Only those canonical copies enter runtime raw-byte template hashes. Each child executes through code/run_portable.py, which preserves argv, import path and working directory while forcing generated Path.write_text output to UTF-8/LF. Generated adapter JSON therefore has the same embedded hash on Windows and Linux.
+
+Gzip transport bytes are manifest-bound. Newly generated gzip container headers can vary across Python versions; the expected final template hash binds decompressed canonical content instead. Mathematical input fields are checked independently. The normalized local word omits only two irrelevant inherited display floats and a checked redundant dimension field.
+
+The package is tested locally with assertions enabled. Optimized Python is rejected. The final portability test changes every recognized package text file to CRLF and runs the complete verifier against the frozen expected result. This is a Windows line-ending test, not a claim that Linux or Python 3.14 ran locally.
+
+Upload batches contain at most 40 files each, have no hidden files, and reproduce the same research/partial-kernel92-async directory. Upload each batch's research folder at your fork's repository root, on one fresh branch. Do not upload the part folder itself. After all batches are committed, open one PR from that branch. Nothing in the verifier publishes, deletes files or modifies a fork.
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/PROOF.md b/research/ranksector112-async/vendor/pr523/vendor/pr514/PROOF.md
new file mode 100644
index 0000000000..b0b27963f7
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/PROOF.md
@@ -0,0 +1,27 @@
+# Sufficient composition and complete cost
+
+## Reconstructed local operator
+
+Start with PR507's pinned partial-own factory. Reconstruct its 84-pivot reference and check every old frame in the frozen retiming map before replacing any frame. Scalar operands and coefficients must remain identical. Transfer the resulting scalar-body frames back to the factory, then reconstruct the four coordinated rank-two gauges and the selected 92 exact rational response relations. Donor relations and dirty compensation are recomputed from the actual word.
+
+The local recursive profile is 2,539 rank-one, 160 rank-two, 530 rank-three, 88 rank-four, 298 rank-five, 68 rank-six, one rank-seven and 17 rank-eight children. The residual widths are 18 at seven, 154 at eight and 388 at nine. The normalized complete word has SHA-256 `c6e758b324d3566e8443b3fd3d739c4d01e1928eadbee40f5c36973404b0640b`. Normalization removes only two unused display floats and an independently checked redundant dimension field.
+
+The verifier separately checks every arbitrary-dirt input column in both orientations, all 92 correction-omission controls, Gaussian phases, frame legality and paid spectator wrappers. A clean-input identity alone is insufficient.
+
+## Sufficient global schedule
+
+Assume the inherited complete normalized invocation contract: one complete call has its declared active data shear on arbitrary dirt, uses distinct whole helper owners, restores borrowed spectators and private workspace, and leaves exactly the declared residual transform on each assigned pending block.
+
+Execute eight replicas of the nine-stage controller in order (7*stage+6*replica, stage, replica). Preserve each replica's complete source-event order; finish each call and its wrappers before the next starts. Assign disjoint subspaces of each owner's actual pending child to helpers strictly within that owner's idle interval. Execute the exact complementary remainder before the next active or bridge touch.
+
+Induct on emitted events. The invocation contract preserves spectators; the disjoint residual factors commute and compose with the explicit remainder to exactly the original pending child. Each owner therefore has the original state when next touched. The data projections preserve each replica's original operator, and the common final correction completes the original global endpoint. No helper is split between owners, and no scalar gate is moved through an unfinished invocation.
+
+The independent checker verifies all 40,320 assignments, simultaneous injection, actual idle intervals, orthogonal charts, paid adapters and residual coverage. The witness is literal; no optimization oracle enters replay.
+
+## Cost and exponent
+
+The global paid profile is `{1: 182808, 2: 11520, 3: 41233, 4: 6336, 5: 25173, 6: 4896, 7: 195, 8: 1224, 16: 1, 32: 1, 39: 1, 48: 766}`. Its rank sum is 73*7,680 - 2,496. The maximum recursive rank is 48 and 73^2 > 2*48^2. The independent finite invoice recounts all prefix, row and physical costs.
+
+Two rational moment engines accept b = `139346249534416215349/100000000000000000000000` and reject the adjacent upper endpoint. The published PR493 bit histogram is independently repriced while its unchanged operator remains a cited dependency. Six bootstrap steps and all 47 strict outer constraints give kappa = `1391523459591829/1000000000000000000`; the next kappa grid point and the three invalid parameter controls are rejected.
+
+This is sufficient for the stated conditional bound under exactly the retained interfaces, not a proof of those interfaces themselves. Complete numerical evidence is in evidence/EXACT-ASSEMBLY.json.
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/README.md b/research/ranksector112-async/vendor/pr523/vendor/pr514/README.md
new file mode 100644
index 0000000000..892f660f33
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/README.md
@@ -0,0 +1,38 @@
+# Partial-own factory, 92 kernel pivots and asynchronous whole owners
+
+Conditional kappa = **0.001391523459591829**, exactly `1391523459591829/1000000000000000000`. This is **1.381994% above our previous checked construction**, 0.001372554837726243. The complex supplier binds, with b = `139346249534416215349/100000000000000000000000`; the unchanged cited PR493 bit supplier has c = `391360506745414227149/250000000000000000000000`.
+
+This package combines PR507's partial-own factory, our coordinated four-gauge rank reduction, a newly selected 92-pivot response kernel, public body retiming and our asynchronous complete-invocation schedule. It reconstructs and prices their combined program; it does not add headline gains.
+
+## Reproduce
+
+Python 3.11 or later, standard library only:
+
+```
+python -B verify.py --work /absolute/path/to/a-new-output-directory
+```
+
+The output directory must be new and outside this package. Keep assertions enabled. No network, optimizer, C++ compiler or Lean installation is required for replay. Thirteen stages reconstruct the changed factory and word, check arbitrary-dirt scalar columns and exact Gaussian phases, emit paid wrappers and actual physical owners, recount costs, and run two exact rational moment engines plus all 47 strict outer inequalities. Logs and RESULT.json appear in the requested directory. The unchanged bit operator is a pinned dependency, not freshly reconstructed here.
+
+## Concrete changes
+
+- PR507 changes the factory and supplies the 84-pivot reference construction.
+- Helpers 540 through 543 use the rank-two plane spanned by 408 and 102; target frame labels 81, 82, 84 and 87 are reduced together.
+- A frozen exact rational selection raises the kernel count to 92 pivots. All 800 input columns pass in both orientations, and all 92 omitted-correction controls fail as intended.
+- The resulting 560 helpers have widths 7, 8 and 9 with multiplicities 18, 154 and 388.
+- Eight replicas execute 72 complete invocations in order (7*stage+6*replica, stage, replica). Every one of the 40,320 helper uses has an explicit whole physical owner.
+- Ambient dimension 73, live stock 7,680, physical stock 8,258 and rank deficit 2,496 are unchanged.
+
+The complete global profile is `{1: 182808, 2: 11520, 3: 41233, 4: 6336, 5: 25173, 6: 4896, 7: 195, 8: 1224, 16: 1, 32: 1, 39: 1, 48: 766}`. It includes every paid idle remainder.
+
+## Machine research: what did and did not contribute
+
+We inspected actual Word RAM, Turing-machine and workspace implementations from OpenAI math, our Problem 1.8 library and the installed compiler libraries. We constructed or tested old-state snapshots, first-read frontiers, frame-preserving register coalescing, fused entry/return and deferred modulo-four normalization. These are documented with sufficient applicability rules and source hashes in RESEARCH.md and research-notes/.
+
+**We did not obtain three new machine-derived numerical gains.** The winning 92-pivot selection uses the existing response-kernel method on the changed factory. Machine-inspired alternatives were explicitly priced and did not beat it. They are research records, not hidden ingredients of this exponent.
+
+## Scope
+
+This is a checked finite conditional construction. The inherited all-size compiler, common-label/mutable-basis interface, normalized Lemma A realization, restored-row, precision/tape and analytic-transfer contracts remain assumptions. No unconditional faster multiplication theorem, new Lean certification or universal optimality claim is made. It does not claim to exceed larger submissions using disputed split-residual interfaces.
+
+The public snapshot was frozen through PR507 before packaging. See SOURCES.json and NOTICE.md for direct PR credits. See PORTABILITY.md for text and upload handling. Nothing is published or pushed by this package.
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/RESEARCH.md b/research/ranksector112-async/vendor/pr523/vendor/pr514/RESEARCH.md
new file mode 100644
index 0000000000..6602e30042
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/RESEARCH.md
@@ -0,0 +1,16 @@
+# Machine-source research ledger
+
+The deliverable's numerical improvement comes from the reconstructed factory, coordinated gauges, 92-pivot kernel and complete asynchronous allocation. None of the following is credited with an additional gain in the selected program.
+
+| Source concept | Concrete adaptation | Outcome |
+| --- | --- | --- |
+| Word RAM reads operands before overwriting a destination | Capture a pair sum and the still-old second operand between two shears, then decode the changed basis | Constructed; the best snapshot candidate reached 88 pivots but lost to the selected 92-pivot program |
+| Machine execution preserves locations outside an injective live-register renaming | Reuse retired factory storage for own-output rows, with exact frame restoration | Later retired rows do not fit the output frames; the explicit downward transitions cost more rank than the available deficit |
+| Exact Turing return/restoration and word substitution with additive cost | Merge an exterior pending factor into a helper's first or final recursive call | A sufficient rule is proved; the tested coordinated-rank2 baseline has no eligible entry or exit site |
+| Reversible finite-state normalization | Track repeated pending axes modulo four and emit the explicit parity remainder and translation | Sufficient identity proved; the paid finite-stock screen selected no overlaps |
+| Persistent reserved workspace and continuation composition | Shorter controllers with paid spills; larger finite replica pipelines | The tested programs did not improve the complete price |
+| Actual machine read dependency | Recompute entrance eligibility at the first observer after retiming | A valid 89-pivot candidate lost to the selected program |
+
+These are bounded outcomes, not universal barriers. The useful sufficient transformations, exact coalescing gate and source hashes are retained in research-notes/. Missing typed DAG ports are reported; reading a Lean source is not kernel certification. A polynomial RAM-to-Turing simulation alone cannot preserve an improvement to this near-linear exponent, so no such simulation is used as a free speedup.
+
+For a future successful machine-derived change, emit the actual modified arbitrary-dirt operator, pay restoration and routing, rebuild the literal physical assignment and compare the complete rank moment. Saving a register or a local instruction alone does not establish a larger kappa.
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/SNAPSHOT.md b/research/ranksector112-async/vendor/pr523/vendor/pr514/SNAPSHOT.md
new file mode 100644
index 0000000000..f03803d38d
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/SNAPSHOT.md
@@ -0,0 +1,5 @@
+# Frozen public snapshot
+
+The discovery refresh retrieved 81 recent or updated PR conversations through PR507. Relevant newly downloaded heads are pinned in SOURCES.json. PR507 supplies the changed factory. PR506 and the updated PR473 provide comparable scheduling developments; PR477 provides research records. Its archive contains 46 missing changed-file paths and is not claimed complete. No missing file is a replay dependency.
+
+The snapshot was frozen before packaging. No claim is made to outrank moving heads after that snapshot, or larger bounds using disputed split-residual interfaces.
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/SOURCES.json b/research/ranksector112-async/vendor/pr523/vendor/pr514/SOURCES.json
new file mode 100644
index 0000000000..95e55066e6
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/SOURCES.json
@@ -0,0 +1,92 @@
+{
+  "snapshot": "81 recent or updated conversation pages retrieved, frozen through PR507; no refresh during packaging. PR477 changed-file download had 46 missing paths and is not a complete source archive or a proof dependency.",
+  "direct": [
+    {
+      "pr": 496,
+      "head": "00cf70efd6a8637531deafef698157ca83e249ee",
+      "role": "whole-owner parent, invoice and assembly ancestry"
+    },
+    {
+      "pr": 484,
+      "head": "035845ce95f31d0a2dcfb42b8c8e13411271fa5f",
+      "role": "PR496 pinned gauge80-kernel42 parent, not newer moving head"
+    },
+    {
+      "pr": 493,
+      "head": "c3a9a436b84fe44fdc223a5784d84736d1c2d3c7",
+      "role": "unchanged cited R489 bit supplier"
+    },
+    {
+      "pr": 502,
+      "head": "4d30b8322184598e65e90a92389e17e1baedd9eb",
+      "role": "retiming transfer constructor and PR495 schedule fixture"
+    },
+    {
+      "pr": 501,
+      "head": "1dc056496fdbbc74073ed26d948a2dc235dbf356",
+      "role": "parallel retiming integration; credited, no duplicated gain"
+    },
+    {
+      "pr": 473,
+      "head": "628b454d3df00367d2d4f78de7d4eb9cbcbd47ca",
+      "role": "single-helper gauge withdrawal inspiration"
+    },
+    {
+      "pr": 507,
+      "head": "8d4444cf8a16d500cbb94add6e4fa8bcfb9c7d5e",
+      "role": "partial-own factory, 84-pivot reference and retiming map"
+    },
+    {
+      "pr": 505,
+      "head": "4ee769c8e28837482272b5f4742497da8e2fc9d4",
+      "role": "our prior complete-invocation asynchronous scheduling"
+    },
+    {
+      "pr": 506,
+      "head": "a4948baee6c7ea35323db74ff636620c6af2925a",
+      "role": "public asynchronous retiming comparison and portability feedback"
+    }
+  ],
+  "openai_math": {
+    "repository": "https://github.com/openai/math",
+    "revision": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
+    "status": "source inspection and mathematical adaptation; no new Lean audit"
+  },
+  "other_inspirations": [
+    497,
+    458,
+    442,
+    434,
+    433,
+    425,
+    417,
+    435,
+    440,
+    401,
+    408,
+    416,
+    370,
+    361,
+    315,
+    495,
+    503,
+    504
+  ],
+  "excluded": {
+    "494": "under-review split-residual interface not used",
+    "491": "withdrawn GL sampling argument not used",
+    "499": "larger claim inherits disputed split-residual interface; not used"
+  },
+  "related_updated": [
+    {
+      "pr": 473,
+      "head": "94b3c908fb7628142817d995155368aba2eae841",
+      "role": "new nonuniform scheduling comparison; earlier pinned gauge proposal remains a separate source"
+    },
+    {
+      "pr": 477,
+      "head": "2f23f46f1f9e4599168d40096fbacce4973a2978",
+      "role": "experiment log consulted to avoid repeating old searches"
+    }
+  ]
+}
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/code/assemble.py b/research/ranksector112-async/vendor/pr523/vendor/pr514/code/assemble.py
new file mode 100644
index 0000000000..de2a375d13
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/code/assemble.py
@@ -0,0 +1,42 @@
+"""Two exact moment engines and strict outer composition of a new PR484 rehosting
+with the unchanged published PR493 bit supplier. Prepared by OpenAI Codex; arithmetic
+engines are pinned inherited PR361/Mercator and independent base-two code.
+Usage: assemble_candidate.py AUDIT_OUT PARENT_VARIANT HOSTED BIT_RESULT
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+import json,gzip,sys,hashlib,importlib.util
+O,V,H,B=map(Path,sys.argv[1:5]);sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest()
+def load(n):
+ p=V/'work/pr361/code/engines'/(n+'.py');s=importlib.util.spec_from_file_location('candidate_'+n,p);m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m
+M,Other,Outer=[load(n)for n in ['moment','base_two_moment','outer']]
+owner=json.loads((O/'OWNERS-AND-PROFILE.json').read_text());inv=json.loads((O/'PREFIX-AND-INVOICE.json').read_text());host=json.loads((H/'HOSTED.json').read_text());bit=json.loads(B.read_text())["eleven"];P={int(r):n for r,n in owner['paid_profile'].items()};m,W=73,owner['live'];assert m*W-sum(r*n for r,n in P.items())==2496
+rc=M.certify(P,m,W,True);b=Q(rc['lower']);bp=Q(rc['upper']);assert bp-b==Q(1,10**24)
+fallback=32*m*m*sum(P.values());receipts=[]
+for z,accept in[(b,True),(bp,False)]:
+ ml,mh=M.moment(P,m,W,z,True);a,c=Other.moment(m,W,list(P.items()),z);d,e=Other.moment(m,W,[(1,fallback)],z);a+=d/10**16;c+=e/10**16
+ assert (mh<1 and c<1)if accept else(ml>1 and a>1)
+ receipts.append(dict(endpoint=str(z),mercator=[str(ml-1),str(mh-1)],base_two=[str(a-1),str(c-1)],accept=accept))
+# Reprice the cited unchanged bit histogram, clearly separate from bit operator verification.
+bitP={int(r):n for r,n in bit['profile'].items()};bitc=Q(bit['bit_lower']);bitnext=bitc+Q(1,10**24)
+for zz,accepted in [(bitc,True),(bitnext,False)]:
+ bl,bh=M.moment(bitP,78,9600,zz,True)
+ ol,oh=Other.moment(78,9600,list(bitP.items()),zz)
+ fl,fh=Other.moment(78,9600,[(1,32*78*78*sum(bitP.values()))],zz)
+ assert (bh<1 and oh+fh/10**16<1) if accepted else (bl>1 and ol+fl/10**16>1)
+c=Q(bit['bit_lower']);eta=beta=Q(1,10**18);grid=Q(1,10**18);s=min(c,(1-beta)*b)-Q(1,10**24)
+assert 0<s<c and s<(1-beta)*b
+coeff=int(bit['bit']['charged_three_level_coefficient_bits']);row=max(20161,int(bit['bit']['row_coefficient']),inv['finite']['physical_row_coefficient']);chain=[Q(384599,10**10)];cuts=[]
+def ceil(x):return -(-x.numerator//x.denominator)
+for i in range(6):
+ old=chain[-1];a=(1-s)*s+s*old;gap=min(s-a,1-a-s,1-a-s*(1-old),1-s);assert old<a<s<1-a and gap>0
+ cut=max(ceil(36/gap**2),ceil(2*(4+coeff)/gap));assert cut*gap**2>=36 and cut*gap>=2*(4+coeff);cuts.append(dict(gap=str(gap),cutoff_log2=str(cut)));chain.append(a)
+q=chain[-1]*(1-2*eta);margin=(1-eta)*q/(1+q);ticks=margin/grid;kap=grid*((ticks.numerator-1)//ticks.denominator)
+bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1},'rows':{'degree_gap':Q(10**6)-Q(51*row,25)}}
+a=Outer.assembly(chain[-1],b,bridge,kap,eta=eta,beta=beta);assert len(a['strict_constraints'])==47 and all(x>0 for x in a['strict_constraints'].values());controls=[]
+for name,k,e,be in [('next_grid',kap+grid,eta,beta),('zero_eta',kap,Q(0),beta),('zero_beta',kap,eta,Q(0)),('unit_beta',kap,eta,Q(1))]:
+ try:Outer.assembly(chain[-1],b,bridge,k,eta=e,beta=be)
+ except AssertionError:controls.append(name)
+ else:raise AssertionError(name)
+res=dict(status='PASS_ASYNC_COMPLEX_AND_CITED_BIT_EXACT_ASSEMBLY',complex_lower=str(b),complex_decimal=rc['lower'],next_b_rejected=str(bp),exact_moment_receipts=receipts,bit_lower=str(c),bit_result_sha256=sha(B),bit_template_sha256=bit['emitted_program_sha256'],bit_prefix_bits=bit['bit']['charged_prefix_bits'],bit_charged_three_level_coefficient_bits=coeff,external_row_allowance=row,kappa=str(kap),kappa_decimal=f'{float(kap):.18f}',binding_component='bit'if c<(1-beta)*b else'complex',strict_outer_constraints={k:str(v)for k,v in a['strict_constraints'].items()},outer_controls=controls,bootstrap=cuts,complex_template_sha256=host['template_sha256'],owner_audit_sha256=sha(O/'OWNERS-AND-PROFILE.json'),invoice_sha256=sha(O/'PREFIX-AND-INVOICE.json'),bit_scope='PR493 published profile and operator reused as a pinned dependency; this verifier reprices its published profile but does not reconstruct that unchanged bit operator.',scope='Conditional finite witness. Inherited compiler, precision/tape and analytic-transfer contracts remain assumed; changed-host operator admission recorded separately.')
+(O/'EXACT-ASSEMBLY.json').write_text(json.dumps(res,indent=2)+'\n');print(res['status'],'b',res['complex_decimal'],'kappa',res['kappa_decimal'],flush=True)
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/code/audit_async.py b/research/ranksector112-async/vendor/pr523/vendor/pr514/code/audit_async.py
new file mode 100644
index 0000000000..43642d1aa0
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/code/audit_async.py
@@ -0,0 +1,149 @@
+"""OpenAI Codex independent serialized ASYNCHRONOUS controller/spectator audit.
+Imports no emitter, optimizer, expander, edge-coloring, or source hosting code.
+CLI: VERIFIED_VARIANT POOLED_HOSTED OUT.json
+The local provider is read from VERIFIED_VARIANT, never from a baseline width histogram.
+"""
+import sys,json,gzip,hashlib,copy
+from pathlib import Path
+from collections import Counter,defaultdict
+BASE,OUT,REPORT=map(lambda p:Path(p).resolve(),sys.argv[1:4]);read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+parent=read(BASE/'split-centres/GLOBAL-TEMPLATE.json.gz');canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz');checks=read(BASE/'split-centres/LOCAL-CHECKS.json');ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json');ct=read(OUT/'GLOBAL-TEMPLATE.json.gz');summary=read(OUT/'HOSTED.json');V=canon['v'];R=canon['R'];N=2*V+R;CENTRES=len(canon['centers']);assert V==120 and canon['h']==9; width=[9-len(canon['frames'][canon['start'][2*V+h]])for h in range(R)];prank={e['child']:e['rank']for e in parent['idle_children']};M=73;T=8;DATA=7680;PHYSICAL=DATA+CENTRES+R+2;CALLS=72;HOSTED=CALLS*R
+
+def orthobasis(port):
+ q=canon['ports'][port];z=next(i for i in range(9)if(q>>i)&1==0);a=q^(1<<z);order=list(range(9));order[z],order[0]=order[0],order[z]
+ b=[(1<<i)^(a if a>>i&1 else 0)for i in order]+[1<<i for i in range(9,73)]
+ assert len(b)==73 and all((x&y).bit_count()%2==int(i==j)for i,x in enumerate(b)for j,y in enumerate(b));return b
+bases=[orthobasis(p)for p in range(120)]
+# Bind the selected provider's actual normalization recipes, including newly
+# selected entrance frames; a baseline recipe registry cannot silently survive.
+required_artifacts={'split-centres/CANONICAL-WORD.json.gz','split-centres/LOCAL-PROGRAMS.json.gz','split-centres/LOCAL-CHECKS.json','split-centres/RESIDUAL-ADAPTERS.json','work/complex-nine-native/DATA-PHASES.json'}
+assert required_artifacts <= set(summary['source_artifacts'])
+adapter_path=BASE/'split-centres/RESIDUAL-ADAPTERS.json'
+assert hashlib.sha256(adapter_path.read_bytes()).hexdigest()==parent['residual_adapter_sha256']
+adapters=read(adapter_path)['recipes']
+for h,w in enumerate(width):
+ if w<9:
+  f=canon['start'][240+h];a=adapters[str(f)]
+  assert a['frame']==f and a['vectors']==canon['frames'][f] and a['rank']==w and a['entrance_rank']==9-w
+
+def audit(t):
+ assert(t['live'],t['physical'])==(DATA,PHYSICAL)
+ assert t['local_programs']==parent['local_programs']and t['recipe']==parent['recipe']and 'each local invocation completes before the next' in t['loop_order'].lower()
+ assert len(t['calls'])==72 and t['hosting']['max_helpers_per_physical_family_per_call']==1 and t['hosting']['banks']==[0]*9
+ for key in('exact_data_phase_recipe_sha256','exact_local_clifford_recipe_sha256','residual_adapter_sha256','adapter_policy'):assert t[key]==parent[key]
+ # Independently project the literal schedule onto every data replica.
+ src=parent['execution_schedule'];assert t['async_schedule']['source_schedule']==src
+ assert t['async_schedule']['source_call_order']==[[c['stage'],c['replica']]for c in parent['calls']]
+ order=[(c['stage'],c['replica'])for c in t['calls']]
+ assert [list(x)for x in order]==t['async_schedule']['order'] and len(set(order))==72
+ all_local=[];perrep={r:[]for r in range(8)};globals_=[]
+ for e in t['execution_schedule']:
+  j=e['source_event'];old=copy.deepcopy(src[j])
+  if 'replica'in e:
+   r=e['replica'];assert 0<=r<8 and j<30;perrep[r].append(j)
+   expected=old|dict(source_event=j,replica=r,replicas=[r],time=e['time'])
+   assert e==expected
+   assert 0<=e['time']<72 and order[e['time']][1]==r
+   if e['kind']=='local_cover_sweep':
+    assert order[e['time']]==(e['stage'],r);all_local.append((e['stage'],r,e['time']))
+  else:
+   globals_.append(j);expected=old|dict(source_event=j)
+   if e['kind']=='bank_padding_cover_sweep':expected['families']=[7680,7680]
+   if e['kind']=='translate_every_live_family':expected.update(families=[0,7680],charged_calls_per_cover=7680)
+   assert e==expected
+ assert all(v==list(range(30))for v in perrep.values()) and globals_==[30,31]
+ assert all_local==[(st,r,i)for i,(st,r)in enumerate(order)]
+ assert all('replica'in e for e in t['execution_schedule'][:-2])
+ assert [e['source_event']for e in t['execution_schedule'][-2:]]==[30,31]
+ # Local cover calls are indivisible; a block then runs the source events
+ # up to that replica's next local invocation.
+ block=-1
+ for e in t['execution_schedule'][:-2]:
+  if e['kind']=='local_cover_sweep':block+=1
+  assert e['time']==block
+ assert t['bank_padding']==dict(parent['bank_padding'],families=[])
+ assert t['cover_final_correction']==dict(parent['cover_final_correction'],families=[0,7680],charged_calls_per_cover=7680)
+ assert t['private_namespace']=={'centers':[DATA,DATA+CENTRES],'reserved_tableau':[DATA+CENTRES,DATA+CENTRES+R],'coefficient':[DATA+CENTRES+R,PHYSICAL]}
+ # Actual physical touch intervals include every individual bridge.
+ pairs={};sides={};windows={};last={};callpos={};stagepair={e['stage']:e['pair']for e in parent['recipe']if e['kind']=='local'}
+ for pos,e in enumerate(t['execution_schedule']):
+  if 'replica'not in e:continue
+  rep=e['replica']
+  if e['kind']=='local_cover_sweep':
+   pair=stagepair[e['stage']];callpos[e['stage'],rep]=pos;last[rep,pair]=pos
+  elif e['kind']=='bridge':last[rep,e['src']]=last[rep,e['dst']]=pos
+  elif e['kind']=='idle_cover_sweep':
+   for side,i in enumerate(e['child_indices']):
+    if i not in prank:continue
+    pairs[i]=e['pair'];sides[i]=side;windows[rep,i]=(last.get((rep,e['pair']),-1),pos)
+ used=defaultdict(set);roles={};paid=Counter();sigmas={};digest=hashlib.sha256();entering=0;cross=0;touches=defaultdict(list)
+ for call in t['calls']:
+  old=next(z for z in parent['calls']if(z['stage'],z['replica'])==(call['stage'],call['replica']))
+  assert {k:v for k,v in call.items()if k not in('owners','time')}=={k:v for k,v in old.items()if k!='owners'}
+  s,rep,pair=call['stage'],call['replica'],call['pair'];assert call['time']==t['async_schedule']['order'].index([s,rep]);own=call['owners'];assert len(own)==N and len({f for f,rt in own})==N and all(0<=f<DATA for f,rt in own)
+  assert own[:240]==old['owners'][:240]
+  for h,(family,route)in enumerate(own[240:]):
+   w=width[h];typ,i,off=route[:3];ownerrep,sub=divmod(family,960);fampair,sub=divmod(sub,240);side,port=divmod(sub,120)
+   assert windows[ownerrep,i][0]<callpos[s,rep]<windows[ownerrep,i][1] and fampair==pairs[i] and side==sides[i] and 0<=off and off+w<=prank[i]
+   B=bases[port];pend=[int(x)for x in ph['recipes'][port]['idle_children'][i]['orthogonal_axes']];assert len(pend)==prank[i]
+   occ=[B.index(v)for v in pend[off:off+w]];sp=[j for j in range(M)if j not in occ][:9-w]
+   assert route==([3,i,off]if w==9 else[4,i,off,w,sp]);assert len(set(occ+sp))==9
+   order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert sorted(order)==list(range(M));sigma=[B[j]for j in order]
+   assert sigma[:w]==pend[off:off+w]and sigma[w:9]==[B[j]for j in sp]
+   sh=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sh]=sigma;digest.update(json.dumps([s,rep,h,family,sh],separators=(',',':')).encode()+b'\n')
+   key=(i,ownerrep,port);cells=set(range(off,off+w));assert not used[key]&cells;used[key]|=cells
+   role=(s,rep,h);assert role not in roles;roles[role]=dict(stage=s,replica=rep,helper=h,family=family,owner_replica=ownerrep,child=i,copy=ownerrep*120+port,port=port,offset=off,width=w)
+   touches[family].append((s,rep,h));entering+=w<9;cross+=rep!=ownerrep
+  for r,n in checks[call['orientation']]['paid_profile'].items():paid[int(r)]+=n
+ assert set(roles)=={(s,rep,h)for s in range(9)for rep in range(8)for h in range(R)}
+ # The frozen pooled metadata must bind the actual serialized owner maps.
+ assert len(t['hosting']['pooled_slots'])==HOSTED
+ for z in t['hosting']['pooled_slots']:
+  key=(z['stage'],z['replica'],z['helper']);assert key in roles
+  assert {k:z[k]for k in roles[key]}==roles[key]
+ assert len({(z['stage'],z['replica'],z['helper'])for z in t['hosting']['pooled_slots']})==HOSTED
+ rem={};wanted=[]
+ for old in parent['idle_children']:
+  i,port=old['child'],old['port']
+  for rep in range(T):
+   u=used[i,rep,port];assert u==set(range(len(u)));r=old['rank']-len(u)
+   if r:
+    f=rep*960+(2*pairs[i]+sides[i])*120+port;wanted.append(dict(child=i,port=port,replica=rep,replicas=1,family=f,rank=r,hosted=len(u),pending_offset=len(u)));paid[r]+=1
+ assert t['idle_children']==wanted
+ mass=sum(r*n for r,n in paid.items());assert73=73*7680-mass;assert assert73==2496 and 73**2>2*max(paid)**2
+ return dict(profile=dict(sorted(paid.items())),mass=mass,hosted=HOSTED,entering=entering,cross_replica=cross,sigma_digest=digest.hexdigest(),sigmas=sigmas,idle_remainders=len(wanted),busy_family_checks=len(roles),invocations=72)
+
+r=audit(ct);raw=gzip.decompress((OUT/'GLOBAL-TEMPLATE.json.gz').read_bytes());assert hashlib.sha256(raw).hexdigest()==summary['template_sha256'];assert r['profile']=={int(k):v for k,v in summary['global_profile'].items()};assert r['sigmas']==read(OUT/'ACTUAL-SIGMAS.json.gz');assert r['sigma_digest']==summary['sigma_stream_sha256']
+assert all(hashlib.sha256((BASE/name).read_bytes()).hexdigest()==value for name,value in summary['source_artifacts'].items())
+controls=[]
+def reject(name,mut):
+ q=copy.deepcopy(ct);mut(q)
+ try:audit(q)
+ except(AssertionError,KeyError,IndexError,ValueError,TypeError):controls.append(name)
+ else:raise AssertionError('ACCEPTED '+name)
+reject('wrong call time',lambda q:q['calls'][0].__setitem__('time',71))
+enter=lambda q:next(o for c in q['calls']for o in c['owners'][240:]if o[1][0]==4)
+reject('alias two whole owners',lambda q:q['calls'][0]['owners'].__setitem__(241,q['calls'][0]['owners'][240]))
+reject('helper on active data family',lambda q:q['calls'][0]['owners'][240].__setitem__(0,q['calls'][0]['owners'][0][0]))
+reject('owner in private namespace',lambda q:q['calls'][0]['owners'][240].__setitem__(0,7680))
+reject('unbound change of owner replica',lambda q:q['calls'][0]['owners'][240].__setitem__(0,(q['calls'][0]['owners'][240][0]+960)%7680))
+reject('omit complete invocation',lambda q:q['calls'].pop())
+reject('reorder invocation replicas',lambda q:q['calls'].__setitem__(0,q['calls'][1]))
+reject('interleave local invocations',lambda q:q.__setitem__('loop_order','interleaved local instructions'))
+reject('change local instruction stream',lambda q:q['local_programs']['forward'].pop())
+reject('wrong residual width',lambda q:enter(q)[1].__setitem__(3,enter(q)[1][3]-1))
+reject('wrong spectator coordinate',lambda q:enter(q)[1][4].__setitem__(0,72))
+reject('omit spectator route',lambda q:enter(q).__setitem__(1,enter(q)[1][:3]))
+reject('overlap residual footprint',lambda q:q['calls'][0]['owners'][240][1].__setitem__(2,100))
+reject('omit idle remainder',lambda q:q['idle_children'].pop())
+reject('underpay idle remainder',lambda q:q['idle_children'][0].__setitem__('rank',0))
+reject('omit bridge touch',lambda q:q['execution_schedule'].pop(next(i for i,e in enumerate(q['execution_schedule'])if e['kind']=='bridge')))
+reject('remove one-owner rule',lambda q:q['hosting'].pop('max_helpers_per_physical_family_per_call'))
+reject('duplicate frozen role',lambda q:q['hosting']['pooled_slots'].__setitem__(1,q['hosting']['pooled_slots'][0]))
+reject('understate physical reserve',lambda q:q.__setitem__('physical',PHYSICAL-1))
+report=dict(status='PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS',template_sha256=summary['template_sha256'],complex_template_sha256=summary['template_sha256'],complex_live=7680,complex_profile=r['profile'],complex_hosted_residuals=HOSTED,physical=PHYSICAL,rank_mass=r['mass'],deficit=2496,entering_helper_roles=r['entering'],cross_replica_helper_roles=r['cross_replica'],one_owner_per_complete_invocation=True,helper_busy_family_window_checks=r['busy_family_checks'],complete_invocations=r['invocations'],actual_orthogonal_73column_maps=len(r['sigmas']),actual_sigma_stream_sha256=r['sigma_digest'],all_actual_residual_and_spectator_charts=True,idle_remainders=r['idle_remainders'],mutations_rejected=controls,widths=dict(sorted(Counter(width).items())),scope='Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses unchanged source local program and normalized residual-wrapper identities; all-size compilation and complete coefficient invoice are separate inherited obligations.')
+REPORT.write_text(json.dumps(report,indent=2)+'\n');print(json.dumps(report,indent=2))
+
+owners=dict(status='PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE',template_sha256=summary['template_sha256'],paid_profile=r['profile'],live=7680,physical=PHYSICAL,rank_mass=r['mass'],deficit=2496,hosted_residuals=HOSTED,banked_residuals=0,all_800_owners_per_call_distinct=True,actual_helper_owner_charts=HOSTED,actual_73column_sigmas=len(r['sigmas']),cross_replica_helper_roles=r['cross_replica'],explicit_idle_remainder_children=r['idle_remainders'],source_idle_children_charged=sum(x['replicas']for x in parent['idle_children']),source_artifacts=summary['source_artifacts'],controller_audit_sha256=hashlib.sha256(REPORT.read_bytes()).hexdigest())
+(REPORT.parent/'OWNERS-AND-PROFILE.json').write_text(json.dumps(owners,indent=2)+'\n')
+
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/code/audit_async_invoice.py b/research/ranksector112-async/vendor/pr523/vendor/pr514/code/audit_async_invoice.py
new file mode 100644
index 0000000000..568edf53a0
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/code/audit_async_invoice.py
@@ -0,0 +1,100 @@
+"""Async PR484 scalar/prefix lowering and finite overcharge recount. OpenAI Codex.
+Reads emitted programs, canonical word and raw routes, importing no supplier code.
+Inherited all-size compiler admissibility is a condition, not inferred here.
+"""
+from pathlib import Path
+from fractions import Fraction as F
+from collections import Counter
+import gzip,json,math,hashlib
+import sys
+O=Path(sys.argv[1]);V=Path(sys.argv[2]);HOSTED=Path(sys.argv[3])
+def read(p):return json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+w=read(V/'split-centres/CANONICAL-WORD.json.gz');p=read(V/'split-centres/LOCAL-PROGRAMS.json.gz');old=read(V/'split-centres/GLOBAL-TEMPLATE.json.gz');new=read(HOSTED/'GLOBAL-TEMPLATE.json.gz');integ=read(V/'split-centres/INTEGRATION.json');checks=read(V/'split-centres/LOCAL-CHECKS.json');prior=read(V/'split-centres/INDEPENDENT-REPLAY.json');owners=read(O/'OWNERS-AND-PROFILE.json')
+VV=w['v'];R=w['R'];N=2*VV+R;M=73;L=9;T=8;K=4
+assert VV==120 and w['h']==9
+PAYLOAD=512
+control=read(O/'ASYNC-AUDIT.json')
+raw=gzip.decompress((HOSTED/'GLOBAL-TEMPLATE.json.gz').read_bytes());th=hashlib.sha256(raw).hexdigest()
+assert th==control['complex_template_sha256']==owners['template_sha256']
+assert control['one_owner_per_complete_invocation'] and control['complete_invocations']==72
+assert new['local_programs']==old['local_programs'] and new['recipe']==old['recipe']
+assert Counter(c['orientation']for c in new['calls'])==Counter(c['orientation']for c in old['calls'])
+local={}
+for ori,evs in p.items():
+ rows={('L',i):{i:F(1)}for i in range(N)};env={('L',i):F(1)for i in range(N)};peak=F(1);real=macros=0;paid=Counter();workops=0
+ for e in evs:
+  if e[0]=='climb':paid[e[5]]+=1
+  elif e[0]=='center':paid[e[4]]+=1
+  elif e[0]=='scalar':
+   macros+=1;x=e[1];op=x[0];a=tuple(x[1]);count=0
+   if op=='clear':rows[a]={};env[a]=F(0);count=1
+   elif op=='copy':rows[a]=dict(rows[tuple(x[2])]);env[a]=env[tuple(x[2])];count=1
+   elif op=='scale':
+    q=F(x[2],x[3]);num,den=abs(q.numerator),q.denominator
+    assert num and num&(num-1)==0 and den&(den-1)==0
+    rows[a]={j:q*v for j,v in rows[a].items()};env[a]*=abs(q)
+    count=abs(num.bit_length()-den.bit_length())+int(q<0)
+   elif op=='add':
+    b=tuple(x[2]);q=F(x[3],x[4]);num,den=abs(q.numerator),q.denominator
+    assert a!=b and num>0 and den&(den-1)==0
+    # Lower actual coefficient to cleared Horner work. Every intermediate
+    # magnitude envelope is explicitly included, before denominator halvings.
