From c0f52b5b18bba78a6a5e8057edf9571bade88549 Mon Sep 17 00:00:00 2001 From: DaysSky Date: Sat, 24 Oct 2026 23:28:50 +0900 Subject: [PATCH] Price the p19 coded-reverse chain: conditional kappa 0.0033999964 The p19 coded-reverse chain is materialised, replayed and priced. Its factorized diagonal realises the invoiced target multiset exactly at p=3,4,5,8,19, so the census the invoice prices is the census of the word itself. Conditional endpoint kappa = 951999/280000000 = 0.0033999964, +12.31% over the selected record 605457647/200000000000 and +12.58% over 60403/20000000. Complex supplier 0.007578535190; the BIT supplier 17/5000 binds the endpoint. Word: 259 gates, 77 recodings, 17,248 monomial field maps, 68,992 scalar adds, 1,232 owned clears, no recursive Gaussian children; replay differs on 0 of 2,179,072 entries at p=19. One limitation is recorded rather than discharged: the inherited producer/compiler contract must admit this composition, and P19_PRECOMPILATION.json reports that no serialized chain-to-event compiler exists in the repository. Six superseded routes are quarantined. --- research/coded-reverse-word-p19/LIFT.json | 26 + .../OP-RECORD-SCHEMA.md | 58 + .../coded-reverse-word-p19/P19_ATTACH.json | 41 + .../coded-reverse-word-p19/P19_AUDIT.json | 321 + research/coded-reverse-word-p19/P19_BANK.json | 21 + .../coded-reverse-word-p19/P19_BINDING.json | 45 + .../coded-reverse-word-p19/P19_BRIDGE.json | 105 + .../coded-reverse-word-p19/P19_CALLER.json | 451 + .../coded-reverse-word-p19/P19_CASCADE.json | 86 + .../coded-reverse-word-p19/P19_CLAIM.json | 298 + .../coded-reverse-word-p19/P19_CONTRACT.json | 56 + .../P19_DESIGNWORD.json | 366 + research/coded-reverse-word-p19/P19_DIAG.json | 101 + .../P19_DIAGCENSUS.json | 1296 ++ .../coded-reverse-word-p19/P19_FACTOR.json | 102 + .../coded-reverse-word-p19/P19_FAMILY.json | 71 + .../P19_FORWARD_PROGRAM.json | 9853 ++++++++++ .../coded-reverse-word-p19/P19_FRAMES.json | 139 + .../coded-reverse-word-p19/P19_GAUGE.json | 809 + .../coded-reverse-word-p19/P19_INVARIANT.json | 497 + research/coded-reverse-word-p19/P19_LIFT.json | 24 + .../P19_LOWERBOUND.json | 183 + .../coded-reverse-word-p19/P19_LOWERING.json | 31 + .../P19_MACRO_RESOURCES.json | 33 + .../P19_NATIVE_APPLY.json | 107 + .../P19_NATIVE_MACRO.json.gz | Bin 0 -> 566236 bytes .../P19_NATIVE_MACRO_REPLAY.json | 6005 +++++++ .../coded-reverse-word-p19/P19_P3FRAMES.json | 147 + .../coded-reverse-word-p19/P19_PLAIN.json | 182 + .../P19_PRECOMPILATION.json | 66 + .../P19_RECODING_PROGRAM.json | 14963 ++++++++++++++++ .../coded-reverse-word-p19/P19_REPRICE.json | 71 + .../P19_REVERSE_PROGRAM.json | 1633 ++ .../coded-reverse-word-p19/P19_ROWFRAME.json | 94 + .../P19_STATE_TRACE.json | 8265 +++++++++ .../coded-reverse-word-p19/P19_SYMBOLIC.json | 427 + .../coded-reverse-word-p19/P19_TARGETS.json | 81 + .../coded-reverse-word-p19/P19_UNITS.json | 192 + research/coded-reverse-word-p19/P19_WORD.json | 69 + research/coded-reverse-word-p19/PR-DRAFT.md | 54 + research/coded-reverse-word-p19/PR.md | 56 + research/coded-reverse-word-p19/README.md | 146 + research/coded-reverse-word-p19/RESULT.json | 1150 ++ research/coded-reverse-word-p19/SOURCES.json | 98 + research/coded-reverse-word-p19/TASK.json | 158 + research/coded-reverse-word-p19/VALIDATION.md | 23 + research/coded-reverse-word-p19/VERIFY.json | 62 + .../full_p19_diagonalization.py | 19 + research/coded-reverse-word-p19/p19_attach.py | 107 + research/coded-reverse-word-p19/p19_audit.py | 147 + research/coded-reverse-word-p19/p19_bank.py | 183 + .../coded-reverse-word-p19/p19_binding.py | 93 + research/coded-reverse-word-p19/p19_bridge.py | 142 + research/coded-reverse-word-p19/p19_caller.py | 144 + .../coded-reverse-word-p19/p19_cascade.py | 111 + research/coded-reverse-word-p19/p19_claim.py | 486 + .../coded-reverse-word-p19/p19_contract.py | 131 + .../coded-reverse-word-p19/p19_designword.py | 124 + .../coded-reverse-word-p19/p19_diagcensus.py | 129 + .../p19_factor_search.py | 117 + research/coded-reverse-word-p19/p19_family.py | 89 + .../p19_forward_program.py | 175 + research/coded-reverse-word-p19/p19_frames.py | 118 + research/coded-reverse-word-p19/p19_gates.py | 187 + research/coded-reverse-word-p19/p19_gauge.py | 163 + .../coded-reverse-word-p19/p19_invariant.py | 99 + research/coded-reverse-word-p19/p19_lift.py | 148 + .../coded-reverse-word-p19/p19_lowerbound.py | 76 + .../coded-reverse-word-p19/p19_lowering.py | 132 + .../p19_macro_resources.py | 68 + .../p19_native_apply.py | 198 + .../p19_native_emitter.py | 137 + .../p19_native_macro_replay.py | 121 + .../p19_native_symbolic.py | 149 + .../coded-reverse-word-p19/p19_p3frames.py | 123 + research/coded-reverse-word-p19/p19_plain.py | 165 + .../p19_precompilation.py | 139 + .../coded-reverse-word-p19/p19_query_reuse.py | 155 + .../p19_recoding_program.py | 154 + .../coded-reverse-word-p19/p19_reprice.py | 103 + .../p19_reverse_program.py | 82 + .../p19_reverse_segment.py | 123 + .../coded-reverse-word-p19/p19_rowframe.py | 106 + .../coded-reverse-word-p19/p19_sparseT.py | 195 + .../coded-reverse-word-p19/p19_state_trace.py | 112 + .../coded-reverse-word-p19/p19_targets.py | 113 + research/coded-reverse-word-p19/p19_units.py | 160 + research/coded-reverse-word-p19/p19_word.py | 265 + .../physical_gauge_lift.py | 310 + research/coded-reverse-word-p19/verify.py | 270 + 90 files changed, 55430 insertions(+) create mode 100644 research/coded-reverse-word-p19/LIFT.json create mode 100644 research/coded-reverse-word-p19/OP-RECORD-SCHEMA.md create mode 100644 research/coded-reverse-word-p19/P19_ATTACH.json create mode 100644 research/coded-reverse-word-p19/P19_AUDIT.json create mode 100644 research/coded-reverse-word-p19/P19_BANK.json create mode 100644 research/coded-reverse-word-p19/P19_BINDING.json create mode 100644 research/coded-reverse-word-p19/P19_BRIDGE.json create mode 100644 research/coded-reverse-word-p19/P19_CALLER.json create mode 100644 research/coded-reverse-word-p19/P19_CASCADE.json create mode 100644 research/coded-reverse-word-p19/P19_CLAIM.json create mode 100644 research/coded-reverse-word-p19/P19_CONTRACT.json create mode 100644 research/coded-reverse-word-p19/P19_DESIGNWORD.json create mode 100644 research/coded-reverse-word-p19/P19_DIAG.json create mode 100644 research/coded-reverse-word-p19/P19_DIAGCENSUS.json create mode 100644 research/coded-reverse-word-p19/P19_FACTOR.json create mode 100644 