Research: bound PR1154 packing headroom

research/pr1154-packing-relaxation/README.md

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+# PR1154 adaptive T16 word: packing relaxation
+
+## Question and result
+
+Does the fixed aggregate paid profile in the merged PR1154 adaptive rank-seven
+T16 construction still have room under the standard nine-stage complex packing
+relaxation? The profile is named and source-pinned; this is a different word
+from the selected PR1094 word and from the staged544 supplier in PR3815.
+
+The answer is yes, but the remaining headroom is small. From PR1154's frozen
+owner-audit receipt, subtracting its idle histogram from the complete profile
+gives the following average local paid profile over 144 calls:
+
+```text
+H1=42949/18, H2=8135/18, H3=15623/36,
+H4=4753/36, H5=82, H8=8
+```
+
+Applying `research/complex-local-word-ceiling/ceiling.py::ceiling()` with
+`m=73`, `families=896`, `stages=9`, `centre=64`, and grid `10^-15` brackets
+the relaxed complex saving root by
+
+```text
+421850048701/250000000000000 <= a* <= 337480038961/200000000000000.
+```
+
+Thus the retained transfer gives the PR1154 word a packing cap
+`kappa <= a*/(1+a*) <= 0.001684557671861340916...`. Its source-reported
+`kappa=0.001673260706543984` realizes 99.3293809% of the cap. This is an
+upper bound from a fractional idle relaxation, not an attained packing optimum
+or a supplier-admission result.
+
+## Derivation and scope
+
+The source receipt gives the complete rank profile
+`{1:344363,2:65097,3:62855,4:19012,5:11808,7:8,8:1152,11:2,48:4873}` and
+idle profile `{1:771,2:17,3:363,7:8,11:2,48:4873}`. Their difference is the
+aggregate local profile. Rank mass is 1,041,408, exactly `72*14336 + 64*144`;
+the idle mass is 58,969/36 per call and the local mass is 201,383/36 per call.
+The outer halving guard permits idle rank at most 51.
+
+The ceiling proof uses only aggregate local counts. Even though PR1154 selects
+different local prefixes on different calls, their moment contributions add.
+For each `a >= 0`, the cost per unit of idle rank,
+`(r/73)^(1-a)/r`, is non-increasing in `r`; therefore every idle histogram
+with rank at most 51 costs at least the fractional placement of all remaining
+mass at rank 51. The exact interval engine certifies the two sides of the root
+bracket. This covers every repacking of PR1154's fixed aggregate local profile
+under this coverage law and guard. It does not cover changes to the local word,
+port count, coverage law, template, centre charge, or outer recipe.
+
+The candidate's exact complex saving in `expected/EXACT-PRICE.json` is
+`1676065200585730447963/10^24`, below the ceiling. Its required saving for the
+reported kappa is `104578794158999/62395421205841001`. The selected bit
+supplier's source-bound saving remains
+`1733427039589844234749/10^24`, above that requirement, so the complex side
+still binds for this comparison. The selected-record baseline is a bindings
+and arithmetic check only.
+
+PR1154 remains a partially reviewed archive. Its whole-head native/provider,
+physical-owner, and complete-admission obligations were not rerun here. The
+source `OWNER-AUDIT.json` and exact-price receipt are hash-checked and their
+profile arithmetic is reconstructed; their underlying owner/native replay is
+not independently reproduced by this package. No kappa is selected or
+promoted.
+
+## Reproduce
+
+From the repository root:
+
+```sh
+python3 -B research/pr1154-packing-relaxation/verify.py --write
+python3 scripts/research_package.py --package research/pr1154-packing-relaxation --check-only
+python3 scripts/research_package.py --package research/pr1154-packing-relaxation
+```
+
+The first command regenerates `RESULT.json`; the default verifier checks it.
+The calculation uses Python's standard library and the pinned ceiling module.
+The registered hook checks input hashes, the coverage identity, rank split,
+exact interval endpoints, the candidate and bit-side comparison, and three
+failure controls. It does not run PR1154's full replay.
+
+## Open next questions
+
+Can an independent source-level reconstruction of PR1154's adaptive local
+profiles and idle histogram reproduce the hash-pinned owner-audit receipt?
+This matters because the present cap trusts that receipt as its input. The
+first step is to run `research/adaptive-kernel-demotion/audit_owner_table.py`
+against its frozen inputs in a separately budgeted audit. Its remaining blocker
+is the inherited native/provider and complete supplier-admission chain.
+
+## Credit
+
+PR1154 was contributed by Dugongue, building on PR1117, PR1111, and the
+retained T16 supplier lineage. The packing-ceiling lemma and exact interval
+engine come from `research/complex-local-word-ceiling/`, credited there to
+Douglas Colkitt with Claude assistance. This scoped application was prepared
+with OpenAI Codex assistance. The source construction retains its Apache-2.0
+license and notices; this new result is Apache-2.0.