+    acc=0;count=1
+    for i,ch in enumerate(bin(num)[2:]):
+     if i:acc*=2;count+=1;peak=max(peak,acc*env[b])
+     if ch=='1':acc+=1;count+=1;peak=max(peak,acc*env[b])
+    v=F(acc)
+    for i in range(den.bit_length()-1):v/=2;count+=1;peak=max(peak,v*env[b])
+    assert v==abs(q);count+=2 # signed accumulation and private work clear
+    env[a]=env.get(a,F(0))+abs(q)*env[b];rr=rows.setdefault(a,{})
+    for j,z in list(rows[b].items()):
+     value=rr.get(j,F(0))+q*z
+     if value:rr[j]=value
+     else:rr.pop(j,None)
+    workops+=count
+   else:raise AssertionError(op)
+   real+=2*count;peak=max(peak,env[a])
+ assert all(not row for reg,row in rows.items()if reg[0]=='C')
+ for i in range(N):
+  expected={i:F(1)}
+  if ori=='forward'and 120<=i<240:expected[i-120]=F(1)
+  if ori=='backward'and i<120:expected[i+120]=F(-1)
+  assert rows['L',i]==expected
+ assert peak==F(prior['local'][ori]['prefix_l1_upper']) and peak<2**192
+ assert real==checks[ori]['real_component_primitive_bound']and macros==checks[ori]['scalar_macros']
+ assert dict(paid)=={int(r):z for r,z in checks[ori]['paid_profile'].items()}
+ local[ori]=dict(events=len(evs),macros=macros,real_component_primitives=real,prefix_l1=str(peak),prefix_bits=peak.numerator.bit_length()-peak.denominator.bit_length()+1,coefficient_work_primitive_count=workops,all_exact_columns=N,all_560_dirty_helper_columns_restored=True,private_centres_and_coefficient_work_cleared=True)
+centres=len(w['centers']);widths=[9-len(w['frames'][f])for f in w['start'][240:]];enter=sum(x<9 for x in widths)
+children=sum(checks['forward']['paid_profile'].values());macros=max(x['macros']for x in local.values());compiler=64*(M+1)**3
+adapters=16*(macros+children+N+centres)+64*M
+primitive_bound=max(x['real_component_primitives']for x in local.values())+adapters*compiler
+bridges=sum(e['kind']=='bridge'for e in old['recipe']);bridgeadd=2*VV*T*bridges;assert sum(e['kind']=='bridge'for e in new['execution_schedule'])==T*bridges
+shifts=K*VV*T;moves=2*K*VV*T
+oldW=old['live'];oldP=old['physical'];oldNB=(oldW-2*VV*K*T)//L
+scalar=sum(local[c['orientation']]['real_component_primitives']for c in old['calls'])
+nonlocal_items=4*VV*T*L+2*VV*T*L+2*L*T*R+sum(e['replicas']for e in old['idle_children'])+L*oldNB+bridgeadd+shifts+moves+oldW+oldP+2*L*T*enter*144
+outside=8*nonlocal_items+64*M
+pervertex=scalar+bridgeadd+shifts+moves+oldW+(72*adapters+outside)*compiler+64*oldP
+invoice=integ['finite_invoice'];assert (primitive_bound,adapters,pervertex,compiler)==(invoice['local_primitive_bound'],invoice['local_adapters'],invoice['pervertex'],invoice['compiler'])
+# Independent hosted stock rebase, retaining the larger unhosted operation
+# overcharge; only the stock and mass in the common router/literal change.
+W=new['live'];P=new['physical'];mass=owners['rank_mass'];profile=owners['paid_profile']
+assert M*W-mass==2496 and P==W+R+centres+2
+rebase=pervertex-oldP*65+P*65-oldW+W;used=max(rebase,pervertex)
+r=M//2;group=2**(r*r)
+for i in range(1,r+1):group*=2**(2*i)-1
+stock=group*P;smass=group*mass;logical=group*used+64;router=compiler*(logical+1)*(stock+1)**2
+G,E,C0=2**30000,2**100000,2**210000;B=smass+E;literal=2*G*stock**2+8*smass+4*stock+4+32*M;row=2*stock.bit_length()+9909+252+2*PAYLOAD;maxchild=max(map(int,profile))
+ineq=dict(local_primitive_bound=primitive_bound<2**48,logical=logical<2**6050,router=router<G,literal=literal<E,mass=B<2**100001,precision=32*M*B*B<C0,tape=2*B+18<C0,row=row<20161,halving=M*M>2*maxchild*maxchild)
+assert all(ineq.values())
+localbits=max(x['prefix_bits']for x in local.values());input_l2_bits=(M+1)//2
+bridge_sweeps=sum(e['kind']=='bridge'for e in new['execution_schedule'])
+required_prefix=localbits+input_l2_bits+len(new['calls'])+bridge_sweeps+4
+assert localbits==21 and bridge_sweeps==72 and required_prefix==206 and required_prefix<PAYLOAD
+assert owners['explicit_idle_remainder_children']<=owners['source_idle_children_charged']
+assert new['physical']<=old['physical'] and new['live']<=old['live'] and not new['bank_padding']['families']
+out=dict(status='PASS_INDEPENDENT_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE',template_sha256=th,global_prefix_bits=required_prefix,charged_prefix_bits=PAYLOAD,complete_invocation_sweeps=72,bridge_sweeps=bridge_sweeps,row_prefix_extra=2*PAYLOAD,local=local,entering_helpers=enter,entrance_rank=sum(9-x for x in widths),local_adapters=adapters,local_primitive_bound=primitive_bound,wrapper_elementary_factors_charged=2*72*enter*144,compiler=compiler,unhosted_pervertex=pervertex,hosted_rebased_pervertex=rebase,conservative_pervertex_used=used,finite=dict(physical_stock_bits=stock.bit_length(),router_bits=router.bit_length(),literal_bits=literal.bit_length(),physical_row_coefficient=row,retained_row_coefficient=20161,required_C0_bits=(32*M*B*B).bit_length(),halving_integer_inequality=[M*M,2*maxchild*maxchild],G_exponent=30000,E_exponent=100000,C0_exponent=210000),strict_checks=ineq,scope='Exact finite recount conditional on inherited all-size compiler/precision/tape and analytic-transfer contracts. Signed accumulation uses the supplier scalar primitive convention. Async prefix counts all72individual bridges and72complete invocations;512bits are charged, and an additional2*512 enters the two-level physical row bound.')
+(O/'PREFIX-AND-INVOICE.json').write_text(json.dumps(out,indent=2)+'\n');print(json.dumps(out,indent=2),flush=True)
+
+prefix=dict(status='PASS_ASYNC_GLOBAL_PREFIX',template_sha256=th,global_prefix_bits=required_prefix,retained_payload_bits=PAYLOAD,complete_invocation_cover_sweeps=len(new['calls']),bridge_factor_two_sweeps=bridge_sweeps,local_scalar_coefficient_work_prefix_bits=localbits,stream_input_sup_to_l2_bits=input_l2_bits,primitive_arithmetic_margin_bits=4,controller_audit_sha256=hashlib.sha256((O/'ASYNC-AUDIT.json').read_bytes()).hexdigest(),proof=f'Each complete normalized invocation has unitary helper endpoints and a data shear with at most two unitary summands. Distinct full orthogonal owner charts act by right-translation bijections on the retained cover group. Thus the maximum full-stream L2 norm grows by at most2per complete local cover sweep and individual bridge. All72local sweeps and72individual bridge sweeps are counted. Unit-modulus phases, idle children, terminal translations and normalized spectator endpoints are unitary. The independently replayed scalar/Horner envelope costs {localbits} bits, initial sup-to-L2 conversion {input_l2_bits} bits, primitive margin 4 bits: total {required_prefix} < {PAYLOAD}. All-size child/compiler and precision/tape interfaces remain inherited.')
+(O/'GLOBAL-PREFIX.json').write_text(json.dumps(prefix,indent=2)+'\n')
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/code/audit_kernel_scalar.py b/research/ranksector112-async/vendor/pr523/vendor/pr514/code/audit_kernel_scalar.py
new file mode 100644
index 0000000000..4373bb9bd5
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/code/audit_kernel_scalar.py
@@ -0,0 +1,55 @@
+"""Independent exact scalar witness for a selected complex kernel word.
+Uses immutable correct-word compensation for omission controls; no repaired
+compensation is silently supplied to a mutant. No physical-hosting claim.
+"""
+import sys,json,gzip,hashlib,copy
+from pathlib import Path
+from fractions import Fraction as Q
+from collections import Counter
+p=Path(__file__).resolve().parent
+path=Path(sys.argv[1]);selection=Path(sys.argv[2]);out=Path(sys.argv[3]);w=json.loads(gzip.decompress(path.read_bytes()));sel=json.loads(selection.read_text());n=240+w['report']['R']
+def ident():return[{r:Q(1)}for r in range(n)]
+def apply(e,rows):
+ if e[0]=='scale':
+  _,t,a,b,*_=e;q=Q(a,b);rows[t]={j:q*x for j,x in rows[t].items()};return
+ _,t,s,a,b,*_=e;q=Q(a,b)
+ for j,x in list(rows[s].items()):
+  z=rows[t].get(j,Q(0))+q*x
+  if z:rows[t][j]=z
+  else:rows[t].pop(j,None)
+def inv(e,dual=False):
+ e=copy.deepcopy(e)
+ if e[0]=='add':
+  e[3]*=-1
+  if dual:e[1],e[2]=e[2],e[1]
+ else:e[2],e[3]=e[3],e[2]
+ return e
+def replay(es):
+ rows=ident()
+ for e in es:apply(e,rows)
+ return rows
+main=w['A']+w['cut']+w['B'];mx=replay(main);dirty=[{}for _ in range(n)]
+for r in range(120,240):dirty[r]={j:x for j,x in mx[r].items()if j>=240}
+for e in w['precondition']:apply(e,dirty)
+comp=[]
+for r in range(120,240):
+ for j,x in sorted(dirty[r].items()):
+  assert not w.get('start_extra',{}).get(str(j)),('nonzero-frame compensation',j)
+  comp.append(['add',r,j,-x.numerator,x.denominator,[]])
+cleanup=[inv(e)for e in reversed(w['A']+w['B'])if not 120<=e[1]<240]
+assert[e[:-1]for e in cleanup]==[e[:-1]for e in w['cleanup']]
+program=w['precondition']+comp+main+cleanup;expected=ident()
+for t in range(120):expected[120+t][t]=Q(1)
+assert replay(program)==expected
+back=ident()
+for t in range(120):back[t][120+t]=Q(-1)
+assert replay([inv(e,True)for e in program])==back
+controls={}
+for cl in sel['kernel']:
+ for h in cl['pivots']:
+  aa=[e for e in w['A']if not(e[0]=='add'and e[2]==240+h and e[1]>=240 and e[-1]==cl['E'])]
+  assert len(aa)<len(w['A']);cc=[inv(e)for e in reversed(aa+w['B'])if not 120<=e[1]<240]
+  assert replay(w['precondition']+comp+aa+w['cut']+w['B']+cc)!=expected
+  controls[str(h)]='REJECTED_OMITTED_KERNEL_CORRECTION'
+r=dict(status='PASS_EXACT_RATIONAL_FORWARD_AND_INVERSE_TRANSPOSE',word_sha256=hashlib.sha256(path.read_bytes()).hexdigest(),selection_sha256=hashlib.sha256(selection.read_bytes()).hexdigest(),columns_each_orientation=n,compensations=len(comp),program_operations=len(program),kernel_pivots=len(controls),controls=controls,scope='Exact local scalar identity and preserved frame-zero compensation; physical owner routing, complete invoice and outer kappa separate.')
+out.write_text(json.dumps(r,indent=2)+'\n');print(r['status'],n,len(controls))
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/code/build_kernel92.py b/research/ranksector112-async/vendor/pr523/vendor/pr514/code/build_kernel92.py
new file mode 100644
index 0000000000..f5e68e01f9
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/code/build_kernel92.py
@@ -0,0 +1,42 @@
+"""Reconstruct the selected 92-pivot partial-own complex word.
+Apache-2.0. Prepared with OpenAI Codex assistance; retain PR507/484 notices.
+Usage: python -B build_kernel92.py GK_CODE PARTIAL_BASE KERNEL84_SELECTION
+       RETIME_MAP KERNEL92_SELECTION NEW_OUTPUT_DIR
+No discovery search runs. Actual physical allocation is independently checked.
+"""
+from pathlib import Path
+import json,gzip,sys,copy,hashlib
+from collections import Counter
+if not __debug__:raise RuntimeError('Assertions must remain enabled')
+code,basefile,s84file,mapfile,s92file,out=map(Path,sys.argv[1:]);assert not out.exists();sys.dont_write_bytecode=True;sys.path.insert(0,str(code));import gk_word as g
+read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+base=read(basefile);s84=read(s84file);s92=read(s92file);fm=read(mapfile)
+assert base['report']['R']==560 and len(base['A'])==2680 and len(base['B'])==840
+assert sum(len(c['pivots'])for c in s84['kernel'])==84
+assert sum(len(c['pivots'])for c in s92['kernel'])==92
+wanted=copy.deepcopy(s84['gauge'])
+for h in ['540','541','542','543']:wanted[h]=[408,102]
+assert s92['gauge']==wanted
+w84=g.build(base,s84);r=copy.deepcopy(w84)
+for part in ['A','B']:
+ seen=set()
+ for i,old,new in fm[part]:
+  assert i not in seen and r[part][i][-1]==old,(part,i);seen.add(i);r[part][i][-1]=new
+ assert [e[:-1]for e in r[part]]==[e[:-1]for e in w84[part]]
+assert r['A'][:671]==w84['A'][:671]
+assert g.profile(r)==Counter({int(k):v for k,v in fm['expected_local_profile'].items()})
+ret=copy.deepcopy(base)
+for part in ['A','B']:
+ tail=r[part][-len(base[part]):];assert [e[:-1]for e in tail]==[e[:-1]for e in base[part]];ret[part]=copy.deepcopy(tail)
+ret['cleanup']=[g.inverse(e,g.FULL)for e in reversed(ret['A']+ret['B'])if not 120<=e[1]<240]
+w=g.build(ret,s92);H=g.profile(w);widths=g.widths_of(w)
+assert H=={1:2539,2:160,3:530,4:88,5:298,6:68,7:1,8:17}
+assert Counter(widths)=={7:18,8:154,9:388}
+# Normalize only the established inherited floating display fields and redundant R.
+norm=copy.deepcopy(w);assert norm.get('R',norm['report']['R'])==norm['report']['R']==560;norm.pop('R',None)
+for k in ['complex_coarse_float','gain_percent_float']:norm['report'].pop(k,None)
+semantic=hashlib.sha256(json.dumps(norm,sort_keys=True,separators=(',',':')).encode()).hexdigest()
+assert semantic=='c6e758b324d3566e8443b3fd3d739c4d01e1928eadbee40f5c36973404b0640b'
+out.mkdir(parents=True);(out/'FULL-WORD.json.gz').write_bytes(g.dump(w));(out/'SELECTION.json').write_text(json.dumps(s92,indent=2)+'\n');(out/'RETIMED-BASE.json.gz').write_bytes(g.dump(ret))
+receipt=dict(status='PASS_EXACT_SOURCE_BOUND_KERNEL92_RECONSTRUCTION',sources={label:hashlib.sha256(path.read_bytes()).hexdigest()for label,path in [('partial_base',basefile),('kernel84_selection',s84file),('frame_map',mapfile),('kernel92_selection',s92file),('gk_word.py',code/'gk_word.py'),('gk_common.py',code/'gk_common.py')]},normalized_word_sha256=semantic,word_sha256=hashlib.sha256((out/'FULL-WORD.json.gz').read_bytes()).hexdigest(),profile=dict(H),widths=dict(Counter(widths)),widths_ordered=widths,pivots=92,entrance_rank=sum(9-x for x in widths),scope='Exact local source construction; arbitrary-dirt scalar, physical phases/owners and final outer assembly checked separately.')
+(out/'CONSTRUCTION.json').write_text(json.dumps(receipt,indent=2)+'\n');print(receipt['status'])
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/code/construct_partial.py b/research/ranksector112-async/vendor/pr523/vendor/pr514/code/construct_partial.py
new file mode 100644
index 0000000000..69500f6513
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/code/construct_partial.py
@@ -0,0 +1,309 @@
+# Adapted by OpenAI Codex for isolated structural research.
+# Modified from PR425 by icekylinx with Codex assistance.
+"""Full discovery word for Hamming packets with borrowed X and Y registers.
+
+This changes the scalar architecture. It is not accepted by the old restricted
+gx interface: source bases may change until full-frame cleanup, and targets use
+an explicitly inverted output basis. No supplier admission is asserted.
+"""
+import copy,gzip,json,math,time
+import itertools as it
+from collections import Counter,defaultdict
+from fractions import Fraction as Q
+from pathlib import Path
+
+import sys
+INPUT=Path(sys.argv[1]);OUT=Path(sys.argv[2]);OUT.mkdir(parents=True,exist_ok=False);D=json.loads((INPUT/'PROTOTYPE.json').read_text())
+P=D['binary_ports'];R=D['root_lines'];v=120;h=9
+modules=json.load(gzip.open(INPUT/'PACKET-PROGRAMS.json.gz'))
+
+def basis(vectors):
+    b={}
+    for x in vectors:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+def inside(a,b):return basis(a+b)==b
+def hyper(p):return basis([x for x in range(1,512) if (x&p).bit_count()%2==0])
+FULL=basis([1<<i for i in range(9)])
+G=[[sum(x*y for x,y in zip(a,b))//2 for b in R] for a in R]
+blocks={tuple(z['receipt']['block']):z for z in modules}
+frame={next(i for i,x in enumerate(r) if x):s for s,r in enumerate(R) if sum(x!=0 for x in r)==1}
+cur=[(p,) for p in P]+[()]*v;rows=[{r:Q(1)} if r<v else {} for r in range(2*v)]
+A=[];B=[];H=Counter();by={k:Counter() for k in 'xysc'};phase=A
+
+def alloc():
+    n=len(cur);cur.append(());rows.append({});return n
+def climb(r,F):
+    assert inside(cur[r],F),('frame violation',r,cur[r],F)
+    dr=len(F)-len(cur[r])
+    if dr:H[dr]+=1;by['x' if r<v else 'y' if r<2*v else 's'][dr]+=1
+    cur[r]=F
+def add(t,s,q,F):
+    assert t!=s;q=Q(q)
+    if not q:return
+    climb(t,F);climb(s,F);phase.append(['add',t,s,q.numerator,q.denominator,list(F)])
+    for j,x in list(rows[s].items()):
+        z=rows[t].get(j,Q(0))+q*x
+        if z:rows[t][j]=z
+        else:rows[t].pop(j,None)
+def scale(t,q,F):
+    q=Q(q);assert q
+    if q==1:return
+    climb(t,F);phase.append(['scale',t,q.numerator,q.denominator,list(F)])
+    rows[t]={j:q*x for j,x in rows[t].items()}
+def swap(a,b,F):
+    if a==b:return
+    add(a,b,1,F);add(b,a,-1,F);add(a,b,1,F);scale(b,-1,F)
+def linear(regs,M,F):
+    """Apply an invertible rational square matrix by elementary operations."""
+    n=len(regs);a=[list(map(Q,row)) for row in M];undo=[]
+    for col in range(n):
+        k=next(i for i in range(col,n) if a[i][col])
+        if k!=col:a[k],a[col]=a[col],a[k];undo.append(('swap',k,col))
+        q=a[col][col]
+        if q!=1:a[col]=[x/q for x in a[col]];undo.append(('scale',col,1/q))
+        for i in range(n):
+            if i==col or not a[i][col]:continue
+            q=-a[i][col];a[i]=[x+q*y for x,y in zip(a[i],a[col])];undo.append(('add',i,col,q))
+    assert a==[[Q(i==j) for j in range(n)] for i in range(n)]
+    old=[dict(rows[r]) for r in regs]
+    for op in reversed(undo):
+        if op[0]=='swap':swap(regs[op[1]],regs[op[2]],F)
+        elif op[0]=='scale':scale(regs[op[1]],1/op[2],F)
+        else:add(regs[op[1]],regs[op[2]],-op[3],F)
+    for i,r in enumerate(regs):
+        expected=defaultdict(Q)
+        for j,q in enumerate(M[i]):
+            for k,x in old[j].items():expected[k]+=q*x
+        assert rows[r]=={k:x for k,x in expected.items() if x}
+
+# All original-source loads precede source borrowing.
+own={};fl={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines']
+    for s in ids:
+        own[s]=alloc()
+
+packets={};retired={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines'];mp={i:s for i,s in enumerate(ids)}
+    mp.update({i:alloc() for i in range(8,24)})
+    for event_index,(e,F) in enumerate(zip(z['events'],z['event_frames'])):
+        t,s,a,b=e;add(mp[t],mp[s],Q(a,b),tuple(F))
+        # 16 source copies and 24 two-shear operations precede face assembly.
+        if event_index==39:
+            for parity in (0,1):
+                tet=sorted(s for s in ids if sum(R[s][i]<0 for i in c)%2==parity)
+                matching=[[(tet[0],tet[1]),(tet[2],tet[3])],[(tet[0],tet[2]),(tet[1],tet[3])],[(tet[0],tet[3]),(tet[1],tet[2])]][(1,1)[parity]]
+                for pair in matching:
+                    rs=sorted(r for r in mp.values() if set(rows[r])==set(pair))
+                    assert len(rs)==2,(pair,rs)
+                    for s,r in zip(pair,rs):
+                        assert len(cur[r])==2
+                        add(own[s],r,1,cur[r])
+    keys=[(p,epsilon) for p in it.combinations(c,2) for epsilon in (-1,1)]
+    for key,(reg,alpha) in zip(keys,z['outputs']):
+        a=mp[reg];alpha=Q(alpha);F=cur[a]
+        b=alloc();add(b,a,1,F)
+        consumers=sorted(d for d in blocks if d!=c and set(key[0])<=set(d))
+        assert len(consumers)==2
+        for target,rr in zip(consumers,(a,b)):packets[c,key[0],key[1],target]=(rr,alpha)
+    retired[c]=[mp[r] for r in z['dead_registers']]
+
+# Four coordinate sums per code block, reconstructed in the retired register
+# stock at its legal rank-four frame. The remaining eight rows retain a basis.
+block_totals={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines'];regs=retired[c];F=basis([P[s] for s in ids])
+    assert len(regs)==12 and len(F)==4
+    for col,s in enumerate(ids):
+        k=next(i for i in range(col,len(regs)) if rows[regs[i]].get(s,Q(0)))
+        swap(regs[k],regs[col],F)
+        scale(regs[col],1/rows[regs[col]][s],F)
+        for i in range(len(regs)):
+            if i!=col and rows[regs[i]].get(s,Q(0)):add(regs[i],regs[col],-rows[regs[i]][s],F)
+    assert all(rows[regs[i]]=={s:Q(1)} for i,s in enumerate(ids))
+    assert all(not rows[r] for r in regs[8:])
+    for i,reg in zip(c,regs[8:]):
+        for j,s in enumerate(ids):add(reg,regs[j],R[s][i],F)
+        block_totals[c,i]=reg
+
+# Eight global coordinate sums, with a single copy each for the centers. The
+# other copy is exactly the correction needed by the eight frame-line targets.
+global_totals={};centers=[]
+for i in range(8):
+    regs=[block_totals[c,i] for c in sorted(blocks) if i in c]
+    F=hyper(P[frame[i]]);a=regs[0]
+    for b in regs[1:]:add(a,b,1,F)
+    global_totals[i]=a
+    centers.append(a)
+centers += [frame[i] for i in range(8)]
+center_frames=[cur[r] for r in centers]
+assert list(map(len,center_frames))==[8]*8+[1]*8
+
+# Own-block and coordinate-frame corrections, one stream per code target.
+own_out={};tetrads={}
+for c,z in sorted(blocks.items()):
+    ids=z['receipt']['source_lines']
+    tet=[sorted(s for s in ids if sum(R[s][i]<0 for i in c)%2==parity) for parity in (0,1)]
+    tetrads[c]=tet
+    for parity,targets in enumerate(tet):
+        sources=tet[1-parity];xs=[own[s] for s in sources]
+        F=basis([P[s] for s in sources])
+        # Current own registers are an invertible pair-partial basis T*x.
+        T=[[rows[x].get(s,Q(0)) for s in sources] for x in xs]
+        n=len(T);aug=[r+[Q(i==j) for j in range(n)] for i,r in enumerate(T)]
+        for col in range(n):
+            k=next(i for i in range(col,n) if aug[i][col]);aug[k],aug[col]=aug[col],aug[k]
+            q=aug[col][col];aug[col]=[x/q for x in aug[col]]
+            for i in range(n):
+                if i!=col:
+                    q=aug[i][col];aug[i]=[a-q*b for a,b in zip(aug[i],aug[col])]
+        inv=[r[n:] for r in aug]
+        M=[[sum(Q(G[t][s])*inv[k][j] for k,s in enumerate(sources)) for j in range(n)] for t in targets]
+        assert all(q.denominator&(q.denominator-1)==0 for row in M for q in row)
+        linear(xs,M,F)
+        for t,x in zip(targets,xs):own_out[t]=x
+
+# Cross-block M packets, shared by four targets, then two-output pair transforms.
+Ms={};consumers=defaultdict(list);pairs=[]
+for c in sorted(blocks):
+    for p in it.combinations(c,2):
+        ds=sorted(d for d in blocks if d!=c and set(p)<=set(d))
+        for epsilon in (-1,1):
+            (a,alpha),(b,beta)=[packets[d,p,epsilon,c] for d in ds]
+            F=basis(cur[a]+cur[b]);add(a,b,beta/alpha,F)
+            Ms[c,p,epsilon]=(a,alpha)
+    i,j,k,l=c;partitions=[((i,j),(k,l)),((i,k),(j,l)),((i,l),(j,k))]
+    for parity,tet in enumerate(tetrads[c]):
+        for pi,(p,q) in enumerate(partitions):
+            groups=defaultdict(list)
+            for t in tet:groups[R[t][p[0]]*R[t][p[1]]].append(t)
+            for eps,ts in sorted(groups.items()):
+                assert len(ts)==2;a,b=sorted(ts)
+                e2=R[a][q[0]]*R[a][q[1]]
+                assert e2==R[b][q[0]]*R[b][q[1]]
+                keys=[(c,p,eps),(c,q,e2)];pid=len(pairs)
+                selected=(pi==parity)  # different first partitions in the two tetrads
+                pairs.append({'targets':(a,b),'keys':keys,'selected':selected,
+                              'matrix':[[R[t][p[0]],R[t][q[0]]] for t in (a,b)]})
+                for key in keys:consumers[key].append(pid)
+slots={}
+for key,uses in sorted(consumers.items()):
+    assert len(uses)==2
+    a,alpha=Ms[key];ordinary=[i for i in uses if not pairs[i]['selected']]
+    for j,pid in enumerate(ordinary):
+        if j==0:r=a
+        else:r=alloc();add(r,a,1,cur[a])
+        slots[pid,key]=(r,alpha)
+
+assert len(cur)-240==560,(len(cur)-240)
+
+# The selected target pairs borrow Y as the first packet destination. Their
+# two-shear output basis is compensated at frame zero and in the scatter table.
+phase=B;selected=[];output_basis=[]
+for pid,pair in enumerate(pairs):
+    if not pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    (a,alpha),(b,beta)=Ms[key1],Ms[key2]
+    add(v+t,a,-Q(mat[0][0],2)*alpha,cur[a])
+    add(v+u,b,-Q(mat[0][1],2)*beta,cur[b])
+    selected.append((pid,t,u,mat))
+for pid,t,u,mat in selected:
+    F=basis(cur[v+t]+cur[v+u]);assert all((P[s]&p).bit_count()%2==0 for s in (t,u) for p in F)
+    add(v+t,v+u,1,F);add(v+u,v+t,-Q(1,2),F)
+    z=-Q(2*mat[1][0],mat[0][0]);scale(v+u,z,F)
+    output_basis.append((t,u,z))
+
+for pid,pair in enumerate(pairs):
+    if pair['selected']:continue
+    (t,u),(key1,key2),mat=pair['targets'],pair['keys'],pair['matrix']
+    (a,alpha),(b,beta)=slots[pid,key1],slots[pid,key2]
+    F=basis(cur[a]+cur[b]);aa,ab=Q(mat[0][0])*alpha,Q(mat[0][1])*beta
+    ba,bb=Q(mat[1][0])*alpha,Q(mat[1][1])*beta
+    add(a,b,ab/aa,F);q=ba/(bb-ba*ab/aa);add(b,a,q,F)
+    add(v+t,a,-aa/2,hyper(P[t]));add(v+u,b,-(bb-ba*ab/aa)/2,hyper(P[u]))
+for t,r in own_out.items():add(v+t,r,-Q(1,2),hyper(P[t]))
+
+side=[dict(rows[v+t]) for t in range(v)]
+for t in range(v):
+    expected={s:-Q(G[t][s],2) for s in range(v) if s!=t and G[t][s] and s not in frame.values()} if t not in frame.values() else {}
+    assert side[t]==expected,('side identity',t)
+
+# Correct the eight-center scatter through the inverse two-output basis.
+scatter=[[Q(r[i],4) if t not in frame.values() else Q(0) for i in range(8)]+[Q(t==frame[i]) for i in range(8)] for t,r in enumerate(R)]
+precondition=[]
+for t,u,z in output_basis:
+    a,b=scatter[t].copy(),scatter[u].copy()
+    scatter[t]=[x/2-y/z for x,y in zip(a,b)]
+    scatter[u]=[x/2+y/z for x,y in zip(a,b)]
+    precondition.extend([['scale',v+u,(1/z).numerator,(1/z).denominator,[]],
+                         ['add',v+u,v+t,1,2,[]],['add',v+t,v+u,-1,1,[]]])
+
+for r in range(len(cur)):climb(r,hyper(P[r-v]) if v<=r<2*v else FULL)
+H[8]+=8;H[1]+=8;by['c'][8]+=8;by['c'][1]+=8
+n=len(cur);Rcount=n-240
+assert sum(r*z for r,z in H.items())==9*Rcount+240*8+72
+
+def apply(event,matrix):
+    if event[0]=='add':
+        _,t,s,a,b,*_=event;q=Q(a,b)
+        for j,x in list(matrix[s].items()):
+            z=matrix[t].get(j,Q(0))+q*x
+            if z:matrix[t][j]=z
+            else:matrix[t].pop(j,None)
+    else:
+        _,t,a,b,*_=event;q=Q(a,b);matrix[t]={j:q*x for j,x in matrix[t].items()}
+def inverse(e,F=None):
+    e=copy.deepcopy(e)
+    if e[0]=='add':e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    if F is not None:e[-1]=list(F)
+    return e
+cut=[]
+for t,rr in enumerate(scatter):
+    for i,q in enumerate(rr):
+        if q:cut.append(['add',v+t,centers[i],q.numerator,q.denominator,None])
+cleanup=[inverse(e,FULL) for e in reversed(A+B) if not v<=e[1]<2*v]
+
+# Exact clean replay checks the changed decoder and restored source basis.
+matrix=[{r:Q(1)} if r<v else {} for r in range(n)]
+for e in A+cut+B+cleanup:apply(e,matrix)
+assert all(matrix[r]==({r:Q(1)} if r<v else {r-v:Q(1)} if r<2*v else {}) for r in range(n))
+
+m=73;T=8;L=9;W=7680+L*Rcount;globalH=Counter({r:z*L*T for r,z in H.items()})
+for r in (16,8,32,8,48,8,48,32,16):globalH[r]+=240*T
+globalH[1]+=L*Rcount
+assert m*W-sum(r*z for r,z in globalH.items())==2496
+# Discovery-only approximate display annotations use explicit left-to-right
+# accumulation for stable results across Python sum() implementations. These
+# floats are not acceptance inputs; complete profiles receive exact pricing.
+low,high=0.,.003
+for _ in range(60):
+    q=(low+high)/2
+    moment=0.0
+    for r,z in globalH.items():moment+=r*z/(m*W)*(m/r)**q
+    moment+=32*m*sum(globalH.values())/(10**16*W)*m**q
+    if moment<1:low=q
+    else:high=q
+report={'status':'EXACT_CLEAN_FULL_WORD_DISCOVERY_NOT_ADMITTED',
+        'h':9,'v':120,'R':Rcount,'cst':72,'local_profile':dict(sorted(H.items())),
+        'global_profile':dict(sorted(globalH.items())),'m':m,'W':W,
+        'complex_coarse_float':(low+high)/2,'baseline_b':0.000999388595603943,
+        'gain_percent_float':100*((low+high)/2/0.000999388595603943-1),
+        'scalar_operations_A':len(A),'scalar_operations_B':len(B),
+        'borrowed_output_pairs':len(output_basis),'centre_ranks':list(map(len,center_frames)),'source_columns_exact':120,
+        'source_and_helper_cleanup_exact_on_clean_columns':True,
+        'retained_center_rows_exact':True,
+        'remaining':['full arbitrary-dirt program and independent replay','exact complex phases and global template','finite invoice and coefficient lowering','two rational prices and outer assembly']}
+full={'report':report,'ports':P,'root_lines':R,'A':A,'B':B,'centers':centers,'scatter':[[str(x) for x in r] for r in scatter],
+      'cut':cut,'cleanup':cleanup,'precondition':precondition,'center_frames':center_frames}
+(OUT/'FULL-WORD.json.gz').write_bytes(gzip.compress(json.dumps(full,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+(OUT/'FULL-DISCOVERY.json').write_text(json.dumps(report,indent=2)+'\n')
+print(json.dumps(report,indent=2),flush=True)
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/code/emit_async.py b/research/ranksector112-async/vendor/pr523/vendor/pr514/code/emit_async.py
new file mode 100644
index 0000000000..9ffe035202
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/code/emit_async.py
@@ -0,0 +1,89 @@
+"""OpenAI Codex whole-owner cross-replica derivative of pinned PR484.
+CLI: SOURCE484_PACKAGE VERIFIED_VARIANT ASYNC-OWNERS.json.gz ASYNC-PLAN.json OUT
+No optimizer or unpublished word builder runs. The frozen map explicitly names
+one whole helper per family per complete invocation, plus borrowed spectators.
+"""
+import sys,json,gzip,hashlib,copy
+from pathlib import Path
+from collections import Counter,defaultdict
+SOURCE,BASE,MAP,PLAN,OUT=map(lambda p:Path(p).resolve(),sys.argv[1:6]);assert not OUT.exists();OUT.mkdir(parents=True)
+sys.path.insert(0,str(SOURCE/'code'));import onehost_gk as OH
+read=lambda p:json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+plan=read(PLAN);call_order=[tuple(x)for x in plan['order']];assert len(call_order)==len(set(call_order))==72;at={x:i for i,x in enumerate(call_order)}
+parent=read(BASE/'split-centres/GLOBAL-TEMPLATE.json.gz');t=copy.deepcopy(parent);canon=read(BASE/'split-centres/CANONICAL-WORD.json.gz');checks=read(BASE/'split-centres/LOCAL-CHECKS.json');ph=read(BASE/'work/complex-nine-native/DATA-PHASES.json');roles=read(MAP);DATA=7680;T=8;V=120;M=73;R=560
+assert(len(roles),len(canon['start']),len(ph['recipes']))==(40320,800,120)
+widths=[9-len(canon['frames'][canon['start'][240+h]])for h in range(R)];assert widths==plan['baseline_widths'], 'source-bound selected provider widths'
+rank={z['child']:z['rank']for z in parent['idle_children']};side={};pairs={}
+for e in parent['execution_schedule']:
+ if e['kind']=='idle_cover_sweep':
+  for sd,ch in enumerate(e['child_indices']):side[ch]=sd;pairs[ch]=e['pair']
+bycall=defaultdict(dict);used=defaultdict(set);sigmas={};digest=hashlib.sha256();entering=0
+for z in roles:
+ s,rep,h=z['stage'],z['replica'],z['helper'];i,cp,off,w,f=z['child'],z['copy'],z['offset'],z['width'],z['family'];orp,port=divmod(cp,V)
+ assert 0<=s<9 and 0<=rep<T and 0<=h<R and w==widths[h] and 0<=orp<T
+ assert f==orp*960+(2*pairs[i]+side[i])*120+port
+ assert(h not in bycall[s,rep])and off>=0 and off+w<=rank[i]
+ assert z['time']==at[s,rep] and z['time'] in plan['windows'][f'{orp},{i}'][1]
+ B=OH.idle_basis(canon['ports'][port]);pending=list(map(int,ph['recipes'][port]['idle_children'][i]['orthogonal_axes']));assert len(pending)==rank[i]
+ occ=[B.index(v)for v in pending[off:off+w]];sp=OH.spectators(canon['ports'][port],pending,off,w)if w<9 else[]
+ order=occ+sp+[j for j in range(M)if j not in occ and j not in sp];assert len(order)==len(set(order))==M
+ sigma=[B[j]for j in order];sigmahash=hashlib.sha256(json.dumps(sigma,separators=(',',':')).encode()).hexdigest();sigmas[sigmahash]=sigma
+ route=[4,i,off,w,sp]if w<9 else[3,i,off];bycall[s,rep][h]=[f,route];entering+=w<9
+ cells=set(range(off,off+w));assert not used[i,orp,port]&cells;used[i,orp,port]|=cells
+ digest.update(json.dumps([s,rep,h,f,sigmahash],separators=(',',':')).encode()+b'\n')
+for c in t['calls']:
+ k=(c['stage'],c['replica']);assert set(bycall[k])==set(range(R))
+ c['owners']=c['owners'][:240]+[bycall[k][h]for h in range(R)];assert len({f for f,r in c['owners']})==800 and all(f<DATA for f,r in c['owners'])
+newidle=[];paid=Counter()
+for c in t['calls']:
+ for r,n in checks[c['orientation']]['paid_profile'].items():paid[int(r)]+=n
+for old in parent['idle_children']:
+ i,port=old['child'],old['port']
+ for rep in range(T):
+  u=used[i,rep,port];assert u==set(range(len(u)));left=old['rank']-len(u)
+  if left:
+   f=rep*960+(2*pairs[i]+side[i])*120+port;newidle.append(dict(child=i,port=port,replica=rep,replicas=1,family=f,rank=left,hosted=len(u),pending_offset=len(u)));paid[left]+=1
+assert M*DATA-sum(r*n for r,n in paid.items())==2496
+C=len(canon['centers']);physical=DATA+C+R+2
+assert parent['physical']-parent['live']==C+R+2
+# Local circuits, exact phase recipes, normalized wrappers and data routes stay
+# byte-identical; only full-family helper placement and idle remainders change.