research/coded-reverse-word-p19/P19_FAMILY.json create mode 100644 research/coded-reverse-word-p19/P19_FORWARD_PROGRAM.json create mode 100644 research/coded-reverse-word-p19/P19_FRAMES.json create mode 100644 research/coded-reverse-word-p19/P19_GAUGE.json create mode 100644 research/coded-reverse-word-p19/P19_INVARIANT.json create mode 100644 research/coded-reverse-word-p19/P19_LIFT.json create mode 100644 research/coded-reverse-word-p19/P19_LOWERBOUND.json create mode 100644 research/coded-reverse-word-p19/P19_LOWERING.json create mode 100644 research/coded-reverse-word-p19/P19_MACRO_RESOURCES.json create mode 100644 research/coded-reverse-word-p19/P19_NATIVE_APPLY.json create mode 100644 research/coded-reverse-word-p19/P19_NATIVE_MACRO.json.gz create mode 100644 research/coded-reverse-word-p19/P19_NATIVE_MACRO_REPLAY.json create mode 100644 research/coded-reverse-word-p19/P19_P3FRAMES.json create mode 100644 research/coded-reverse-word-p19/P19_PLAIN.json create mode 100644 research/coded-reverse-word-p19/P19_PRECOMPILATION.json create mode 100644 research/coded-reverse-word-p19/P19_RECODING_PROGRAM.json create mode 100644 research/coded-reverse-word-p19/P19_REPRICE.json create mode 100644 research/coded-reverse-word-p19/P19_REVERSE_PROGRAM.json create mode 100644 research/coded-reverse-word-p19/P19_ROWFRAME.json create mode 100644 research/coded-reverse-word-p19/P19_STATE_TRACE.json create mode 100644 research/coded-reverse-word-p19/P19_SYMBOLIC.json create mode 100644 research/coded-reverse-word-p19/P19_TARGETS.json create mode 100644 research/coded-reverse-word-p19/P19_UNITS.json create mode 100644 research/coded-reverse-word-p19/P19_WORD.json create mode 100644 research/coded-reverse-word-p19/PR-DRAFT.md create mode 100644 research/coded-reverse-word-p19/PR.md create mode 100644 research/coded-reverse-word-p19/README.md create mode 100644 research/coded-reverse-word-p19/RESULT.json create mode 100644 research/coded-reverse-word-p19/SOURCES.json create mode 100644 research/coded-reverse-word-p19/TASK.json create mode 100644 research/coded-reverse-word-p19/VALIDATION.md create mode 100644 research/coded-reverse-word-p19/VERIFY.json create mode 100644 research/coded-reverse-word-p19/full_p19_diagonalization.py create mode 100644 research/coded-reverse-word-p19/p19_attach.py create mode 100644 research/coded-reverse-word-p19/p19_audit.py create mode 100644 research/coded-reverse-word-p19/p19_bank.py create mode 100644 research/coded-reverse-word-p19/p19_binding.py create mode 100644 research/coded-reverse-word-p19/p19_bridge.py create mode 100644 research/coded-reverse-word-p19/p19_caller.py create mode 100644 research/coded-reverse-word-p19/p19_cascade.py create mode 100644 research/coded-reverse-word-p19/p19_claim.py create mode 100644 research/coded-reverse-word-p19/p19_contract.py create mode 100644 research/coded-reverse-word-p19/p19_designword.py create mode 100644 research/coded-reverse-word-p19/p19_diagcensus.py create mode 100644 research/coded-reverse-word-p19/p19_factor_search.py create mode 100644 research/coded-reverse-word-p19/p19_family.py create mode 100644 research/coded-reverse-word-p19/p19_forward_program.py create mode 100644 research/coded-reverse-word-p19/p19_frames.py create mode 100644 research/coded-reverse-word-p19/p19_gates.py create mode 100644 research/coded-reverse-word-p19/p19_gauge.py create mode 100644 research/coded-reverse-word-p19/p19_invariant.py create mode 100644 research/coded-reverse-word-p19/p19_lift.py create mode 100644 research/coded-reverse-word-p19/p19_lowerbound.py create mode 100644 research/coded-reverse-word-p19/p19_lowering.py create mode 100644 research/coded-reverse-word-p19/p19_macro_resources.py create mode 100644 research/coded-reverse-word-p19/p19_native_apply.py create mode 100644 research/coded-reverse-word-p19/p19_native_emitter.py create mode 100644 research/coded-reverse-word-p19/p19_native_macro_replay.py create mode 100644 research/coded-reverse-word-p19/p19_native_symbolic.py create mode 100644 research/coded-reverse-word-p19/p19_p3frames.py create mode 100644 research/coded-reverse-word-p19/p19_plain.py create mode 100644 research/coded-reverse-word-p19/p19_precompilation.py create mode 100644 research/coded-reverse-word-p19/p19_query_reuse.py create mode 100644 research/coded-reverse-word-p19/p19_recoding_program.py create mode 100644 research/coded-reverse-word-p19/p19_reprice.py create mode 100644 research/coded-reverse-word-p19/p19_reverse_program.py create mode 100644 research/coded-reverse-word-p19/p19_reverse_segment.py create mode 100644 research/coded-reverse-word-p19/p19_rowframe.py create mode 100644 research/coded-reverse-word-p19/p19_sparseT.py create mode 100644 research/coded-reverse-word-p19/p19_state_trace.py create mode 100644 research/coded-reverse-word-p19/p19_targets.py create mode 100644 research/coded-reverse-word-p19/p19_units.py create mode 100644 research/coded-reverse-word-p19/p19_word.py create mode 100644 research/coded-reverse-word-p19/physical_gauge_lift.py create mode 100644 research/coded-reverse-word-p19/verify.py diff --git a/research/coded-reverse-word-p19/LIFT.json b/research/coded-reverse-word-p19/LIFT.json new file mode 100644 index 0000000000..058d7caaf7 --- /dev/null +++ b/research/coded-reverse-word-p19/LIFT.json @@ -0,0 +1,26 @@ +{ + "commuting_letters": [ + "I", + "R" + ], + "p19_entries": 2179072, + "p19_recodings": { + "even-gauge": 77, + "odd-gauge": 77 + }, + "p2_entries": 229376, + "p2_recodings": { + "coded-all/R": 14, + "even-gauge/R": 9, + "odd-gauge/I": 9, + "odd-gauge/R": 9, + "transient/D": 6 + }, + "rejected_letters": [ + "D", + "Q" + ], + "scope": "exact operator identity and local gauge bill; no tariff, compiler or kappa claim", + "status": "PASS_CODED_REVERSE_GLOBAL_GAUGE_LIFT", + "thin_source": "S = Q D C^-1 Q^-1 D^-1 = C^-1" +} diff --git a/research/coded-reverse-word-p19/OP-RECORD-SCHEMA.md b/research/coded-reverse-word-p19/OP-RECORD-SCHEMA.md new file mode 100644 index 0000000000..551c45bfda --- /dev/null +++ b/research/coded-reverse-word-p19/OP-RECORD-SCHEMA.md @@ -0,0 +1,58 @@ +# The frozen native op stream: the specification, and what it covers + +## Where the specification is + +`research/kappa-lean-verification-20261022/` holds the PR4470/PR4610 lineage's own transcription of +the native word. It is the authority for the record encoding, and it is pinned in +`P19_NATIVE_APPLY.json` by path and SHA-256: + +| file | what it defines | +|---|---| +| `NativeCore.lean` | the event kinds, the `step` transition with its frame guards, the `scalarAllowance` tariff, and `checkSegment` — all checked by ordinary kernel reduction | +| `native_generate.py` | the record -> event `encode`, the `paid_index`/`warp_index` catalogues, and the chunked state loop | + +Upstream these run under Lean on the word whose payload SHA-256 is +`4409d2d9328fffbd276bb03fb800f59a33ec3b2ab15f79a330a7af66e75110cc` +(the word frozen in `research/warp-interface-20261022/`, present here). + +## The schema + +Event kinds, from `NativeCore.lean`: `0 marker, 1 climb, 2 center, 3 warp, 4 add, 5 scale, 6 clear, +7 copy, 8 adapter`. Persistent roles are `0..631`; role `632` is the owned C₀. A record maps to a +nine-field event `(kind, role, source, input, output, reference, operator, numerator, denominator)`: + +| record | event | +|---|---| +| `["phase", name]` | kind 0, no state change | +| `["adapter", name, a, b]` | kind 8, no state change | +| `["climb", tag, role, from, to, rank]` | kind 1: the role moves `from -> to`, `paid[rank] += 1`; must be ascending | +| `["center", a, b, rank, …]` | kind 2: role 632 moves `a -> b`, `paid[rank] += 1` | +| `["warp", ["L", role], op, from, to]` | kind 3: the role moves `from -> to` under operator `op` (negative = inverse) | +| `["scalar", ["add", dst, src, ca, cb], field]` | kind 4, both roles must hold frame `field` | +| `["scalar", ["scale", dst, num, den], field]` | kind 5 | +| `["scalar", ["clear", dst], field]` | kind 6, targets role 632 | +| `["scalar", ["copy", dst, src], field]` | kind 7 | + +## What the specification deliberately excludes + +`NativeCore.lean`'s own docstring: *"This file deliberately does not model amplitudes, Clifford +phases, or the free noncommutative endpoint algebra."* So it certifies the **frame trace, the paid +histogram and the scalar tariff** — not operator equality. + +## What this package does with it + +`p19_native_apply.py` re-implements `encode` + `step` + `scalarAllowance` in Python, independently of +the Lean run, and executes both orientations of the frozen word this package prices: 21,449 records +and 20,991 state steps each, every declared input frame equal to the role's current frame, the +persistent roles ending on `canonical.final`, and the paid histogram `{1:2201, 2:412, 3:510, 4:127, +5:40, 8:8}` plus the tariff (158,120 forward / 158,168 backward) **derived** from the trace. As a +control the lineage word derives its own `{1:2201, 2:412, 3:506, 4:135, 5:36, 8:8}`. + +The operator side is covered separately by `P19_LOWERING.json`, which binds each emitted gate to the +primitive stated in `research/coded-native-caller/PHYSICAL.md`. + +## What is still missing + +Encoding the 259 p19 chain gates *into* this event stream — i.e. the producer's own operator/phase +lowering of a unit. That artefact exists upstream, not in this repository, so producer instantiation +of the chain remains an inherited premise. diff --git a/research/coded-reverse-word-p19/P19_ATTACH.json b/research/coded-reverse-word-p19/P19_ATTACH.json new file mode 100644 index 0000000000..a7ba40a49a --- /dev/null +++ b/research/coded-reverse-word-p19/P19_ATTACH.json @@ -0,0 +1,41 @@ +{ + "D_mass": 68782, + "D_status": "inherited paid profile, unchanged and not derived", + "T_mass": 12008, + "T_realised": { + "153": 1232, + "17": 336, + "25": 336, + "33": 336, + "4": 532, + "41": 336, + "49": 336, + "57": 336, + "65": 336, + "7": 133, + "73": 336, + "8": 893, + "9": 6530 + }, + "complex_root_invoiced": 0.00757853519, + "complex_root_realised": 0.20984141991109154, + "guards": { + "alpha": 0.7000523544831928, + "alpha_limit": "999999999/1000000000", + "alpha_pass": true, + "delta": 0.6689557772031509, + "delta_limit": "97/100", + "delta_pass": true, + "gamma": 0.6775343896533879, + "gamma_limit": "97/100", + "gamma_pass": true + }, + "kappa": "951999/280000000", + "kappa_decimal": 0.0033999964285714285, + "note": "the realised census has a larger complex root than the invoice model, so the complex side has more slack at the BIT-capped endpoint; the delta guard is the one test that can tighten, and it is reported explicitly", + "raw_moment_sign_at_tested": "positive", + "status": "SUPERSEDED_DIAGNOSTIC", + "superseded_because": "attachment computed from the row-closure census", + "tested_saving": "2380001/700000000", + "used_for_active_claim": false +} diff --git a/research/coded-reverse-word-p19/P19_AUDIT.json b/research/coded-reverse-word-p19/P19_AUDIT.json new file mode 100644 index 0000000000..d0b2b10c8d --- /dev/null +++ b/research/coded-reverse-word-p19/P19_AUDIT.json @@ -0,0 +1,321 @@ +{ + "cases": { + "p3_IT": { + "cancelled_keys": 0, + "denominator_clearing_invariant": true, + "designed_per_role": [ + [ + 1, + 3, + 5 + ], + [ + 1, + 3, + 5 + ], + [ + 1 + ], + [ + 1 + ], + [ + 5 + ], + [ + 5 + ] + ], + "designed_sizes": { + "1": 4, + "3": 2 + }, + "full_equals_thinned": true, + "full_sizes_all_stages": { + "3": 3, + "7": 3 + }, + "full_sizes_retained": { + "1": 3, + "3": 3 + }, + "merged_keys": 0, + "thin_is_quotient_of_combined": true, + "thinned_sizes_retained": { + "1": 3, + "3": 3 + }, + "witness_rows": { + "0": { + "entries": [ + { + "coef": "1", + "col": 0, + "key": [ + -1, + 0, + 1, + 0, + 0, + 0, + 0, + 0 + ] + }, + { + "coef": "1", + "col": 2, + "key": [ + -1, + 0, + 1, + 0, + 0, + 0, + 0, + 0 + ] + }, + { + "coef": "-1", + "col": 2, + "key": [ + -1, + 0, + 1, + 0, + 1, + 0, + 1, + 0 + ] + } + ], + "frame_all": [ + 1, + 3, + 5 + ], + "frame_retained": [ + 1, + 3, + 5 + ] + }, + "1": { + "entries": [ + { + "coef": "1", + "col": 1, + "key": [ + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0 + ] + } + ], + "frame_all": [ + 1 + ], + "frame_retained": [ + 1 + ] + }, + "2": { + "entries": [ + { + "coef": "1", + "col": 2, + "key": [ + -1, + 0, + 1, + 0, + 1, + 0, + 1, + 0 + ] + } + ], + "frame_all": [ + 1, + 3, + 5 + ], + "frame_retained": [ + 1, + 3, + 5 + ] + }, + "3": { + "entries": [ + { + "coef": "1", + "col": 1, + "key": [ + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0 + ] + }, + { + "coef": "-1", + "col": 1, + "key": [ + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0 + ] + }, + { + "coef": "1", + "col": 3, + "key": [ + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0 + ] + } + ], + "frame_all": [ + 1, + 3, + 5 + ], + "frame_retained": [ + 1, + 3, + 5 + ] + }, + "4": { + "entries": [ + { + "coef": "1", + "col": 4, + "key": [ + -1, + 0, + 0, + 0, + 0, + 0, + 1, + 0 + ] + } + ], + "frame_all": [ + 5 + ], + "frame_retained": [ + 5 + ] + }, + "5": { + "entries": [ + { + "coef": "1", + "col": 5, + "key": [ + 1, + 0, + 0, + 0, + 0, + 0, + 1, + 0 + ] + } + ], + "frame_all": [ + 5 + ], + "frame_retained": [ + 5 + ] + } + } + }, + "p4_IIT": { + "cancelled_keys": 0, + "denominator_clearing_invariant": true, + "designed_sizes": { + "1": 4, + "2": 2, + "4": 2 + }, + "full_equals_thinned": true, + "full_sizes_all_stages": { + "3": 3, + "5": 1, + "9": 4 + }, + "full_sizes_retained": { + "1": 3, + "2": 1, + "4": 4 + }, + "merged_keys": 0, + "thin_is_quotient_of_combined": true, + "thinned_sizes_retained": { + "1": 3, + "2": 1, + "4": 4 + } + }, + "p5_IITT": { + "cancelled_keys": 0, + "denominator_clearing_invariant": true, + "designed_sizes": { + "1": 4, + "2": 4, + "5": 2 + }, + "full_equals_thinned": true, + "full_sizes_all_stages": { + "3": 3, + "5": 3, + "11": 4 + }, + "full_sizes_retained": { + "1": 3, + "2": 3, + "5": 4 + }, + "merged_keys": 0, + "thin_is_quotient_of_combined": true, + "thinned_sizes_retained": { + "1": 3, + "2": 3, + "5": 4 + } + } + }, + "conclusion": "the frames are computed from the fully combined controller matrix, thinning is exactly the retained-stage projection, coefficients are exact and the frame survives denominator clearing; the witnessed p=3 rows are the raw combined monomials", + "status": "PASS_FRAME_INVARIANT_CONFIRMED" +} diff --git a/research/coded-reverse-word-p19/P19_BANK.json b/research/coded-reverse-word-p19/P19_BANK.json new file mode 100644 index 0000000000..88e7a6606d --- /dev/null +++ b/research/coded-reverse-word-p19/P19_BANK.json @@ -0,0 +1,21 @@ +{ + "addresses_per_role": 131072, + "binding": "the trace gate list and the controller matrix agree on every address of every role at the smallest faithful ambient (two blocks plus the shared centre)", + "decoder_contract": "literal stage IDs and indicator vectors agree on all 36 retained p=19 idles and on the boundary cases", + "differing_entries": [ + 0, + 0, + 0, + 0 + ], + "gates": 20, + "p": 2, + "pattern": "T", + "retained_stages": [ + 1, + 3 + ], + "roles": 4, + "scope": "p=19 needs 2**153 addresses, so the address-level check is done at p=2 and the p=19 word is certified by the trace identity in the controller algebra", + "status": "PASS_ADDRESS_LEVEL_TRACE_REPLAY" +} diff --git a/research/coded-reverse-word-p19/P19_BINDING.json b/research/coded-reverse-word-p19/P19_BINDING.json new file mode 100644 index 0000000000..2603de6d45 --- /dev/null +++ b/research/coded-reverse-word-p19/P19_BINDING.json @@ -0,0 +1,45 @@ +{ + "binding": "inherited operation vocabulary and invocation-budget binding: each chain gate is an invocation of the frozen program or of a kind it already contains, and the raw budget is explicit", + "chain_counts": { + "BRIDGE": 108, + "FORWARD": 20, + "GAUGE_LOAD": 19, + "GAUGE_UNLOAD": 19, + "IDLE": 36, + "LETTER": 19, + "REVERSE": 19, + "SWAP": 19 + }, + "does_not_show": "field-level equality between one invocation and the frozen program operator, which needs the program semantics that this package does not implement", + "fraction_of_allowance": 0.000837, + "invocation_inventory": { + "backward": 21449, + "forward": 21449 + }, + "invocation_kinds": { + "backward": { + "adapter": 448, + "center": 8, + "climb": 3290, + "phase": 10, + "scalar": 17453, + "warp": 240 + }, + "forward": { + "adapter": 448, + "center": 8, + "climb": 3290, + "phase": 10, + "scalar": 17453, + "warp": 240 + } + }, + "invocations_at_p19": { + "backward": 19, + "forward": 20 + }, + "not_full_lowering": "this is not a lowering proof. The remaining obligation is that one generated invocation is semantically equal to the frozen native invocation, including field state, ownership, scratch, precision, adapters, phases and output gauges", + "raw_allowance": 1000000000, + "raw_operation_budget": 836511, + "status": "PASS_INHERITED_VOCABULARY_AND_INVOCATION_BUDGET" +} diff --git a/research/coded-reverse-word-p19/P19_BRIDGE.json b/research/coded-reverse-word-p19/P19_BRIDGE.json new file mode 100644 index 0000000000..2b4fe838e8 --- /dev/null +++ b/research/coded-reverse-word-p19/P19_BRIDGE.json @@ -0,0 +1,105 @@ +{ + "adapter_count_per_direction": { + "backward": 448, + "forward": 448 + }, + "adapter_positions": { + "new_to_old": [ + 15611, + 15834 + ], + "old_to_new": [ + 6038, + 6261 + ] + }, + "between_inventory": { + "center": 8, + "climb": 2907, + "phase": 6, + "scalar": 6332, + "warp": 96 + }, + "center_free_inventory": { + "backward": { + "adapter": 448, + "climb": 3290, + "phase": 10, + "scalar": 24057, + "warp": 240 + }, + "forward": { + "adapter": 448, + "climb": 3290, + "phase": 10, + "scalar": 24057, + "warp": 240 + } + }, + "deletion_argument": "count level only: the pricer is blind to the deleted operations, so the census and root are untouched -- but the position analysis shows the deleted adapters bracket the middle section, so the deletion does not preserve the operator", + "finding": "the adapters convert the chart before and after a middle section of 9349 operations, so they are a conjugation of that section rather than removable normalizers. Deleting them leaves the middle running in the old chart, which is a different operator", + "frozen_inventory": { + "backward": { + "adapter": 448, + "center": 8, + "climb": 3290, + "phase": 10, + "scalar": 17453, + "warp": 240 + }, + "forward": { + "adapter": 448, + "center": 8, + "climb": 3290, + "phase": 10, + "scalar": 17453, + "warp": 240 + } + }, + "invoice_dependency": { + "checked_statically": true, + "consequence": "the deleted adapters cannot enter the T/D census or the root", + "forbidden_identifiers_absent": [ + "adapter", + "inventory", + "recoding", + "operation", + "schedule", + "field_bill", + "programs" + ], + "reads": "the pattern, the retained stages, the two rank histograms and the paid profile H", + "signature": "invoice(p, pat, thick, prof)" + }, + "listing_to_native": { + "BRIDGE": "scalar", + "FORWARD": "scalar", + "GAUGE_LOAD": "adapter", + "GAUGE_UNLOAD": "adapter", + "IDLE": "climb", + "LETTER": "warp", + "REVERSE": "scalar", + "SWAP": "scalar", + "checked": "every mapped native kind is present in the pinned program" + }, + "normalizer_charge_in_PHYSICAL": "448 monomial maps per native invocation", + "operations_between": 9349, + "reduced_inventory": { + "backward": { + "center": 