research/pr1154-packing-relaxation/RESULT.json

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+{
+  "controls": {
+    "idle_rank_52": "rejected",
+    "local_profile_mass_over_coverage": "rejected",
+    "one_rank_unit_added_to_complete_profile": "rejected"
+  },
+  "limits": [
+    "The hash-pinned PR1154 owner-audit and exact-price receipts are inputs; their underlying owner/native replay was not independently reproduced.",
+    "PR1154 remains partially reviewed and is not a selected supplier.",
+    "The selected bit value is source-bound by the selected certificate; the full bit circuit was not replayed in this session."
+  ],
+  "model": {
+    "calls": 144,
+    "centre": 64,
+    "coverage_identity": "rank_mass = 72*live_stock + 64*calls",
+    "deficit": 5120,
+    "families": 896,
+    "idle_rank_cap": 51,
+    "live_stock": 14336,
+    "m": 73,
+    "rank_mass": "1041408",
+    "stages": 9
+  },
+  "packing_cap": {
+    "a_lower": "421850048701/250000000000000",
+    "a_root_lower_relaxation": [
+      "115792089237316018834055606565245307022430145434682530476350785458923278827839/115792089237316195423570985008687907853269984665640564039457584007913129639936",
+      "28948022309329004708513901641311326755607536358670632619087696364730819706969/28948022309329048855892746252171976963317496166410141009864396001978282409984"
+    ],
+    "a_root_upper_relaxation": [
+      "57896044618658177796543724602433634590596981195715896928494734661634808457269/57896044618658097711785492504343953926634992332820282019728792003956564819968",
+      "115792089237316355593087449204867269181193962391431793856989469323269616914575/115792089237316195423570985008687907853269984665640564039457584007913129639936"
+    ],
+    "a_upper": "337480038961/200000000000000",
+    "a_upper_decimal": "0.001687400194805000",
+    "candidate_a_fraction_realized": "1676065200585730447963/1687400194805000000000",
+    "candidate_a_fraction_realized_decimal": "0.993282569094061618",
+    "candidate_kappa_fraction_of_cap": "20951052087327073381748760039/21092502435062500000000000000",
+    "candidate_kappa_fraction_of_cap_decimal": "0.993293809107245103",
+    "kappa_upper": "337480038961/200337480038961",
+    "kappa_upper_decimal": "0.001684557671861340"
+  },
+  "profiles": {
+    "complete": {
+      "1": 344363,
+      "11": 2,
+      "2": 65097,
+      "3": 62855,
+      "4": 19012,
+      "48": 4873,
+      "5": 11808,
+      "7": 8,
+      "8": 1152
+    },
+    "idle": {
+      "1": 771,
+      "11": 2,
+      "2": 17,
+      "3": 363,
+      "48": 4873,
+      "7": 8
+    },
+    "idle_mass_per_call": "58969/36",
+    "local_mass_per_call": "201383/36",
+    "local_per_call": {
+      "1": "42949/18",
+      "2": "8135/18",
+      "3": "15623/36",
+      "4": "4753/36",
+      "5": "82",
+      "8": "8"
+    }
+  },
+  "scope": "Upper bound for all repackings of PR1154's fixed aggregate local profile under the 73-rank, 896-family, nine-stage, centre-64 coverage model and rank-51 halving guard. Fractional idle placement is allowed. Not an attained optimum, supplier admission, or bound for changed words or models.",
+  "source": {
+    "merge_commit": "998a33b0df8af40aa672c72585c61ad7e1bbe701",
+    "pr": 1154,
+    "pr_head": "390de2866a03758e7f4ddbb2846e5b2ee4e72154",
+    "selected_kappa": "836330098538459/500000000000000000",
+    "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129",
+    "supplier_source_head": "342b67f23dfa8f41a520a0d58978b2875e9eb0dd",
+    "task_base": "20ecf2891d80b5acf18d980b2164fb44ea7faa90"
+  },
+  "status": "PASS_PR1154_AGGREGATE_PACKING_RELAXATION",
+  "supplier_comparison": {
+    "candidate_complex_a_lower": "1676065200585730447963/1000000000000000000000000",
+    "candidate_kappa": "104578794158999/62500000000000000",
+    "candidate_kappa_decimal": "0.001673260706543984",
+    "candidate_required_a": "104578794158999/62395421205841001",
+    "complex_side_binds_for_this_comparison": true,
+    "selected_bit_a_lower": "1733427039589844234749/1000000000000000000000000",
+    "selected_bit_margin_over_candidate_required_a": "3579116105803355341226851043813143749/62395421205841001000000000000000000000000"
+  }
+}