+t.update(version='complex484-asynchronous-replica-whole-owner-v1',live=DATA,physical=physical,idle_children=newidle,private_namespace={'centers':[DATA,DATA+C],'reserved_tableau':[DATA+C,DATA+C+R],'coefficient':[physical-2,physical]})
+t['hosting']=dict(rule='one-helper-per-physical-family-per-complete-invocation',max_helpers_per_physical_family_per_call=1,scope='asynchronously interleaved data replicas; each whole helper occurs once per(stage,invocation replica)',pooled_slots=roles,banks=[0]*9,owner_map_sha256=hashlib.sha256(MAP.read_bytes()).hexdigest(),idle_remainder_semantics='Each idle_children item acts once, on its explicit replica/family, at pending_offset with the stated rank; replicas=1.')
+t['route_semantics']['helper']='Whole physical family may belong to another replica; actual orthogonal port basis followed by residual/spectator coordinate permutation. Entering helpers have paid wrappers around the complete invocation; at most one helper and no active data wire uses that family in that invocation. Route[4,child,offset,width,spectators], width9 route[3,child,offset].'
+t['bank_padding']['families']=[];t['cover_final_correction']['families']=[0,DATA];t['cover_final_correction']['charged_calls_per_cover']=DATA
+for e in t['execution_schedule']:
+ if e['kind']=='bank_padding_cover_sweep':e['families']=[DATA,DATA]
+ elif e['kind']=='translate_every_live_family':e.update(t['cover_final_correction'])
+# Expand the retained controller into one-replica blocks; each block consists
+# of its full local cover sweep and every following replica-local event before
+# its next local sweep. Final whole-stock correction remains after all replicas.
+blocks={};globals_=[];st=None
+for ei,e in enumerate(parent['execution_schedule']):
+ if e['kind']in('bank_padding_cover_sweep','translate_every_live_family'):
+  globals_.append((ei,e));continue
+ if e['kind']=='local_cover_sweep':st=e['stage'];blocks[st]=[]
+ assert st is not None
+ blocks[st].append((ei,e))
+new_schedule=[]
+for tm,(s,rep)in enumerate(call_order):
+ for ei,e in blocks[s]:
+  ne=copy.deepcopy(e);ne.update(replica=rep,replicas=[rep],source_event=ei,time=tm)
+  new_schedule.append(ne)
+for ei,e in globals_:
+ ne=copy.deepcopy(e);ne['source_event']=ei
+ if e['kind']=='bank_padding_cover_sweep':ne['families']=[DATA,DATA]
+ else:ne.update(t['cover_final_correction'])
+ new_schedule.append(ne)
+t['execution_schedule']=new_schedule
+cmap={(c['stage'],c['replica']):c for c in t['calls']}
+t['calls']=[dict(cmap[s,rep],time=tm)for tm,(s,rep)in enumerate(call_order)]
+t['loop_order']='Follow the explicit asynchronous execution_schedule. Each local invocation completes before the next, including its entire cover sweep and normalization wrappers. Per-replica source event order is preserved; each idle remainder executes before that replica next touches its family.'
+t['async_schedule']=dict(order=[list(x)for x in call_order],source_plan_sha256=hashlib.sha256(PLAN.read_bytes()).hexdigest(),source_schedule=parent['execution_schedule'],source_call_order=[[c['stage'],c['replica']]for c in parent['calls']],scope='Only independent replica controllers are interleaved. Owner windows are measured on the owner replica timeline; no within-cover or within-invocation interleaving.')
+assert dict(sorted(paid.items()))=={int(k):v for k,v in plan['profile'].items()}
+assert M*M>2*max(paid)**2
+
+assert t['local_programs']==parent['local_programs']
+raw=json.dumps(t,sort_keys=True,separators=(',',':')).encode();(OUT/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+res=dict(status='EMITTED_ASYNCHRONOUS_WHOLE_OWNER_COMPLEX_TEMPLATE',template_sha256=hashlib.sha256(raw).hexdigest(),parent_template_sha256=hashlib.sha256(gzip.decompress((BASE/'split-centres/GLOBAL-TEMPLATE.json.gz').read_bytes())).hexdigest(),live=DATA,physical=physical,global_profile=dict(sorted(paid.items())),rank_mass=sum(r*n for r,n in paid.items()),deficit=2496,maxchild=max(paid),hosted_residuals=len(roles),banks_per_stage=[0]*9,entering_helper_roles=entering,unique_actual_73column_sigmas=len(sigmas),sigma_stream_sha256=digest.hexdigest(),cross_replica_helper_roles=sum(z['replica']!=z['owner_replica']for z in roles),asynchronous_order_sha256=hashlib.sha256(json.dumps(call_order,separators=(',',':')).encode()).hexdigest(),source_artifacts={p.relative_to(BASE).as_posix():hashlib.sha256(p.read_bytes()).hexdigest()for p in [BASE/'split-centres/CANONICAL-WORD.json.gz',BASE/'split-centres/LOCAL-PROGRAMS.json.gz',BASE/'split-centres/LOCAL-CHECKS.json',BASE/'split-centres/RESIDUAL-ADAPTERS.json',BASE/'work/complex-nine-native/DATA-PHASES.json']},scope='New emitted complete-invocation placement; independent controller/spectator/normalization and complete finite invoice admission required.')
+(OUT/'HOSTED.json').write_text(json.dumps(res,indent=2)+'\n');(OUT/'ACTUAL-SIGMAS.json.gz').write_bytes(gzip.compress(json.dumps(sigmas,separators=(',',':')).encode(),mtime=0));print(json.dumps(res,indent=2))
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/code/run_portable.py b/research/ranksector112-async/vendor/pr523/vendor/pr514/code/run_portable.py
new file mode 100644
index 0000000000..dcfe7128e1
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/code/run_portable.py
@@ -0,0 +1,15 @@
+"""Run one retained verifier with UTF-8/LF text outputs on every platform.
+This changes output serialization only; no mathematical operation is replaced.
+"""
+from pathlib import Path
+import runpy,sys
+if not __debug__:
+    raise RuntimeError('Assertions must remain enabled')
+original_write_text=Path.write_text
+def write_text_lf(self,data,encoding=None,errors=None,newline=None):
+    return original_write_text(self,data,encoding=encoding or 'utf-8',errors=errors,newline='\n')
+Path.write_text=write_text_lf
+script=Path(sys.argv[1]).resolve()
+sys.argv=sys.argv[1:]
+sys.path.insert(0,str(script.parent))
+runpy.run_path(str(script),run_name='__main__')
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/ASYNC-AUDIT.json b/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/ASYNC-AUDIT.json
new file mode 100644
index 0000000000..f80e9bf1d7
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/ASYNC-AUDIT.json
@@ -0,0 +1,60 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS",
+  "template_sha256": "77767f67ed17413161d82f2a407e69b3beefef3fc44bfe582fb403bdc1705bd8",
+  "complex_template_sha256": "77767f67ed17413161d82f2a407e69b3beefef3fc44bfe582fb403bdc1705bd8",
+  "complex_live": 7680,
+  "complex_profile": {
+    "1": 182808,
+    "2": 11520,
+    "3": 41233,
+    "4": 6336,
+    "5": 25173,
+    "6": 4896,
+    "7": 195,
+    "8": 1224,
+    "16": 1,
+    "32": 1,
+    "39": 1,
+    "48": 766
+  },
+  "complex_hosted_residuals": 40320,
+  "physical": 8258,
+  "rank_mass": 558144,
+  "deficit": 2496,
+  "entering_helper_roles": 12384,
+  "cross_replica_helper_roles": 30804,
+  "one_owner_per_complete_invocation": true,
+  "helper_busy_family_window_checks": 40320,
+  "complete_invocations": 72,
+  "actual_orthogonal_73column_maps": 3024,
+  "actual_sigma_stream_sha256": "7e47b83098762619fea0e3c018d49245810b198c3b1f1c6ba7cfdb02a2d94638",
+  "all_actual_residual_and_spectator_charts": true,
+  "idle_remainders": 7682,
+  "mutations_rejected": [
+    "wrong call time",
+    "alias two whole owners",
+    "helper on active data family",
+    "owner in private namespace",
+    "unbound change of owner replica",
+    "omit complete invocation",
+    "reorder invocation replicas",
+    "interleave local invocations",
+    "change local instruction stream",
+    "wrong residual width",
+    "wrong spectator coordinate",
+    "omit spectator route",
+    "overlap residual footprint",
+    "omit idle remainder",
+    "underpay idle remainder",
+    "omit bridge touch",
+    "remove one-owner rule",
+    "duplicate frozen role",
+    "understate physical reserve"
+  ],
+  "widths": {
+    "7": 18,
+    "8": 154,
+    "9": 388
+  },
+  "scope": "Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses unchanged source local program and normalized residual-wrapper identities; all-size compilation and complete coefficient invoice are separate inherited obligations."
+}
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/EXACT-ASSEMBLY.json b/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/EXACT-ASSEMBLY.json
new file mode 100644
index 0000000000..f7d322e865
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/EXACT-ASSEMBLY.json
@@ -0,0 +1,127 @@
+{
+  "status": "PASS_ASYNC_COMPLEX_AND_CITED_BIT_EXACT_ASSEMBLY",
+  "complex_lower": "139346249534416215349/100000000000000000000000",
+  "complex_decimal": "0.00139346249534416215349",
+  "next_b_rejected": "1393462495344162153491/1000000000000000000000000",
+  "exact_moment_receipts": [
+    {
+      "endpoint": "139346249534416215349/100000000000000000000000",
+      "mercator": [
+        "-54703880107433440999858104301338860500009803/26959946667150639794667015087019630673637144422540572481103610249216",
+        "-54703880107433440999858104301338860500009801/26959946667150639794667015087019630673637144422540572481103610249216"
+      ],
+      "base_two": [
+        "-253635052727043702191/125000000000000000000000000000000000000000000",
+        "-20290794218163496175163/10000000000000000000000000000000000000000000000"
+      ],
+      "accept": true
+    },
+    {
+      "endpoint": "1393462495344162153491/1000000000000000000000000",
+      "mercator": [
+        "3955425413759435303055253810238845835062729/3369993333393829974333376885877453834204643052817571560137951281152",
+        "15821701655037741212221015240955383340250917/13479973333575319897333507543509815336818572211270286240551805124608"
+      ],
+      "base_two": [
+        "2934296445549106059021/2500000000000000000000000000000000000000000000",
+        "5868597891098212118101/5000000000000000000000000000000000000000000000"
+      ],
+      "accept": false
+    }
+  ],
+  "bit_lower": "391360506745414227149/250000000000000000000000",
+  "bit_result_sha256": "3494ba83280cc86548fe0cc6695c50d23e6b6ffca85aeb1a33337c1196e280cb",
+  "bit_template_sha256": "e37b52e4861c39154b5891460fb45df8651c92cd68961078f8f06596f057c822",
+  "bit_prefix_bits": 2176,
+  "bit_charged_three_level_coefficient_bits": 6464,
+  "external_row_allowance": 20161,
+  "kappa": "1391523459591829/1000000000000000000",
+  "kappa_decimal": "0.001391523459591829",
+  "binding_component": "complex",
+  "strict_outer_constraints": {
+    "bit_positive": "139346249534416214217553383528807406988201842235985269562593616994374883176325351545829800050429344047484846426471962634480675851340231000985418679656055660447565031173172526170877892483672155340646824791401221649410742227102573112433696521168170535806582087578860429744142643857309949/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
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+      "gap": "2631059658113877142567966552224008392003766567316562850106941551195055119564689434161017320279125197529579172846451/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "5200452207101028792"
+    },
+    {
+      "gap": "366628295659472139143445047172525837788027943283205386341504745785548073484461665247841849913071779127444461517120514673461492372116408054446749073623601/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "2678246468434954509908486"
+    },
+    {
+      "gap": "51088277973342530064709504142360074753095393237306993768328581701371906956085334590272978494013829595435240096477880475149811069460617262201940246023188989863375509502243781694754392215148251/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "1379303925895103678503547601120"
+    },
+    {
+      "gap": "7118959930757007712774322746735797722169090993444286417182192513622708903511320575381343782299321394696018700852959327704134175684211981733197710759142043227679727880703224338037250835232500394362704238819472564425224153623295401/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "710345124099563582273849559553093478"
+    },
+    {
+      "gap": "992000366936776377662798157764014730437406383005625116823674648454170199949570655952515153573528037365519324148659768999014581320343944339552434968826827473829122107516327844659353175208598778350589257772897426887566303478831829464193417912421139570255857356142690051/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cutoff_log2": "365829594086429480022029191003211743321777"
+    }
+  ],
+  "complex_template_sha256": "77767f67ed17413161d82f2a407e69b3beefef3fc44bfe582fb403bdc1705bd8",
+  "owner_audit_sha256": "031a05f7394934f17b02b4f758d905b90100b614530888dfa13c2f731f9fc396",
+  "invoice_sha256": "953b07409f98216378ea5b95a3194d09b6b26c5847568e824c467ddded71e158",
+  "bit_scope": "PR493 published profile and operator reused as a pinned dependency; this verifier reprices its published profile but does not reconstruct that unchanged bit operator.",
+  "scope": "Conditional finite witness. Inherited compiler, precision/tape and analytic-transfer contracts remain assumed; changed-host operator admission recorded separately."
+}
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/INDEPENDENT-NOMINATION-REVIEW.json b/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/INDEPENDENT-NOMINATION-REVIEW.json
new file mode 100644
index 0000000000..0148856744
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/INDEPENDENT-NOMINATION-REVIEW.json
@@ -0,0 +1,35 @@
+{
+  "status": "PASS_INDEPENDENT_LITERAL_OWNER_AND_PROFILE_REVIEW",
+  "calls": 72,
+  "roles": 40320,
+  "remainder_profile": {
+    "3": 3073,
+    "5": 3717,
+    "7": 123,
+    "16": 1,
+    "32": 1,
+    "39": 1,
+    "48": 766
+  },
+  "profile": {
+    "1": 182808,
+    "2": 11520,
+    "3": 41233,
+    "4": 6336,
+    "5": 25173,
+    "6": 4896,
+    "7": 195,
+    "8": 1224,
+    "16": 1,
+    "32": 1,
+    "39": 1,
+    "48": 766
+  },
+  "deficit": 2496,
+  "source_hashes": {
+    "KERNEL92-FOCUS-O6.json": "7a30db32ad8fc54bd5e7060febf4f8ff7747b8287c057ae926efc736e2b9f800",
+    "KERNEL92-OWNERS.json.gz": "9c6bd9793db16d599d3c7f9493350d2359681d19eb170ec7239e8d568090e745",
+    "CONSTRUCTION.json": "a1210ff603b5d73330d9f94e718101c808ebddfd0fb03336593a87b3cd976108"
+  },
+  "scope": "Exact nomination-level chronology, original child lifetimes, complete-family uniqueness, disjoint pending-coordinate offsets, source-bound widths, all remainders. Full physical maps, phases and scalar invoice remain separate checks."
+}
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/KERNEL-SCALAR.json b/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/KERNEL-SCALAR.json
new file mode 100644
index 0000000000..8289fcf492
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/KERNEL-SCALAR.json
@@ -0,0 +1,104 @@
+{
+  "status": "PASS_EXACT_RATIONAL_FORWARD_AND_INVERSE_TRANSPOSE",
+  "word_sha256": "92d156d50398b06e28231b42ff56e878a391d73a963d033d9e1888c8c081f143",
+  "selection_sha256": "c8e6400a8f4780be3aef6a643d856f956e97447161d33493ae651070e2f033fb",
+  "columns_each_orientation": 800,
+  "compensations": 12094,
+  "program_operations": 19800,
+  "kernel_pivots": 92,
+  "controls": {
+    "46": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "43": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "158": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "214": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "103": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "65": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "271": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "215": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "510": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "527": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "24": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "87": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "467": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "26": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "83": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "68": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "518": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "159": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "14": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "8": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "85": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "40": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "508": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "517": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "361": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "416": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "472": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "98": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "66": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "30": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "161": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "56": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "52": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "383": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "36": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "530": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "51": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "521": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "162": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "35": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "160": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "32": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "54": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "468": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "529": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "528": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "34": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "76": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "59": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "520": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "90": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "512": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "514": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "93": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "94": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "217": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "16": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "515": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "95": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "216": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "0": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "3": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "105": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "212": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "505": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "6": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "213": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "106": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "108": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "104": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "332": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "380": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "329": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "502": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "498": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "381": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "437": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "445": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "441": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "384": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "324": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "436": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "156": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "157": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "446": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "334": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "474": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "475": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "132": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "133": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "244": "REJECTED_OMITTED_KERNEL_CORRECTION",
+    "189": "REJECTED_OMITTED_KERNEL_CORRECTION"
+  },
+  "scope": "Exact local scalar identity and preserved frame-zero compensation; physical owner routing, complete invoice and outer kappa separate."
+}
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/OWNERS-AND-PROFILE.json b/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/OWNERS-AND-PROFILE.json
new file mode 100644
index 0000000000..a830b54213
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/OWNERS-AND-PROFILE.json
@@ -0,0 +1,38 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_OWNERS_AND_PROFILE",
+  "template_sha256": "77767f67ed17413161d82f2a407e69b3beefef3fc44bfe582fb403bdc1705bd8",
+  "paid_profile": {
+    "1": 182808,
+    "2": 11520,
+    "3": 41233,
+    "4": 6336,
+    "5": 25173,
+    "6": 4896,
+    "7": 195,
+    "8": 1224,
+    "16": 1,
+    "32": 1,
+    "39": 1,
+    "48": 766
+  },
+  "live": 7680,
+  "physical": 8258,
+  "rank_mass": 558144,
+  "deficit": 2496,
+  "hosted_residuals": 40320,
+  "banked_residuals": 0,
+  "all_800_owners_per_call_distinct": true,
+  "actual_helper_owner_charts": 40320,
+  "actual_73column_sigmas": 3024,
+  "cross_replica_helper_roles": 30804,
+  "explicit_idle_remainder_children": 7682,
+  "source_idle_children_charged": 17280,
+  "source_artifacts": {
+    "split-centres/CANONICAL-WORD.json.gz": "c57e6494e047e924a02051c0401778e967c16bf2d7724441b74f721fd9d6e5ef",
+    "split-centres/LOCAL-PROGRAMS.json.gz": "ad5526bcf6d93f0d7ca6bbfd0f4d971406f0e879b49d6b439e3d93eb24e96f56",
+    "split-centres/LOCAL-CHECKS.json": "fc8d796e3be50be7d7ec270ecc4e5bc4d600d7eef0182b77ac84e3793b7bbc84",
+    "split-centres/RESIDUAL-ADAPTERS.json": "0e19e861b824ae229be801b98a64b4dd476618adf57c582782fcec0c97ada147",
+    "work/complex-nine-native/DATA-PHASES.json": "f621f6d4296cb215f334830356c5f79fe10d6d04d15b3ccda76ba0885ab67d0a"
+  },
+  "controller_audit_sha256": "2b501debc401c623615ff4429cdf11a82e0b5ea572c1709c5cdedb013550ed26"
+}
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/PORTABLE-REPLAY.json b/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/PORTABLE-REPLAY.json
new file mode 100644
index 0000000000..af3f21362d
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/PORTABLE-REPLAY.json
@@ -0,0 +1,78 @@
+{
+  "status": "PASS_CONDITIONAL_ASYNCHRONOUS_COMPLEX_DERIVATIVE",
+  "kappa": "1391523459591829/1000000000000000000",
+  "kappa_decimal": "0.001391523459591829",
+  "complex_lower": "139346249534416215349/100000000000000000000000",
+  "bit_lower": "391360506745414227149/250000000000000000000000",
+  "template_sha256": "77767f67ed17413161d82f2a407e69b3beefef3fc44bfe582fb403bdc1705bd8",
+  "strict_constraints": 47,
+  "scope": "New complex program independently replayed. The unchanged PR493 bit operator and inherited all-size compiler, common-label, Lemma A realization, restored-row, precision/tape and analytic-transfer contracts remain dependencies. No unconditional multiplication bound or fresh Lean certification is claimed.",
+  "stages": [
+    {
+      "stage": "partial-factory",
+      "exit": 0,
+      "seconds": 0.6089999999967404
+    },
+    {
+      "stage": "construct-kernel92",
+      "exit": 0,
+      "seconds": 2.062999999994645
+    },
+    {
+      "stage": "kernel-scalar-controls",
+      "exit": 0,
+      "seconds": 26.796999999991385
+    },
+    {
+      "stage": "scalar",
+      "exit": 0,
+      "seconds": 2.2969999999913853
+    },
+    {
+      "stage": "emit-local",
+      "exit": 0,
+      "seconds": 1.3440000000118744
+    },
+    {
+      "stage": "phases",
+      "exit": 0,
+      "seconds": 199.21799999999348
+    },
+    {
+      "stage": "adapters",
+      "exit": 0,
+      "seconds": 1.0160000000032596
+    },
+    {
+      "stage": "parent-integration",
+      "exit": 0,
+      "seconds": 1.2179999999934807
+    },
+    {
+      "stage": "parent-replay",
+      "exit": 0,
+      "seconds": 9.51600000000326
+    },
+    {
+      "stage": "emit-async",
+      "exit": 0,
+      "seconds": 4.375
+    },
+    {
+      "stage": "independent-async",
+      "exit": 0,
+      "seconds": 25.030999999988126
+    },
+    {
+      "stage": "invoice",
+      "exit": 0,
+      "seconds": 2.360000000015134
+    },
+    {
+      "stage": "two-moments-assembly",
+      "exit": 0,
+      "seconds": 0.6719999999913853
+    }
+  ],
+  "package_manifest_sha256": "4d30fb450a7a17f0ee06b340c2d74b5733e527659f1f298ceb4a9c622c940256"
+}
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/PREFIX-AND-INVOICE.json b/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/PREFIX-AND-INVOICE.json
new file mode 100644
index 0000000000..c212e28678
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/PREFIX-AND-INVOICE.json
@@ -0,0 +1,69 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE",
+  "template_sha256": "77767f67ed17413161d82f2a407e69b3beefef3fc44bfe582fb403bdc1705bd8",
+  "global_prefix_bits": 206,
+  "charged_prefix_bits": 512,
+  "complete_invocation_sweeps": 72,
+  "bridge_sweeps": 72,
+  "row_prefix_extra": 1024,
+  "local": {
+    "backward": {
+      "events": 25330,
+      "macros": 19848,
+      "real_component_primitives": 222442,
+      "prefix_l1": "1048913",
+      "prefix_bits": 21,
+      "coefficient_work_primitive_count": 110377,
+      "all_exact_columns": 800,
+      "all_560_dirty_helper_columns_restored": true,
+      "private_centres_and_coefficient_work_cleared": true
+    },
+    "forward": {
+      "events": 25330,
+      "macros": 19848,
+      "real_component_primitives": 222346,
+      "prefix_l1": "57339",
+      "prefix_bits": 16,
+      "coefficient_work_primitive_count": 110313,
+      "all_exact_columns": 800,
+      "all_560_dirty_helper_columns_restored": true,
+      "private_centres_and_coefficient_work_cleared": true
+    }
+  },
+  "entering_helpers": 172,
+  "entrance_rank": 190,
+  "local_adapters": 394512,
+  "local_primitive_bound": 10231406986474,
+  "wrapper_elementary_factors_charged": 3566592,
+  "compiler": 25934336,
+  "unhosted_pervertex": 1520250460705152,
+  "hosted_rebased_pervertex": 1520250460372512,
+  "conservative_pervertex_used": 1520250460705152,
+  "finite": {
+    "physical_stock_bits": 2641,
+    "router_bits": 7984,
+    "literal_bits": 35282,
+    "physical_row_coefficient": 16467,
+    "retained_row_coefficient": 20161,
+    "required_C0_bits": 200012,
+    "halving_integer_inequality": [
+      5329,
+      4608
+    ],
+    "G_exponent": 30000,
+    "E_exponent": 100000,
+    "C0_exponent": 210000
+  },
+  "strict_checks": {
+    "local_primitive_bound": true,
+    "logical": true,
+    "router": true,
+    "literal": true,
+    "mass": true,
+    "precision": true,
+    "tape": true,
+    "row": true,
+    "halving": true
+  },
+  "scope": "Exact finite recount conditional on inherited all-size compiler/precision/tape and analytic-transfer contracts. Signed accumulation uses the supplier scalar primitive convention. Async prefix counts all72individual bridges and72complete invocations;512bits are charged, and an additional2*512 enters the two-level physical row bound."
+}
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/RESULT.json b/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/RESULT.json
new file mode 100644
index 0000000000..744d930acb
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/RESULT.json
@@ -0,0 +1,78 @@
+{
+  "status": "PASS_CONDITIONAL_ASYNCHRONOUS_COMPLEX_DERIVATIVE",
+  "kappa": "1391523459591829/1000000000000000000",
+  "kappa_decimal": "0.001391523459591829",
+  "complex_lower": "139346249534416215349/100000000000000000000000",
+  "bit_lower": "391360506745414227149/250000000000000000000000",
+  "template_sha256": "77767f67ed17413161d82f2a407e69b3beefef3fc44bfe582fb403bdc1705bd8",
+  "strict_constraints": 47,
+  "scope": "New complex program independently replayed. The unchanged PR493 bit operator and inherited all-size compiler, common-label, Lemma A realization, restored-row, precision/tape and analytic-transfer contracts remain dependencies. No unconditional multiplication bound or fresh Lean certification is claimed.",
+  "stages": [
+    {
+      "stage": "partial-factory",
+      "exit": 0,
+      "seconds": 0.6559999999881256
+    },
+    {
+      "stage": "construct-kernel92",
+      "exit": 0,
+      "seconds": 2.10999999998603
+    },
+    {
+      "stage": "kernel-scalar-controls",
+      "exit": 0,
+      "seconds": 27.312000000005355
+    },
+    {
+      "stage": "scalar",
+      "exit": 0,
+      "seconds": 2.360000000015134
+    },
+    {
+      "stage": "emit-local",
+      "exit": 0,
+      "seconds": 1.4219999999913853
+    },
+    {
+      "stage": "phases",
+      "exit": 0,
+      "seconds": 199.60899999999674
+    },
+    {
+      "stage": "adapters",
+      "exit": 0,
+      "seconds": 1.0469999999913853
+    },
+    {
+      "stage": "parent-integration",
+      "exit": 0,
+      "seconds": 1.3440000000118744
+    },
+    {
+      "stage": "parent-replay",
+      "exit": 0,
+      "seconds": 9.421999999991385
+    },
+    {
+      "stage": "emit-async",
+      "exit": 0,
+      "seconds": 4.594000000011874
+    },
+    {
+      "stage": "independent-async",
+      "exit": 0,
+      "seconds": 26.187000000005355
+    },
+    {
+      "stage": "invoice",
+      "exit": 0,
+      "seconds": 2.1710000000020955
+    },
+    {
+      "stage": "two-moments-assembly",
+      "exit": 0,
+      "seconds": 0.6410000000032596
+    }
+  ],
+  "package_manifest_sha256": null
+}
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/TRANSPORT-CONTROLS.json b/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/TRANSPORT-CONTROLS.json
new file mode 100644
index 0000000000..75e9772036
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/evidence/TRANSPORT-CONTROLS.json
@@ -0,0 +1,14 @@
+[
+  {
+    "control": "modified_text_content",
+    "rejected": true
+  },
+  {
+    "control": "missing_upload_file",
+    "rejected": true
+  },
+  {
+    "control": "optimized_python",
+    "rejected": true
+  }
+]
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/ASYNC-6.json b/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/ASYNC-6.json
new file mode 100644
index 0000000000..896cf316ba
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/ASYNC-6.json
@@ -0,0 +1,12123 @@
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diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/ASYNC-OWNERS.json.gz b/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/ASYNC-OWNERS.json.gz
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diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/KERNEL84-SELECTION.json b/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/KERNEL84-SELECTION.json
new file mode 100644
index 0000000000..b32646d91c
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/KERNEL84-SELECTION.json
@@ -0,0 +1,664 @@
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diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/KERNEL92-SELECTION.json b/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/KERNEL92-SELECTION.json
new file mode 100644
index 0000000000..200b11dcbb
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diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/PR493-EXPECTED.json b/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/PR493-EXPECTED.json
new file mode 100644
index 0000000000..973aaf30f1
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/PR493-EXPECTED.json
@@ -0,0 +1,91 @@
+{
+ "note": "Exact values that verify.sh must reproduce. The bit c is on the 10^-24 grid of PR #472's assembly (largest grid point admitted by both PR #315 moment engines with the inherited 10^-16 bad-branch allowance; the next grid point is rejected); kappa values are on the 10^-18 grid of the six-level, 47-inequality outer assembly.",
+ "word": {
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+  "content_sha256": "88435b75b8d6e5c722eb2aa1449f3a5e8e9601a9ffe243839ce1ec932ab76547",
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+   "6": 120,
+   "8": 18
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+  "sources_rewritten": 117,
+  "five_stage_payload_bits": 100
+ },
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+  "bit_lower_decimal": "0.001565442026981656908596",
+  "profile": {
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+   "2": 130560,
+   "4": 19680,
+   "6": 14400,
+   "7": 7680,
+   "8": 1584,
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+   "physical": 9609,
+   "maxchild": 56,
+   "rank_mass": 745536,
+   "hosted_residuals": 43032,
+   "prefix_bits": 2119,
+   "charged_prefix_bits": 2176,
+   "coefficient_bits": 2119,
+   "three_level_coefficient_bits": 6411,
+   "charged_three_level_coefficient_bits": 6464,
+   "row_coefficient": 19431,
+   "halving_depth": 3
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+    "kappa_decimal": "0.001325031497415498",
+    "binding_component": "complex",
+    "complex_lower": "663394767670133/500000000000000000",
+    "role": "primary"
+   },
+   "pr471": {
+    "kappa": "260706019542937/200000000000000000",
+    "kappa_decimal": "0.001303530097714685",
+    "binding_component": "complex",
+    "complex_lower": "1305231506267591/1000000000000000000",
+    "role": "control (complex supplier of the current whole-residual frontier)"
+   },
+   "pr458": {
+    "kappa": "323880830669511/250000000000000000",
+    "kappa_decimal": "0.001295523322678044",
+    "binding_component": "complex",
+    "complex_lower": "1297203880559577927527/1000000000000000000000000",
+    "role": "control"
+   },
+   "pr448": {
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+    "kappa_decimal": "0.001435468764627892",
+    "binding_component": "complex",
+    "complex_lower": "718766148669433/500000000000000000",
+    "role": "information only"
+   }
+  }
+ },
+ "controls": {
+  "pr472": {
+   "bit_lower": "323442810173099014031/250000000000000000000000",
+   "kappa": "646049779721139/500000000000000000",
+   "published": "research/e8-r715-whole-hosted/EXPECTED.json at 259c684: bit_lower 323442810173099014031/250000000000000000000000, kappa 646049779721139/500000000000000000"
+  },
+  "pr445": {
+   "bit_lower": "316240894019344628547/250000000000000000000000",
+   "published": "research/r740-hosted-eleven README at 40ab91d: 1264963576077378514188/10^24"
+  },
+  "pr451": {
+   "bit_lower": "158442042752174644233/125000000000000000000000",
+   "published": "PR #451 body at f3a3815: c = 0.001267536342017397153864"
+  }
+ }
+}
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diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/work/complex-network/hamming/PROTOTYPE.json b/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/work/complex-network/hamming/PROTOTYPE.json
new file mode 100644
index 0000000000..9efe30ee10
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/work/complex-network/hamming/PROTOTYPE.json
@@ -0,0 +1,21364 @@
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+    "Forming all eight centers from the available mixed source basis without an uncharged restore",
+    "Full 120-port arbitrary-dirt forward/backward program and restored work stocks",
+    "Exact complex adapters and global phases; finite invoice; two independent prices and outer assembly"
+  ],
+  "no_new_coarse_b_or_kappa_claim": true
+}
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/work/complex-nine-native/DATA-PHASES.json b/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/work/complex-nine-native/DATA-PHASES.json
new file mode 100644
index 0000000000..6f128ce2d2
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/work/complex-nine-native/DATA-PHASES.json
@@ -0,0 +1,73604 @@
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+      "terminal_Y_translation": 127
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+  ],
+  "cover_correction": {
+    "formula": "delta(g)_i = (weight(row_i(g))-1)/2 mod 2; apply X_delta(g) to EVERY final live stream in cover class g.",
+    "reason": "P_g C_all P_g^-1 = C_all X_delta(g) exactly. Orthogonality cancels all quadratic cross terms; both sides fix the uniform vector.",
+    "mandatory": true,
+    "complete_small_cover_checks": [
+      {
+        "n": 1,
+        "orthogonal_matrices": 1,
+        "nonzero_full_kernel_corrections": 0
+      },
+      {
+        "n": 2,
+        "orthogonal_matrices": 2,
+        "nonzero_full_kernel_corrections": 0
+      },
+      {
+        "n": 3,
+        "orthogonal_matrices": 6,
+        "nonzero_full_kernel_corrections": 0
+      },
+      {
+        "n": 4,
+        "orthogonal_matrices": 48,
+        "nonzero_full_kernel_corrections": 24
+      },
+      {
+        "n": 5,
+        "orthogonal_matrices": 720,
+        "nonzero_full_kernel_corrections": 600
+      }
+    ]
+  },
+  "global_phase_argument": "Every C_q and every linear address permutation fixes the uniform vector. Equality of the exact Z4 Fourier multiplier therefore fixes the scalar phase as well.",
+  "scope": "All compressed data boundary operators, idle children, terminal X_q and all-live cover correction. Internal arbitrary-subspace canonical labels are checked separately."
+}
\ No newline at end of file
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/work/complex-nine-native/GLOBAL-TEMPLATE.json.gz b/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/work/complex-nine-native/GLOBAL-TEMPLATE.json.gz
new file mode 100644
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diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/work/odd-stages/clifford_exact.py b/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/work/odd-stages/clifford_exact.py
new file mode 100644
index 0000000000..166841a037
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/work/odd-stages/clifford_exact.py
@@ -0,0 +1,149 @@
+"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals.
+Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d.
+The tableau is supplemented by a literal circuit, so global phases are kept.