8, + "climb": 3290, + "phase": 10, + "scalar": 17453, + "warp": 240 + }, + "forward": { + "center": 8, + "climb": 3290, + "phase": 10, + "scalar": 17453, + "warp": 240 + } + }, + "status": "PASS_ADAPTERS_ARE_PART_OF_THE_INHERITED_UNIT", + "what_this_shows": "the adapters number 448 per direction, exactly the normalizer charge, and their deletion is a pure count-level sub-multiset" +} diff --git a/research/coded-reverse-word-p19/P19_CALLER.json b/research/coded-reverse-word-p19/P19_CALLER.json new file mode 100644 index 0000000000..0c0000a9f9 --- /dev/null +++ b/research/coded-reverse-word-p19/P19_CALLER.json @@ -0,0 +1,451 @@ +{ + "base_condition": "research/coded-native-caller/PHYSICAL.md:59 - productive main ranks depend on the completed caller, its initial/final gauges and every paid correction", + "completed_caller": { + "ambient_rank": 153, + "gates": 259, + "kinds": { + "BRIDGE": 108, + "FORWARD": 20, + "GAUGE_LOAD": 19, + "GAUGE_UNLOAD": 19, + "IDLE": 36, + "LETTER": 19, + "REVERSE": 19, + "SWAP": 19 + }, + "replay_entries": 2179072, + "roles": 38, + "stages": 39, + "units": 19 + }, + "derivation": { + "conclusion": "the abstract/controller caller, its endpoint, its census and every paid-correction record are exhibited, and the ranks follow for that endpoint through the four links above. Encoding this p19 chain into the producer native event stream remains an INHERITED PREMISE, so the admitted physical caller is not covered here", + "step 1: the caller computes the standard word": { + "claim": "the 259 gates replayed against the standard word differ on 0 of the replayed entries", + "entries": 2179072, + "receipt": "P19_WORD.json", + "residual": 0 + }, + "step 2: the word is the controller operator for every block count": { + "claim": "Phi is a ring homomorphism on the retained-stage monomial ring and every gate kind is the Phi-image of its monomial, so the gate list realises the operator at every block count", + "exponent_pairs": 263169, + "receipt": "P19_LIFT.json", + "status": "PASS_LIFTING_LEMMA" + }, + "step 3: the operator has the design target census": { + "claim": "the factorisation diagonal of that operator holds exactly the design multiset at p=3,4,5,8,19", + "receipt": "P19_DIAGCENSUS.json", + "status": "PASS_DIAGONAL_CENSUS_IS_INVOICED" + }, + "step 4: the census is the invoice": { + "claim": "T measured on the diagonal equals the invoiced target histogram rank by rank", + "equality": true, + "receipt": "P19_DIAGCENSUS.json" + } + }, + "explicitly_not_proved": "that this p19 chain is encoded into the producer native event stream, hence that it is an admitted physical caller", + "final_gauge": { + "order": "unload then signed swap, so the roles are uncoded when the swap is applied", + "per_unit": true, + "swap_signs": [ + -1 + ], + "swaps": [ + [ + "SWAP", + 0, + 1, + -1 + ], + [ + "SWAP", + 2, + 3, + -1 + ], + [ + "SWAP", + 4, + 5, + -1 + ], + [ + "SWAP", + 6, + 7, + -1 + ], + [ + "SWAP", + 8, + 9, + -1 + ], + [ + "SWAP", + 10, + 11, + -1 + ], + [ + "SWAP", + 12, + 13, + -1 + ], + [ + "SWAP", + 14, + 15, + -1 + ], + [ + "SWAP", + 16, + 17, + -1 + ], + [ + "SWAP", + 18, + 19, + -1 + ], + [ + "SWAP", + 20, + 21, + -1 + ], + [ + "SWAP", + 22, + 23, + -1 + ], + [ + "SWAP", + 24, + 25, + -1 + ], + [ + "SWAP", + 26, + 27, + -1 + ], + [ + "SWAP", + 28, + 29, + -1 + ], + [ + "SWAP", + 30, + 31, + -1 + ], + [ + "SWAP", + 32, + 33, + -1 + ], + [ + "SWAP", + 34, + 35, + -1 + ], + [ + "SWAP", + 36, + 37, + -1 + ] + ], + "type": "C followed by the signed exchange, denominators [1] standard / [1, 13] coded", + "unload_roles": [ + 1, + 3, + 5, + 7, + 9, + 11, + 13, + 15, + 17, + 19, + 21, + 23, + 25, + 27, + 29, + 31, + 33, + 35, + 37 + ], + "unloads": [ + [ + "GAUGE_UNLOAD", + 1, + "C" + ], + [ + "GAUGE_UNLOAD", + 3, + "C" + ], + [ + "GAUGE_UNLOAD", + 5, + "C" + ], + [ + "GAUGE_UNLOAD", + 7, + "C" + ], + [ + "GAUGE_UNLOAD", + 9, + "C" + ], + [ + "GAUGE_UNLOAD", + 11, + "C" + ], + [ + "GAUGE_UNLOAD", + 13, + "C" + ], + [ + "GAUGE_UNLOAD", + 15, + "C" + ], + [ + "GAUGE_UNLOAD", + 17, + "C" + ], + [ + "GAUGE_UNLOAD", + 19, + "C" + ], + [ + "GAUGE_UNLOAD", + 21, + "C" + ], + [ + "GAUGE_UNLOAD", + 23, + "C" + ], + [ + "GAUGE_UNLOAD", + 25, + "C" + ], + [ + "GAUGE_UNLOAD", + 27, + "C" + ], + [ + "GAUGE_UNLOAD", + 29, + "C" + ], + [ + "GAUGE_UNLOAD", + 31, + "C" + ], + [ + "GAUGE_UNLOAD", + 33, + "C" + ], + [ + "GAUGE_UNLOAD", + 35, + "C" + ], + [ + "GAUGE_UNLOAD", + 37, + "C" + ] + ] + }, + "initial_gauge": { + "every_role_odd": true, + "gates": [ + [ + "GAUGE_LOAD", + 1, + "C^-1" + ], + [ + "GAUGE_LOAD", + 3, + "C^-1" + ], + [ + "GAUGE_LOAD", + 5, + "C^-1" + ], + [ + "GAUGE_LOAD", + 7, + "C^-1" + ], + [ + "GAUGE_LOAD", + 9, + "C^-1" + ], + [ + "GAUGE_LOAD", + 11, + "C^-1" + ], + [ + "GAUGE_LOAD", + 13, + "C^-1" + ], + [ + "GAUGE_LOAD", + 15, + "C^-1" + ], + [ + "GAUGE_LOAD", + 17, + "C^-1" + ], + [ + "GAUGE_LOAD", + 19, + "C^-1" + ], + [ + "GAUGE_LOAD", + 21, + "C^-1" + ], + [ + "GAUGE_LOAD", + 23, + "C^-1" + ], + [ + "GAUGE_LOAD", + 25, + "C^-1" + ], + [ + "GAUGE_LOAD", + 27, + "C^-1" + ], + [ + "GAUGE_LOAD", + 29, + "C^-1" + ], + [ + "GAUGE_LOAD", + 31, + "C^-1" + ], + [ + "GAUGE_LOAD", + 33, + "C^-1" + ], + [ + "GAUGE_LOAD", + 35, + "C^-1" + ], + [ + "GAUGE_LOAD", + 37, + "C^-1" + ] + ], + "per_unit": true, + "roles": [ + 1, + 3, + 5, + 7, + 9, + 11, + 13, + 15, + 17, + 19, + 21, + 23, + 25, + 27, + 29, + 31, + 33, + 35, + 37 + ], + "type": "the code C^-1 applied per unit on its own odd role" + }, + "p": 19, + "paid_corrections": { + "adapter_charge_per_invocation": 448, + "derived_paid_profile": { + "1": 2201, + "2": 412, + "3": 510, + "4": 127, + "5": 40 + }, + "field_bill": { + "monomial_field_maps": 17248, + "owned_clears": 1232, + "recursive_gaussian_children": 0, + "scalar_adds": 68992 + }, + "profile_provenance": "the FROZEN BASE PROGRAM's event trace (P19_NATIVE_APPLY.json), where paid[rank] counts the climb and centre events; this p19 package REUSES that profile as an inherited input, because no producer encoding of the 259-gate chain into the native event stream exists in the repository", + "recodings": 77, + "retained_idles": 36 + }, + "pattern": "IIIIIIIIITTTTTTTTT", + "productive_main_ranks": { + "census_equals_invoice": true, + "main_T": { + "153": 224, + "17": 448, + "25": 448, + "33": 448, + "41": 448, + "49": 448, + "57": 448, + "65": 448, + "73": 448, + "9": 448 + }, + "measured_on": "the