research/pr1154-packing-relaxation/SOURCES.json

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+{
+  "schema_version": 1,
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "input",
+      "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81",
+      "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+    },
+    {
+      "path": "research/community-frontier1094-audit/ASSEMBLY.json",
+      "usage": "input",
+      "git_blob": "5fd676df060f3b450782fdf5ff5f6beb63a5eeb0",
+      "sha256": "1122cb3a575f8c788345fc1bf4c108ac7c3250fb81a5988671f5eb04b3ab3045"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5",
+      "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0"
+    },
+    {
+      "path": "research/adaptive-kernel-demotion/MANIFEST.json",
+      "usage": "input",
+      "git_blob": "902eca929548ad2b56e86e9cd07e17ee14de4035",
+      "sha256": "500ad2de1456f788783d10fb5570db80891451d36c081a0934cfad86a853e25b"
+    },
+    {
+      "path": "research/adaptive-kernel-demotion/README.md",
+      "usage": "input",
+      "git_blob": "d6180f40044ce63577618e21c227d2e8c16de1f2",
+      "sha256": "7731ec24896362dc45709279946c47b39a4b4e7207c826c220d85f270e0f769b"
+    },
+    {
+      "path": "research/adaptive-kernel-demotion/data/SOURCE-BINDING.json",
+      "usage": "input",
+      "git_blob": "87a2d5ae89f2c5fd3cd060cf8eedc9acea02047f",
+      "sha256": "818b400c402ad376dcf5ddde7e97b3727c3778e66b7bc765c3f5b290dc225853"
+    },
+    {
+      "path": "research/adaptive-kernel-demotion/expected/EXACT-PRICE.json",
+      "usage": "input",
+      "git_blob": "93ff6101ae1d7cfe21c8496fc74a87af23c10381",
+      "sha256": "3883ea5f2a3802bc13ba6b2c33ac749ad738b45bed13ae0f0fd6399d30b48a1a"
+    },
+    {
+      "path": "research/adaptive-kernel-demotion/expected/OWNER-AUDIT.json",
+      "usage": "input",
+      "git_blob": "0a5bb027b42c5280cca336acf8b253f9ed5343c8",
+      "sha256": "e7dc4874fa7d671765caab0f747519e2fd9f3f821a5daf58bba9b3a34f276ed9"
+    },
+    {
+      "path": "research/complex-local-word-ceiling/README.md",
+      "usage": "input",
+      "git_blob": "f5f742f8196da29d2c3f4dffb3c27685ca9401f6",
+      "sha256": "b60be039cb0e03e064a27407d0bce9e58908d793da5ee405c876de5aebfa5f81"
+    },
+    {
+      "path": "research/complex-local-word-ceiling/ceiling.py",
+      "usage": "input",
+      "git_blob": "6c0f54527d879396f689523bfde19928a9b6157c",
+      "sha256": "86a1432870b3b21d8454106ec9162fddc0471472d9214c590a1420f2426cedfc"
+    }
+  ]
+}