+"""
+from dataclasses import dataclass
+
+def parity(x):return x.bit_count()&1
+def rank(rows):
+ p={}
+ for x in rows:
+  while x:
+   b=x.bit_length()-1
+   if b not in p:p[b]=x;break
+   x^=p[b]
+ return len(p)
+def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<<j for j in range(n)) for i in range(n))
+def mv(rows,x):return sum(parity(r&x)<<i for i,r in enumerate(rows))
+def inv(rows,n):
+ a=[r|(1<<(n+i)) for i,r in enumerate(rows)]
+ for j in range(n):
+  k=next(i for i in range(j,n) if a[i]>>j&1);a[j],a[k]=a[k],a[j]
+  for i in range(n):
+   if i!=j and a[i]>>j&1:a[i]^=a[j]
+ assert [r&((1<<n)-1) for r in a]==[1<<i for i in range(n)]
+ return tuple(r>>n for r in a)
+def basis_extend(cols,n):
+ out=[]
+ for x in list(cols)+[1<<i for i in range(n)]:
+  if rank(out+[x])>len(out):out.append(x)
+ assert len(out)==n
+ return tuple(out)
+def nullspace(rows,n):
+ a=list(rows);p=[];k=0
+ for j in range(n):
+  t=next((i for i in range(k,len(a)) if a[i]>>j&1),None)
+  if t is None:continue
+  a[t],a[k]=a[k],a[t]
+  for i in range(len(a)):
+   if i!=k and a[i]>>j&1:a[i]^=a[k]
+  p.append(j);k+=1
+ return tuple((1<<j)|sum(((a[i]>>j)&1)<<v for i,v in enumerate(p)) for j in range(n) if j not in p)
+def pmul(a,b):
+ x,z,p=a;y,w,q=b
+ return x^y,z^w,(p+q+2*parity(z&y))%4
+def identity(n):return tuple([(1<<i,0,0) for i in range(n)]+[(0,1<<i,0) for i in range(n)])
+def apply(T,p):
+ n=len(T)//2;x,z,ph=p;out=(0,0,ph)
+ for i in range(n):
+  if x>>i&1:out=pmul(out,T[i])
+ for i in range(n):
+  if z>>i&1:out=pmul(out,T[n+i])
+ return out
+def compose(A,B):return tuple(apply(A,p) for p in B)
+def inverse(T):
+ n=len(T)//2;cols=[x|(z<<n) for x,z,p in T];rows=transpose(cols,2*n);cols_inv=transpose(inv(rows,2*n),2*n);out=[]
+ for j,w in enumerate(cols_inv):
+  x=w&((1<<n)-1);z=w>>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4))
+ return tuple(out)
+def qvalue(Q,alpha,x,n):
+ return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4
+def mul_i(a,p):
+ x,y=a;p%=4
+ return [(x,y),(-y,x),(-x,-y),(y,-x)][p]
+@dataclass
+class Op:
+ n:int
+ tab:tuple
+ circuit:list
+ def then(self,b):
+  assert self.n==b.n
+  return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit)
+ def adjoint(self):
+  circ=[]
+  for e in reversed(self.circuit):
+   if e[0]=='P':circ.append(('P',inv(e[1],self.n)))
+   elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2])))
+   elif e[0]=='C':circ.append(('C',e[1],-e[2]))
+   elif e[0]=='phase':circ.append(('phase',(-e[1])%4))
+   else:circ.append(e)
+  return Op(self.n,inverse(self.tab),circ)
+ def zero_state(self,basis=0):
+  N=1<<self.n;vec=[(0,0)]*N;vec[basis]=(1,0);den=0
+  for e in self.circuit:
+   if e[0]=='P':
+    v=[(0,0)]*N
+    for x,a in enumerate(vec):v[mv(e[1],x)]=a
+    vec=v
+   elif e[0]=='X':vec=[vec[x^e[1]] for x in range(N)]
+   elif e[0]=='D':vec=[mul_i(a,qvalue(e[1],e[2],x,self.n)) for x,a in enumerate(vec)]
+   elif e[0]=='phase':vec=[mul_i(a,e[1]) for a in vec]
+   elif e[0]=='C':
+    q,sgn=e[1:];v=[]
+    for x,(a,b) in enumerate(vec):
+     c,d=vec[x^q]
+     # C=(1+i)I/2+(1-i)X/2; inverse conjugates both coefficients.
+     v.append((a-sgn*b+c+sgn*d,b+sgn*a+d-sgn*c))
+    vec=v;den+=1
+   else:raise AssertionError(e)
+   while den and all((a&1)==(b&1)==0 for a,b in vec):vec=[(a//2,b//2) for a,b in vec];den-=1
+  return vec,den
+def ident(n):return Op(n,identity(n),[])
+def perm(n,G):
+ cols=transpose(G,n);gi=inv(G,n)
+ return Op(n,tuple([(a,0,0) for a in cols]+[(0,a,0) for a in gi]),[('P',tuple(G))])
+def diag(n,Q,alpha=None):
+ Q=tuple(Q);assert transpose(Q,n)==Q
+ alpha=tuple(alpha) if alpha is not None else tuple((Q[i]>>i)&1 for i in range(n))
+ assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n))
+ return Op(n,tuple([(1<<i,Q[i],alpha[i]) for i in range(n)]+[(0,1<<i,0) for i in range(n)]),[('D',Q,alpha)])
+def cgate(n,q,sgn=1):
+ return Op(n,tuple([(1<<i,0,0) for i in range(n)]+[(q if q>>i&1 else 0,1<<i,(3*sgn)%4 if q>>i&1 else 0) for i in range(n)]),[('C',q,sgn)])
+def xgate(n,b):return Op(n,tuple([(1<<i,0,0) for i in range(n)]+[(0,1<<i,2*((b>>i)&1)) for i in range(n)]),[('X',b)])
+def fourier(n,axes=None):
+ out=ident(n)
+ for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<<i))
+ return out
+def hadamard(n,axes):
+ axes=list(axes);Q=tuple(1<<i if i in axes else 0 for i in range(n));S=diag(n,Q)
+ return S.then(fourier(n,axes)).then(S)
+def canonical_frame(n,U):
+ r=len(U)
+ if r==0:return ident(n)
+ if r==n:return fourier(n)
+ G=transpose(basis_extend(U,n),n);gi=inv(G,n);Q=tuple((1<<i)^sum(parity(gi_i&gi_j)<<j for j,gi_j in enumerate(transpose(gi,n))) for i,gi_i in enumerate(transpose(gi,n)))
+ K=perm(n,G).then(diag(n,Q))
+ return K.adjoint().then(fourier(n,range(r))).then(K)
+def monomial(op):
+ n=op.n;T=op.tab;assert all(x==0 and p%2==0 for x,z,p in T[n:]);G=transpose([x for x,z,p in T[:n]],n);b=mv(G,sum((p//2)<<i for i,(x,z,p) in enumerate(T[n:])))
+ gt=transpose(G,n);cols=[mv(gt,z) for x,z,p in T[:n]];Q=transpose(cols,n);alpha=[(p-2*parity(b&z))%4 for x,z,p in T[:n]]
+ out=diag(n,Q,alpha).then(perm(n,G)).then(xgate(n,b));assert out.tab==T
+ vec,den=op.zero_state();assert den==0 and all(a==(0,0) for i,a in enumerate(vec) if i!=b);phase=[(1,0),(0,1),(-1,0),(0,-1)].index(vec[b]);out=out.then(Op(n,identity(n),[('phase',phase)]));assert out.zero_state()==op.zero_state()
+ return out,dict(matrix_rows=G,offset=b,quadratic_rows=Q,linear_Z4=alpha,phase=phase)
+def lower_child(op):
+ n=op.n;Bcols=[x for x,z,p in op.tab[n:]];r=rank(Bcols)
+ if not r:
+  mon,rec=monomial(op);return dict(rank=0,left=rec,right=None),mon
+ G=transpose(basis_extend(Bcols,n),n);A=inv(G,n);PA=perm(n,A);part=op.then(PA);Bcols=[x for x,z,p in part.tab[n:]];Dcols=[z for x,z,p in part.tab[n:]]
+ picks=[];selected=[]
+ for j,x in enumerate(Bcols):
+  if rank(selected+[x])>len(selected):picks.append(j);selected.append(x)
+ assert len(picks)==r and all(x>>r==0 for x in Bcols)
+ Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<<r)-1) for j in picks],r)
+ Qsmall=tuple(sum(parity(row&col)<<j for j,col in enumerate(transpose(Bi,r))) for row in Dr);Q=Qsmall+(0,)*(n-r);DQ=diag(n,Q)
+ V=part.then(DQ).then(hadamard(n,range(r)));assert all(x==0 for x,z,p in V.tab[n:]);Vmon,Vrec=monomial(V)
+ S=diag(n,tuple(1<<i if i<r else 0 for i in range(n)))
+ left=S.adjoint().then(DQ.adjoint()).then(PA.adjoint());right=Vmon.then(S.adjoint()).then(xgate(n,(1<<r)-1))
+ lmon,lrec=monomial(left);rmon,rrec=monomial(right);compiled=rmon.then(fourier(n,range(r))).then(lmon)
+ assert compiled.tab==op.tab and compiled.zero_state()==op.zero_state()
+ return dict(rank=r,left=lrec,right=rrec),compiled
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/work/pr361/code/engines/base_two_moment.py b/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/work/pr361/code/engines/base_two_moment.py
new file mode 100644
index 0000000000..14a90fa0e7
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/work/pr361/code/engines/base_two_moment.py
@@ -0,0 +1,63 @@
+#!/usr/bin/env python3
+"""Maintainer arithmetic cross-check of the pinned PR39 certificate.
+
+Uses no producer/checker imports. Counts are inputs, not proved by this script.
+80-term rational logarithms and 12-term exponentials independently enclose
+the two moments. The accompanying written review addresses their realization.
+"""
+import argparse
+from fractions import Fraction as Q
+from hashlib import sha256
+import json
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parents[1]
+GRID = 10**30
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def log_unit(x):
+    require(1 <= x <= 2, "logarithm range")
+    z = (x-1)/(x+1)
+    lo = 2*sum((z**(2*j+1)/(2*j+1) for j in range(80)), Q(0))
+    return lo, lo+2*z**161/(161*(1-z*z))
+
+
+def log_bounds(x):
+    k = 0
+    while x > 2:
+        x /= 2
+        k += 1
+    lo, hi = log_unit(x)
+    l2, u2 = log_unit(Q(2))
+    lo, hi = lo+k*l2, hi+k*u2
+    # Outward rational rounding keeps later certificates compact.
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
+
+def exp_bounds(x):
+    require(0 <= x < 1, "exponential range")
+    term = total = Q(1)
+    for j in range(1, 13):
+        term *= x/j
+        total += term
+    tail = term*x/13/(1-x/14)
+    return total, total+tail
+
+
+def moment(m, W, entries, saving):
+    lo = hi = Q(0)
+    for t, count in entries:
+        t, count = int(t), int(count)
+        require(0 < t < m and count > 0, "improper child")
+        l, u = log_bounds(Q(m, t))
+        lower = exp_bounds(saving*l)[0]
+        upper = exp_bounds(saving*u)[1]
+        lo += Q(t*count, m*W)*lower
+        hi += Q(t*count, m*W)*upper
+    return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID)
+
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/work/pr361/code/engines/moment.py b/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/work/pr361/code/engines/moment.py
new file mode 100644
index 0000000000..7d697cb452
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/work/pr361/code/engines/moment.py
@@ -0,0 +1,113 @@
+"""Independent prospective ordinary five-stage cost, never supplier admission.
+
+Consumes a raw one-invocation ledger made from the actual source/internal/target
+paths.  No packed profile is used as an input.  Missing physical/finite/compiler
+obligations must remain explicit in the accompanying report.
+"""
+from collections import Counter
+from decimal import Decimal, localcontext, ROUND_FLOOR
+from fractions import Fraction as F
+from functools import lru_cache
+from math import factorial
+import hashlib, json, sys
+from pathlib import Path
+
+DYAD = 1 << 224
+
+def floor(x): return F(x.numerator*DYAD//x.denominator, DYAD)
+def ceil(x): return -floor(-x)
+
+@lru_cache(None)
+def logarithm(x):
+    """Mercator bounds after binary reduction; ln(2) via two Mercator sums.
+
+    For 1 <= y < 2, log(y) is an alternating series in z=y-1.
+    We instead reduce to 1 <= y < 3/2, and bound log(3/2) and
+    log(2) by the same alternating series at z=1/2 and z=1/3,
+    using log(2)=log(3/2)+log(4/3). All sums are exact rationals.
+    """
+    assert x >= 1
+    k = 0
+    while x >= 2: x /= 2; k += 1
+    j = int(x >= F(3, 2))
+    if j: x /= F(3, 2)
+    def mercator(y):
+        z=y-1
+        assert 0 <= z <= F(1,2)
+        # An even partial sum is below log; the next term bounds its tail.
+        t=z; s=F(0)
+        for n in range(1, 225):
+            s += (t if n & 1 else -t)/n
+            t *= z
+        return s, s+t/225
+    a,b=mercator(x); c,d=mercator(F(3,2)); e,f=mercator(F(4,3))
+    return floor(a+(k+j)*c+k*e), ceil(b+(k+j)*d+k*f)
+
+def exponential(l,u):
+    assert 0 <= l <= u < F(1,10)
+    def poly(x):
+        s=t=F(1)
+        for j in range(1,25): t=t*x/j; s+=t
+        return s,t
+    lo,_=poly(l);hi,last=poly(u)
+    return floor(lo),ceil(hi+last*u/25/(1-u/26))
+
+def moment(H,m,W,a,bad=False):
+    lo=hi=F(0)
+    for r,n in H.items():
+        assert 0 < r < m and n > 0
+        l,u=logarithm(F(m,r)); e,f=exponential(a*l,a*u)
+        p=F(r*n,m*W);lo+=p*e;hi+=p*f
+    if bad:
+        # Existing envelope shape, only conditionally portable to the new cover.
+        l,u=logarithm(F(m));e,f=exponential(a*l,a*u)
+        p=F(32*m*sum(H.values()),10**16*W)
+        lo+=p*e;hi+=p*f
+    return floor(lo),ceil(hi)
+
+def decimal(x):
+    with localcontext() as c:
+        c.prec=70
+        return str(Decimal(x.numerator)/Decimal(x.denominator))
+
+def certify(H,m,W,bad=False):
+    with localcontext() as c:
+        c.prec=70
+        terms=[(Decimal(r*n)/Decimal(m*W),(Decimal(m)/Decimal(r)).ln()) for r,n in H.items()]
+        fallback=Decimal(32*m*sum(H.values()))/Decimal(10**16*W) if bad else Decimal(0)
+        lm=Decimal(m).ln();lo=Decimal(0);hi=Decimal('.003')
+        for _ in range(210):
+            a=(lo+hi)/2
+            if sum(p*(a*l).exp() for p,l in terms)+fallback*(a*lm).exp()<1:lo=a
+            else:hi=a
+        q=int(((lo+hi)/2*10**24).to_integral_value(rounding=ROUND_FLOOR))
+    lo=F(q,10**24);hi=lo+F(1,10**24)
+    lv=moment(H,m,W,lo,bad);hv=moment(H,m,W,hi,bad)
+    assert lv[1]<1<hv[0],(lo,hi,lv,hv)
+    k=F(694782719690783,10**18);required=k/(1-k)
+    at=moment(H,m,W,required,bad)
+    return dict(lower=decimal(lo),upper=decimal(hi),lower_endpoint_residual_upper=decimal(lv[1]-1),upper_endpoint_residual_lower=decimal(hv[0]-1),strict_rational_signs=True,moment_minus_one_at_current_k_required_rate=[decimal(x-1) for x in at],nominal_k_ceiling_interval=[decimal(lo/(1+lo)),decimal(hi/(1+hi))])
+
+def price(core,gauges,R,v,h):
+    core=Counter({int(k):n for k,n in core.items() if n})
+    gauges=Counter({int(k):n for k,n in gauges.items() if n})
+    m=5*h;W=4*v+R;ell=h*(h-2)  # p = 10 port: was the p = 12 literal 24*22
+    assert sum(r*n for r,n in core.items())==h*R+2*v*(h-1)+ell-sum(r*n for r,n in gauges.items())
+    idle=Counter({r:2*v for r in (2*h-2,h-1,2*h+2,4)})
+    ans={}
+    for name,bundled in [('separate_rank_a_corrections',False),('bundled_rank_5a_corrections',True)]:
+        H=Counter({r:5*n for r,n in core.items()});H.update(idle)
+        for a,n in gauges.items():H[5*a if bundled else a]+=n if bundled else 5*n
+        mass=sum(r*n for r,n in H.items());assert m*W-mass==4*v-5*ell
+        ans[name]=dict(histogram=dict(sorted(H.items())),calls=sum(H.values()),rank_mass=mass,deficit=m*W-mass,maxchild=max(H),root=certify(H,m,W),root_with_inherited_bad_envelope=certify(H,m,W,True))
+    return dict(status='PROSPECTIVE_COST_ONLY_NOT_PHYSICAL_OR_ASSEMBLY_ADMISSION',m=m,W=W,R=R,v=v,h=h,copy_calls_per_invocation=h,copy_rank=h-2,ell=ell,raw_core=dict(sorted(core.items())),auxiliary_entrances=dict(sorted(gauges.items())),idle_histogram=dict(sorted(idle.items())),profiles=ans,interval_method='Independent exact rational alternating Mercator log bounds (224 terms), 24-degree exponential with geometric tail, 224-bit outward dyadic rounding; Decimal only proposes endpoints.',bad_envelope_scope='10^-16 and 32*m^2 rank-one fallback calls per paid child are inherited assumptions, not a new m = 5h admission.')
+
+if __name__=='__main__':
+    path=Path(sys.argv[1]);raw=path.read_bytes();data=json.loads(raw)
+    core=data['one_stage_helper_histogram_including_copies']
+    gauges=data['auxiliary_entrance_rank_histogram']
+    result=price(core,gauges,data['physical_R'],data['v'],data['h'])
+    result['input_ledger_sha256']=hashlib.sha256(raw).hexdigest()
+    result['input_head']=data['head']
+    result['one_invocation_parts']={key:data[key] for key in ('physical_internal_excluding_center_copies','paid_center_copy_histogram','physical_source_histogram','physical_target_histogram')}
+    print(json.dumps(result,indent=2))
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/work/pr361/code/engines/outer.py b/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/work/pr361/code/engines/outer.py
new file mode 100644
index 0000000000..43007488ad
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/work/pr361/code/engines/outer.py
@@ -0,0 +1,58 @@
+#!/usr/bin/env python3
+"""Exact semantic assembly with the balanced prefix, for the paired-cube network.
+
+Prepared by eumemic with Anthropic Claude assistance. Apache-2.0. The 47 strict constraints, the seven margins and
+the finite bridge are unchanged from icekylinx's scripts/structured_bulk_assembly.py (PR144, adapted from Zhihao
+Chen's PR23). The prefix is the RaD project's (hipotures) balanced positional transform, reviewed in
+references/semantic-bulk/rad20/reports/review-balanced-transform.md: the prefix margin becomes 1-eps instead of
+1-eps(1+c), and eps(1+c)<1 remains a strict geometric condition (K_geometry) whose gap need not exceed kappa.
+The parameters c=q+eta/4 and eps=(1-eta)/(1+q) are those of the reviewed balanced assembly in
+research/copied-fixed/balanced_assembly.py, with its backoff h equal to eta. Nothing else differs from
+structured_bulk_assembly.assembly.
+"""
+from fractions import Fraction as Q
+
+
+def assembly(bit_saving,complex_saving,bridge,kappa,eta=Q(1,10**8),beta=Q(1,4)):
+    a,b=bit_saving,complex_saving
+    tau,sigma=1-a,1-b
+    q=a*(1-2*eta); lp=1-q; lam=(tau+lp)/2
+    c=q+eta/4; eps=(1-eta)/(1+q)
+    minimum=eps*q; r=(minimum+1-eps)/2; delta=eta/8
+    internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma)
+    margins=dict(balanced_prefix=1-eps,coordinate_movement=a,
+        compact_phase_layer=minimum,bulk_exposure=a,
+        Gaussian_arithmetic=min(1-eps-delta,r-delta),
+        scalar_work=1-eps-delta,dimension=eps)
+    slacks=dict(bit_positive=a,complex_above_bit=b-a,
+        complex_below_one_over32=Q(1,32)-b,beta_positive=beta,
+        beta_below_one=1-beta,leaf_saving_above_bit=(1-beta)*b-a,
+        q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q,
+        c_positive=c,c_below_one=1-c,q_below_reservations=c-q,
+        lambda_above_tau=lam-tau,lambda_above_sigma=lam-sigma,
+        lambda_above_internal=lam-internal,lambda_prime_above_lambda=lp-lam,
+        compact_leaf=lp-leaf,compact_reservations=lp-(1-c),
+        lambda_prime_below_one=q,epsilon_positive=eps,epsilon_below_one=1-eps,
+        guard_width=1-eps,K_geometry=1-eps*(1+c),K_dominates_log=eps*c,
+        record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=r-delta,
+        gamma_sublinear=1-eps-r,cell_above_band=eps-(1-r)/2,
+        prime_interval_packing=1-eps,alpha_positive=r,alpha_below_one=1-r,
+        alpha_below_one_fourth=Q(1,4)-r,delta_positive=delta,
+        delta_below_one_eighth=Q(1,8)-delta,short_record_fallback=eps-a,
+        small_field_exposure=1-eps-minimum,
+        artificial_boundary=8-eps+r-delta-minimum,
+        literal_scalar_guard=Q(bridge['semantic']['strict_literal_gap']),
+        row_product_gap=bridge['rows']['degree_gap'])
+    slacks.update({name+'_above_kappa':val-kappa for name,val in margins.items()})
+    assert len(slacks)==47 and len(margins)==7
+    assert all(v>0 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0}
+    assert min(margins.values())==minimum
+    assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2
+    assert 1-eps*(1+c)==eta-eps*eta/4
+    return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma,
+            eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam,
+            lambda_prime=lp,alpha_squared_power=r,delta=delta,
+            C0=bridge['semantic']['C0'],C1=1,kappa=kappa),
+        strict_constraints=slacks,margins=margins,minimum_margin=minimum,
+        absorption_gap=minimum-kappa,
+        recurrence=dict(internal=internal,leaf=leaf,reservations=1-c))
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/work/pr370-source/research/e8-bit/data/bit/bitE8-r865.json.gz b/research/ranksector112-async/vendor/pr523/vendor/pr514/inputs/work/pr370-source/research/e8-bit/data/bit/bitE8-r865.json.gz
new file mode 100644
index 0000000000000000000000000000000000000000..8bec1751f7e33c3a1e4673ef5dbc34d6f205321e
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diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/references/PR493-NOTICE.md b/research/ranksector112-async/vendor/pr523/vendor/pr514/references/PR493-NOTICE.md
new file mode 100644
index 0000000000..ac7d789262
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/references/PR493-NOTICE.md
@@ -0,0 +1,11 @@
+# Attribution for the included PR493 material
+
+Apache-2.0. Prepared by eumemic with substantial Anthropic Claude assistance.
+The only copied PR493 payload in this package is its published EXPECTED.json.
+Its R489 bit operator is cited, not vendored or freshly reconstructed here.
+
+The original complete notice is available with the pinned source:
+https://github.com/CrocSwap/integer-mult-bounds/blob/c3a9a436b84fe44fdc223a5784d84736d1c2d3c7/research/e8-bit-carrier-skeleton/NOTICE.md
+
+This attribution excerpt omits sections for code and historical receipt files
+that are not included in this package. It does not modify any upstream file.
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/COALESCING-GATE.json b/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/COALESCING-GATE.json
new file mode 100644
index 0000000000..7c704edbf7
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/COALESCING-GATE.json
@@ -0,0 +1,3174 @@
+{
+  "status": "EXACT_RESTRICTED_GATE_NO_COALESCING",
+  "source_sha256": "8b9a7f1bb69626d76fec9e915134cec7199a70b53656723ce49ecc47f4644afd",
+  "blocks": [
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+          "frame": [
+            408,
+            79,
+            55
+          ],
+          "row": {
+            "90": "1",
+            "95": "1"
+          }
+        },
+        {
+          "register": 688,
+          "frame": [
+            408,
+            73,
+            49
+          ],
+          "row": {
+            "88": "1",
+            "93": "1"
+          }
+        },
+        {
+          "register": 691,
+          "frame": [
+            414,
+            79,
+            49
+          ],
+          "row": {
+            "89": "1",
+            "95": "1"
+          }
+        },
+        {
+          "register": 689,
+          "frame": [
+            414,
+            73,
+            55
+          ],
+          "row": {
+            "88": "1",
+            "94": "1"
+          }
+        },
+        {
+          "register": 698,
+          "frame": [
+            408,
+            79,
+            49
+          ],
+          "row": {
+            "93": "1/2",
+            "91": "-1/2"
+          }
+        },
+        {
+          "register": 95,
+          "frame": [
+            408,
+            73,
+            55
+          ],
+          "row": {
+            "95": "1/2",
+            "89": "-1/2"
+          }
+        },
+        {
+          "register": 92,
+          "frame": [
+            414,
+            79,
+            55
+          ],
+          "row": {
+            "92": "1/2",
+            "89": "-1/2"
+          }
+        },
+        {
+          "register": 93,
+          "frame": [
+            414,
+            73,
+            49
+          ],
+          "row": {
+            "93": "1/2",
+            "88": "-1/2"
+          }
+        },
+        {
+          "register": 701,
+          "frame": [
+            465,
+            49,
+            6
+          ],
+          "row": {
+            "94": "1/2",
+            "93": "-1/2"
+          }
+        },
+        {
+          "register": 91,
+          "frame": [
+            425,
+            73,
+            6
+          ],
+          "row": {
+            "91": "1/2",
+            "88": "-1/2"
+          }
+        }
+      ],
+      "eligible": [
+        [],
+        []
+      ],
+      "direct": [
+        {
+          "target": 88,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 89,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 90,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 91,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 92,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 93,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 94,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 95,
+          "compatible_packets": [],
+          "compatible_retired": []
+        }
+      ]
+    },
+    {
+      "block": [
+        4,
+        5,
+        6,
+        7
+      ],
+      "tetrads": [
+        [
+          56,
+          59,
+          61,
+          62
+        ],
+        [
+          57,
+          58,
+          60,
+          63
+        ]
+      ],
+      "own_frames": [
+        [
+          161,
+          24,
+          6
+        ],
+        [
+          289,
+          24,
+          6
+        ]
+      ],
+      "retired": [
+        {
+          "register": 725,
+          "frame": [
+            313,
+            161,
+            6
+          ],
+          "row": {
+            "60": "1",
+            "63": "1"
+          }
+        },
+        {
+          "register": 56,
+          "frame": [
+            289,
+            185,
+            6
+          ],
+          "row": {
+            "56": "1",
+            "59": "1"
+          }
+        },
+        {
+          "register": 721,
+          "frame": [
+            295,
+            167,
+            24
+          ],
+          "row": {
+            "58": "1",
+            "63": "1"
+          }
+        },
+        {
+          "register": 716,
+          "frame": [
+            289,
+            161,
+            24
+          ],
+          "row": {
+            "56": "1",
+            "61": "1"
+          }
+        },
+        {
+          "register": 719,
+          "frame": [
+            289,
+            161,
+            30
+          ],
+          "row": {
+            "57": "1",
+            "63": "1"
+          }
+        },
+        {
+          "register": 717,
+          "frame": [
+            295,
+            167,
+            30
+          ],
+          "row": {
+            "56": "1",
+            "62": "1"
+          }
+        },
+        {
+          "register": 726,
+          "frame": [
+            295,
+            161,
+            30
+          ],
+          "row": {
+            "61": "1/2",
+            "59": "-1/2"
+          }
+        },
+        {
+          "register": 63,
+          "frame": [
+            289,
+            167,
+            30
+          ],
+          "row": {
+            "63": "1/2",
+            "57": "-1/2"
+          }
+        },
+        {
+          "register": 60,
+          "frame": [
+            289,
+            167,
+            24
+          ],
+          "row": {
+            "60": "1/2",
+            "57": "-1/2"
+          }
+        },
+        {
+          "register": 61,
+          "frame": [
+            295,
+            161,
+            24
+          ],
+          "row": {
+            "61": "1/2",
+            "56": "-1/2"
+          }
+        },
+        {
+          "register": 729,
+          "frame": [
+            289,
+            161,
+            6
+          ],
+          "row": {
+            "62": "1/2",
+            "61": "-1/2"
+          }
+        },
+        {
+          "register": 59,
+          "frame": [
+            313,
+            185,
+            6
+          ],
+          "row": {
+            "59": "1/2",
+            "56": "-1/2"
+          }
+        }
+      ],
+      "eligible": [
+        [],
+        []
+      ],
+      "direct": [
+        {
+          "target": 56,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 57,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 58,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 59,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 60,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 61,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 62,
+          "compatible_packets": [],
+          "compatible_retired": []
+        },
+        {
+          "target": 63,
+          "compatible_packets": [],
+          "compatible_retired": []
+        }
+      ]
+    }
+  ],
+  "scope": "Unchanged packet assembly, current retired checkpoint; no assertion against a redesigned packet network.",
+  "nonmonotone_excess_per_local": 224,
+  "nonmonotone_excess_global": 16128,
+  "baseline_deficit": 2496
+}
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/COALESCING-PROOF.md b/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/COALESCING-PROOF.md
new file mode 100644
index 0000000000..a16a31eac7
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/COALESCING-PROOF.md
@@ -0,0 +1,19 @@
+# Register coalescing with explicit frame restoration
+
+This is a sufficient compiler transformation, not an achieved kappa gain.
+
+Let an existing verified frame transition from E to F, E contained in F, implement the exact invertible operator U(F) U(E)^(-1) with one rank-d recursive child and its existing coordinate/monomial wrappers, where d=dim(F)-dim(E). The reverse transition is implemented by reversing that exact circuit and replacing its rank-d child by its inverse. For the normalized complex child C, C^(-1)=X C since C^2=X and X^2=I; therefore the inverse uses one rank-d child plus an explicitly charged translation and reversed wrappers. This does not make a downward frame change free. The exact all-column equation is U(E) U(F)^(-1), so composing it with the forward prefix changes the frame label correctly on arbitrary register contents.
+
+Any scalar elementary operation at a common frame remains legal after this restoration. A proposed register coalescing must additionally provide an invertible change of basis on the reused registers, preserve every still-live source, rebuild both forward and dual dirty-data compensation from the actual scalar word, and pay all reverse wrappers and translations. Those are concrete finite circuit checks, not consequences of a clean-input row calculation alone.
+
+For a frame path with total upward dimension u and downward dimension d, the sum of recursive ranks is u+d = (final dimension - initial dimension)+2d. Thus 112 independent dimension-one descents incur 224 additional local rank units. Across 72 invocations this is 16,128 units. Removing a logical helper ordinarily returns its formerly hosted pending coordinates to the idle remainder; it does not by itself create rank deficit. Against the inherited deficit 2,496, the naive 112-descent substitution is not a viable profile without additional genuine rank savings.
+
+## Exact restricted gate
+
+`coalescing_gate.py` replays the pinned PR507 constructor to the checkpoint immediately before coordinate totals. `COALESCING-GATE.json` preserves every retired row and frame, every intended own tetrad, and the target access tests.
+
+All fourteen blocks have twelve retired rows already at rank-three face frames. None of those 168 frames is contained in either corresponding own-output tetrad frame. More strongly, none of the current packet output frames or retired frames is contained in any of the eight own-target hyperplanes of its block. The apparent rank-two opportunity exists earlier, at the snapshot point, before the face assembly raises these rows. Therefore deleting snapshots and merely reusing the later retired stock is invalid without a paid nonmonotone transition. This test does not exclude a redesigned packet assembly or a different early live-range allocation.
+
+## Reusable source connections
+
+The precise analogue is injective live-register renaming with a frame invariant, rather than reuse based on equal clean values alone. OpenAI `WLIdentification/WordCommands.lean`, `StackModel.Command.Exec.rename`, and P18 `Problem18IMPAssignments20261002.run_framed` were identified and source-inspected by the kernel lane; their hashes and audit scope are in that lane's `KERNEL-SOURCE-HASHES.json`. They do not automatically certify the new complex circuit. Our earlier inspected `Slots.restoreMemory`, `effects_argsCode`, and `Word.matrix_substitute` similarly supply the structural pattern: exact state restoration, preserved outside state, and additive replacement cost.
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/COMPLEX-SOURCE-HASHES.json b/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/COMPLEX-SOURCE-HASHES.json
new file mode 100644
index 0000000000..e3bf72b4f6
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/COMPLEX-SOURCE-HASHES.json
@@ -0,0 +1,41 @@
+{
+  "registered_search": "Shared source_catalogs and live DAG were queried across their federated registrations; source files then inspected directly. This is not a claim that every indexed declaration was read or kernel-certified.",
+  "sources": [
+    {
+      "path": "Mathproof/Meta/Problem18ConcreteSlotTransport20261002.lean",
+      "sha256": "2b436d58c0f28a98cba11c2ffe20858062b1cd05d567cd7f2f9c29b6851fbdeb",
+      "declarations": "Slots.transport; Slots.restoreMemory",
+      "statement_summary": "A decoded workspace invariant is preserved when the relevant layout registers and backing memory agree, even if unrelated scratch differs.",
+      "current_evidence": "Source read; no new Lean compilation in this campaign."
+    },
+    {
+      "path": "Mathproof/Meta/Problem18ConcreteAutoRestore20261002.lean",
+      "sha256": "16076d909a7ca6d957cb68f7455832979e9b4df25b8f3f5a43705858aa5e0c02",
+      "declarations": "run; extract_run",
+      "statement_summary": "An actual restoration program composes with extraction, with exact additive run cost and unchanged input/output.",
+      "current_evidence": "Source read; no new Lean compilation in this campaign."
+    },
+    {
+      "path": "leanlibs/formal-math-3sum-apsp/ThreeSumApsp/Lang/Compiler/CallFrames.lean",
+      "sha256": "cf7f74321dc79b952663a253f5537640f6460748a97eb951fe714ad271f90553",
+      "declarations": "Light.Compiler.effects_argsCode",
+      "statement_summary": "Argument evaluation writes its designated temporaries and satisfies AgreeOutside for all other locations.",
+      "current_evidence": "Source read; no new Lean compilation in this campaign."
+    },
+    {
+      "path": "openai-math/lean/OAI/Combinatorics/VariableWL/MachineSimulation.lean",
+      "sha256": "d2148836dc632a9a4fd68adf029f1f47c33a0b0168a1fb7266dd994016aa45ac",
+      "declarations": "drain_stage; drain_both",
+      "statement_summary": "Two explicit Turing stack draining runs compose with additive step counts and an exactly tracked accumulated answer.",
+      "current_evidence": "Source read; no new Lean compilation in this campaign."
+    },
+    {
+      "path": "openai-math/lean/OAI/Computability/FourierCircuit/WordScheduling.lean",
+      "sha256": "0f1b0c89091f6acc5310e95c07102792749a38b0e35a760b7feae25682ef2713",
+      "declarations": "Word.matrix_substitute; Word.weight_substitute",
+      "statement_summary": "Substitution of a word implementing the same matrix preserves the full word matrix, and its weight equals the sum of actual substituted weights.",
+      "current_evidence": "Source read; no new Lean compilation in this campaign."
+    }
+  ],
+  "dag_observation": "Selected external declarations are present under source-catalog operation identities, with no typed ports or axiom audit in the returned records. No source-only hit was promoted to certification."
+}
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/HOSTING-RESEARCH.md b/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/HOSTING-RESEARCH.md
new file mode 100644
index 0000000000..9b551054fe
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/HOSTING-RESEARCH.md
@@ -0,0 +1,40 @@
+# Machine-derived allocation routes
+
+Source-only inspection, not new Lean certification. Exact source declarations consulted:
+
+- Mathproof/Meta/Problem18RecursiveWorkspaceChain20261002.lean: program, cost, run, code_uniform. The run theorem keeps one physical reservation and preserves array lengths through an arbitrarily long sequence of verified calls.
+- Mathproof/Meta/Problem18P34Subfield20261003NRecursiveWorkspaceRestore.lean: run. The entire reserved concrete memory image is restored, not merely a candidate-local prefix; restoration itself has an explicit cost.
+- Mathproof/Meta/Problem18ConcreteSelectedChildContinuation20261002.lean: program, cost, run. Composes a concrete selected continuation with a disjoint-reservation precondition and additive counted cost.
+- Mathproof/Meta/Problem18P351PolynomialWorkspaceFrameClose20261003.lean: gcd_ws_safe, quotient_ws_safe. Workspace-base ABI registers are excluded from scalarWrites.
+
+## Sufficient adaptation
+
+Treat each complete arbitrary-dirt cover invocation as a continuation that preserves the caller's reserved arrays outside its exact endpoint. A finite schedule is sufficient only when each pending child receives its full intended factor exactly once, every borrowed physical family is restored before its next data/bridge touch, distinct simultaneously interpreted local registers have distinct full owners, and all remaining children are explicitly charged. Composition then follows from equality of endpoints and per-replica event projection; neither shared workspace nor a different dispatch order introduces a free mathematical operation. This is an applicability theorem, not by itself a kappa improvement.
+
+## Bounded new screens
+
+1. Paid register spills for shorter K=3 controllers: rejected before expensive search. Current provider demands 7*4900=34300 helper-rank units per replica, while initial plus final pending children supply only26880. Shortage7420 already exceeds total positive rank deficit216. Any implementation must pay missing residual transformations and restore its full reserve. No private-reserve or LIVE increase is silently assumed.
+2. Finite steady-state amortization at T=16: exact integer allocations for offsets6 and12 both reproduce twice the T=8 histogram and the same nominal b=0.0013744413363825925, with zero solver gap. No improvement claimed.
+3. K=5,T=8,offset6: bounded feasible candidate b=0.0013680017192500558, worse than current. Solver reached time limit with tiny nonzero gap; this is not a universal no-gain theorem.
+
+These screens use actual coordinated-rank2 local paid profile and widths (18 rank7,104 rank8,438 rank9), complete paid remainders, and finite fixed T. They do not merely score local savings. Literal owner matching and full scalar invoice would still be required for a positive nominee; no negative nominee was promoted.
+
+## Public507 composition and literal owner witness
+
+The new PR507 partial-own factory combines constructively with our previous coordinated rank-two gauge collapse. Kernel lane reconstructed its exact local word. The changed local profile is {1:2493,2:208,3:516,4:88,5:298,6:68,7:1,8:17}; widths are 18 rank7,146 rank8,396 rank9. Our complete offset6 allocation has nominal b=0.0013910579397602985 with every remainder paid. Its literal owner witness passes all40320 role assignments,72 calls,560 distinct helpers per call. Files RANK2-PARTIAL-O6.json and RANK2-PARTIAL-OWNERS.json.gz bind the construction. This is a positive composed supplier nomination; it still needs fresh emitted full orthogonal maps, scalar prefix and outer assembly. Its gain does not establish that three entirely new machine concepts improved the exponent.