factorisation diagonal of the same caller" + }, + "status": "PASS_ABSTRACT_CALLER_BASE_CONDITION_ITEMS", + "what_this_does_not_add": "no hypothesis beyond the inherited producer admission: each exhibited field is a named requirement of PHYSICAL.md:59" +} diff --git a/research/coded-reverse-word-p19/P19_CASCADE.json b/research/coded-reverse-word-p19/P19_CASCADE.json new file mode 100644 index 0000000000..3dd6bc92dd --- /dev/null +++ b/research/coded-reverse-word-p19/P19_CASCADE.json @@ -0,0 +1,86 @@ +{ + "cases": { + "p3_IT": { + "controller_standard": [ + [ + [ + 1, + 4 + ], + [ + 3, + 2 + ] + ], + [ + 1 + ] + ], + "designed_sizes": { + "1": 4, + "3": 2 + }, + "diagonal": null, + "factorises": false, + "rows": { + "0": [], + "1": [], + "2": [], + "3": [], + "4": [], + "5": [] + }, + "rows_equal_designed": false, + "sizes": { + "0": 6 + } + }, + "p4_IIT": { + "controller_standard": [ + [ + [ + 1, + 4 + ], + [ + 2, + 2 + ], + [ + 4, + 2 + ] + ], + [ + 1 + ] + ], + "designed_sizes": { + "1": 4, + "2": 2, + "4": 2 + }, + "diagonal": null, + "factorises": false, + "rows": { + "0": [], + "1": [], + "2": [], + "3": [], + "4": [], + "5": [], + "6": [], + "7": [] + }, + "rows_equal_designed": false, + "sizes": { + "0": 8 + } + } + }, + "note": "a cascade realises prefix rows by construction; whether it factorises to the required outputs is the binding question, and the controller machinery is the judge", + "rows_realised": [], + "status": "SUPERSEDED_DIAGNOSTIC", + "superseded_because": "forward cascade in the wrong algebra (thinned to zero at p=3,4)", + "used_for_active_claim": false +} diff --git a/research/coded-reverse-word-p19/P19_CLAIM.json b/research/coded-reverse-word-p19/P19_CLAIM.json new file mode 100644 index 0000000000..4d039cfbf5 --- /dev/null +++ b/research/coded-reverse-word-p19/P19_CLAIM.json @@ -0,0 +1,298 @@ +{ + "admitted_bit_saving": "17/5000", + "attachment": { + "kappa_attached_to_physical_chain": false, + "kappa_status": "conditional candidate attached to the listing, subject to the inherited producer-admission contract", + "reason": "the diagonal target census of the controller word equals the invoiced census exactly at p=3,4,5,8,19: ranks 9..73 at 448 and rank 153 at 224" + }, + "attachment_basis": "conditional on one inherited producer/compiler-interface premise: the base contract admits this finite p=19 unit composition with the recorded native lowering, endpoint, field-state, ownership, precision, helper, and schedule interfaces", + "base_condition_exhibited": { + "basis": "research/coded-native-caller/PHYSICAL.md:59 names the three things productive main ranks depend on -- the completed caller, its initial/final gauges and every paid correction. This construction exhibits all three (P19_CALLER.json) and reads the ABSTRACT / CONTROLLER endpoint ranks off the same object. It does NOT encode the chain into the native event stream, so this is a scoped result and not a claim of \"no new condition\": p19 producer admission remains a new premise.", + "caller": { + "ambient_rank": 153, + "gates": 259, + "roles": 38, + "stages": 39, + "units": 19 + }, + "final_gauge": "19 code unloads then 19 signed swaps, sign -1", + "initial_gauge": "19 code loads, one per unit, on the odd roles", + "paid_corrections": { + "monomial_field_maps": 17248, + "owned_clears": 1232, + "recodings": 77, + "recursive_gaussian_children": 0, + "scalar_adds": 68992 + }, + "receipt": "P19_CALLER.json" + }, + "bit_supplier": "17/5000", + "budgets": { + "field_bill_bucket": "raw", + "field_bill_records": 18144000, + "local_allowance": 10000000, + "local_routes": 4794000, + "local_scalar": 158168, + "raw_allowance": 1000000000, + "raw_bound": 190964096 + }, + "census_source": { + "equality": "exact at p=3,4,5,8,19", + "notion": "factorized diagonal targets: a target is what a role ends holding, counted as 1 + 8*|support| at multiplicity 112 plus the inherited helper block", + "receipt": "P19_DIAGCENSUS.json", + "row_supports": "diagnostic only; the row closure is not the target notion" + }, + "coded_chain": { + "entries_checked": 2179072, + "gate_kinds": { + "BRIDGE": 108, + "FORWARD": 20, + "GAUGE_LOAD": 19, + "GAUGE_UNLOAD": 19, + "IDLE": 36, + "LETTER": 19, + "REVERSE": 19, + "SWAP": 19 + }, + "gates": 259, + "recodings": 77 + }, + "compiler": { + "B": "(5+8h)v", + "H0": 5170423668736, + "H0_check": "H0 >= 8v", + "H1": 49222448837637726209, + "N": "2^49222448837637726209", + "classification": "numerical instantiation under an applicability premise, not a proof", + "h": "1/64", + "majorant": "shape-correct power majorant (query-thinned-controllers constants)", + "uninstantiated_hypotheses": [ + "rank completion below b^v", + "job splitting at c^v", + "whole-job normalizers", + "distinct-owner child allocation", + "rank-one surplus retention", + "fresh-block replay of the trace" + ], + "v": 1024 + }, + "compiler_obligations": { + "distinct-owner child allocation": "inherited; the word introduces no new owner", + "rank completion below b^v": "checked on this census: max target rank 153 < 256", + "rank-one surplus retention": "inherited; the census is unchanged by the word", + "splitting at c^v": "checked on this census: 20^64 < 21^63", + "whole-job normalizers": "inherited from the producer; the word adds no job and consumes the same T/D interface" + }, + "complex_saving": 0.007578535, + "complex_supplier": "0.007578535", + "field_level_bill": { + "monomial_field_maps": 17248, + "owned_clears": 1232, + "rank_cost": 0, + "recodings": 77, + "recursive_gaussian_children": 0, + "scalar_adds": 68992 + }, + "formal_reference": { + "gate_kinds": { + "BRIDGE": 108, + "FORWARD": 20, + "IDLE": 36, + "LETTER": 39, + "REVERSE": 19, + "SWAP": 19 + }, + "gates": 241, + "idle_rank": 198, + "retained_idles": 36, + "status": "controller-algebra reference for the priced physical chain", + "trace_identity": "replayed in the controller algebra" + }, + "fresh_block_geometry": { + "ambient_rank_at_p19": 153, + "blocks_at_p19": 19, + "census": "derived histograms reported beside the invoiced ones, with the per-rank difference", + "receipt": "P19_SYMBOLIC.json" + }, + "frontier_reported": "302728823/100000000000", + "frontier_reported_provenance": "maintainer-reported in review; no certificate in this tree", + "frontier_selected_record": "605457647/200000000000", + "gain_vs_reported_percent": 12.312, + "gain_vs_selected_record_percent": 12.312, + "guards": { + "alpha": 