research/pr1154-packing-relaxation/TASK.json

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+{
+  "schema_version": 1,
+  "task_id": "selected-packing",
+  "priority_revision": 6,
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "original_card": {
+    "id": "selected-packing",
+    "question": "Is there a genuinely unsearched, explicitly bounded improvement to the selected packing?",
+    "starting_points": [
+      "certificates/selected-result.json",
+      "research/heterogeneous-owner-assembly/README.md",
+      "research/complex-local-word-ceiling/README.md"
+    ],
+    "methods": [
+      "Search a named unclaimed canonical candidate domain with a reproducible partition.",
+      "Prove a stronger scoped relaxation or exact optimum for one named residual subproblem."
+    ],
+    "acceptance_gate": "Check live PR overlap first, price both suppliers and distinguish a search best from an optimum. Report the word's packing cap from ceiling.ceiling() and the fraction of it realized; label packing gains as such.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Locate the selected packing source in the review and check live PRs for the same residual problem.",
+      "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Define an unclaimed canonical domain and a favorable bound before starting a new search.",
+    "bottleneck_link": "An actual paid-profile gain can improve the frontier up to the other supplier cap.",
+    "allowed_variations": [
+      "One bounded residual packing instance or exact relaxation.",
+      "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope."
+    ],
+    "scope_change_triggers": [
+      "Rerunning an existing search with only a different seed as a separate mathematical contribution."
+    ],
+    "overlap_terms": [
+      "T16",
+      "owner exchange",
+      "packing"
+    ],
+    "existing_checks": [
+      {
+        "scope": "Packing-independent ceiling for the selected paid profile under the one-unpaid-coordinate coverage and halving guard.",
+        "evidence": "docs/research/community-efficient1000-review.md",
+        "remaining": "A changed word or model requires new pricing; a local packing search must name uncovered scope.",
+        "status": "reviewed",
+        "source_commit": "836b19bfa309ceafbc8ee32a15e8c4b10dde7e11",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      }
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "For PR1154's fixed adaptive rank-seven T16 word, derive the aggregate local paid profile from its frozen complete and idle histograms and certify the remaining nine-stage packing cap under the one-unpaid-coordinate law and rank-51 halving guard.",
+  "scope_change_reason": "The selected PR1094 word and recent staged544/T488 packing scopes already have direct current coverage. PR1154 is a named alternate local word; the live queue ceiling census explicitly left it unscreened, and no current #1166 claim matched this aggregate-profile bound.",
+  "bottleneck_link": "This prices the complex-side headroom of a named candidate against the unchanged selected bit-side saving. It can reject further packing-only effort for this word if its ceiling is exhausted; it does not admit the candidate.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop if the source profile split fails its mass identity, if the source call count does not match 896/9 live families per call, or if the rank-51 halving guard is not valid. Do not extend to another word in this session.",
+  "outcome": "partial",
+  "evidence": "research/pr1154-packing-relaxation/RESULT.json certifies the aggregate PR1154 relaxation bracket and compares its cap with the source-reported candidate kappa and the selected bit-side lower saving. Exact inputs and the ceiling engine are pinned in SOURCES.json.",
+  "author": "macbook-16 Codex agent",
+  "ai_assistance": "OpenAI Codex assistance for source inspection, exact derivation, verifier and report.",
+  "open_questions": [
+    {
+      "question": "Can an independent source-level reconstruction of PR1154's adaptive local profiles and idle histogram reproduce its hash-pinned owner-audit receipt?",
+      "why_it_matters": "The packing ceiling uses that receipt as its fixed aggregate input; an independent reconstruction would check the receipt boundary without expanding the word search.",
+      "first_step": "Run research/adaptive-kernel-demotion/audit_owner_table.py against its frozen inputs and compare the complete and idle histograms with expected/OWNER-AUDIT.json.",
+      "blocked_by": "A full supplier-admission review still needs the inherited native/provider and complete physical-owner chain; this session did not rerun that chain."
+    }
+  ]
+}

research/pr1154-packing-relaxation/VERIFY.json

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+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "certificates/selected-result.json",
+    "research/adaptive-kernel-demotion/MANIFEST.json",
+    "research/adaptive-kernel-demotion/README.md",
+    "research/adaptive-kernel-demotion/data/SOURCE-BINDING.json",
+    "research/adaptive-kernel-demotion/expected/EXACT-PRICE.json",
+    "research/adaptive-kernel-demotion/expected/OWNER-AUDIT.json",
+    "research/complex-local-word-ceiling/README.md",
+    "research/complex-local-word-ceiling/ceiling.py",
+    "research/community-frontier1094-audit/ASSEMBLY.json"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Source pins; profile split, mass identity, halving guard; exact ceiling bracket; both-supplier comparison; three rejected mutations."
+    }
+  ]
+}