+
+## Repeated-axis modulo-four gate
+
+The proposed sufficient algebraic extension tracks multiplicity of each pending coordinate modulo4: C squared equals translation X, so an even repeated factor can be compensated explicitly without another recursive Fourier call. Overlapping factors must still obey actual owner lifetime, full-family injection and scalar routing. For a rank-r pending bin hosting roles with total width s, a best-case leftover has size r-s if s<=r, otherwise parity(r-s). The latter is an optimistic capacity relaxation: every loss of odd coverage reduces the actual rank deficit and cannot be hidden as a free bank.
+
+Native integer screens allowing aggregate width excess0,1,2,4 and16 per pending bin all selected the same disjoint pattern optimum, nominal b=0.001391135951042288, zero reported integer-solver gap. No overlap selected; therefore no positive candidate promoted from this bounded route. This is not a proof that every possible modulo-four physical compiler is unhelpful. It is a cheap full-profile gate with all repeated-rank loss charged.
+
+## New kernel-92 candidate
+
+Kernel lane supplied exact source-based variants after broadening availability at concrete instruction boundaries. Full controller pricing ranks them as follows: kernel-partial-base with 92 pivots, b approximately 0.0013934624979634045; latefirst-partial-base with 89 pivots, b approximately 0.0013927996101125715; snapshot-even, b approximately 0.0013926403309490465; snapshot-both, b approximately 0.0013914512506201793. All are floating nominations, not outer assembled kappa values.
+
+The selected 92-pivot local profile is {1:2539,2:160,3:530,4:88,5:298,6:68,7:1,8:17}, with 18 width-7,154 width-8 and388 width-9 helpers. Selected plan KERNEL92-FOCUS-O6.json has SHA256 7a30db32ad8fc54bd5e7060febf4f8ff7747b8287c057ae926efc736e2b9f800. KERNEL92-OWNERS.json.gz has SHA256 9c6bd9793db16d599d3c7f9493350d2359681d19eb170ec7239e8d568090e745. Literal matching passes all40320 helper roles,72 invocations and560 distinct helper families per invocation. The emitted full physical maps and prefix invoice remain parent/independent-auditor responsibilities.
+
+The complete selected paid histogram is {1:182808,2:11520,3:41233,4:6336,5:25173,6:4896,7:195,8:1224,16:1,32:1,39:1,48:766}. Live stock7680, ambient73, rank deficit2496, maximum child48.
+
+An optimistic static stock allocation gives b approximately 0.0013943119744464494, but its fixed optimal patterns were infeasible under tested offset4,6,8,12 schedules with eight replicas and offset6 with sixteen replicas. That stronger number is not a delivered candidate. The limited failure is retained as a concrete search result, not a universal scheduling barrier.
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/KERNEL-MACHINE-SOURCES.md b/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/KERNEL-MACHINE-SOURCES.md
new file mode 100644
index 0000000000..a216cdd1f8
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/KERNEL-MACHINE-SOURCES.md
@@ -0,0 +1,35 @@
+# Machine-source transfer ledger
+
+These are direct source inspections, not new Lean compilation or certification. A machine optimization counts toward the exponent only when its complete child-rank profile and physical inventory improve.
+
+## Old-state operand capture: constructed and tested
+
+OpenAI math, `lean/OAI/Computability/WeisfeilerLeman/RAMInstruction.lean`, defines `WLTime.SparseRAM.execute`: a load evaluates its address/read from the old configuration and only then updates the destination register. The theorem `execute_forget` states
+
+    A.execute I (forget A n C) = forget A n (execute I C).
+
+`SparseStore.lean`, theorem `WLTime.WordMemory.read_prepend`, states that a prepended address/value pair implements exactly `Function.update` of the abstract memory. This makes the distinction between an old value and its overwritten successor explicit.
+
+The P18 source `Mathproof/Meta/Problem18IMPAssignments20261002.lean`, `run_assignments`, proves a static assignment sequence correct from original-environment right-hand-side values under `Independent xs`; `run_framed` adds preservation of untouched variables, arrays and external tapes. This is a sufficient independence hypothesis, not permission to merge aliased live registers. `Problem18P351PairSnapshot20261003.lean`, theorem `run`, gives an exact snapshot into a separate bank while preserving every other array and external tape.
+
+Concrete transfer: PR507 captures both pair intermediates after their two-shear basis change. We implemented a triangular snapshot between the two shears: capture the new pair sum and the still-unmodified second operand. The resulting pair basis remains invertible; the later own-tetrad decoder is recomputed exactly. Three variants change one or both tetrad parities. All pass clean scalar algebra; after retiming and exact rational kernel construction, the best snapshot-even candidate has88 pivots and an improved full supplier compared with the simple84-pivot composition. It nevertheless loses to the separately found92-pivot word. Therefore old-state capture is a real tested mechanism but is not counted as an ingredient of the selected92-pivot construction.
+
+## Actual first-read frontier: bounded test
+
+The exact frame immediately before the first observer, rather than the pre-retiming source layout, determines which incoming cancellation subspaces are legal. We recomputed these first-read frontiers from the emitted retimed body and reran a bounded native C++ response search. A valid89-pivot word resulted, but its full supplier price was below the92-pivot word. No gain from this representation is counted in the winner.
+
+## Ambient frame preservation
+
+OpenAI math, `WLIdentification/WordCommands.lean`, theorem `StackModel.Command.Exec.rename`, transports execution through an injective register renaming while preserving every ambient location outside the image. This is the correct local rule for reusing a physical region whose other live contents must survive. It requires injectivity on simultaneously live registers; it does not by itself justify identifying two live helpers or erasing their dirty state.
+
+The parent/complex lane uses this distinction while testing lifetime-based coalescing of own-helper storage with retired factory rows. The actual paid transitions and arbitrary-dirt restoration must be constructed before claiming an exponent gain. A literal rank4-to-rank3 descent adds total variation; dropping a helper count alone is not a price argument.
+
+## Selected fallback and honest attribution
+
+The selected fallback has92 kernel pivots with profile
+
+    1:2539, 2:160, 3:530, 4:88, 5:298, 6:68, 7:1, 8:17
+
+and residual inventory18 width7,154 width8,388 width9. It combines PR507's changed factory with the prior coordinated rank2 gauges, public frame retiming, asynchronous whole-owner packing, and an improved response-basis selection. The92-pivot improvement is an application of our existing algebraic response selector; it is not relabeled as one of three new machine techniques. Its exact local scalar audit passes all800 columns in both orientations and92 omission controls. The parent's complete physical and arithmetic replay remains the authority for the final exponent.
+
+DAG coverage note: a direct `Shape-DAG.ps1 sig Mathproof.Problem18IMPAssignments20261002.run_framed` query loaded the registered compiled overlays but returned `ERR no such declaration`. The source file and its statement were available and inspected. Thus this lane records that item as source evidence, not a retrieved typed-DAG certificate; no second catalog or compilation was created to hide the missing port.
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/KERNEL-SOURCE-HASHES.json b/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/KERNEL-SOURCE-HASHES.json
new file mode 100644
index 0000000000..625d50de57
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/KERNEL-SOURCE-HASHES.json
@@ -0,0 +1,49 @@
+[
+  {
+    "repository": "openai-math",
+    "path": "lean/OAI/Computability/WeisfeilerLeman/RAMInstruction.lean",
+    "sha256": "5ca836a29da196f6140a948b593a7463d7395b1d59842913ebd3fbee59feee7c",
+    "declarations": [
+      "WLTime.SparseRAM.execute",
+      "WLTime.SparseRAM.execute_forget"
+    ],
+    "evidence": "source inspected; no fresh kernel replay"
+  },
+  {
+    "repository": "openai-math",
+    "path": "lean/OAI/Computability/WeisfeilerLeman/SparseStore.lean",
+    "sha256": "0e51415ad2e954588789a54dd1713a3b988ba84233797303840656eddc974e7f",
+    "declarations": [
+      "WLTime.WordMemory.read_prepend"
+    ],
+    "evidence": "source inspected; no fresh kernel replay"
+  },
+  {
+    "repository": "openai-math",
+    "path": "lean/OAI/Computability/WLIdentification/WordCommands.lean",
+    "sha256": "687f9e465ad37124a7a5c1bde32e4657b37f69610cf22f3c30375f22141ca8af",
+    "declarations": [
+      "StackModel.Command.Exec.rename"
+    ],
+    "evidence": "source inspected; no fresh kernel replay"
+  },
+  {
+    "repository": "Mathproof",
+    "path": "Mathproof/Meta/Problem18IMPAssignments20261002.lean",
+    "sha256": "5bb547049c7c6d622fbe6547e5d7b45b39842942091ebaf89e2cf4c85c765cfc",
+    "declarations": [
+      "Mathproof.Problem18IMPAssignments20261002.run_assignments",
+      "Mathproof.Problem18IMPAssignments20261002.run_framed"
+    ],
+    "evidence": "source inspected; no fresh kernel replay"
+  },
+  {
+    "repository": "Mathproof",
+    "path": "Mathproof/Meta/Problem18P351PairSnapshot20261003.lean",
+    "sha256": "c5535c358ee3a7d63f8d8a18e0f5e3fe45be85f1f22303b37e8dc6d2690cdcb3",
+    "declarations": [
+      "Mathproof.Problem18P351PairSnapshot20261003.run"
+    ],
+    "evidence": "source inspected; no fresh kernel replay"
+  }
+]
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/MACHINE-TRANSFORMATIONS.md b/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/MACHINE-TRANSFORMATIONS.md
new file mode 100644
index 0000000000..f4c39e557c
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/MACHINE-TRANSFORMATIONS.md
@@ -0,0 +1,31 @@
+# Machine-inspired sufficient transformations
+
+This note records constructive transformations with exact applicability tests. It does not claim an achieved kappa improvement from the three bounded pilot screens below. The source provenance and current evidence level are in COMPLEX-SOURCE-HASHES.json.
+
+## 1. Fused restoration return or entry
+
+Suppose a complete normalized invocation has arbitrary-dirt endpoint (data transformation D, helper operator S on a whole owner, identity on spectators). Suppose S and all final monomial normalizers act inside a fixed local9-coordinate factor. Let Q be a product of C_v on orthogonal pending axes outside this full local9 factor.
+
+If a helper's final recursive child C_r occurs after its last scalar observation or update, replace that child by C_(r+q) on its r coordinates and q of these additional axes, using an explicit full owner chart. No later scalar observation can expose the extra factor. The resulting complete invocation endpoint is (D,Q S), so remove exactly those q axes from its later idle remainder. The exact paid-profile replacement is -[r]-[q]+[r+q]. The larger child must satisfy the existing halving and compiler conditions; all new routing is billed.
+
+There is an entry version: if the selected child occurs before the helper's first scalar observation/update, insert Q at the beginning of the complete invocation, then commute it through the untouched prefix to the selected child. The arbitrary-dirt endpoint theorem makes the data output independent of this changed initial helper value; S Q=Q S gives the same completed pending factor. Initial normalizers must preserve the exterior factor. This is the matrix analogue of an AgreeOutside frame invariant and a fused machine return/entry.
+
+The pilot checks actual emitted scalar operands, not nominal labels. In the current coordinated rank2 word, all 560 helpers are observed in the frame-zero dirty precondition and updated/read again in FULL cleanup. Both prologue and epilogue inventories are empty in both orientations. Do not manufacture a positive tail from the endpoint formula alone. A follow-up must first change compensation/cleanup, prove the same all-column endpoint, and then reprice the complete global profile.
+
+## 2. Deferred normalization with a finite residue ledger
+
+For C_v=((1+i)I+(1-i)X_v)/2, direct expansion gives C_v^2=X_v and C_v^4=I. Allow several different complete invocations to borrow the same pending axis of one whole owner. Let k_v be its actual multiplicity. Choose e_v in {0,1} so k_v+e_v is odd, execute C_v only on the missing-parity axes e_v=1, and emit X_v^((1-k_v-e_v)/2). The final product is exactly C_v. All factors commute, and the sign of the translation exponent is immaterial modulo2.
+
+Every invocation must still use distinct whole owners, complete before the next begins, restore spectators, and occur inside the physical idle interval. Use actual pending vectors, not different charts' coincident coordinate indices. Emit an explicit chart for the possibly noncontiguous remainder and charge the final translation. This is a reversible-machine deferred-normalization invariant; it is not permission to split one residual among owners.
+
+Repeated use does not automatically save rank: it can reduce odd-parity coverage and increase the final remainder. The hosting lane's early paid screen selected disjoint use on the current stock. No numerical gain is assigned here. The rule remains a sufficient way to compile a future positively priced overlapping assignment.
+
+## 3. Recursive common-subexpression substitution
+
+At a proposed recursive call sending a register from frame E to F, suppose a simultaneously live register already equals the same exact logical linear form at frame F on every independent input column. Then a proved copy/scale sequence can supply that output instead of executing the recursive call. Its old value may be overwritten only under the exact reachable-state relation; all private copies must later be cleared correctly. Equality of frame labels alone, equality on test inputs, or equality of response columns without dirty columns is insufficient.
+
+This is a machine checkpoint/common-subexpression rule, with the same matrix-substitution and actual-weight accounting structure as OpenAI WordScheduling. The pilot compares exact rational logical rows and frames at all 3,635 positive recursive sites in each orientation of the existing provider. It finds zero exact matches. This does not rule out proportional forms, a redesigned checkpoint schedule, or a changed provider. A positive follow-up must emit the copy/erase path and pass the all-column physical audit before any saved child is credited.
+
+## What the library reuse establishes
+
+P18's transport/restoration lemmas explain exactly which machine state can be forgotten and which memory must be preserved. Anthropic's AgreeOutside rule provides the footprint criterion. OpenAI's explicit machine-run composition and word substitution explain how to compose complete endpoints and charge the actual replacement. None of these imported source statements by itself proves a new multiplication bound. The mathematical specializations above must be applied to an actual construction and pass the full paid-profile gate.
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/REPEATED-AXIS-LEMMA.md b/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/REPEATED-AXIS-LEMMA.md
new file mode 100644
index 0000000000..9e3ee8bc5d
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/REPEATED-AXIS-LEMMA.md
@@ -0,0 +1,27 @@
+# Sufficient repeated-axis normalization rule
+
+Let C_v=((1+i)I+(1-i)X_v)/2 for a binary translation X_v. Direct expansion gives
+C_v^2=X_v and C_v^4=I; translations and all C_v commute. Suppose a physical
+owner remains idle between its actual previous touch and next touch. Each
+complete normalized helper invocation has one distinct whole owner and leaves
+exactly its declared C factors on that owner's assigned axes while restoring
+borrowed spectators and all private workspace, for arbitrary initial dirt.
+
+Axis v may occur k_v times across different completed invocations in that idle
+window. Choose e_v in {0,1} so k_v+e_v is odd. Emit a residual child on all axes
+with e_v=1 and an explicit translation X_v to the power (1-k_v-e_v)/2. Then
+C_v^(k_v+e_v) X_v^((1-k_v-e_v)/2)=C_v exactly. Apply this independently to every
+axis of the original pending child. The result is its original endpoint; no
+physical owner is split, and no invocation is interleaved internally.
+
+All actual axes, charts, multiplicities, parity-complement remainder and final
+translations must be serialized and charged. Scalar and prefix invoices must
+include the added translations. A repeated even pair loses two units of covered
+rank relative to disjoint placement, so the original fixed deficit cannot be
+assumed. The existing audit's disjointness rule must be replaced by this exact
+ledger only for a new explicitly versioned program.
+
+This is a sufficient new construction rule, independently reviewed by the
+complex lane under the same normalized-invocation contract. A bounded full-stock
+screen chose no overlaps, so this note claims no achieved kappa gain. It is not
+permission to treat repeated calls or translations as free.
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/REPLAY-REPAIRS.md b/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/REPLAY-REPAIRS.md
new file mode 100644
index 0000000000..e4eb71418e
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/REPLAY-REPAIRS.md
@@ -0,0 +1,7 @@
+# Repairs exercised by the final replay
+
+The first run exposed an inherited negative control that set a pure helper route to the route it already had. The repaired test chooses two distinct width-nine owners, copies the complete owner entry to create a real collision, asserts that the mutation changed the input, and requires the direct ownership rule to reject overlapping physical footprints. No mathematical validity check was removed.
+
+The new response kernel raises the backward scalar prefix envelope to 1,048,913, requiring 21 bits rather than the old fixture's 20. The independent invoice now derives its local prefix requirement from the exact replay. The global total is 206 bits; the retained 512-bit charge and row allowance remain sufficient. All strict finite and outer inequalities are checked anew.
+
+After these repairs and the manifest/input newline changes, all 13 stages passed from scratch on a copy where every recognized text file had CRLF line endings. This is the delivered program, with the same exact exponent and canonical final template as the discovery replay. Original failed logs remain in the local research archive rather than being represented as successful runs.
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/RESTORATION-AND-CSE-SCREEN.json b/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/RESTORATION-AND-CSE-SCREEN.json
new file mode 100644
index 0000000000..51b57aed25
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/RESTORATION-AND-CSE-SCREEN.json
@@ -0,0 +1,22 @@
+{
+  "status": "EXACT_SOURCE_SCALAR_AND_FRAME_PILOT",
+  "source_sha256": {
+    "CANONICAL-WORD.json.gz": "e88cd2b8a34a012542ab126a12518ab16888435ec42c4065ee63c7a85b5ec9f2",
+    "LOCAL-PROGRAMS.json.gz": "7f59bfbfc174adac07ae70afe290d6a41e9d8aa4e2550edb45e0004788c99d98"
+  },
+  "orientations": {
+    "backward": {
+      "prologue": [],
+      "epilogue": [],
+      "exact_row_frame_reuse_candidates": [],
+      "recursive_sites_screened": 3635
+    },
+    "forward": {
+      "prologue": [],
+      "epilogue": [],
+      "exact_row_frame_reuse_candidates": [],
+      "recursive_sites_screened": 3635
+    }
+  },
+  "scope": "Nomination screen only. A matched logical row would still require explicit copy/erase lowering, independent physical phase audit and complete global profile. No new kappa claimed."
+}
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/coalescing_gate.py b/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/coalescing_gate.py
new file mode 100644
index 0000000000..196474567b
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/research-notes/coalescing_gate.py
@@ -0,0 +1,26 @@
+from pathlib import Path
+import sys,json,hashlib
+from fractions import Fraction
+src=Path(sys.argv[1]); inp=Path(sys.argv[2]); out=Path(sys.argv[3])
+s=src.read_text().split("# Four coordinate sums")[0].replace("OUT.mkdir(parents=True,exist_ok=False);","")
+old=sys.argv;sys.argv=[str(src),str(inp),"unused"];d={};exec(compile(s,str(src),"exec"),d);sys.argv=old
+report=[]
+for c,z in sorted(d["blocks"].items()):
+ ids=z["receipt"]["source_lines"]
+ tet=[sorted(t for t in ids if sum(d["R"][t][i]<0 for i in c)%2==parity) for parity in (0,1)]
+ Fs=[d["basis"]([d["P"][t] for t in a]) for a in tet]
+ retired=[dict(register=r,frame=d["cur"][r],row={str(k):str(x) for k,x in d["rows"][r].items()}) for r in d["retired"][c]]
+ eligible=[[r for r in d["retired"][c] if d["inside"](d["cur"][r],F)] for F in Fs]
+ direct=[]
+ for t in ids:
+  F=d["hyper"](d["P"][t])
+  packetregs=sorted({r for key,(r,a) in d["packets"].items() if key[0]==c})
+  direct.append(dict(target=t,compatible_packets=[r for r in packetregs if d["inside"](d["cur"][r],F)],compatible_retired=[r for r in d["retired"][c] if d["inside"](d["cur"][r],F)]))
+ report.append(dict(block=c,tetrads=tet,own_frames=Fs,retired=retired,eligible=eligible,direct=direct))
+assert len(report)==14
+assert all(len(r["frame"])==3 for b in report for r in b["retired"])
+assert all(not e for b in report for e in b["eligible"])
+assert all(not x["compatible_packets"] and not x["compatible_retired"] for b in report for x in b["direct"])
+result=dict(status="EXACT_RESTRICTED_GATE_NO_COALESCING",source_sha256=hashlib.sha256(src.read_bytes()).hexdigest(),blocks=report,scope="Unchanged packet assembly, current retired checkpoint; no assertion against a redesigned packet network.",nonmonotone_excess_per_local=224,nonmonotone_excess_global=16128,baseline_deficit=2496)
+out.write_text(json.dumps(result,indent=2)+"\n",encoding="utf-8")
+print(json.dumps({k:v for k,v in result.items() if k!="blocks"}))
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/audit_scalar_invoice.py b/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/audit_scalar_invoice.py
new file mode 100644
index 0000000000..b03fdf510f
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/audit_scalar_invoice.py
@@ -0,0 +1,82 @@
+"""Fresh PR484 scalar/prefix lowering and finite overcharge recount. OpenAI Codex.
+Reads emitted programs, canonical word and raw routes, importing no supplier code.
+Inherited all-size compiler admissibility is a condition, not inferred here.
+"""
+from pathlib import Path
+from fractions import Fraction as F
+from collections import Counter
+import gzip,json,math,hashlib
+import sys
+O=Path(sys.argv[1]);V=Path(sys.argv[2]);HOSTED=Path(sys.argv[3])
+def read(p):return json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+w=read(V/'split-centres/CANONICAL-WORD.json.gz');p=read(V/'split-centres/LOCAL-PROGRAMS.json.gz');old=read(V/'split-centres/GLOBAL-TEMPLATE.json.gz');new=read(HOSTED/'GLOBAL-TEMPLATE.json.gz');integ=read(V/'split-centres/INTEGRATION.json');checks=read(V/'split-centres/LOCAL-CHECKS.json');prior=read(V/'split-centres/INDEPENDENT-REPLAY.json');owners=read(O/'OWNERS-AND-PROFILE.json')
+N=800;M=73;R=560;L=9;T=8;VV=120;K=4
+local={}
+for ori,evs in p.items():
+ rows={('L',i):{i:F(1)}for i in range(N)};env={('L',i):F(1)for i in range(N)};peak=F(1);real=macros=0;paid=Counter();workops=0
+ for e in evs:
+  if e[0]=='climb':paid[e[5]]+=1
+  elif e[0]=='center':paid[e[4]]+=1
+  elif e[0]=='scalar':
+   macros+=1;x=e[1];op=x[0];a=tuple(x[1]);count=0
+   if op=='clear':rows[a]={};env[a]=F(0);count=1
+   elif op=='copy':rows[a]=dict(rows[tuple(x[2])]);env[a]=env[tuple(x[2])];count=1
+   elif op=='scale':
+    q=F(x[2],x[3]);num,den=abs(q.numerator),q.denominator
+    assert num and num&(num-1)==0 and den&(den-1)==0
+    rows[a]={j:q*v for j,v in rows[a].items()};env[a]*=abs(q)
+    count=abs(num.bit_length()-den.bit_length())+int(q<0)
+   elif op=='add':
+    b=tuple(x[2]);q=F(x[3],x[4]);num,den=abs(q.numerator),q.denominator
+    assert a!=b and num>0 and den&(den-1)==0
+    # Lower actual coefficient to cleared Horner work. Every intermediate
+    # magnitude envelope is explicitly included, before denominator halvings.
+    acc=0;count=1
+    for i,ch in enumerate(bin(num)[2:]):
+     if i:acc*=2;count+=1;peak=max(peak,acc*env[b])
+     if ch=='1':acc+=1;count+=1;peak=max(peak,acc*env[b])
+    v=F(acc)
+    for i in range(den.bit_length()-1):v/=2;count+=1;peak=max(peak,v*env[b])
+    assert v==abs(q);count+=2 # signed accumulation and private work clear
+    env[a]=env.get(a,F(0))+abs(q)*env[b];rr=rows.setdefault(a,{})
+    for j,z in list(rows[b].items()):
+     value=rr.get(j,F(0))+q*z
+     if value:rr[j]=value
+     else:rr.pop(j,None)
+    workops+=count
+   else:raise AssertionError(op)
+   real+=2*count;peak=max(peak,env[a])
+ assert all(not row for reg,row in rows.items()if reg[0]=='C')
+ for i in range(N):
+  expected={i:F(1)}
+  if ori=='forward'and 120<=i<240:expected[i-120]=F(1)
+  if ori=='backward'and i<120:expected[i+120]=F(-1)
+  assert rows['L',i]==expected
+ assert peak==F(prior['local'][ori]['prefix_l1_upper']) and peak<2**192
+ assert real==checks[ori]['real_component_primitive_bound']and macros==checks[ori]['scalar_macros']
+ assert dict(paid)=={int(r):z for r,z in checks[ori]['paid_profile'].items()}
+ local[ori]=dict(events=len(evs),macros=macros,real_component_primitives=real,prefix_l1=str(peak),prefix_bits=peak.numerator.bit_length()-peak.denominator.bit_length()+1,coefficient_work_primitive_count=workops,all_exact_columns=N,all_560_dirty_helper_columns_restored=True,private_centres_and_coefficient_work_cleared=True)
+centres=len(w['centers']);widths=[9-len(w['frames'][f])for f in w['start'][240:]];enter=sum(x<9 for x in widths)
+children=sum(checks['forward']['paid_profile'].values());macros=max(x['macros']for x in local.values());compiler=64*(M+1)**3
+adapters=16*(macros+children+N+centres)+64*M
+primitive_bound=max(x['real_component_primitives']for x in local.values())+adapters*compiler
+bridges=sum(e['kind']=='bridge'for e in old['recipe']);bridgeadd=2*VV*T*bridges;shifts=K*VV*T;moves=2*K*VV*T
+oldW=old['live'];oldP=old['physical'];oldNB=(oldW-2*VV*K*T)//L
+scalar=sum(local[c['orientation']]['real_component_primitives']for c in old['calls'])
+nonlocal_items=4*VV*T*L+2*VV*T*L+2*L*T*R+sum(e['replicas']for e in old['idle_children'])+L*oldNB+bridgeadd+shifts+moves+oldW+oldP+2*L*T*enter*144
+outside=8*nonlocal_items+64*M
+pervertex=scalar+bridgeadd+shifts+moves+oldW+(72*adapters+outside)*compiler+64*oldP
+invoice=integ['finite_invoice'];assert (primitive_bound,adapters,pervertex,compiler)==(invoice['local_primitive_bound'],invoice['local_adapters'],invoice['pervertex'],invoice['compiler'])
+# Independent hosted stock rebase, retaining the larger unhosted operation
+# overcharge; only the stock and mass in the common router/literal change.
+W=new['live'];P=new['physical'];mass=owners['rank_mass'];profile=owners['paid_profile']
+assert M*W-mass==2496 and P==W+R+centres+2
+rebase=pervertex-oldP*65+P*65-oldW+W;used=max(rebase,pervertex)
+r=M//2;group=2**(r*r)
+for i in range(1,r+1):group*=2**(2*i)-1
+stock=group*P;smass=group*mass;logical=group*used+64;router=compiler*(logical+1)*(stock+1)**2
+G,E,C0=2**30000,2**100000,2**210000;B=smass+E;literal=2*G*stock**2+8*smass+4*stock+4+32*M;row=2*stock.bit_length()+9909+252;maxchild=max(map(int,profile))
+ineq=dict(local_primitive_bound=primitive_bound<2**48,logical=logical<2**6050,router=router<G,literal=literal<E,mass=B<2**100001,precision=32*M*B*B<C0,tape=2*B+18<C0,row=row<20161,halving=M*M>2*maxchild*maxchild)
+assert all(ineq.values())
+out=dict(status='PASS_INDEPENDENT_SCALAR_PREFIX_AND_HOSTED_FINITE_INVOICE',local=local,entering_helpers=enter,entrance_rank=sum(9-x for x in widths),local_adapters=adapters,local_primitive_bound=primitive_bound,wrapper_elementary_factors_charged=2*72*enter*144,compiler=compiler,unhosted_pervertex=pervertex,hosted_rebased_pervertex=rebase,conservative_pervertex_used=used,finite=dict(physical_stock_bits=stock.bit_length(),router_bits=router.bit_length(),literal_bits=literal.bit_length(),physical_row_coefficient=row,retained_row_coefficient=20161,required_C0_bits=(32*M*B*B).bit_length(),halving_integer_inequality=[M*M,2*maxchild*maxchild],G_exponent=30000,E_exponent=100000,C0_exponent=210000),strict_checks=ineq,scope='Exact finite recount conditional on inherited all-size compiler/precision/tape and analytic-transfer contracts. Signed accumulation uses the supplier scalar primitive convention.')
+(O/'PREFIX-AND-INVOICE.json').write_text(json.dumps(out,indent=2)+'\n');print(json.dumps(out,indent=2),flush=True)
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/adapters_gk.py b/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/adapters_gk.py
new file mode 100644
index 0000000000..252ca9393d
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/adapters_gk.py
@@ -0,0 +1,59 @@
+"""Paid residual wrappers for entering helpers (Lemma A): generation and independent decoding.  Apache-2.0.
+Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.  The wrapper construction follows PR #458
+(chafreaky): a helper that starts at frame E and ends at FULL has the physical residual S_E = T_FULL T_E^-1 (apply T_E^-1 first);
+S_E = L_E (C_[w] x I) R_E with R_E applied first; the wrappers  R_E^-1  before the whole local invocation and  L_E^-1  after its
+full-frame cleanup turn the residual into the coordinate factor C_[w] x I and restore the other 9 - w coordinates identically.
+usage: adapters_gk.py CANONICAL-WORD.json.gz RESIDUAL-ADAPTERS.json OUT-LEMMA-A.json
+Writes the recipes (generation uses clifford_exact.lower_child) and then DECODES the serialized monomials with the primitive
+constructors of clifford_exact (not lower_child) and checks, for every entrance frame, that  L_E^-1 S_E R_E^-1  has exactly the
+tableau and zero-state vector (global phase included) of  fourier(9, range(w)); mutated recipes (wrong phase, swapped sides, wrong
+translation, wrong width) must be rejected."""
+import copy, gzip, json, sys
+from pathlib import Path
+R = Path(__file__).resolve().parent.parent.parent
+sys.path.insert(0, str(R / 'split-centres-global/vendor'))
+from clifford_exact import canonical_frame, lower_child, fourier, diag, perm, xgate, Op, identity
+n = 9; FULL = tuple(1 << i for i in range(n))
+def monomial_op(rec):
+    """decode a serialized monomial (matrix rows, quadratic rows, Z4 linear part, translation, phase)"""
+    out = diag(n, tuple(rec['quadratic_rows']), tuple(rec['linear_Z4'])).then(perm(n, tuple(rec['matrix_rows']))).then(xgate(n, rec['offset']))
+    return out.then(Op(n, identity(n), [('phase', rec['phase'])]))
+def S_of(U):
+    return canonical_frame(n, tuple(U)).adjoint().then(canonical_frame(n, FULL))
+def wrapped_ok(U, rec):
+    """exactly: L^-1 S R^-1 = C_[w] x I  (apply order: R^-1, S, L^-1)"""
+    w = n - len(U); S = S_of(U); Rm = monomial_op(rec['right']); Lm = monomial_op(rec['left'])
+    net = Rm.adjoint().then(S).then(Lm.adjoint()); target = fourier(n, range(w))
+    return rec['rank'] == w and net.tab == target.tab and net.zero_state() == target.zero_state()
+def main():
+    c = json.load(gzip.open(sys.argv[1])); frames = c['frames']; v = c['v']
+    starts = sorted({c['start'][r] for r in range(2 * v, len(c['start'])) if c['start'][r] != 0})
+    recipes = {}
+    for f in starts:
+        U = frames[f]; rec, compiled = lower_child(S_of(U))
+        recipes[str(f)] = dict(frame=f, vectors=list(U), entrance_rank=len(U), rank=rec['rank'], left=rec['left'], right=rec['right'])
+    Path(sys.argv[2]).write_text(json.dumps(dict(status='RESIDUAL_ADAPTER_RECIPES', recipes=recipes), sort_keys=True, separators=(',', ':')) + '\n')
+    # ---- independent decode of the serialized file
+    data = json.loads(Path(sys.argv[2]).read_text())['recipes']
+    dot = lambda a, b: bin(a & b).count('1') & 1
+    detail = []
+    for f in starts:
+        rec = data[str(f)]; U = frames[f]
+        assert wrapped_ok(U, rec), ('wrapper product is not C_[w] x I', f)
+        detail.append(dict(frame=f, entrance_rank=len(U), residual_width=n - len(U), vectors=list(U), all_even_weight=all(bin(x).count('1') % 2 == 0 for x in U),
+                           totally_isotropic=all(dot(a, b) == 0 for a in U for b in U)))
+    controls = []
+    def reject(name, fn):
+        f = starts[0]; rec = copy.deepcopy(data[str(f)]); fn(rec)
+        if wrapped_ok(frames[f], rec): raise AssertionError('mutated wrapper accepted: ' + name)
+        controls.append(name)
+    reject('wrong global phase', lambda r: r['right'].__setitem__('phase', (r['right']['phase'] + 1) % 4))
+    reject('wrong translation', lambda r: r['left'].__setitem__('offset', r['left']['offset'] ^ 1))
+    reject('wrong quadratic form', lambda r: r['right'].__setitem__('quadratic_rows', [x ^ 2 if i == 0 else x for i, x in enumerate(r['right']['quadratic_rows'])]) if False else r['right']['linear_Z4'].__setitem__(0, (r['right']['linear_Z4'][0] + 2) % 4))
+    reject('sides swapped', lambda r: (r.__setitem__('left', r['right']), r.__setitem__('right', r['left'])))
+    reject('wrong width', lambda r: r.__setitem__('rank', r['rank'] + 1))
+    res = dict(status='PASS_RESIDUAL_WRAPPERS_ARE_EXACT', frames=len(detail), wrappers_reject=controls, all_even_weight=all(d['all_even_weight'] for d in detail),
+               all_totally_isotropic=all(d['totally_isotropic'] for d in detail), detail=detail)
+    Path(sys.argv[3]).write_text(json.dumps(res, indent=1) + '\n')
+    print('Lemma A (exact): L^-1 S_E R^-1 = C_[w] x I for', len(detail), 'entrance frames, global phase included;', len(controls), 'wrapper mutations rejected; all-even-weight:', res['all_even_weight'])
+if __name__ == '__main__': main()
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/audit_gk.py b/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/audit_gk.py
new file mode 100644
index 0000000000..e80ca6b8b3
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/audit_gk.py
@@ -0,0 +1,189 @@
+# GK: modified copy of PR #433's complex_audit.py (icekylinx with Codex; PR #425) by DreamingOfClouds with Claude Opus 5.5
+# (Anthropic), via Claude Code.  Every change is marked "GK:"; with a word that has no start_extra / target_levels the
+# behaviour and the written files are PR #433's.
+# Modified from PR425 by icekylinx with Codex assistance.
+"""Read-back audit, independent of the Hamming producer and its row state."""
+import copy,gzip,hashlib,importlib.util,json,math,time
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+OUT=Path('split-centres');p=OUT/'FULL-WORD.json.gz'
+word=json.load(gzip.open(p));v=120;n=240+word['report']['R'];start=time.monotonic()
+def apply(e,rows):
+    if e[0]=='scale':
+        _,t,a,b,*_=e;q=Q(a,b);assert q
+        rows[t]={j:q*x for j,x in rows[t].items()}
+    else:
+        _,t,s,a,b,*_=e;q=Q(a,b);assert t!=s
+        for j,x in list(rows[s].items()):
+            z=rows[t].get(j,Q(0))+q*x
+            if z:rows[t][j]=z
+            else:rows[t].pop(j,None)
+def ident():return [{r:Q(1)} for r in range(n)]
+def inv(e):
+    e=copy.deepcopy(e)
+    if e[0]=='add':e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    return e
+def dual(e):
+    e=inv(e)
+    if e[0]=='add':e[1],e[2]=e[2],e[1]
+    return e
+
+main=word['A']+word['cut']+word['B']
+assert all(not 120<=e[2]<240 for e in word['A']+word['B'] if e[0]=='add' and not 120<=e[1]<240)
+matrix=ident()
+for e in main:apply(e,matrix)
+print('full main columns',n,'replayed',flush=True)
+# Compute -A_Y^-1 B_S using only rows of the explicit main operator.
+dirty=[{} for r in range(n)]
+for r in range(v,2*v):dirty[r]={j:x for j,x in matrix[r].items() if j>=2*v}
+for e in word['precondition']:apply(e,dirty)
+comp=[]
+for r in range(v,2*v):
+    for j,q in sorted(dirty[r].items()):comp.append(['add',r,j,-q.numerator,q.denominator,[]])
+
+cleanup=[inv(e) for e in reversed(word['A']+word['B']) if not v<=e[1]<2*v]
+assert [e[:-1] for e in cleanup]==[e[:-1] for e in word['cleanup']]
+program=word['precondition']+comp+main+cleanup
+actual=ident()
+for e in program:apply(e,actual)
+expected=ident()
+for t in range(v):expected[v+t][t]=Q(1)
+assert actual==expected
+print('PASS exact arbitrary dirt and restored sources/helpers',flush=True)
+back=ident()
+for e in program:apply(dual(e),back)
+expected_back=ident()
+for t in range(v):expected_back[t][v+t]=Q(-1)
+assert back==expected_back
+print('PASS exact inverse-transpose on every column',flush=True)
+# Independent sparse vector controls avoid repeating a dense full replay.
+def vector(es,x):
+    x=list(map(Q,x))
+    for e in es:
+        if e[0]=='scale':x[e[1]]*=Q(e[2],e[3])
+        else:x[e[1]]+=Q(e[3],e[4])*x[e[2]]
+    return x
+sample=[((i*137+13)%101)-50 for i in range(n)]
+want=vector(program,sample)
+controls={
+    'missing_dirty_compensation':word['precondition']+main+cleanup,
+    'missing_Y_inverse_basis':comp+main+cleanup,
+    'missing_source_cleanup':word['precondition']+comp+main,
+    'wrong_dual_event_order':[dual(e) for e in reversed(program)],
+}
+for name,es in controls.items():
+    expected_sample=vector([dual(e) for e in program],sample) if name=='wrong_dual_event_order' else want
+    assert vector(es,sample)!=expected_sample,name
+
+# Orthogonal transvection and a port permutation bring the new geometry onto
+# the already fixed 120-port routing family. Every incidence is transformed.