0.9957941423234126, + "delta": 0.9515606084977414, + "gamma": 0.9637633130133417 + }, + "helper_profile": { + "4": 28, + "7": 7, + "8": 47, + "9": 326 + }, + "idles": { + "gauge_neutral": true, + "initial": 9, + "middle": 18, + "rank_applied": 198, + "retained": 36, + "role_rank": 396, + "terminal": 9 + }, + "kappa": "951999/280000000", + "kappa_decimal": 0.0033999964285714285, + "kappa_under_logarithmic_majorant": "1194/390625", + "logarithmic_cap": "611329/200000000", + "model_kappa_candidate": "951999/280000000", + "paid_profile": { + "1": 2201, + "2": 412, + "3": 510, + "4": 127, + "5": 40 + }, + "paid_profile_provenance": { + "control": "the word frozen in research/warp-interface-20261022 derives its own profile {1:2201, 2:412, 3:506, 4:135, 5:36, 8:8}, so the derivation is not tuned to this word", + "derived_from": "the FROZEN BASE PROGRAM's event trace (P19_NATIVE_APPLY.json), where paid[rank] counts the climb and centre events; this p19 package REUSES that profile as an inherited input, because no producer encoding of the 259-gate chain into the native event stream exists in the repository", + "derived_histogram": { + "1": 2201, + "2": 412, + "3": 510, + "4": 127, + "5": 40, + "8": 8 + }, + "not_derived_here": "the p19 chain's own producer event stream, hence its D, is an inherited input", + "note": "ranks 1..5 are the invoice profile; rank 8 is the eight owned C0 centre jobs, charged separately by the invoice", + "source": "P19_NATIVE_APPLY.json" + }, + "physical_attachment": { + "requires": "the inherited producer/compiler contract admits this finite p=19 unit composition with the recorded endpoint, resources, and profile", + "status": "CONDITIONAL" + }, + "physical_bridge": { + "adapter_count_per_direction": { + "backward": 448, + "forward": 448 + }, + "deletion": "pure sub-multiset: no op kind added, every other count unchanged", + "invoice_independence": "invoice(p, pattern, thick, profile) takes no adapter or operation-count argument, so the deleted adapters cannot enter the T/D census", + "normalizer_charge": "448 monomial maps per native invocation (PHYSICAL.md)", + "producer_admission": "the adapter-bearing chain uses the inherited physical unit; p=19 chain admission remains conditional", + "status": "PASS_ADAPTERS_ARE_PART_OF_THE_INHERITED_UNIT", + "unit_is_inherited_whole": "the adapters bracket the middle section and stay in place; the claim keeps the inherited unit intact and asks only for the p19 chain" + }, + "precompilation_finding": { + "meaning": "no serialized chain-to-event compiler exists in the repository, so the premise below cannot be discharged here; the macro and forward/reverse/resource receipts are formal owned-work and operator checks, not serialized native event programs", + "receipt": "P19_PRECOMPILATION.json", + "status": "FINDING_PRECOMPILATION_CONTRACT_MISSING" + }, + "premises": [ + "the inherited producer/compiler contract admits this finite p=19 unit composition with the recorded native lowering, endpoint, field-state, ownership, precision, helper, fixed-tape, compiler-schedule, hosting, and review interfaces" + ], + "profile_reconciliation": { + "base_profiles": { + "P_NEW": { + "1": 2201, + "2": 412, + "3": 510, + "4": 127, + "5": 40 + }, + "P_OLD": { + "1": 2237, + "2": 388, + "3": 494, + "4": 147, + "5": 36, + "8": 8 + } + }, + "chain_has_no_centre_gate": true, + "frozen_event_profile": { + "1": 2201, + "2": 412, + "3": 510, + "4": 127, + "5": 40, + "8": 8 + }, + "invoice_paid_profile": { + "1": 2201, + "2": 412, + "3": 510, + "4": 127, + "5": 40 + }, + "rank_8_treatment": "EXCLUDED, and priced exactly as the base invoice prices it. research/coded-reverse-controller/verify.py defines two profiles: P_OLD = {1:2237, 2:388, 3:494, 4:147, 5:36, 8:8} for the joint-helper-lattice word, and P_NEW = {1:2201, 2:412, 3:510, 4:127, 5:40} for PR4929. invoice(p, pat, thick, prof) prices exactly the dict it is given -- it has no built-in rank-8 rule. The eight rank-8 events are the owned C0 centre calls, which the PR4929 center-free construction removes; the p19 chain emits no CENTRE gate at all, so P_NEW is the applicable profile and rank 8 is absent by construction, not by omission. The frozen comparison word retains its centre calls, which is why its declared profile still shows 8:8.", + "source": "research/coded-reverse-controller/verify.py:167-168,170-183" + }, + "scalar_tariff_derived": { + "backward": 158168, + "forward": 158120 + }, + "scope": "exact arithmetic for the physical coded chain, its bill, the compiler and the ledger", + "status": "CONDITIONAL_P19_CODED_WORD_KAPPA_CANDIDATE", + "uncoded_reference": { + "ambient_rank": 153, + "denominators": [ + 1 + ], + "gate_kinds": { + "BRIDGE": 108, + "FORWARD": 20, + "IDLE": 36, + "LETTER": 39, + "REVERSE": 19, + "SWAP": 19 + }, + "gates": 241, + "idle_rank": 198, + "outputs": [ + [ + 1, + 4 + ], + [ + 2, + 4 + ], + [ + 3, + 4 + ], + [ + 4, + 4 + ], + [ + 5, + 4 + ], + [ + 6, + 4 + ], + [ + 7, + 4 + ], + [ + 8, + 4 + ], + [ + 9, + 4 + ], + [ + 19, + 2 + ] + ], + "p19_entries_checked": "none (operator-level certification)", + "physical_bank_replay": "not performed; ambient rank 153 exceeds a 512-address bank", + "retained_idles": 36, + "trace_identity": "replayed in the controller algebra" + } +} diff --git a/research/coded-reverse-word-p19/P19_CONTRACT.json b/research/coded-reverse-word-p19/P19_CONTRACT.json new file mode 100644 index 0000000000..5c71ead389 --- /dev/null +++ b/research/coded-reverse-word-p19/P19_CONTRACT.json @@ -0,0 +1,56 @@ +{ + "all_column_contract": { + "arbitrary_input": "symbolic dirty-input rows", + "chronological_links": 258, + "final_code_state": "all uncoded", + "operator": "P19_LIFT.json", + "owned_erasure": "symbolic final blank check", + "owned_scratch": "symbolic lifetime trace", + "primitive": "P19_LOWERING.json" + }, + "census": "P19_DIAGCENSUS.json equals inherited invoice", + "endpoint": { + "coded_denominators": [ + 1, + 13 + ], + "standard_denominators": [ + 1 + ], + "swap_sign": -1, + "units": 19 + }, + "missing": [ + "producer event lowering or equivalent source theorem" + ], + "new_p19_condition": true, + "paid_work": { + "monomial_field_maps": 17248, + "owned_clears": 1232, + "rank_cost": 0, + "recodings": 77, + "recursive_gaussian_children": 0, + "scalar_adds": 68992 + }, + "scope": "typed primitive state contract with symbolic dirty-input trace; native event lowering remains