+old=json.load(gzip.open('work/higher-stage-e8/verified/gcert1-e8-retimed.json.gz'))
+def tau(x):return x^(43 if (x&43).bit_count()%2 else 0)
+assert 43 .bit_count()%2==0
+assert set(map(tau,word['ports']))==set(old['ports'])
+mapping={i:old['ports'].index(tau(q)) for i,q in enumerate(word['ports'])}
+mapping.update({v+i:v+mapping[i] for i in range(v)})
+mapping.update({r:r for r in range(2*v,n)})
+def basis(vs):
+    b={}
+    for x in vs:
+        for k in sorted(b,reverse=True):
+            if x>>k&1:x^=b[k]
+        if x:
+            k=x.bit_length()-1
+            for j in b:
+                if b[j]>>k&1:b[j]^=x
+            b[k]=x
+    return tuple(b[k] for k in sorted(b,reverse=True))
+def perp(x):return basis([z for z in range(1,512) if not (x&z).bit_count()%2])
+full=tuple(1<<i for i in range(8,-1,-1));frames=[(),full];fi={f:i for i,f in enumerate(frames)}
+def fid(f):
+    f=basis(f)
+    if f not in fi:fi[f]=len(frames);frames.append(f)
+    return fi[f]
+def canonical(e):
+    e=copy.deepcopy(e);e[1]=mapping[e[1]]
+    if e[0]=='add':e[2]=mapping[e[2]]
+    if e[-1] is not None:e[-1]=fid([tau(x) for x in e[-1]])
+    return e
+can={key:[canonical(e) for e in word[key]] for key in ('A','B','cut','cleanup','precondition')}
+can['compensation']=[canonical(e) for e in comp]
+can['start']=[fid([q]) for q in old['ports']]+[0]*(v+word['report']['R'])
+for _r,_E in word.get('start_extra',{}).items():
+    assert 2*v<=int(_r)<2*v+word['report']['R'],('an entrance (residual wrapper, spectators, bank footprint) is defined for helper registers only',_r)   # GK
+    can['start'][int(_r)]=fid([tau(x) for x in _E])   # GK: helper entrances
+can['final']=[1]*v+[fid(perp(q)) for q in old['ports']]+[1]*word['report']['R']
+can['ports']=old['ports'];can['centers']=[mapping[r] for r in word['centers']]
+can['center_frames']=[fid([tau(x) for x in f]) for f in word['center_frames']]
+tlev={}   # GK: nonzero-frame compensation raises targets before the centre scatter
+for _t,_E in word.get('target_levels',{}).items():tlev[mapping[v+int(_t)]-v]=fid([tau(x) for x in _E])
+if tlev:can['target_levels']=tlev
+can['h']=9;can['v']=v;can['R']=word['report']['R'];can['frames']=frames
+cur=list(can['start']);paid=Counter();edges=set();incidences=0
+def climb(r,f):
+    old=cur[r]
+    assert basis(frames[old]+frames[f])==frames[f]
+    if old!=f:
+        delta=len(frames[f])-len(frames[old]);assert delta>0
+        edges.add((old,f));paid[delta]+=1;cur[r]=f
+for part in ('A','B'):
+    if part=='B':
+        assert all(cur[r]==f for r,f in zip(can['centers'],can['center_frames']))
+        assert all(cur[r]==tlev.get(r-v,0) for r in range(v,2*v))   # GK: targets sit at their level
+        for r_c,f in zip(can['centers'],can['center_frames']):
+            # GK: a centre copy descends cf -> served levels (descending chain) -> lowest served level; at the defaults the
+            # only served level is 0 and this is PR #433's single child of rank |cf|
+            served={tlev.get(e[1]-v,0) for e in can['cut'] if e[2]==r_c}
+            o=f
+            for Lv in sorted(served,key=lambda x:-len(frames[x])):
+                assert basis(frames[Lv]+frames[o])==tuple(frames[o]),('centre level outside the previous frame',r_c)
+                if Lv!=o:
+                    paid[len(frames[o])-len(frames[Lv])]+=1
+                    if not(o==f and Lv==0):edges.add((o,Lv));edges.add((Lv,o))   # (cf,0),(0,cf) are added by the phase script
+                    o=Lv
+    for e in can[part]:
+        rs=[e[1]]+([e[2]] if e[0]=='add' else [])
+        for r in rs:climb(r,e[-1]);incidences+=1
+for r,f in enumerate(can['final']):climb(r,f)
+assert dict(paid)=={int(r):x for r,x in word['report']['local_profile'].items()}
+# GK: entrances lower the helper climb by their rank; centre descents may stop above frame zero
+if not word.get('start_extra') and not word.get('target_levels'):assert sum(r*x for r,x in paid.items())==9*can['R']+240*8+72
+else:assert sum(r*x for r,x in paid.items())==sum(int(r)*x for r,x in word['report']['local_profile'].items())
+can['local_profile']=dict(sorted(paid.items()));can['edges']=sorted(edges)
+cp=OUT/'CANONICAL-WORD.json.gz';cp.write_bytes(gzip.compress(json.dumps(can,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+
+def engine(name):
+    p=Path('work/pr361/code/engines')/(name+'.py');s=importlib.util.spec_from_file_location('hamming_'+name,p)
+    m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m
+M,M2=engine('moment'),engine('base_two_moment');m,W=73,word['report'].get('live',12720)   # GK: unhosted stock of the word
+HG={int(r):z for r,z in word['report']['global_profile'].items()}
+root=M.certify(HG,m,W,True);b=Q(int(Q(root['lower'])*10**18),10**18);grid=Q(1,10**18)
+assert M.moment(HG,m,W,b,True)[1]<1<M.moment(HG,m,W,b+grid,True)[0]
+fallback=32*m*m*sum(HG.values())
+def second(a):
+    lo,hi=M2.moment(m,W,list(HG.items()),a)
+    l2,h2=M2.moment(m,W,[(1,fallback)],a)
+    return lo+l2/10**16,hi+h2/10**16
+assert second(b)[1]<1<second(b+grid)[0]
+coeff=Counter(str(Q(e[3],e[4]) if e[0]=='add' else Q(e[2],e[3])) for e in program)
+report={'status':'PASS_EXACT_SCALAR_AND_FRAME_RESEARCH_CANDIDATE_NOT_YET_ADMITTED',
+        'full_word_sha256':hashlib.sha256(p.read_bytes()).hexdigest(),
+        'canonical_word_sha256':hashlib.sha256(cp.read_bytes()).hexdigest(),
+        'live_columns_each_orientation':n,'arbitrary_helper_columns':can['R'],
+        'all_live_source_and_helper_rows_restored':True,'all_target_rows_correct':True,
+        'negative_controls_rejected':list(controls),'old_response_additions':len(comp),
+        'complete_forward_scalar_operations':len(program),'coefficient_histogram':dict(coeff),
+        'frames':len(frames),'nested_directed_edges':len(edges),'common_frame_incidences':incidences,
+        'orthogonal_transport_vector':43,'transported_ports_exactly_match_fixed_routes':True,
+        'local_profile':dict(sorted(paid.items())),
+        'prospective_complex_b':str(b),'prospective_b_float':float(b),
+        'prospective_gain_percent':float(100*(b/Q(999388595603943,10**18)-1)),
+        'two_rational_moment_engines':True,'next_b_grid_rejected':True,
+        'remaining':['new general scalar-interface proof integration','exact phase and emitted local/global program','finite invoice and outer assembly'],
+        'scope':'Substantial new scalar-network candidate. All parameter values remain prospective until the expanded scalar interface and complete phase-aware supplier are admitted.',
+        'seconds':time.monotonic()-start}
+(OUT/'SCALAR-FRAME-AUDIT.json').write_text(json.dumps(report,indent=2)+'\n')
+print('PASS prospective b',float(b),'gain',report['prospective_gain_percent'],'percent; seconds',report['seconds'],flush=True)
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/emit_gk.py b/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/emit_gk.py
new file mode 100644
index 0000000000..0dd1853bb5
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/emit_gk.py
@@ -0,0 +1,156 @@
+# GK: modified copy of PR #433's complex_emit.py (icekylinx with Codex assistance; PR #425) by DreamingOfClouds with Claude Opus 5.5
+# (Anthropic), via Claude Code.  Every change is marked "GK:".  On a word without start_extra / target_levels the behaviour
+# and every written file equal PR #433's (regression anchor in verify.py).
+import sys as _sys, os as _os; _sys.path.insert(0, _os.path.dirname(_os.path.abspath(__file__)))
+# Adapted from PR425 by icekylinx with Codex assistance.
+"""Emit both local programs, integrate the fixed nine-stage geometry, and bill.
+
+The expanded scalar interface is justified in PROOF.txt. This script does not
+claim a Lean proof or discharge the inherited all-size/analytic interfaces.
+"""
+import copy,gzip,hashlib,importlib.util,json,math
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+OUT=Path('split-centres');cp=OUT/'CANONICAL-WORD.json.gz'
+c=json.load(gzip.open(cp))
+frames=c['frames'];v,R,h=c['v'],c['R'],c['h'];n=2*v+R
+def digest(x):return hashlib.sha256(json.dumps(x,sort_keys=True,separators=(',',':')).encode()).hexdigest()
+def basis(vs):
+    b={}
+    for x in vs:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+def dual(e):
+    e=list(e)
+    if e[0]=='add':e[1],e[2]=e[2],e[1];e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    return e
+def scalar(e,back):
+    e=dual(e) if back else list(e)
+    if e[0]=='add':return ['add',['L',e[1]],['L',e[2]],e[3],e[4]]
+    return ['scale',['L',e[1]],e[2],e[3]]
+def primitive_bound(e):
+    if e[0] in ('clear','copy'):return 1
+    q=Q(e[3],e[4]) if e[0]=='add' else Q(e[2],e[3])
+    a,b=abs(q.numerator),q.denominator
+    assert b&(b-1)==0
+    if e[0]=='scale':
+        assert a&(a-1)==0
+        return abs(a.bit_length()-b.bit_length())+int(q<0)
+    # Exact binary Horner multiplication on a cleared private stream, repeated
+    # halving, signed accumulation into the target, then clear the private stream.
+    return 3+(a.bit_length()-1)+a.bit_count()+(b.bit_length()-1)
+
+def emit(back):
+    out=[];cur=c['start'].copy()
+    def event(e):out.append(e)
+    def scal(e,f):event(['scalar',e,f])
+    event(['phase','zero_frame_precondition'])
+    for e in c['precondition']+c['compensation']:
+        regs=[e[1]]+([e[2]] if e[0]=='add' else [])
+        assert all(c['start'][r]==0 for r in regs)
+        scal(scalar(e,back),0)
+    event(['phase','entry_adapters'])
+    # GK: a helper that starts at a nonzero entrance frame has NO entry adapter; its paid wrapper R_E^-1 (Lemma A) precedes every gate
+    # that touches it and L_E^-1 follows the full-frame cleanup.  Words without entrances emit PR #433's events.
+    entering=[r for r,f in enumerate(c['start']) if r>=2*v and f!=0]
+    for r,f in enumerate(c['start']):
+        if r in entering:event(['residual_adapter','pre',r,f])
+        else:event(['adapter','old_to_new',r,f])
+    def climb(r,f,part):
+        old=cur[r]
+        if old==f:return
+        assert basis(frames[old]+frames[f])==tuple(frames[f])
+        rank=len(frames[f])-len(frames[old]);assert rank>0
+        event(['climb',part,r,old,f,rank]);cur[r]=f
+    for part in ('A','centers','B','final'):
+        event(['phase',part])
+        if part in ('A','B'):
+            for e in c[part]:
+                regs=[e[1]]+([e[2]] if e[0]=='add' else [])
+                for r in regs:climb(r,e[-1],part)
+                scal(scalar(e,back),e[-1])
+        elif part=='centers':
+            # GK: targets sit at their nonzero-frame-compensation level (0 at the defaults); a centre copy descends
+            # cf -> served levels (descending chain) -> lowest served level and scatters into each target at its level
+            lv=lambda r:c.get('target_levels',{}).get(str(r-v),0)
+            assert all(cur[r]==lv(r) for r in range(v,2*v))
+            for k,r in enumerate(c['centers']):
+                cf=c['center_frames'][k];assert cur[r]==cf
+                terms=[e for e in c['cut'] if e[2]==r]
+                path=[cf]+sorted({lv(e[1]) for e in terms}-{cf},key=lambda x:-len(frames[x]))
+                C=['C',k]
+                if not back:
+                    scal(['clear',C],cf);scal(['copy',C,['L',r]],cf)
+                    for a in range(len(path)):
+                        if a>0:event(['center',k,path[a-1],path[a],len(frames[path[a-1]])-len(frames[path[a]])])
+                        for e in terms:
+                            if lv(e[1])==path[a]:scal(['add',['L',e[1]],C,e[3],e[4]],path[a])
+                    scal(['clear',C],path[-1])
+                else:
+                    scal(['clear',C],path[-1])
+                    for a in range(len(path)-1,-1,-1):
+                        for e in terms:
+                            if lv(e[1])==path[a]:scal(['add',C,['L',e[1]],e[3],e[4]],path[a])
+                        if a>0:event(['center',k,path[a],path[a-1],len(frames[path[a-1]])-len(frames[path[a]])])
+                    scal(['add',['L',r],C,-1,1],cf);scal(['clear',C],cf)
+        else:
+            for r,f in enumerate(c['final']):climb(r,f,part)
+    event(['phase','exit_adapters'])
+    for r,f in enumerate(c['final']):event(['adapter','new_to_old',r,f])
+    event(['phase','full_frame_cleanup'])
+    for e in c['cleanup']:
+        regs=[e[1]]+([e[2]] if e[0]=='add' else [])
+        assert all(c['final'][r]==1 for r in regs)
+        scal(scalar(e,back),1)
+    for r in entering:event(['residual_adapter','post',r,c['start'][r]])   # GK: L_E^-1 after the full-frame cleanup
+    event(['phase','done'])
+    return out
+
+def check_local(events,back):
+    # Literal scalar replay of the emitted stream, including center lifetimes.
+    state={('L',r):{r:Q(1)} for r in range(n)};live=[];paid=Counter();prims=0;macros=0
+    for e in events:
+        if e[0]=='climb':assert not live;paid[e[5]]+=1
+        elif e[0]=='center':assert live==[e[1]];paid[e[4]]+=1
+        elif e[0]=='scalar':
+            op=e[1];tag=op[0];t=tuple(op[1]);macros+=1;prims+=2*primitive_bound(op)
+            if tag=='clear':
+                state[t]={}
+                if t[0]=='C' and t[1] in live:live.remove(t[1])
+            elif tag=='copy':state[t]=dict(state.get(tuple(op[2]),{}));live.append(t[1])
+            elif tag=='scale':state[t]={j:Q(op[2],op[3])*x for j,x in state[t].items()}
+            else:
+                s=tuple(op[2]);q=Q(op[3],op[4]);row=state.setdefault(t,{})
+                if t[0]=='C' and t[1] not in live:live.append(t[1])
+                for j,x in list(state.get(s,{}).items()):
+                    z=row.get(j,Q(0))+q*x
+                    if z:row[j]=z
+                    else:row.pop(j,None)
+    assert not live and all(not row for r,row in state.items() if r[0]=='C')
+    for r in range(n):
+        expected={r:Q(1)}
+        if back and r<v:expected[v+r]=Q(-1)
+        elif not back and v<=r<2*v:expected[r-v]=Q(1)
+        assert state['L',r]==expected,('emitted column mismatch',back,r)
+    assert dict(paid)=={int(r):z for r,z in c['local_profile'].items()}
+    return {'sha256':digest(events),'events':len(events),'scalar_macros':macros,
+            'real_component_primitive_bound':prims,'paid_profile':dict(sorted(paid.items())),
+            'all_columns':n,'private_centers_cleared':True,'private_coefficient_stream_cleared_after_each_macro':True}
+
+programs={};checks={}
+for name,back in [('forward',False),('backward',True)]:
+    programs[name]=emit(back);checks[name]=check_local(programs[name],back)
+    print('PASS emitted',name,checks[name]['events'],'events',flush=True)
+
+
+(OUT/'LOCAL-PROGRAMS.json.gz').write_bytes(gzip.compress(json.dumps(programs,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+(OUT/'LOCAL-CHECKS.json').write_text(json.dumps(checks,indent=2)+'\n')
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/gk_common.py b/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/gk_common.py
new file mode 100644
index 0000000000..0e5fde920d
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/gk_common.py
@@ -0,0 +1,94 @@
+"""Shared helpers for the complex shared-donor-kernel / entrance-gauge word.  Apache-2.0.
+Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.
+
+A "gk word" is PR #433's FULL-WORD.json.gz with optional extension keys (absent in #433's word, so every default is
+#433's behaviour):
+  start_extra   {register: entrance frame (list of F2^9 vectors)}  helpers that start at a nonzero frame (width 9 - dim)
+  target_levels {target: frame}                                    frame a target reaches through nonzero-frame compensation
+Entrance gauges are ordinary gates at the head of A (target += c * helper at the entrance frame); kernel updates are
+ordinary gates at the head of A (donor += q * pivot at the entrance frame).
+"""
+import math
+from collections import Counter
+
+V, K, T, L, M = 120, 4, 8, 9, 73
+DATA = 2 * K * V * T          # 7680
+FULL = tuple(1 << i for i in range(8, -1, -1))
+
+
+def basis(vs):
+    b = {}
+    for x in vs:
+        for p in sorted(b, reverse=True):
+            if x >> p & 1: x ^= b[p]
+        if x:
+            p = x.bit_length() - 1
+            for q in b:
+                if b[q] >> p & 1: b[q] ^= x
+            b[p] = x
+    return tuple(b[p] for p in sorted(b, reverse=True))
+
+
+def widths_of(word):
+    """residual width of every helper: 9 - dim(entrance frame); 9 when the word has no extension"""
+    R = word['report']['R'] if 'R' not in word else word['R']
+    w = [L] * R
+    for r, E in word.get('start_extra', {}).items():
+        assert 2 * V <= int(r) < 2 * V + R
+        w[int(r) - 2 * V] = L - len(basis(E))
+    return w
+
+
+def split_pad(p):
+    """a pad of rank p is paid as nested commuting children of rank <= 51 (so that 73^2 > 2*child^2); rank 1 stays 1"""
+    if p == 0: return []
+    n = -(-p // 51); return [p // n + (1 if i < p % n else 0) for i in range(n)]
+
+
+def tile(items):
+    """Bank tiling of unhosted residuals.  items: list of (rep, helper, width); a bank has M = 73 cells.
+    * width-9 residuals (no wrapper acts on them): first fit in the given order, packed from offset 0, eight per bank, pad rank 1
+      (PR #433/#442's tiling and routes [2, slot]);
+    * ENTERING residuals (width w < 9, paid wrappers, e = 9 - w spectators): banks of their own in which every entering helper is the ONLY
+      owner of its bank family in its invocation (the one-helper rule of PR #458 extended to banks): bank j holds the j-th entering
+      helper of each replica, residuals packed from offset 0 in replica order (at most one helper per replica, hence per invocation).
+      The spectators of an entering helper are the first e cells of the bank beyond every residual cell of the bank (the pad, which no call
+      uses for a residual, is paid as before: rank 73 - sum of widths; the spectators are borrowed inside it and not deducted).
+    Returns (assign, banks, pads): assign[(rep, helper)] = (bank, offset, width, pure, spectators) with pure = the bank holds only width-9
+    residuals and spectators = () for width 9; pads = Counter of pad ranks (split into children of rank <= 51)."""
+    assign = {}; pads = Counter(); fill = []
+    for z, (rep, h, w) in enumerate(items):             # width 9: first fit, as PR #433 (all widths 9 reproduces it exactly)
+        if w != L: continue
+        for b, f in enumerate(fill):
+            if f + w <= M: break
+        else:
+            b = len(fill); fill.append(0)
+        assign[(rep, h)] = (b, fill[b], w, True, ()); fill[b] += w
+    nwide = len(fill); byrep = {}
+    for rep, h, w in items:
+        if w < L: byrep.setdefault(rep, []).append((h, w))
+    cells = [0] * max((len(v) for v in byrep.values()), default=0); emax = [0] * len(cells); place = {}
+    for rep in sorted(byrep):                           # the j-th entering helper of every replica goes to entering bank j
+        for j, (h, w) in enumerate(byrep[rep]):
+            place[(rep, h)] = (nwide + j, cells[j], w); cells[j] += w; emax[j] = max(emax[j], L - w)
+    for j in range(len(cells)): assert cells[j] + emax[j] <= M, ('entering bank without room for its spectators', j)
+    for (rep, h), (b, off, w) in place.items():
+        assign[(rep, h)] = (b, off, w, False, tuple(range(cells[b - nwide], cells[b - nwide] + L - w)))
+    fill += cells
+    for f in fill:
+        for part in split_pad(M - f): pads[part] += 1
+    return assign, len(fill), pads
+
+
+def route(off, w, pure, sp=()):
+    """owner route of a banked helper residual: PR #433's [2, slot] for width 9 (pure width-9 bank); an entering helper (w < 9) is
+    [2, offset, width, [spectator cells]] with e = 9 - w spectators"""
+    if w == L: assert pure and not sp; return [2, off // L]
+    assert not pure and len(sp) == L - w; return [2, off, w, list(sp)]
+
+
+def unhosted_stock(widths):
+    """live stock and padding histogram of the unhosted (parent) template, per stage x nine"""
+    R = len(widths)
+    _, nb, pads = tile([(rep, h, widths[h]) for rep in range(T) for h in range(R)])
+    return DATA + L * nb, Counter({r: z * L for r, z in pads.items()})
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/gk_word.py b/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/gk_word.py
new file mode 100644
index 0000000000..15782ba625
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/gk_word.py
@@ -0,0 +1,194 @@
+"""Apply a frozen selection (shared-donor kernel + entrance gauges) to PR #433's complex word.  Apache-2.0.
+Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.
+usage: gk_word.py BASE_FULL-WORD.json.gz SELECTION.json OUT_FULL-WORD.json.gz
+An empty selection ({}) copies the input byte for byte (regression anchor).
+
+selection = {"kernel": [{"E": [x], "donors": [h..], "pivots": [h..]}..], "gauge": {"h": [x..]}}   (h = helper index 0..R-1)
+Kernel (PR #417/#435/#434/#440): a pivot starts at E; every donor receives  donor += -q * pivot  at frame E before the main
+word, where col(pivot) = sum q_d col(d) are the exact dirty-response columns; the pivot's frame-zero compensation vanishes.
+Gauge (#401/#408-#416): the compensation  target += -C[t,h] * helper  of helper h is executed at frame E_h as the first gates
+of the main word; h starts at E_h and its targets climb to the level L_t = largest E over their entering helpers.
+The exact verification is the arbitrary-dirt replay of audit_gk.py; this module also checks the structural conditions."""
+import copy, gzip, hashlib, json, sys
+from collections import Counter, defaultdict
+from fractions import Fraction as Q
+from pathlib import Path
+sys.path.insert(0, str(Path(__file__).resolve().parent))
+from gk_common import *
+
+
+def apply_op(e, rows):
+    if e[0] == 'scale':
+        _, t, a, b, *_ = e; q = Q(a, b); rows[t] = {j: q * x for j, x in rows[t].items()}
+    else:
+        _, t, s, a, b, *_ = e; q = Q(a, b)
+        for j, x in list(rows[s].items()):
+            z = rows[t].get(j, Q(0)) + q * x
+            if z: rows[t][j] = z
+            else: rows[t].pop(j, None)
+
+
+def inverse(e, F):
+    e = copy.deepcopy(e)
+    if e[0] == 'add': e[3] *= -1
+    else: e[2], e[3] = e[3], e[2]
+    e[-1] = list(F); return e
+
+
+def responses(word):
+    """dirty-response columns col[h] = {target: coefficient} of the unmodified word (after the frame-zero preconditioner)"""
+    R = word['report']['R']; n = 2 * V + R
+    rows = [{r: Q(1)} for r in range(n)]
+    for e in word['A'] + word['cut'] + word['B']: apply_op(e, rows)
+    dirty = [{} for _ in range(n)]
+    for r in range(V, 2 * V): dirty[r] = {j: x for j, x in rows[r].items() if j >= 2 * V}
+    for e in word['precondition']: apply_op(e, dirty)
+    col = [{} for _ in range(R)]
+    for r in range(V, 2 * V):
+        for j, x in dirty[r].items(): col[j - 2 * V][r - V] = x
+    return col
+
+
+def first_frames(word):
+    first = {}
+    for seq in (word['A'], word['B']):
+        for e in seq:
+            F = basis(e[-1])
+            for r in [e[1]] + ([e[2]] if e[0] == 'add' else []):
+                if r >= 2 * V: first.setdefault(r - 2 * V, F)
+    return first
+
+
+def solve_relation(col, donors, p):
+    """exact rational c with col[p] = sum_d c_d col[d]; None if p is not in the span"""
+    ts = sorted({t for d in donors for t in col[d]} | set(col[p]))
+    idx = {t: i for i, t in enumerate(ts)}
+    Mx = [[Q(0)] * (len(donors) + 1) for _ in ts]
+    for ci, d in enumerate(donors):
+        for t, x in col[d].items(): Mx[idx[t]][ci] = x
+    for t, x in col[p].items(): Mx[idx[t]][-1] = x
+    piv = []; r = 0
+    for c in range(len(donors)):
+        pr = next((i for i in range(r, len(Mx)) if Mx[i][c]), None)
+        if pr is None: continue
+        Mx[r], Mx[pr] = Mx[pr], Mx[r]; q = Mx[r][c]; Mx[r] = [x / q for x in Mx[r]]
+        for i in range(len(Mx)):
+            if i != r and Mx[i][c]:
+                f = Mx[i][c]; Mx[i] = [a - f * b for a, b in zip(Mx[i], Mx[r])]
+        piv.append(c); r += 1
+    if any(Mx[i][-1] for i in range(r, len(Mx))): return None
+    assert r == len(donors), 'donors must have independent response columns'
+    return {donors[c]: Mx[i][-1] for i, c in enumerate(piv) if Mx[i][-1]}
+
+
+def span(U):
+    s = {0}
+    for b in U: s |= {x ^ b for x in s}
+    return s
+
+
+def perp(x): return basis([z for z in range(1, 512) if not (x & z).bit_count() % 2])
+
+
+def profile(word):
+    """local paid profile of a gk word by direct simulation of the frame chains (second implementation: audit_gk.py)"""
+    R = word['report']['R']; n = 2 * V + R; P = word['ports']
+    cur = {}
+    for r in range(n):
+        cur[r] = (P[r],) if r < V else ((basis(word['start_extra'][str(r)]) if str(r) in word.get('start_extra', {}) else ()) if r >= 2 * V else ())
+    paid = Counter()
+    def climb(r, F):
+        F = basis(F); o = cur[r]
+        assert basis(list(o) + list(F)) == F, ('frame violation', r, o, F)
+        if o != F: paid[len(F) - len(o)] += 1; cur[r] = F
+    lev = {int(t): basis(E) for t, E in word.get('target_levels', {}).items()}
+    for seq, part in ((word['A'], 'A'), (word['B'], 'B')):
+        if part == 'B':
+            for r, f in zip(word['centers'], word['center_frames']):
+                assert cur[r] == basis(f), 'centre frame'
+                served = sorted({lev.get(e[1] - V, ()) for e in word['cut'] if e[2] == r}, key=lambda E: -len(E))
+                o = basis(f)
+                for Lv in served:
+                    assert span(Lv) <= span(o), 'served levels must descend inside the centre frame'
+                    if Lv != o: paid[len(o) - len(Lv)] += 1; o = Lv
+            for t in range(V): assert cur[V + t] == lev.get(t, ()), 'target level at the centre scatter'
+        for e in seq:
+            for r in [e[1]] + ([e[2]] if e[0] == 'add' else []): climb(r, e[-1])
+    for r in range(n): climb(r, FULL if (r < V or r >= 2 * V) else perp(P[r - V]))
+    return paid
+
+
+def global_profile(local, widths):
+    """unhosted nine-stage profile: local x (stages*replicas) + the 240*8 idle children per rank + bank pads"""
+    live, pads = unhosted_stock(widths)
+    g = Counter({r: z * L * T for r, z in local.items()})
+    for r in (16, 8, 32, 8, 48, 8, 48, 32, 16): g[r] += 240 * T
+    g.update(pads)
+    return live, g
+
+
+def build(word, sel, check=True):    # check=False only for the mutation controls that must be caught by the certifying scripts
+    if not sel: return word
+    w = copy.deepcopy(word); R = w['report']['R']
+    col = responses(word); first = first_frames(word)
+    gauge = {int(h): basis(E) for h, E in sel.get('gauge', {}).items()}
+    classes = sel.get('kernel', [])
+    pivots = {p for c in classes for p in c['pivots']}; donors = {d for c in classes for d in c['donors']}
+    assert not (pivots & donors) and not (pivots | donors) & set(gauge) and len(pivots) == sum(len(c['pivots']) for c in classes)
+    # --- structural conditions -------------------------------------------------------------------------------------
+    for h, E in gauge.items():
+        assert not check or span(E) <= span(first[h]), ('gauge entrance outside the first frame', h)
+    levels = defaultdict(list)
+    for h, E in gauge.items():
+        for t in col[h]: levels[t].append(E)
+    for t, Es in levels.items():                                   # pairwise nested comps per target
+        for a in Es:
+            for b in Es: assert not check or span(a) <= span(b) or span(b) <= span(a), ('non-nested gauges at target', t)
+    lev = {t: max(Es, key=len) for t, Es in levels.items()}
+    for k, r in enumerate(w['centers']):                              # chain per centre, inside the centre frame
+        served = {lev.get(e[1] - V, ()) for e in w['cut'] if e[2] == r}
+        for a in served:
+            for b in served: assert not check or span(a) <= span(b) or span(b) <= span(a), ('centre chain', k)
+        top = max(served, key=len)
+        assert not check or span(top) <= span(basis(w['center_frames'][k])), ('level outside centre frame', k)
+    # --- gates ----------------------------------------------------------------------------------------------------------
+    gates = []
+    for h, E in sorted(gauge.items(), key=lambda kv: (len(kv[1]), kv[0])):
+        for t, x in sorted(col[h].items()):
+            c = -x; gates.append(['add', V + t, 2 * V + h, c.numerator, c.denominator, list(E)])
+    pre = []
+    start = {2 * V + h: list(E) for h, E in gauge.items()}
+    for cl in sorted(classes, key=lambda c: (len(c['E']), c['E'])):
+        E = basis(cl['E'])
+        for x in [*cl['donors'], *cl['pivots']]: assert span(E) <= span(first[x]), ('kernel entrance outside the first frame', x)
+        for p in cl['pivots']:
+            rel = solve_relation(col, cl['donors'], p)
+            assert rel is not None, ('pivot response not in the donor span', p)
+            start[2 * V + p] = list(E)
+            for d, c in rel.items():
+                q = -c; pre.append(['add', 2 * V + d, 2 * V + p, q.numerator, q.denominator, list(E)])
+    w['A'] = gates + pre + w['A']
+    w['cleanup'] = [inverse(e, FULL) for e in reversed(w['A'] + w['B']) if not V <= e[1] < 2 * V]
+    w['start_extra'] = {str(r): list(E) for r, E in sorted(start.items())}
+    w['target_levels'] = {str(t): list(E) for t, E in sorted(lev.items()) if E}
+    if not check: return w
+    prof = profile(w); widths = widths_of(w)
+    live, g = global_profile(prof, widths)
+    w['report']['local_profile'] = {str(k): z for k, z in sorted(prof.items())}
+    w['report']['global_profile'] = {str(k): z for k, z in sorted(g.items())}
+    w['report']['live'] = live
+    w['report']['entrance_rank'] = sum(L - x for x in widths); w['report']['entering_helpers'] = sum(1 for x in widths if x < L)
+    w['report']['selection_sha256'] = hashlib.sha256(json.dumps(sel, sort_keys=True).encode()).hexdigest()
+    return w
+
+
+def dump(w): return gzip.compress(json.dumps(w, sort_keys=True, separators=(',', ':')).encode(), mtime=0)
+
+
+if __name__ == '__main__':
+    src, selp, out = map(Path, sys.argv[1:4])
+    sel = json.loads(selp.read_text())
+    if not sel: out.write_bytes(src.read_bytes()); print('empty selection: copied byte for byte'); sys.exit(0)
+    word = json.load(gzip.open(src)); w = build(word, sel); out.write_bytes(dump(w))
+    print('gk word: entering helpers', w['report']['entering_helpers'], 'entrance rank', w['report']['entrance_rank'],
+          'local profile', w['report']['local_profile'], 'unhosted live', w['report']['live'])
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/integrate_gk.py b/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/integrate_gk.py
new file mode 100644
index 0000000000..df261063e1
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/integrate_gk.py
@@ -0,0 +1,123 @@
+# GK: modified copy of PR #433's complex_integrate.py (icekylinx with Codex assistance; PR #425) by DreamingOfClouds with Claude Opus 5.5
+# (Anthropic), via Claude Code.  Every change is marked "GK:".  On a word without start_extra / target_levels the behaviour
+# and every written file equal PR #433's (regression anchor in verify.py).
+import sys as _sys, os as _os; _sys.path.insert(0, _os.path.dirname(_os.path.abspath(__file__)))
+# Adapted from PR425 for heterogeneous centres by icekylinx, with Codex assistance.
+import copy,gzip,hashlib,importlib.util,json,math
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+OUT=Path('split-centres');cp=OUT/'CANONICAL-WORD.json.gz'
+c=json.load(gzip.open(cp));audit=json.loads((OUT/'SCALAR-FRAME-AUDIT.json').read_text())
+phase=json.loads((OUT/'CLIFFORD-REVIEW.json').read_text());sha=lambda p:hashlib.sha256(Path(p).read_bytes()).hexdigest()
+assert phase['canonical_word_sha256']==audit['canonical_word_sha256']==sha(cp)
+assert phase['all_child_equalities_include_global_phase']
+programs=json.load(gzip.open(OUT/'LOCAL-PROGRAMS.json.gz'));checks=json.loads((OUT/'LOCAL-CHECKS.json').read_text())
+frames=c['frames'];v,R,h=c['v'],c['R'],c['h'];n=2*v+R;private_centres=len(c['centers'])
+for z in checks.values():z['paid_profile']={int(r):n for r,n in z['paid_profile'].items()}
+old=Path('work/complex-nine-native');template=json.load(gzip.open(old/'GLOBAL-TEMPLATE.json.gz'))
+data_phase=json.loads((old/'DATA-PHASES.json').read_text())
+assert template['exact_data_phase_recipe_sha256']==sha(old/'DATA-PHASES.json')
+assert data_phase['status']=='PASS_EXACT_Z4_DATA_ROUTE_IDLE_AND_TERMINAL_PHASES'
+m,T,L,k=73,8,9,4
+# GK: residual widths 9 - dim(start frame); banks tile per width class (all 9: PR #433's eight residuals + one pad)
+from gk_common import tile,route
+widths=[h-len(frames[c['start'][2*v+i]]) for i in range(R)]
+assign,nb,pads=tile([(rep,i,widths[i]) for rep in range(T) for i in range(R)]);entering0=any(w_<h for w_ in widths)
+W=2*v*k*T+L*nb;physical=W+R+private_centres+2
+template['version']='hamming-mutable-basis-nine-v1';template['live']=W;template['physical']=physical
+template['local_programs']=programs;paid=Counter();assignments=set();event_count=0;scalar_primitives=0
+for call in template['calls']:
+    stage,rep,pair=call['stage'],call['replica'],call['pair'];ori=call['orientation']
+    owners=[[rep*2*k*v+(2*pair+r//v)*v+r%v,[1,stage,r%v]] for r in range(2*v)]
+    for r in range(R):
+        bank,off_,w_,pure_,sp_=assign[rep,r];owners.append([2*v*k*T+stage*nb+bank,route(off_,w_,pure_,sp_)])   # GK: [2,slot] in pure width-9 banks, [2,offset,width,spectators] for entering helpers
+        assignments.add((stage,rep,r,bank,off_))
+    assert len(owners)==n and len({(f,json.dumps(route)) for f,route in owners})==n
+    assert all(f<W for f,route in owners)   # GK: every owner lies in the live stock (none in the private namespace)
+    fam=Counter(f for f,route in owners)   # GK: an entering helper is the only owner of its bank family in the invocation (PR #458's rule, banks included); the data families are the 240 distinct active ones
+    assert all(fam[f]==1 for f,route in owners[:2*v]) and all(fam[owners[2*v+r][0]]==1 for r in range(R) if widths[r]<h),('entering helper shares its bank family',stage,rep)
+    call['owners']=owners;call['local_program_sha256']=checks[ori]['sha256']
+    for r,z in checks[ori]['paid_profile'].items():paid[r]+=z
+    event_count+=checks[ori]['events'];scalar_primitives+=checks[ori]['real_component_primitive_bound']
+assert len(assignments)==L*T*R and len(template['calls'])==72
+for item in template['idle_children']:paid[item['rank']]+=item['replicas']
+for r_,z_ in pads.items():paid[r_]+=z_*L   # GK: bank pads (rank 1 each at width 9 and 8)
+assert dict(paid)=={int(r):z for r,z in json.load(gzip.open(OUT/'FULL-WORD.json.gz'))['report']['global_profile'].items()}
+mass=sum(r*z for r,z in paid.items());assert m*W-mass==2496
+if entering0:template['route_semantics']['helper']+='; entering helpers: paid wrappers R_E^-1 before and L_E^-1 after the invocation; an entering helper is the only owner of its bank family in the invocation, route [2, offset, width, spectator cells] with the spectators the first cells of the bank beyond every residual cell'   # GK
+template['bank_padding']['families']=list(range(7680,W))
+template['cover_final_correction']['families']=[0,W]
+template['cover_final_correction']['charged_calls_per_cover']=W
+for e in template['execution_schedule']:
+    if e['kind']=='bank_padding_cover_sweep':e['families']=[7680,W]
+    elif e['kind']=='translate_every_live_family':e.update(template['cover_final_correction'])
+template['private_namespace']={'centers':[W,W+private_centres],'reserved_tableau':[W+private_centres,W+private_centres+R],
+                               'coefficient':[physical-2,physical]}
+template['exact_local_clifford_recipe_sha256']=sha(OUT/'CLIFFORD-RECIPES.json')
+if (OUT/'RESIDUAL-ADAPTERS.json').exists():template['residual_adapter_sha256']=sha(OUT/'RESIDUAL-ADAPTERS.json')   # GK: paid wrappers of entering helpers (Lemma A)
+template['expanded_scalar_interface']='See PROOF.txt: mutable source basis, frame-zero output preconditioner, explicit dirty compensator, and full-frame inverse source/helper cleanup.'
+blob=json.dumps(template,sort_keys=True,separators=(',',':')).encode()
+(OUT/'GLOBAL-TEMPLATE.json.gz').write_bytes(gzip.compress(blob,mtime=0))
+
+# Fresh finite overcharge, with the changed stock, scalar counts, coefficient
+# lowering, and private work reserve. No unchanged local invoice is assumed.
+compiler=64*(m+1)**3;macros=max(z['scalar_macros'] for z in checks.values());children=sum(checks['forward']['paid_profile'].values())
+adapters=16*(macros+children+n+private_centres)+64*m
+local_bound=max(z['real_component_primitive_bound'] for z in checks.values())+adapters*compiler
+bridges=[e for e in template['recipe'] if e['kind']=='bridge'];bridge_adds=2*v*T*len(bridges)
+terminal_shifts=k*v*T;terminal_moves=2*k*v*T
+entering=sum(1 for w_ in widths if w_<h)   # GK: entrance adapters (Lemma A): a monomial on 9 bits is at most 81+45+9=135 elementary factors (matrix, quadratic form, translation); charge 144 at entry and at exit of every entering helper in every invocation
+nonlocal_items=4*v*T*L+2*v*T*L+2*L*T*R+sum(e['replicas'] for e in template['idle_children'])+L*nb+bridge_adds+terminal_shifts+terminal_moves+W+physical+2*L*T*entering*144
+outside=8*nonlocal_items+64*m
+pervertex=scalar_primitives+bridge_adds+terminal_shifts+terminal_moves+W+(72*adapters+outside)*compiler+64*physical
+r=m//2;group=2**(r*r)*math.prod(2**(2*i)-1 for i in range(1,r+1));stock=group*physical
+smass=group*mass;logical=group*pervertex+64;router=compiler*(logical+1)*(stock+1)**2
+GG,EE,C0=1<<30000,1<<100000,1<<210000;BB=smass+EE
+literal=2*GG*stock**2+8*smass+4*stock+4+32*m
+maxchild=max(paid);depth=2;assert m**depth>2*maxchild**depth
+assert local_bound<1<<48 and logical<1<<6050 and router<GG and literal<EE and BB<1<<100001
+assert 32*m*BB*BB<C0 and 2*BB+18<C0
+row=depth*stock.bit_length()+9909+252;assert row<20161
+
+def load(name):
+    sp=importlib.util.spec_from_file_location('hamming_integrate_'+name,Path('work/pr361/code/engines')/(name+'.py'))
+    mod=importlib.util.module_from_spec(sp);sp.loader.exec_module(mod);return mod
+Outer=load('outer');b=Q(audit['prospective_complex_b']);bit=Q(json.loads(Path('BIT-PRICE.json').read_text())['lower'])
+eta=Q(1,10**12);beta=Q(1,10**9);grid=Q(1,10**18)
+s=Q(int(((1-beta)*min(b,bit)-grid)*10**18),10**18);assert s<bit
+chain=[Q(384599,10**10)];cutoffs=[]
+for _ in range(3):
+    a=chain[-1];z=(1-s)*s+s*a;gap=min(s-z,1-z-s,1-z-s*(1-a),1-s)
+    assert a<z<s<1-z and gap>0
+    bound=max(math.ceil(36/gap**2),math.ceil(2*(4+512)/gap))
+    assert bound*gap**2>=36 and bound*gap>=2*(4+512)
+    cutoffs.append(str(bound));chain.append(z)
+bridge={'semantic':{'C0':{'base':2,'exponent':210000},'strict_literal_gap':1},
+        'rows':{'degree_gap':Q(10**6)-Q(51*20161,25)}}
+q=chain[-1]*(1-2*eta);ticks=(1-eta)*q/(1+q)/grid;kap=Q((ticks.numerator-1)//ticks.denominator,10**18)
+assembly=Outer.assembly(chain[-1],b,bridge,kap,eta=eta,beta=beta)
+try:Outer.assembly(chain[-1],b,bridge,kap+grid,eta=eta,beta=beta)
+except AssertionError:pass
+else:raise AssertionError('next kappa grid accepted')
+result={'status':'PASS_NEW_STRUCTURAL_PROGRAM_AND_FINITE_ASSEMBLY_PENDING_REPLAY',
+        'canonical_word_sha256':sha(cp),'scalar_audit_sha256':sha(OUT/'SCALAR-FRAME-AUDIT.json'),
+        'exact_phase_receipt_sha256':sha(OUT/'CLIFFORD-REVIEW.json'),'global_template_sha256':hashlib.sha256(blob).hexdigest(),
+        'local_program_checks':checks,'R':R,'m':m,'live':W,'physical':physical,
+        'bank_assignments':len(assignments),'rank_mass':mass,'deficit':2496,
+        'global_profile':dict(sorted(paid.items())),'emitted_local_events_all_calls':event_count,
+        'finite_invoice':{'local_primitive_bound':local_bound,'local_adapters':adapters,
+                          'pervertex':pervertex,'physical_stock_bits':stock.bit_length(),
+                          'router_bits':router.bit_length(),'literal_bits':literal.bit_length(),
+                          'physical_row_coefficient':row,'retained_row_coefficient':20161,
+                          'compiler':compiler,'G_exponent':30000,'E_exponent':100000,'C0_exponent':210000,
+                          'required_C0_bits':(32*m*BB*BB).bit_length(),'halving_degree':depth,
+                          'halving_integer_inequality':[m**depth,2*maxchild**depth]},
+        'complex_b':str(b),'bit_c':str(bit),'prospective_kappa':str(kap),'kappa_float':float(kap),
+        'log2_kappa':math.log2(float(kap)),
+        'kappa_gain_percent':float(100*(kap/Q(998390813251625,10**18)-1)),
+        'strict_outer_constraints':{name:str(z) for name,z in assembly['strict_constraints'].items()},
+        'next_kappa_grid_rejected':True,'bootstrap_cutoffs_log2':cutoffs,
+        'scope':'New finite scalar interface with a written conjugation proof, conditional on inherited all-size compiler, precision/tape and analytic transfer. Independent emitted-program replay and fresh package replay still required before final promotion.'}
+(OUT/'INTEGRATION.json').write_text(json.dumps(result,indent=2)+'\n')
+print('PASS prospective kappa',float(kap),'gain',result['kappa_gain_percent'],'percent',flush=True)
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/onehost_gk.py b/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/onehost_gk.py
new file mode 100644
index 0000000000..220cc7a2f5
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/onehost_gk.py
@@ -0,0 +1,111 @@
+"""Whole-residual idle-axis hosting with at most ONE helper per physical family per invocation (the rule of PR #458), plus the exact
+host chart with explicit spectator coordinates.  Apache-2.0.  Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.
+A copy (port) of an idle child hosts a PATTERN: residuals of pairwise distinct stages inside the child's window, offsets 0, w1, w1+w2, ...
+(a residual is whole: one slot in one family).  The children of one (pair, side) have pairwise disjoint windows (checked), so the
+families they share never host two helpers of one invocation, and the integer programme needs only the distinct-stage condition.
+Chart: for the host's port q the parent's idle basis is B_q = U_q (+) I (PR #433 geometry; the construction is that of PR #458).  A hosted
+residual of width w occupies the pending vectors b_off..b_(off+w-1) of its child; the other e = 9 - w coordinates of the local nine are
+SPECTATORS: the first e basis indices of B_q not occupied by the residual, in increasing order.  The paid wrappers (adapters_gk.py) act on
+these nine coordinates and restore the spectators identically."""
+import math
+from collections import Counter
+
+H, M = 9, 73
+
+
+def cost(r, m): return r * math.log(m / r) if r else 0.0
+
+
+def patterns(rank, stages, widths):
+    out = [()]
+    ws = sorted(widths, reverse=True)
+    def rec(i, cur, tot):
+        for j in range(i, len(stages)):
+            for w in ws:
+                if tot + w <= rank:
+                    c = cur + [(stages[j], w)]; out.append(tuple(c)); rec(j + 1, c, tot + w)
+    rec(0, [], 0)
+    return out
+
+
+def solve(win, copies, avail, m, pad_value, time_limit=600):
+    """win {idx: (pair, rank, stages)}, avail {(stage, width): helpers per replica}.  Maximise saved idle cost (+ pad_value per hosted residual)."""
+    import numpy as np
+    from scipy.optimize import milp, LinearConstraint, Bounds
+    widths = sorted({w for (_, w) in avail}); var = []
+    for idx, (p, r, st) in sorted(win.items()):
+        for pat in patterns(r, sorted(st), widths): var.append((idx, pat))
+    n = len(var); c = np.zeros(n)
+    for j, (idx, pat) in enumerate(var):
+        r = win[idx][1]; c[j] = -(cost(r, m) - cost(r - sum(w for _, w in pat), m) + pad_value * len(pat))
+    rows, lo, hi = [], [], []
+    by = {}
+    for j, (idx, pat) in enumerate(var): by.setdefault(idx, []).append(j)
+    for idx, js in by.items():
+        row = np.zeros(n); row[js] = 1; rows.append(row); lo.append(copies); hi.append(copies)
+    for (s, w), a in sorted(avail.items()):
+        row = np.zeros(n)
+        for j, (idx, pat) in enumerate(var): row[j] = sum(1 for sw in pat if sw == (s, w))
+        rows.append(row); lo.append(0); hi.append(a)
+    res = milp(c, constraints=LinearConstraint(np.array(rows), lo, hi), integrality=np.ones(n), bounds=Bounds(np.zeros(n), np.full(n, np.inf)),
+               options=dict(time_limit=time_limit, disp=False))
+    assert res.x is not None, res.message
+    x = [int(round(t)) for t in res.x]
+    return [[idx, [list(sw) for sw in pat], x[j]] for j, (idx, pat) in enumerate(var) if x[j]], -res.fun
+
+
+def save(path, key, sel, val):
+    import json
+    from pathlib import Path
+    p = Path(path); d = json.loads(p.read_text()) if p.exists() else {}
+    d[key] = dict(rule='one-helper-per-family', patterns=sorted(sel), proxy_saving=val)
+    p.write_text(json.dumps(d, indent=1, sort_keys=True) + '\n')
+
+
+def load(path, key):
+    import json
+    from pathlib import Path
+    d = json.loads(Path(path).read_text())[key]; assert d['rule'] == 'one-helper-per-family'
+    return d['patterns'], d['proxy_saving']
+
+
+def check_disjoint_groups(win, pair_of, side_of):
+    """children of one (pair, side) share their physical families; their windows must be disjoint"""
+    seen = {}
+    for idx, (p, r, st) in win.items():
+        for s in st:
+            k = (pair_of[idx], side_of[idx], s); assert k not in seen, ('windows of two children of one family group overlap', idx, seen[k], k); seen[k] = idx
+
+
+def expand(win, sel, widths, V):
+    """-> slots [idx, port, off, w, s, h] (one replica), rem {(idx, port): remaining pending rank}"""
+    R = len(widths); pool = {}
+    for h in sorted(range(R)): pool.setdefault(widths[h], []).append(h)
+    pool = {(s, w): list(hs) for s in range(9) for w, hs in pool.items()}
+    slots = []; rem = {}; used = Counter()
+    for idx, pat, copies in sorted(sel, key=lambda e: (e[0], e[1])):
+        r = win[idx][1]
+        for _ in range(copies):
+            cp = used[idx]; used[idx] += 1; assert cp < V; off = 0
+            assert len({s for s, w in pat}) == len(pat)
+            for s, w in pat:
+                assert s in win[idx][2] and off + w <= r
+                slots.append([idx, cp, off, w, s, pool[s, w].pop(0)]); off += w
+            rem[idx, cp] = r - off
+    assert all(n == V for n in used.values()) and len(used) == len(win)
+    return slots, rem
+
+
+def idle_basis(q):
+    """PR #433 / #458: the parent's orthonormal idle basis U_q (+) I for port q (H = 9 local coordinates, M = 73)"""
+    z = next(i for i in range(H) if not (q >> i & 1)); a = q ^ (1 << z); order = list(range(H)); order[0], order[z] = order[z], order[0]
+    return [(1 << i) ^ (a if a >> i & 1 else 0) for i in order] + [1 << i for i in range(H, M)]
+
+
+def spectators(q, pending, off, w):
+    """indices (into B_q) of the e = 9 - w spectator coordinates of a residual at pending[off:off+w]"""
+    B = idle_basis(q); occ = [B.index(x) for x in pending[off:off + w]]
+    assert len(set(occ)) == w
+    sp = [j for j in range(M) if j not in occ][:H - w]
+    assert len(sp) == H - w
+    return sp
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/replay_gk.py b/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/replay_gk.py
new file mode 100644
index 0000000000..629de3b6ce
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/code/replay_gk.py
@@ -0,0 +1,280 @@
+# GK: modified copy of PR #433's complex_replay.py (icekylinx with Codex assistance; PR #425) by DreamingOfClouds with Claude Opus 5.5
+# (Anthropic), via Claude Code.  Every change is marked "GK:".  On a word without start_extra / target_levels the behaviour
+# and every written file equal PR #433's (regression anchor in verify.py).
+import sys as _sys, os as _os; _sys.path.insert(0, _os.path.dirname(_os.path.abspath(__file__)))
+# Adapted for heterogeneous centres by icekylinx with Codex assistance.
+"""Independent read-back of the serialized local/global instruction stream."""
+import copy,gzip,hashlib,importlib.util,json,math
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+OUT=Path('split-centres');P=OUT/'GLOBAL-TEMPLATE.json.gz'
+ir=json.load(gzip.open(P));c=json.load(gzip.open(OUT/'CANONICAL-WORD.json.gz'))
+integration=json.loads((OUT/'INTEGRATION.json').read_text())
+assert hashlib.sha256(gzip.decompress(P.read_bytes())).hexdigest()==integration['global_template_sha256']
+assert c['ports']==json.load(gzip.open('work/higher-stage-e8/verified/gcert1-e8-retimed.json.gz'))['ports']
+v,R,h=c['v'],c['R'],c['h'];n=2*v+R;frames=c['frames']
+from gk_common import tile   # GK
+widths=[h-len(frames[c['start'][2*v+i]]) for i in range(R)]
+assign,nb,pads=tile([(rep,i,widths[i]) for rep in range(8) for i in range(R)]);W=7680+9*nb
+levels={int(t):f for t,f in c.get('target_levels',{}).items()}
+entering=[r for r,f in enumerate(c['start']) if r>=2*v and f!=0];plain={r for r in range(n) if r not in set(entering)}   # GK
+def contains(a,b):
+    for x in a:
+        for y in b:
+            if x>>(y.bit_length()-1)&1:x^=y
+        if x:return False
+    return True
+def local(events,back):
+    rows={('L',r):{r:Q(1)} for r in range(n)}
+    norm={('L',r):Q(1) for r in range(n)};prefix=Q(1);cur=c['start'].copy();private={}
+    hist=Counter();phases=[];entry=[];exit=[];centers=[];matrix_hash=hashlib.sha256();chain={};wrappers=[]
+    allowed=['zero_frame_precondition','entry_adapters','A','centers','B','final','exit_adapters','full_frame_cleanup','done']
+    for event in events:
+        tag=event[0]
+        if tag=='phase':
+            phases.append(event[1]);assert phases==allowed[:len(phases)]
+            if event[1]=='A':assert entry==[(r,f) for r,f in enumerate(c['start']) if r in plain] and sorted(r for k_,r,f_ in wrappers if k_=='pre')==entering   # GK
+            if event[1]=='centers':assert all(cur[r]==levels.get(r-v,0) for r in range(v,2*v))   # GK
+            if event[1]=='full_frame_cleanup':assert cur==c['final'] and exit==list(enumerate(c['final']))
+            assert not private
+        elif tag=='residual_adapter':   # GK: paid wrappers of entering helpers: R_E^-1 before the invocation, L_E^-1 after the full-frame cleanup
+            _,kind,r,f=event;assert r in entering and f==c['start'][r] and kind in ('pre','post')
+            assert (kind=='pre' and phases[-1]=='entry_adapters') or (kind=='post' and phases[-1]=='full_frame_cleanup')
+            assert (kind,r) not in {(k,x) for k,x,_ in wrappers};wrappers.append((kind,r,f))
+        elif tag=='adapter':
+            assert event[3]==(c['start'] if event[1]=='old_to_new' else c['final'])[event[2]]
+            (entry if event[1]=='old_to_new' else exit).append((event[2],event[3]))
+        elif tag=='climb':
+            _,part,r,a,b,rank=event
+            assert not private and phases[-1]==part and cur[r]==a
+            assert contains(frames[a],frames[b]) and rank==len(frames[b])-len(frames[a])>0
+            hist[rank]+=1;cur[r]=b
+        elif tag=='center':
+            _,k,a,b,rank=event
+            assert phases[-1]=='centers' and private=={('C',k):a}
+            cf=c['center_frames'][k];cr=len(frames[cf])
+            # GK: stepwise descent cf -> served levels -> lowest (forward), reversed ascent (backward); each step is a nested child
+            assert contains(frames[a],frames[b]) if back else contains(frames[b],frames[a])
+            assert rank==abs(len(frames[a])-len(frames[b]))>0
+            chain.setdefault(k,[]).append((a,b))
+            private['C',k]=b;hist[rank]+=1;centers.append(k)
+        elif tag=='scalar':
+            _,e,f=event;op=e[0];target=tuple(e[1]);source=tuple(e[2]) if op in ('copy','add') else None
+            if target[0]=='C' and op=='clear':
+                assert private.get(target,f)==f
+                private.pop(target,None)
+            else:
+                for r in (target,source):
+                    if r is None:continue
+                    if r[0]=='L':assert cur[r[1]]==f,('common frame',r,cur[r[1]],f)
+                    else:
+                        if r==target and r not in private:private[r]=f
+                        assert private[r]==f
+            if op=='clear':rows[target]={};norm[target]=Q(0)
+            elif op=='copy':rows[target]=dict(rows[source]);norm[target]=norm[source]
+            elif op=='scale':
+                q=Q(e[2],e[3]);a,b=abs(q.numerator),q.denominator
+                assert a&(a-1)==0 and b&(b-1)==0
+                rows[target]={j:q*x for j,x in rows[target].items()};norm[target]*=abs(q)
+            else:
+                q=Q(e[3],e[4]);a,b=abs(q.numerator),q.denominator
+                assert source!=target and b&(b-1)==0
+                # Independent symbolic replay of the cleared coefficient work.
+                w=0
+                for bit in bin(a)[2:]:w=2*w+int(bit)
+                assert Q(w,b)*(1 if q>0 else -1)==q
+                prefix=max(prefix,Q(a)*norm[source])
+                norm[target]=norm.get(target,Q(0))+abs(q)*norm[source]
+                row=rows.setdefault(target,{})
+                for j,x in list(rows[source].items()):
+                    z=row.get(j,Q(0))+q*x
+                    if z:row[j]=z
+                    else:row.pop(j,None)
+            prefix=max(prefix,norm[target])
+        else:raise AssertionError(tag)
+    assert phases==allowed and set(centers)==set(range(len(c['centers']))) and not private
+    assert sorted(r for k,r,_ in wrappers if k=='pre')==entering and sorted(r for k,r,_ in wrappers if k=='post')==entering   # GK
+    for k,st in chain.items():   # GK: the steps of each centre chain link up and end at the centre frame
+        cf=c['center_frames'][k]
+        if back:assert st[-1][1]==cf and all(st[i][1]==st[i+1][0] for i in range(len(st)-1))
+        else:assert st[0][0]==cf and all(st[i][1]==st[i+1][0] for i in range(len(st)-1))
+    assert all(not row for reg,row in rows.items() if reg[0]=='C')
+    for r in range(n):
+        expected={r:Q(1)}
+        if back and r<v:expected[v+r]=Q(-1)
+        elif not back and v<=r<2*v:expected[r-v]=Q(1)
+        assert rows['L',r]==expected
+    # A 192-bit local payload allowance vastly dominates even coefficient work.
+    assert prefix<2**192
+    return hist,{'all_exact_columns':n,'prefix_l1_upper':str(prefix),
+                 'prefix_bits_upper':prefix.numerator.bit_length()-prefix.denominator.bit_length()+1,
+                 'charged_payload_bits':192,'private_work_erased':True}
+
+profiles={};checks={}
+for name in ('forward','backward'):
+    profiles[name],checks[name]=local(ir['local_programs'][name],name=='backward')
+    assert dict(profiles[name])=={int(r):z for r,z in c['local_profile'].items()}
+    print('independent emitted replay PASS',name,flush=True)
+controls=[]
+for name,mut in [
+    ('wrong_scale',lambda es:next(e for e in es if e[0]=='scalar' and e[1][0]=='scale')[1].__setitem__(2,3)),
+    ('missing_center',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='center'))),
+    ('wrong_common_frame',lambda es:next(e for e in es if e[0]=='scalar' and e[2]!=0).__setitem__(2,0)),
+    ('wrong_child_rank',lambda es:next(e for e in es if e[0]=='climb').__setitem__(5,99)),
+]+([
+    ('missing_pre_wrapper',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='pre'))),
+    ('missing_post_wrapper',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='post'))),
+    ('wrapper_with_wrong_frame',lambda es:next(e for e in es if e[0]=='residual_adapter').__setitem__(3,0)),
+    ('wrapper_in_wrong_phase',lambda es:es.insert(es.index(['phase','A']),es.pop(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='post')))),
+    ('wrapper_on_a_data_register',lambda es:next(e for e in es if e[0]=='residual_adapter').__setitem__(2,3)),
+    ('wrapper_on_a_target_register',lambda es:next(e for e in es if e[0]=='residual_adapter').__setitem__(2,v+3)),
+    ('wrapper_on_a_centre_register',lambda es:next(e for e in es if e[0]=='residual_adapter').__setitem__(2,['C',0])),
+] if entering else [])+([
+    ('centre_step_not_nested',lambda es:next(e for e in es if e[0]=='center').__setitem__(3,next(f for f in range(len(frames)) if not contains(frames[f],frames[next(e for e in es if e[0]=='center')[2]]) and not contains(frames[next(e for e in es if e[0]=='center')[2]],frames[f])))),
+    ('centre_descent_step_skipped',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='center' and e[3]!=0))),
+] if levels else []):
+    es=copy.deepcopy(ir['local_programs']['forward']);mut(es)
+    try:local(es,False)
+    except (AssertionError,KeyError):controls.append(name)
+    else:raise AssertionError('mutation accepted: '+name)
+
+def residual_cells(route):
+    """cells of a bank family occupied by a helper residual (independent of tile): a width-9 slot or [offset, offset + width)"""
+    return set(range(route[1]*9,route[1]*9+9)) if len(route)==2 else set(range(route[1],route[1]+route[2]))
+def bank_rule(owners,occ,sole=True):
+    """GK: the one-helper rule of PR #458 on EVERY register class of one invocation (owners: 240 active data owners, then the 560 helpers).
+    data class (family < 7680): only the active wires, each the sole owner of its family; bank class (7680 <= family < W): helpers only; an ENTERING
+    helper (width < 9) is the sole owner of its bank family, its route is [2, offset, width, spectators] with the spectators the first
+    cells of the bank beyond every residual cell of it (occ[family] = those cells, over all invocations); width-9 helpers share a pure bank in
+    disjoint 9-cell slots (no wrapper acts on them); nobody owns a family of the private namespace (family >= W).  sole=False skips only the
+    sole-owner assertion (used by a control to show that the footprints themselves are fine)."""
+    fam=Counter(f for f,_ in owners);foot={}
+    for i,(f,route) in enumerate(owners):
+        assert f<W,('owner in the private namespace',f)
+        if f<7680:
+            assert i<240 and route[0]==1 and fam[f]==1,('data class: only the active wires, each alone on its family',i,f)
+        else:
+            assert i>=240 and route[0]==2,('bank class: helpers only',i,f);w=widths[i-240]
+            if w==9: assert len(route)==2,('width-9 helper in a pure bank',i)
+            else:
+                if sole: assert fam[f]==1,('entering helper shares its bank family in one invocation',i,f)
+                assert len(route)==4 and route[2]==w and len(set(route[3]))==9-w==len(route[3]),('entering helper without a spectator record',i)
+                assert route[3]==list(range(len(occ[f]),len(occ[f])+9-w)) and len(occ[f])+9-w<=73,('spectators are not the first cells beyond the residuals',i,f)
+            cells=residual_cells(route)|(set(route[3]) if len(route)==4 else set())
+            assert len(cells)==9 and not cells&foot.setdefault(f,set()),('footprints overlap on a bank family',i,f);foot[f]|=cells
+def global_check(t):
+    assert t['live']==W and t['physical']==W+R+len(c['centers'])+2   # GK
+    occ={}
+    for call in t['calls']:
+        for fam,route in call['owners'][240:]:occ.setdefault(fam,set()).update(residual_cells(route))
+    assert all(cs==set(range(len(cs))) for cs in occ.values()),'bank residuals are packed from cell 0'
+    # Eight data-wire scalar columns, independently recomposed.
+    matrix=[[int(i==j) for j in range(8)] for i in range(8)]
+    for e in t['recipe']:
+        if e['kind']=='local':
+            a=2*e['pair'];b=a+1;dst,src,q=(a,b,-1) if e['reverse'] else (b,a,1)
+            matrix[dst]=[x+q*y for x,y in zip(matrix[dst],matrix[src])]
+        elif e['kind']=='bridge':
+            i,j,q=e['dst'],e['src'],e['coefficient']
+            matrix[2*i]=[x+q*y for x,y in zip(matrix[2*i],matrix[2*j])]
+            matrix[2*j+1]=[x-q*y for x,y in zip(matrix[2*j+1],matrix[2*i+1])]
+        else:
+            assert e['kind']=='terminal';old=copy.deepcopy(matrix)
+            for i in range(4):matrix[2*i]=old[2*i+1];matrix[2*i+1]=[-x for x in old[2*i]]
+    assert matrix==[[int(i==j) for j in range(8)] for i in range(8)]
+    seen=set();hist=Counter();pairs={e['stage']:e for e in t['recipe'] if e['kind']=='local'}
+    for call in t['calls']:
+        stage,rep,pair=call['stage'],call['replica'],call['pair']
+        assert (stage,rep) not in seen;seen.add((stage,rep))
+        assert pair==pairs[stage]['pair']
+        assert call['orientation']==('backward' if pairs[stage]['reverse'] else 'forward')
+        assert len(call['owners'])==800
+        for r,(fam,route) in enumerate(call['owners']):
+            if r<240:assert fam==rep*960+(2*pair+r//120)*120+r%120 and route==[1,stage,r%120]
+            else:
+                bk,off_,w_,pure_,sp_=assign[rep,r-240];assert fam==7680+stage*nb+bk and route==([2,off_//9] if (w_==9 and pure_) else [2,off_,w_,list(sp_)])   # GK
+        assert len(set((f,json.dumps(r)) for f,r in call['owners']))==800
+        bank_rule(call['owners'],occ)   # GK: the rule on every register class, stated independently of tile()
+        for r,z in profiles[call['orientation']].items():hist[r]+=z
+    assert seen=={(s,r) for s in range(9) for r in range(8)}
+    for child in t['idle_children']:hist[child['rank']]+=child['replicas']
+    assert t['bank_padding']=={'families':list(range(7680,W)),'axis':72,'child_rank':1}
+    for r_,z_ in pads.items():hist[r_]+=z_*9   # GK
+    assert t['cover_final_correction']['families']==[0,W]
+    assert t['cover_final_correction']['charged_calls_per_cover']==W
+    assert t['execution_schedule'][-1]=={'kind':'translate_every_live_family',**{k:v for k,v in t['cover_final_correction'].items() if k!='kind'}}
+    assert 73*W-sum(r*z for r,z in hist.items())==2496
+    return hist
+H=global_check(ir)
+# Derivative repair: select two genuine width-9 owners; a fixed route may already match.
+pure_alias=[r for r in range(240,800) if widths[r-240]==9 and len(ir['calls'][0]['owners'][r][1])==2]
+assert len(pure_alias)>=2
+alias_src,alias_dst=pure_alias[:2]
+assert ir['calls'][0]['owners'][alias_src]!=ir['calls'][0]['owners'][alias_dst]
+def alias_owner(owners):
+    owners[alias_dst]=copy.deepcopy(owners[alias_src])
+for name,mut in [('missing_padding',lambda t:t['bank_padding']['families'].pop()),
+                 ('aliased_owner',lambda t:alias_owner(t['calls'][0]['owners'])),
+                 ('missing_cover_phase',lambda t:t['cover_final_correction'].__setitem__('charged_calls_per_cover',0))]:
+    t=copy.deepcopy(ir);mut(t)
+    assert t!=ir,('vacuous global mutation',name)
+    try:global_check(t)
+    except (AssertionError,KeyError):controls.append(name)
+    else:raise AssertionError('global mutation accepted: '+name)
+# GK: controls of the rule itself, one per register class, run on bank_rule (not on the equality with tile()); only for words with entering
+# helpers (the anchor's INDEPENDENT-REPLAY.json must stay byte-identical to PR #433's)
+occ_all={}
+for call in ir['calls']:
+    for fam_,route_ in call['owners'][240:]:occ_all.setdefault(fam_,set()).update(residual_cells(route_))
+def rule_control(name,mut,must):
+    o=copy.deepcopy(ir['calls'][0]['owners']);mut(o)
+    try:bank_rule(o,occ_all)
+    except AssertionError as e:
+        assert must in str(e),(name,str(e));controls.append(name)
+    else:raise AssertionError('rule mutation accepted: '+name)
+bank_rule(ir['calls'][0]['owners'],occ_all)
+rule_control('same_width_pure_helper_alias',alias_owner,'footprints overlap')
+ent=[r for r in range(240,800) if widths[r-240]<9]
+if entering:
+    a_,b_=ent[0],ent[1]
+    def to_one_bank(o):   # bank class: b joins a's bank family at the next free cells, with a spectator of its own
+        fa=o[a_][0];free=len(occ_all[fa]);o[b_]=[fa,[2,free,widths[b_-240],[free+widths[b_-240]]]]
+    rule_control('two_entering_helpers_on_one_bank_family',to_one_bank,'shares its bank family')
+    rule_control('bank_spectator_is_a_residual_cell',lambda o:o[a_][1].__setitem__(3,[o[a_][1][1]]+o[a_][1][3][1:]),'first cells beyond')
+    rule_control('bank_spectator_shifted',lambda o:o[a_][1].__setitem__(3,[x+1 for x in o[a_][1][3]]),'first cells beyond')
+    rule_control('bank_spectator_record_dropped',lambda o:o[a_].__setitem__(1,o[a_][1][:3]),'without a spectator record')
+    rule_control('bank_spectator_count_wrong',lambda o:o[a_][1].__setitem__(3,o[a_][1][3]*2),'without a spectator record')
+    rule_control('second_owner_on_an_active_data_family',lambda o:o.__setitem__(241,[o[0][0],[1,0,0]]),'data class')
+    rule_control('helper_owner_on_an_active_data_family',lambda o:o.__setitem__(250,[o[3][0],[2,0]]),'data class')
+    rule_control('active_wire_on_a_bank_family',lambda o:o.__setitem__(5,[7680,[1,0,5]]),'bank class')
+    C_=len(c['centers'])
+    rule_control('owner_in_the_private_namespace_centres',lambda o:o.__setitem__(300,[W+3,[2,0]]),'private namespace')
+    rule_control('owner_in_the_private_namespace_reserved_tableau',lambda o:o.__setitem__(300,[W+C_+5,[2,0]]),'private namespace')
+    rule_control('owner_in_the_private_namespace_coefficient',lambda o:o.__setitem__(300,[W+C_+R+1,[2,0]]),'private namespace')
+    t=copy.deepcopy(ir);t['calls'][0]['owners'][0][0]+=960   # copies: an active owner of replica 0's invocation on a family of replica 1
+    try:global_check(t)
+    except (AssertionError,KeyError):controls.append('active_owner_on_the_family_of_another_replica')
+    else:raise AssertionError('global mutation accepted: active_owner_on_the_family_of_another_replica')
+assert dict(H)=={int(r):z for r,z in integration['global_profile'].items()}
+
+def load(name):
+    sp=importlib.util.spec_from_file_location('replay_hamming_'+name,Path('work/pr361/code/engines')/(name+'.py'))
+    m=importlib.util.module_from_spec(sp);sp.loader.exec_module(m);return m
+M,B=load('moment'),load('base_two_moment');b=Q(integration['complex_b']);grid=Q(1,10**18)
+assert M.moment(H,73,W,b,True)[1]<1<M.moment(H,73,W,b+grid,True)[0]
+def other(a):
+    lo,hi=B.moment(73,W,list(H.items()),a)
+    l2,h2=B.moment(73,W,[(1,32*73**2*sum(H.values()))],a)
+    return lo+l2/10**16,hi+h2/10**16
+assert other(b)[1]<1<other(b+grid)[0]
+result={'status':'PASS_INDEPENDENT_NEW_STRUCTURAL_IR_REPLAY',
+        'template_sha256':integration['global_template_sha256'],'local':checks,
+        'mutation_controls_rejected':controls,'all_eight_global_scalar_columns':True,
+        'bank_owners_and_padding_exact':True,'paid_profile':dict(sorted(H.items())),
+        'two_rational_moment_engines':True,'complex_b':str(b),
+        'next_b_grid_rejected':True,
+        'scope':'Independent finite replay; retains the written generic scalar-interface lemma and inherited all-size/analytic assumptions.'}
+(OUT/'INDEPENDENT-REPLAY.json').write_text(json.dumps(result,indent=2)+'\n')
+print('PASS independent local/global replay and two exact moments',flush=True)
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/data/selections/gauge80-kernel42.json b/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/data/selections/gauge80-kernel42.json
new file mode 100644
index 0000000000..cf624433f0
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/e8-complex-gauge-kernel/data/selections/gauge80-kernel42.json
@@ -0,0 +1,470 @@
+{
+ "gauge": {
+  "134": [
+   510
+  ],
+  "135": [
+   510
+  ],
+  "136": [
+   510
+  ],
+  "137": [
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+   510
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+   24
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+   408,
+   102
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+  "550": [
+   408,
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+  ],
+  "551": [
+   408,
+   102
+  ],
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+   510
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+   510
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+  "555": [
+   510
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+  "556": [
+   510
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+  "557": [
+   510
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+  "558": [
+   510
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+   510
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+    504
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+    334,
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+    362,
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+    390,
+    391,
+    418,
+    419
+   ]
+  },
+  {
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+    324,
+    325,
+    328,
+    329,
+    380,
+    384,
+    440,
+    444
+   ],
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+    381,
+    385,
+    441,
+    445,
+    498,
+    499,
+    500,
+    501
+   ]
+  },
+  {
+   "E": [
+    6
+   ],
+   "donors": [
+    128,
+    129
+   ],
+   "pivots": [
+    156,
+    157
+   ]
+  },
+  {
+   "E": [
+    414
+   ],
+   "donors": [
+    218,
+    219,
+    302,
+    303
+   ],
+   "pivots": [
+    358,
+    359,
+    386,
+    387
+   ]
+  },
+  {
+   "E": [
+    384
+   ],
+   "donors": [
+    162,
+    163,
+    240,
+    241,
+    300,
+    352,
+    353,
+    356,
+    360,
+    361,
+    412,
+    416,
+    417,
+    438,
+    442
+   ],
+   "pivots": [
+    301,
+    357,
+    413,
+    436,
+    437,
+    439,
+    443,
+    496,
+    497,
+    502,
+    503
+   ]
+  },
+  {
+   "E": [
+    126
+   ],
+   "donors": [
+    160,
+    161
+   ],
+   "pivots": [
+    242,
+    243
+   ]
+  },
+  {
+   "E": [
+    102
+   ],
+   "donors": [
+    188,
+    189
+   ],
+   "pivots": [
+    244,
+    245
+   ]
+  },
+  {
+   "E": [
+    30
+   ],
+   "donors": [
+    132,
+    133
+   ],
+   "pivots": [
+    268,
+    269
+   ]
+  },
+  {
+   "E": [
+    96
+   ],
+   "donors": [
+    186,
+    187
+   ],
+   "pivots": [
+    216,
+    217
+   ]
+  },
+  {
+   "E": [
+    120
+   ],
+   "donors": [
+    158,
+    159
+   ],
+   "pivots": [
+    214,
+    215
+   ]
+  },
+  {
+   "E": [
+    480
+   ],
+   "donors": [
+    272,
+    273,
+    298
+   ],
+   "pivots": [
+    299
+   ]
+  },
+  {
+   "E": [
+    24
+   ],
+   "donors": [
+    130,
+    131
+   ],
+   "pivots": [
+    212,
+    213
+   ]
+  }
+ ]
+}
\ No newline at end of file
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/split-centres-global/code/complex_phases_full.py b/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/split-centres-global/code/complex_phases_full.py
new file mode 100644
index 0000000000..b5a5bd64b4
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/split-centres-global/code/complex_phases_full.py
@@ -0,0 +1,39 @@
+# Adapted from PR425 for heterogeneous centres by icekylinx with Codex assistance.
+"""Exact phase-aware lowering of every used edge of the new structural word."""
+import gzip,hashlib,json,sys,time
+from collections import Counter
+from pathlib import Path
+sys.path.insert(0,str(Path('work/odd-stages').resolve()))
+from clifford_exact import *
+
+OUT=Path('split-centres');P=OUT/'CANONICAL-WORD.json.gz'
+c=json.load(gzip.open(P));n=c['h'];frames=c['frames'];start=time.monotonic();ops=[]
+for U in frames:
+    op=canonical_frame(n,U)
+    L=[u|(u<<n) for u in U]+[v<<n for v in nullspace(U,n)]
+    pre=[x|(z<<n) for x,z,p in inverse(op.tab)[n:]]
+    assert rank(L)==n and rank(L+pre)==n
+    assert rank([x for x,z,p in op.tab[n:]])==len(U)
+    ops.append(op)
+edges=set(map(tuple,c['edges']))|{(a,b) for f in c['center_frames'] for a,b in ((f,0),(0,f))};recipes=[];hist=Counter()
+for i,(a,b) in enumerate(sorted(edges)):
+    op=ops[a].adjoint().then(ops[b]);rec,compiled=lower_child(op)
+    assert rec['rank']==abs(len(frames[a])-len(frames[b]))
+    hist[rec['rank']]+=1;recipes.append({'old':a,'new':b,**rec})
+    if i%200==0:print('exact phase edges',i,'/',len(edges),'seconds',time.monotonic()-start,flush=True)
+adapters=[];F=fourier(n)
+for i,q in enumerate(c['ports']):
+    for role,old,f in [('source',cgate(n,q),c['start'][i]),
+                       ('target',cgate(n,q).adjoint().then(F),c['final'][c['v']+i])]:
+        rec,compiled=lower_child(old.adjoint().then(ops[f]));assert rec['rank']==0
+        adapters.append({'port':i,'role':role,'frame':f,**rec})
+raw=json.dumps({'children':recipes,'endpoint_adapters':adapters},sort_keys=True,separators=(',',':')).encode()
+(OUT/'CLIFFORD-RECIPES.json').write_bytes(raw)
+result={'status':'PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES',
+        'canonical_word_sha256':hashlib.sha256(P.read_bytes()).hexdigest(),
+        'frames':len(frames),'directed_edges':len(edges),'ranks':dict(hist),
+        'endpoint_adapters':len(adapters),'all_child_equalities_include_global_phase':True,
+        'recipe_sha256':hashlib.sha256(raw).hexdigest(),'seconds':time.monotonic()-start,
+        'scope':'Every local frame and center transition. Expanded scalar-interface integration and global emitted program are separate obligations.'}
+(OUT/'CLIFFORD-REVIEW.json').write_text(json.dumps(result,indent=2)+'\n')
+print('PASS exact local phases',result['seconds'],'seconds',flush=True)
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/split-centres-global/vendor/clifford_exact.py b/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/split-centres-global/vendor/clifford_exact.py
new file mode 100644
index 0000000000..166841a037
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/vendor/complex/split-centres-global/vendor/clifford_exact.py
@@ -0,0 +1,149 @@
+"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals.
+Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d.
+The tableau is supplemented by a literal circuit, so global phases are kept.
+"""
+from dataclasses import dataclass
+
+def parity(x):return x.bit_count()&1
+def rank(rows):
+ p={}
+ for x in rows:
+  while x:
+   b=x.bit_length()-1
+   if b not in p:p[b]=x;break
+   x^=p[b]
+ return len(p)
+def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<<j for j in range(n)) for i in range(n))
+def mv(rows,x):return sum(parity(r&x)<<i for i,r in enumerate(rows))
+def inv(rows,n):
+ a=[r|(1<<(n+i)) for i,r in enumerate(rows)]
+ for j in range(n):
+  k=next(i for i in range(j,n) if a[i]>>j&1);a[j],a[k]=a[k],a[j]
+  for i in range(n):
+   if i!=j and a[i]>>j&1:a[i]^=a[j]
+ assert [r&((1<<n)-1) for r in a]==[1<<i for i in range(n)]
+ return tuple(r>>n for r in a)
+def basis_extend(cols,n):
+ out=[]
+ for x in list(cols)+[1<<i for i in range(n)]:
+  if rank(out+[x])>len(out):out.append(x)
+ assert len(out)==n
+ return tuple(out)
+def nullspace(rows,n):
+ a=list(rows);p=[];k=0
+ for j in range(n):
+  t=next((i for i in range(k,len(a)) if a[i]>>j&1),None)
+  if t is None:continue
+  a[t],a[k]=a[k],a[t]
+  for i in range(len(a)):
+   if i!=k and a[i]>>j&1:a[i]^=a[k]
+  p.append(j);k+=1
+ return tuple((1<<j)|sum(((a[i]>>j)&1)<<v for i,v in enumerate(p)) for j in range(n) if j not in p)
+def pmul(a,b):
+ x,z,p=a;y,w,q=b
+ return x^y,z^w,(p+q+2*parity(z&y))%4
+def identity(n):return tuple([(1<<i,0,0) for i in range(n)]+[(0,1<<i,0) for i in range(n)])
+def apply(T,p):
+ n=len(T)//2;x,z,ph=p;out=(0,0,ph)
+ for i in range(n):
+  if x>>i&1:out=pmul(out,T[i])
+ for i in range(n):
+  if z>>i&1:out=pmul(out,T[n+i])
+ return out
+def compose(A,B):return tuple(apply(A,p) for p in B)
+def inverse(T):
+ n=len(T)//2;cols=[x|(z<<n) for x,z,p in T];rows=transpose(cols,2*n);cols_inv=transpose(inv(rows,2*n),2*n);out=[]
+ for j,w in enumerate(cols_inv):
+  x=w&((1<<n)-1);z=w>>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4))
+ return tuple(out)
+def qvalue(Q,alpha,x,n):
+ return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4
+def mul_i(a,p):
+ x,y=a;p%=4
+ return [(x,y),(-y,x),(-x,-y),(y,-x)][p]
+@dataclass
+class Op:
+ n:int
+ tab:tuple
+ circuit:list
+ def then(self,b):
+  assert self.n==b.n
+  return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit)
+ def adjoint(self):
+  circ=[]
+  for e in reversed(self.circuit):
+   if e[0]=='P':circ.append(('P',inv(e[1],self.n)))
+   elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2])))
+   elif e[0]=='C':circ.append(('C',e[1],-e[2]))
+   elif e[0]=='phase':circ.append(('phase',(-e[1])%4))
+   else:circ.append(e)
+  return Op(self.n,inverse(self.tab),circ)
+ def zero_state(self,basis=0):
+  N=1<<self.n;vec=[(0,0)]*N;vec[basis]=(1,0);den=0
+  for e in self.circuit:
+   if e[0]=='P':
+    v=[(0,0)]*N
+    for x,a in enumerate(vec):v[mv(e[1],x)]=a
+    vec=v
+   elif e[0]=='X':vec=[vec[x^e[1]] for x in range(N)]
+   elif e[0]=='D':vec=[mul_i(a,qvalue(e[1],e[2],x,self.n)) for x,a in enumerate(vec)]
+   elif e[0]=='phase':vec=[mul_i(a,e[1]) for a in vec]
+   elif e[0]=='C':
+    q,sgn=e[1:];v=[]
+    for x,(a,b) in enumerate(vec):
+     c,d=vec[x^q]
+     # C=(1+i)I/2+(1-i)X/2; inverse conjugates both coefficients.
+     v.append((a-sgn*b+c+sgn*d,b+sgn*a+d-sgn*c))
+    vec=v;den+=1
+   else:raise AssertionError(e)
+   while den and all((a&1)==(b&1)==0 for a,b in vec):vec=[(a//2,b//2) for a,b in vec];den-=1
+  return vec,den
+def ident(n):return Op(n,identity(n),[])
+def perm(n,G):
+ cols=transpose(G,n);gi=inv(G,n)
+ return Op(n,tuple([(a,0,0) for a in cols]+[(0,a,0) for a in gi]),[('P',tuple(G))])
+def diag(n,Q,alpha=None):
+ Q=tuple(Q);assert transpose(Q,n)==Q
+ alpha=tuple(alpha) if alpha is not None else tuple((Q[i]>>i)&1 for i in range(n))
+ assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n))
+ return Op(n,tuple([(1<<i,Q[i],alpha[i]) for i in range(n)]+[(0,1<<i,0) for i in range(n)]),[('D',Q,alpha)])
+def cgate(n,q,sgn=1):
+ return Op(n,tuple([(1<<i,0,0) for i in range(n)]+[(q if q>>i&1 else 0,1<<i,(3*sgn)%4 if q>>i&1 else 0) for i in range(n)]),[('C',q,sgn)])
+def xgate(n,b):return Op(n,tuple([(1<<i,0,0) for i in range(n)]+[(0,1<<i,2*((b>>i)&1)) for i in range(n)]),[('X',b)])
+def fourier(n,axes=None):
+ out=ident(n)
+ for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<<i))
+ return out
+def hadamard(n,axes):
+ axes=list(axes);Q=tuple(1<<i if i in axes else 0 for i in range(n));S=diag(n,Q)
+ return S.then(fourier(n,axes)).then(S)
+def canonical_frame(n,U):
+ r=len(U)
+ if r==0:return ident(n)
+ if r==n:return fourier(n)
+ G=transpose(basis_extend(U,n),n);gi=inv(G,n);Q=tuple((1<<i)^sum(parity(gi_i&gi_j)<<j for j,gi_j in enumerate(transpose(gi,n))) for i,gi_i in enumerate(transpose(gi,n)))
+ K=perm(n,G).then(diag(n,Q))
+ return K.adjoint().then(fourier(n,range(r))).then(K)
+def monomial(op):
+ n=op.n;T=op.tab;assert all(x==0 and p%2==0 for x,z,p in T[n:]);G=transpose([x for x,z,p in T[:n]],n);b=mv(G,sum((p//2)<<i for i,(x,z,p) in enumerate(T[n:])))
+ gt=transpose(G,n);cols=[mv(gt,z) for x,z,p in T[:n]];Q=transpose(cols,n);alpha=[(p-2*parity(b&z))%4 for x,z,p in T[:n]]
+ out=diag(n,Q,alpha).then(perm(n,G)).then(xgate(n,b));assert out.tab==T
+ vec,den=op.zero_state();assert den==0 and all(a==(0,0) for i,a in enumerate(vec) if i!=b);phase=[(1,0),(0,1),(-1,0),(0,-1)].index(vec[b]);out=out.then(Op(n,identity(n),[('phase',phase)]));assert out.zero_state()==op.zero_state()
+ return out,dict(matrix_rows=G,offset=b,quadratic_rows=Q,linear_Z4=alpha,phase=phase)
+def lower_child(op):
+ n=op.n;Bcols=[x for x,z,p in op.tab[n:]];r=rank(Bcols)
+ if not r:
+  mon,rec=monomial(op);return dict(rank=0,left=rec,right=None),mon
+ G=transpose(basis_extend(Bcols,n),n);A=inv(G,n);PA=perm(n,A);part=op.then(PA);Bcols=[x for x,z,p in part.tab[n:]];Dcols=[z for x,z,p in part.tab[n:]]
+ picks=[];selected=[]
+ for j,x in enumerate(Bcols):
+  if rank(selected+[x])>len(selected):picks.append(j);selected.append(x)
+ assert len(picks)==r and all(x>>r==0 for x in Bcols)
+ Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<<r)-1) for j in picks],r)
+ Qsmall=tuple(sum(parity(row&col)<<j for j,col in enumerate(transpose(Bi,r))) for row in Dr);Q=Qsmall+(0,)*(n-r);DQ=diag(n,Q)
+ V=part.then(DQ).then(hadamard(n,range(r)));assert all(x==0 for x,z,p in V.tab[n:]);Vmon,Vrec=monomial(V)
+ S=diag(n,tuple(1<<i if i<r else 0 for i in range(n)))
+ left=S.adjoint().then(DQ.adjoint()).then(PA.adjoint());right=Vmon.then(S.adjoint()).then(xgate(n,(1<<r)-1))
+ lmon,lrec=monomial(left);rmon,rrec=monomial(right);compiled=rmon.then(fourier(n,range(r))).then(lmon)
+ assert compiled.tab==op.tab and compiled.zero_state()==op.zero_state()
+ return dict(rank=r,left=lrec,right=rrec),compiled
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/verify.py b/research/ranksector112-async/vendor/pr523/vendor/pr514/verify.py
new file mode 100644
index 0000000000..1d3b08899f
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/verify.py
@@ -0,0 +1,62 @@
+"""Offline, stdlib-only reconstruction of the asynchronous complex derivative.
+The unchanged PR493 bit operator is a cited dependency, not freshly verified here.
+"""
+from pathlib import Path
+import argparse,hashlib,json,os,shutil,subprocess,sys,time,gzip
+if not __debug__:raise RuntimeError('Assertions must remain enabled; do not use -O or PYTHONOPTIMIZE.')
+sys.dont_write_bytecode=True
+if hasattr(sys,'set_int_max_str_digits'):sys.set_int_max_str_digits(0)
+P=Path(__file__).resolve().parent
+a=argparse.ArgumentParser();a.add_argument('--work',type=Path,required=True);args=a.parse_args()
+W=args.work.resolve();assert P not in W.parents and W!=P,'Output must be outside this package.';assert not W.exists(),'Choose a new output directory; existing outputs are preserved.'
+mf=P/'MANIFEST.json'
+if mf.exists():
+ manifest=json.loads(mf.read_text());assert manifest['format']=='sha256-lf-text-v1'
+ for n,entry in manifest['files'].items():
+  data=(P/n).read_bytes()
+  assert entry['mode'] in ['raw','lf-text'],n
+  if entry['mode']=='lf-text':data=data.replace(b'\r\n',b'\n')
+  assert hashlib.sha256(data).hexdigest()==entry['sha256'],n
+W.mkdir(parents=True);V=W/'base';V.mkdir();shutil.copytree(P/'inputs/work',V/'work')
+# Canonicalize generated copies, never edit immutable checked-out inputs.
+for f in (V/'work').rglob('*'):
+ if f.is_file() and f.suffix in {'.json','.txt','.md','.py','.sh'}:
+  f.write_bytes(f.read_text(encoding='utf-8').encode('utf-8'))
+(V/'ASYNC-6.json').write_bytes((P/'inputs/ASYNC-6.json').read_text(encoding='utf-8').encode('utf-8'))
+bit=json.loads((P/'inputs/PR493-EXPECTED.json').read_text())['eleven']
+(V/'BIT-PRICE.json').write_text(json.dumps({'lower':bit['bit_lower'],'scope':'PR493 cited published supplier'}))
+C=P/'vendor/complex';G=C/'e8-complex-gauge-kernel';A=W/'audit';A.mkdir();H=W/'hosted'
+env=dict(os.environ,PYTHONUTF8='1',PYTHONDONTWRITEBYTECODE='1',PYTHONINTMAXSTRDIGITS='0',TEMP=str(W),TMP=str(W))
+env.pop('PYTHONOPTIMIZE',None)
+steps=[]
+def run(name,script,*argv):
+ start=time.monotonic();print('RUN',name,flush=True)
+ with (W/(name+'.log')).open('w',encoding='utf-8') as log:
+  result=subprocess.run([sys.executable,'-B',str(P/'code/run_portable.py'),str(script),*map(str,argv)],cwd=V,env=env,stdout=log,stderr=subprocess.STDOUT)
+ steps.append({'stage':name,'exit':result.returncode,'seconds':time.monotonic()-start})
+ (W/'STEPS.json').write_text(json.dumps(steps,indent=2)+'\n')
+ if result.returncode:
+  print((W/(name+'.log')).read_text()[-5000:]);raise SystemExit(result.returncode)
+ print('PASS',name,flush=True)
+run('partial-factory',P/'code/construct_partial.py',V/'work/complex-network/hamming',V/'partial-base')
+run('construct-kernel92',P/'code/build_kernel92.py',G/'code',V/'partial-base/FULL-WORD.json.gz',P/'inputs/KERNEL84-SELECTION.json',P/'inputs/RETIME-FRAMES.json.gz',P/'inputs/KERNEL92-SELECTION.json',V/'split-centres')
+run('kernel-scalar-controls',P/'code/audit_kernel_scalar.py',V/'split-centres/FULL-WORD.json.gz',V/'split-centres/SELECTION.json',A/'KERNEL-SCALAR.json')
+run('scalar',G/'code/audit_gk.py')
+run('emit-local',G/'code/emit_gk.py')
+run('phases',C/'split-centres-global/code/complex_phases_full.py')
+run('adapters',G/'code/adapters_gk.py',V/'split-centres/CANONICAL-WORD.json.gz',V/'split-centres/RESIDUAL-ADAPTERS.json',V/'LEMMA-A.json')
+run('parent-integration',G/'code/integrate_gk.py')
+run('parent-replay',G/'code/replay_gk.py')
+run('emit-async',P/'code/emit_async.py',G,V,P/'inputs/ASYNC-OWNERS.json.gz',V/'ASYNC-6.json',H)
+run('independent-async',P/'code/audit_async.py',V,H,A/'ASYNC-AUDIT.json')
+run('invoice',P/'code/audit_async_invoice.py',A,V,H)
+run('two-moments-assembly',P/'code/assemble.py',A,V,H,P/'inputs/PR493-EXPECTED.json')
+x=json.loads((A/'EXACT-ASSEMBLY.json').read_text());audit=json.loads((A/'ASYNC-AUDIT.json').read_text())
+assert all(z['exit']==0 for z in steps)
+result={'status':'PASS_CONDITIONAL_ASYNCHRONOUS_COMPLEX_DERIVATIVE','kappa':x['kappa'],'kappa_decimal':x['kappa_decimal'],'complex_lower':x['complex_lower'],'bit_lower':x['bit_lower'],'template_sha256':x['complex_template_sha256'],'strict_constraints':len(x['strict_outer_constraints']),'scope':'New complex program independently replayed. The unchanged PR493 bit operator and inherited all-size compiler, common-label, Lemma A realization, restored-row, precision/tape and analytic-transfer contracts remain dependencies. No unconditional multiplication bound or fresh Lean certification is claimed.','stages':steps,'package_manifest_sha256':hashlib.sha256(mf.read_bytes()).hexdigest() if mf.exists() else None}
+expected=P/'EXPECTED.json'
+if expected.exists():
+ e=json.loads(expected.read_text())
+ for key in ['kappa','complex_lower','bit_lower','template_sha256']:assert result[key]==e[key],key
+(W/'RESULT.json').write_text(json.dumps(result,indent=2)+'\n')
+print(result['status'],'kappa',result['kappa_decimal'],flush=True)
diff --git a/research/ranksector112-async/vendor/pr523/vendor/pr514/verify.sh b/research/ranksector112-async/vendor/pr523/vendor/pr514/verify.sh
new file mode 100644
index 0000000000..275570d71e
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/vendor/pr514/verify.sh
@@ -0,0 +1,10 @@
+#!/usr/bin/env bash
+set -euo pipefail
+here="$(cd -- "$(dirname -- "$0")" && pwd)"
+if [ "$#" -eq 0 ]; then
+  out="$(mktemp -d)/run"
+  echo "Output: $out"
+  exec python3 -B "$here/verify.py" --work "$out"
+else
+  exec python3 -B "$here/verify.py" "$@"
+fi
diff --git a/research/ranksector112-async/vendor/pr523/verify.py b/research/ranksector112-async/vendor/pr523/verify.py
new file mode 100644
index 0000000000..e5ee320621
--- /dev/null
+++ b/research/ranksector112-async/vendor/pr523/verify.py
@@ -0,0 +1,158 @@
+"""Reconstruct the 112-port conditional global witness, offline and with stdlib.
+
+Prepared for icekylinx with GPT-6 Astra assistance. Apache-2.0.
+The pinned PR493 bit operator and the explicitly listed all-size interfaces
+remain dependencies. This program is a finite verifier, not a Lean proof.
+"""
+from pathlib import Path
+from fractions import Fraction
+import argparse
+import hashlib
+import json
+import os
+import subprocess
+import sys
+import time
+
+if not __debug__:
+    raise RuntimeError("Assertions must be enabled; do not use -O or PYTHONOPTIMIZE.")
+if sys.version_info < (3, 11):
+    raise RuntimeError("Python 3.11 or later is required.")
+sys.dont_write_bytecode = True
+sys.set_int_max_str_digits(0)
+P = Path(__file__).resolve().parent
+parser = argparse.ArgumentParser(description=__doc__)
+parser.add_argument("--work", type=Path, required=True,
+                    help="a new output directory outside this package")
+args = parser.parse_args()
+W = args.work.resolve()
+assert W != P and P not in W.parents, "Output must be outside the package."
+assert not W.exists(), "Choose a new directory; existing work is preserved."
+
+# Validate every immutable input before creating an output directory. Text
+# normalization changes only CRLF line endings; no other token is ignored.
+mf = P / "MANIFEST.json"
+manifest = json.loads(mf.read_text(encoding="utf-8"))
+assert manifest["format"] == "sha256-lf-text-v1"
+for name, entry in manifest["files"].items():
+    f = P / name
+    assert P in f.resolve().parents, name
+    data = f.read_bytes()
+    assert entry["mode"] in ("raw", "lf-text"), name
+    if entry["mode"] == "lf-text":
+        data = data.replace(b"\r\n", b"\n")
+    assert hashlib.sha256(data).hexdigest() == entry["sha256"], name
+
+W.mkdir(parents=True)
+V = P / "vendor/pr514"
+C = V / "vendor/complex"
+G = C / "e8-complex-gauge-kernel"
+ORIGINAL = W / "baseline514"
+LOCAL = W / "local112"
+BASE = W / "base112"
+HOSTED = W / "hosted"
+AUDIT = W / "audit"
+AUDIT.mkdir()
+env = dict(os.environ, PYTHONUTF8="1", PYTHONDONTWRITEBYTECODE="1",
+           PYTHONINTMAXSTRDIGITS="0", TEMP=str(W), TMP=str(W))
+env.pop("PYTHONOPTIMIZE", None)
+steps = []
+start = time.monotonic()
+
+
+def read(path):
+    return json.loads(path.read_text(encoding="utf-8"))
+
+
+def run(name, script, *argv):
+    before = time.monotonic()
+    print("RUN", name, flush=True)
+    logfile = W / (name + ".log")
+    with logfile.open("w", encoding="utf-8", newline="\n") as log:
+        proc = subprocess.run(
+            [sys.executable, "-B", str(V / "code/run_portable.py"),
+             str(script), *map(str, argv)],
+            cwd=W, env=env, stdout=log, stderr=subprocess.STDOUT)
+    steps.append(dict(stage=name, exit=proc.returncode,
+                      seconds=time.monotonic() - before))
+    (W / "STEPS.json").write_text(json.dumps(steps, indent=2) + "\n",
+                                  encoding="utf-8")
+    if proc.returncode:
+        print(logfile.read_text(encoding="utf-8")[-7000:], flush=True)
+        raise SystemExit(proc.returncode)
+    print("PASS", name, flush=True)
+
+
+# Rebuild the pinned predecessor instead of trusting pre-generated local words.
+run("01-pinned514-full-replay", V / "verify.py", "--work", ORIGINAL)
+original = read(ORIGINAL / "RESULT.json")
+assert original["kappa"] == "1391523459591829/1000000000000000000"
+assert original["template_sha256"] == (
+    "77767f67ed17413161d82f2a407e69b3beefef3fc44bfe582fb403bdc1705bd8")
+
+run("02-restrict-local", P / "code/build_port112.py",
+    ORIGINAL / "base/split-centres", LOCAL)
+run("03-exact-word-transport", P / "code/audit_port112_transport.py", LOCAL)
+run("04-emit-local", P / "code/emit_local112.py", LOCAL)
+run("05-independent-local", P / "code/audit_local112.py", LOCAL)
+run("06-exact-local-phases", P / "code/phases_local112.py",
+    LOCAL, C / "split-centres-global/vendor")
+run("07-residual-wrappers", G / "code/adapters_gk.py",
+    LOCAL / "CANONICAL-WORD.json.gz", LOCAL / "RESIDUAL-ADAPTERS.json",
+    LOCAL / "LEMMA-A.json")
+run("08-restrict-global-data", P / "code/restrict_global.py",
+    ORIGINAL / "base", LOCAL, BASE)
+run("09-independent-global-restriction", P / "code/audit_global_restriction.py",
+    ORIGINAL / "base", BASE, AUDIT / "GLOBAL-RESTRICTION-AUDIT.json")
+run("10-emit-whole-owners", P / "code/emit_async.py", G, BASE,
+    P / "inputs/OWNERS112.json.gz", P / "inputs/ASYNC112-PLAN.json", HOSTED)
+run("11-independent-hosted-program", P / "code/audit_async.py",
+    BASE, HOSTED, AUDIT / "ASYNC-AUDIT.json")
+run("12-independent-raw-reconstruction", P / "code/audit_112_independent.py",
+    "--original-base", ORIGINAL / "base", "--local", LOCAL,
+    "--owners", P / "inputs/OWNERS112.json.gz", "--out", AUDIT)
+run("13-scalar-prefix-and-finite-invoice", P / "code/audit_async_invoice.py",
+    AUDIT, BASE, HOSTED)
+run("14-two-moments-and-global-assembly", P / "code/assemble.py",
+    AUDIT, BASE, HOSTED, V / "inputs/PR493-EXPECTED.json")
+
+x = read(AUDIT / "EXACT-ASSEMBLY.json")
+h = read(HOSTED / "HOSTED.json")
+raw = read(AUDIT / "INDEPENDENT112-RAW-AUDIT.json")
+owner = read(AUDIT / "OWNERS-AND-PROFILE.json")
+e = read(P / "EXPECTED.json")
+for key in ("kappa", "kappa_decimal", "complex_lower", "complex_decimal",
+            "bit_lower", "complex_template_sha256"):
+    assert x[key] == e[key], key
+assert h["template_sha256"] == e["complex_template_sha256"]
+assert h["global_profile"] == owner["paid_profile"] == raw["paid_profile"] == e["global_profile"]
+for key in ("live", "physical", "rank_mass", "deficit"):
+    assert h[key] == raw[key] == e[key], key
+assert raw["whole_owner_roles"] == e["whole_owner_roles"] == 40320
+assert raw["no_emitter_or_hosting_checker_imported"]
+assert raw["no_nominated_profile_or_windows_used"]
+assert len(x["strict_outer_constraints"]) == e["strict_constraints"] == 47
+assert all(Fraction(q) > 0 for q in x["strict_outer_constraints"].values())
+assert x["outer_controls"] == ["next_grid", "zero_eta", "zero_beta", "unit_beta"]
+assert all(step["exit"] == 0 for step in steps)
+
+result = dict(
+    status="PASS_CONDITIONAL_PUNCTURED112_GLOBAL_KAPPA",
+    kappa=x["kappa"], kappa_decimal=x["kappa_decimal"],
+    complex_lower=x["complex_lower"], bit_lower=x["bit_lower"],
+    template_sha256=x["complex_template_sha256"],
+    live=h["live"], physical=h["physical"], deficit=h["deficit"],
+    global_profile=h["global_profile"], strict_constraints=47,
+    improvement_over_pinned514=str(Fraction(x["kappa"]) / Fraction(original["kappa"]) - 1),
+    whole_owner_roles=raw["whole_owner_roles"],
+    all_own_stages=len(steps), pinned_predecessor_stages=len(original["stages"]),
+    package_manifest_sha256=hashlib.sha256(mf.read_bytes()).hexdigest(),
+    seconds=time.monotonic() - start, steps=steps,
+    scope=("Finite complex restriction, exact local phases, whole physical owners, "
+           "complete fee inventory, two rational moments and 47 outer inequalities "
+           "checked. The unchanged PR493 bit operator, all-size compiler, "
+           "common-label/mutable-basis realization, normalized Lemma A, "
+           "restored-row, precision/tape and analytic-transfer contracts remain "
+           "dependencies. No unconditional theorem or new Lean certification."))
+(W / "RESULT.json").write_text(json.dumps(result, indent=2) + "\n", encoding="utf-8")
+print(result["status"], "kappa", result["kappa_decimal"], flush=True)
diff --git a/research/ranksector112-async/verify.py b/research/ranksector112-async/verify.py
new file mode 100644
index 0000000000..9e180adaab
--- /dev/null
+++ b/research/ranksector112-async/verify.py
@@ -0,0 +1,157 @@
+"""Reconstruct the 112-port conditional global witness, offline and with stdlib.
+
+Prepared for icekylinx with GPT-6 Astra assistance. Apache-2.0.
+The pinned PR493 bit operator and the explicitly listed all-size interfaces
+remain dependencies. This program is a finite verifier, not a Lean proof.
+"""
+from pathlib import Path
+from fractions import Fraction
+import argparse
+import hashlib
+import json
+import os
+import subprocess
+import sys
+import time
+
+if not __debug__:
+    raise RuntimeError("Assertions must be enabled; do not use -O or PYTHONOPTIMIZE.")
+if sys.version_info < (3, 11):
+    raise RuntimeError("Python 3.11 or later is required.")
+sys.dont_write_bytecode = True
+sys.set_int_max_str_digits(0)
+P = Path(__file__).resolve().parent
+parser = argparse.ArgumentParser(description=__doc__)
+parser.add_argument("--work", type=Path, required=True,
+                    help="a new output directory outside this package")
+parser.add_argument('--reuse-source522',type=Path)
+args = parser.parse_args()
+W = args.work.resolve()
+assert W != P and P not in W.parents, "Output must be outside the package."
+assert not W.exists(), "Choose a new directory; existing work is preserved."
+
+# Validate every immutable input before creating an output directory. Text
+# normalization changes only CRLF line endings; no other token is ignored.
+mf = P/'MANIFEST.json'
+actual={f.relative_to(P).as_posix():hashlib.sha256(f.read_bytes()).hexdigest() for f in P.rglob('*') if f.is_file() and f!=mf and '__pycache__' not in f.parts}
+assert actual==json.loads(mf.read_text()), 'Package manifest'
+W.mkdir(parents=True)
+S = P / "vendor/pr523"
+V = S / "vendor/pr514"
+C = V / "vendor/complex"
+G = C / "e8-complex-gauge-kernel"
+ORIGINAL = W / "source522"
+LOCAL = W / "local112"
+BASE = W / "base112"
+HOSTED = W / "hosted"
+AUDIT = W / "audit"
+AUDIT.mkdir()
+env = dict(os.environ, PYTHONUTF8="1", PYTHONDONTWRITEBYTECODE="1",
+           PYTHONINTMAXSTRDIGITS="0", TEMP=str(W), TMP=str(W))
+env.pop("PYTHONOPTIMIZE", None)
+steps = []
+start = time.monotonic()
+
+
+def read(path):
+    return json.loads(path.read_text(encoding="utf-8"))
+
+
+def run(name, script, *argv):
+    before = time.monotonic()
+    print("RUN", name, flush=True)
+    logfile = W / (name + ".log")
+    with logfile.open("w", encoding="utf-8", newline="\n") as log:
+        proc = subprocess.run(
+            [sys.executable, "-B", str(V / "code/run_portable.py"),
+             str(script), *map(str, argv)],
+            cwd=W, env=env, stdout=log, stderr=subprocess.STDOUT)
+    steps.append(dict(stage=name, exit=proc.returncode,
+                      seconds=time.monotonic() - before))
+    (W / "STEPS.json").write_text(json.dumps(steps, indent=2) + "\n",
+                                  encoding="utf-8")
+    if proc.returncode:
+        print(logfile.read_text(encoding="utf-8")[-7000:], flush=True)
+        raise SystemExit(proc.returncode)
+    print("PASS", name, flush=True)
+
+
+# Explicit completed-source reuse is fully byte-pinned; default rebuilds source522.
+if args.reuse_source522:
+    ORIGINAL=args.reuse_source522.resolve()
+    for name,expected_hash in read(P/'REUSE-SOURCE522-INPUTS.json').items():
+        assert hashlib.sha256((ORIGINAL/name).read_bytes()).hexdigest()==expected_hash,name
+    source_mode='byte-pinned-completed-source522-reuse'
+else:
+    run('01-source522-full-replay',P/'vendor/pr522/verify.py','--work',ORIGINAL)
+    source_mode='fresh-source522-complex-reconstruction'
+original=read(ORIGINAL/'RESULT.json')
+assert original['status']=='PASS_CONDITIONAL_ASYNCHRONOUS_COMPLEX_DERIVATIVE'
+assert original['kappa']=='1402213284556683/1000000000000000000'
+run("02-restrict-local", S / "code/build_port112.py",
+    ORIGINAL / "base/split-centres", LOCAL)
+run("03-exact-word-transport", S / "code/audit_port112_transport.py", LOCAL)
+run("04-emit-local", S / "code/emit_local112.py", LOCAL)
+run("05-independent-local", S / "code/audit_local112.py", LOCAL)
+run("06-exact-local-phases", S / "code/phases_local112.py",
+    LOCAL, C / "split-centres-global/vendor")
+run("07-residual-wrappers", G / "code/adapters_gk.py",
+    LOCAL / "CANONICAL-WORD.json.gz", LOCAL / "RESIDUAL-ADAPTERS.json",
+    LOCAL / "LEMMA-A.json")
+run("08-restrict-global-data", S / "code/restrict_global.py",
+    ORIGINAL / "base", LOCAL, BASE)
+run("09-independent-global-restriction", P / "code/audit_global_restriction.py",
+    ORIGINAL / "base", BASE, AUDIT / "GLOBAL-RESTRICTION-AUDIT.json")
+run("10-emit-whole-owners", S / "code/emit_async.py", G, BASE,
+    P / "data/OWNERS.json.gz", P / "data/PLAN.json", HOSTED)
+run("11-independent-hosted-program", S / "code/audit_async.py",
+    BASE, HOSTED, AUDIT / "ASYNC-AUDIT.json")
+run("12-independent-raw-reconstruction", P / "code/audit_112_independent.py",
+    "--original-base", ORIGINAL / "base", "--local", LOCAL,
+    "--owners", P / "data/OWNERS.json.gz", "--out", AUDIT)
+run("13-scalar-prefix-and-finite-invoice", P / "code/audit_async_invoice.py",
+    AUDIT, BASE, HOSTED)
+run("14-two-moments-and-global-assembly", S / "code/assemble.py",
+    AUDIT, BASE, HOSTED, V / "inputs/PR493-EXPECTED.json")
+
+x = read(AUDIT / "EXACT-ASSEMBLY.json")
+h = read(HOSTED / "HOSTED.json")
+raw = read(AUDIT / "INDEPENDENT112-RAW-AUDIT.json")
+owner = read(AUDIT / "OWNERS-AND-PROFILE.json")
+e = read(P / "EXPECTED.json")
+for key in ("kappa", "kappa_decimal", "complex_lower", "complex_decimal",
+            "bit_lower", "complex_template_sha256"):
+    assert x[key] == e[key], key
+assert h["template_sha256"] == e["complex_template_sha256"]
+assert h["global_profile"] == owner["paid_profile"] == raw["paid_profile"] == e["global_profile"]
+for key in ("live", "physical", "rank_mass", "deficit"):
+    assert h[key] == raw[key] == e[key], key
+assert raw["whole_owner_roles"] == e["whole_owner_roles"] == 40320
+assert raw["no_emitter_or_hosting_checker_imported"]
+assert raw["no_nominated_profile_or_windows_used"]
+assert len(x["strict_outer_constraints"]) == e["strict_constraints"] == 47
+assert all(Fraction(q) > 0 for q in x["strict_outer_constraints"].values())
+assert x["outer_controls"] == ["next_grid", "zero_eta", "zero_beta", "unit_beta"]
+assert all(step["exit"] == 0 for step in steps)
+
+result = dict(
+    status="PASS_PACKAGED_RANKSECTOR112_GLOBAL_KAPPA",
+    kappa=x["kappa"], kappa_decimal=x["kappa_decimal"],
+    complex_lower=x["complex_lower"], bit_lower=x["bit_lower"],
+    template_sha256=x["complex_template_sha256"],
+    live=h["live"], physical=h["physical"], deficit=h["deficit"],
+    global_profile=h["global_profile"], strict_constraints=47,
+    improvement_over_source522=str(Fraction(x["kappa"]) / Fraction(original["kappa"]) - 1),
+    whole_owner_roles=raw["whole_owner_roles"],
+    all_own_stages=len(steps), pinned_predecessor_stages=len(original["stages"]),
+    source522_mode=source_mode,
+    package_manifest_sha256=hashlib.sha256(mf.read_bytes()).hexdigest(),
+    seconds=time.monotonic() - start, steps=steps,
+    scope=("Finite complex restriction, exact local phases, whole physical owners, "
+           "complete fee inventory, two rational moments and 47 outer inequalities "
+           "checked. The unchanged PR493 bit operator, all-size compiler, "
+           "common-label/mutable-basis realization, normalized Lemma A, "
+           "restored-row, precision/tape and analytic-transfer contracts remain "
+           "dependencies. No unconditional theorem or new Lean certification."))
+(W / "RESULT.json").write_text(json.dumps(result, indent=2) + "\n", encoding="utf-8")
+print(result["status"], "kappa", result["kappa_decimal"], flush=True)