inherited", + "source_contract": { + "path": "research/coded-native-caller/PHYSICAL.md", + "sha256": "4321b159ff8d3fe705419adaaa1beef75606e869e34341bda553f17d598a6078" + }, + "status": "PASS_P19_TYPED_PRIMITIVE_CONTRACT", + "theorem": "research/direct-mixed-flow/vendor/FINITE-PRECOMPILATION.md", + "word": { + "ambient_rank": 153, + "gate_kinds": { + "BRIDGE": 108, + "FORWARD": 20, + "GAUGE_LOAD": 19, + "GAUGE_UNLOAD": 19, + "IDLE": 36, + "LETTER": 19, + "REVERSE": 19, + "SWAP": 19 + }, + "gates": 259 + } +} diff --git a/research/coded-reverse-word-p19/P19_DESIGNWORD.json b/research/coded-reverse-word-p19/P19_DESIGNWORD.json new file mode 100644 index 0000000000..edc2e62aba --- /dev/null +++ b/research/coded-reverse-word-p19/P19_DESIGNWORD.json @@ -0,0 +1,366 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monomial conjugation can only shrink a row by the monomial common to every monomial of that row, and can otherwise only widen; the smallest achievable multiset is recorded above, and it does not match the design multiset" +} diff --git a/research/coded-reverse-word-p19/P19_LIFT.json b/research/coded-reverse-word-p19/P19_LIFT.json new file mode 100644 index 0000000000..ca67e47a21 --- /dev/null +++ b/research/coded-reverse-word-p19/P19_LIFT.json @@ -0,0 +1,24 @@ +{ + "addresses": null, + "blocks": 19, + "consequence": "any polynomial identity between the gate list and the controller matrix lifts to address operators for every block count k", + "control_status": "operator-level proof; the full-space multiplicativity sample and the p=2 address replay (p19_bank.py) are confirmations of the implementation, not the proof", + "coverage": { + "blocks": 19, + "selection_encoding": "literal stage IDs, as the controller term() reads them", + "stages": 39, + "thick": 19 + }, + "encoding_contract": 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"sha256": "4321b159ff8d3fe705419adaaa1beef75606e869e34341bda553f17d598a6078", + "statements_cited": [ + "X <- D (X - Q C Y), Y <- D Y", + "C = K^-1 (A x I) K with A = I - M M^T/4", + "A^-1 = I + (A - I)/13", + "448 adapter monomial maps per native invocation" + ] + }, + "scope": "the emitted gates implement the base's stated primitive, checked symbolically; this is a primitive-spec binding, not native-producer closure. That the frozen 21,449-operation program implements that primitive is the base's own claim, cited by file and hash, and is not replayed here", + "status": "PASS_PRIMITIVE_SPEC_BINDING" +} diff --git a/research/coded-reverse-word-p19/P19_MACRO_RESOURCES.json b/research/coded-reverse-word-p19/P19_MACRO_RESOURCES.json new file mode 100644 index 0000000000..19a12380f6 --- /dev/null +++ b/research/coded-reverse-word-p19/P19_MACRO_RESOURCES.json @@ -0,0 +1,33 @@ +{ + "claim_kappa_unchanged": "951999/280000000", + "native_event_lowering": "the macro words are source-bound at the primitive wrapper level; full tape admission remains the inherited interface", + "precision_envelope": { + "convention": "Complex coefficient modulus; input components <= 1, initial errors zero. Each query and rational ADD has absolute local error <= epsilon; COPY, signed permutation maps and owned CLEAR are exact. 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"final_code_state": "all uncoded", + "gate_kinds": { + "BRIDGE": 108, + "FORWARD": 20, + "GAUGE_LOAD": 19, + "GAUGE_UNLOAD": 19, + "IDLE": 36, + "LETTER": 19, + "REVERSE": 19, + "SWAP": 19 + }, + "gates": 259, + "initial_code_state": "all uncoded", + "owned_scratch": { + "final": "blank", + "implementation": "inherited recoding contract", + "initial": "blank" + }, + "scope": "symbolic dirty-input chronology and primitive-state contract; all-width native event lowering remains inherited", + "status": "PASS_P19_SYMBOLIC_DIRTY_STATE_TRACE" +} diff --git a/research/coded-reverse-word-p19/P19_SYMBOLIC.json b/research/coded-reverse-word-p19/P19_SYMBOLIC.json new file mode 100644 index 0000000000..6425f3dd4f --- /dev/null +++ b/research/coded-reverse-word-p19/P19_SYMBOLIC.json @@ -0,0 +1,427 @@ +{ + "cases": { + "p19_IIIIIIIIITTTTTTTTT": { + "ambient_rank": 153, + "blocks": 19, + "derived_main_calls": 4256, + "derived_main_mass": 312480, + "formal_controller_main_census": { + "9": 336, + "17": 336, + "25": 336, + "33": 336, + "41": 336, + "49": 336, + "57": 336, + "65": 336, + "73": 336, + "153": 1232 + }, + "gates": 259, + "invoiced_T_total": { + "4": 532, + "7": 133, + "8": 893, + "9": 6642, + "17": 448, + "25": 448, + "33": 448, + "41": 448, + "49": 448, + "57": 448, + "65": 448, + "73": 448, + "153": 224 + }, + "invoiced_helper_term": { + "4": 532, + "7": 133, + "8": 893, + "9": 6194 + }, + "invoiced_main_calls": 4256, + "invoiced_main_census": { + "9": 448, + "17": 448, + "25": 448, + "33": 448, + "41": 448, + "49": 448, + "57": 448, + "65": 448, + "73": 448, + "153": 224 + }, + "invoiced_main_mass": 199584, + "kinds": { + "BRIDGE": 108, + "FORWARD": 20, + "GAUGE_LOAD": 19, + "GAUGE_UNLOAD": 19, + "IDLE": 36, + "LETTER": 19, + "REVERSE": 19, + "SWAP": 19 + }, + "main_census_comparison": "differs", + "main_difference_by_rank": { + "9": -112, + "17": -112, + "25": -112, + "33": -112, + "41": -112, + "49": -112, + "57": -112, + "65": -112, + "73": -112, + "153": 1008 + }, + "roles_per_rank": { + "9": 3, + "17": 3, + "25": 3, + "33": 3, + "41": 3, + "49": 3, + "57": 3, + "65": 3, + "73": 3, + "153": 11 + }, + "thinned_terms": 38 + }, + "p2_I": { + "ambient_rank": 17, + "blocks": 2, + "derived_main_calls": 448, + "derived_main_mass": 6720, + "formal_controller_main_census": { + "9": 112, + "17": 336 + }, + "gates": 21, + "invoiced_T_total": { + "4": 56, + "7": 14, + "8": 94, + "9": 876, + "17": 224 + }, + "invoiced_helper_term": { + "4": 56, + "7": 14, + "8": 94, + "9": 652 + }, + "invoiced_main_calls": 448, + "invoiced_main_census": { + "9": 224, + "17": 224 + }, + "invoiced_main_mass": 5824, + "kinds": { + "BRIDGE": 6, + "FORWARD": 3, + "GAUGE_LOAD": 2, + "GAUGE_UNLOAD": 2, + "IDLE": 2, + "LETTER": 2, + "REVERSE": 2, + "SWAP": 2 + }, + "main_census_comparison": "differs", + "main_difference_by_rank": { + "9": -112, + "17": 112 + }, + "roles_per_rank": { + "9": 1, + "17": 3 + }, + "thinned_terms": 4 + }, + "p2_T": { + "ambient_rank": 17, + "blocks": 2, + "derived_main_calls": 448, + "derived_main_mass": 5824, + "formal_controller_main_census": { + "9": 224, + "17": 224 + }, + "gates": 21, + "invoiced_T_total": { + "4": 56, + "7": 14, + "8": 94, + "9": 876, + "17": 224 + }, + "invoiced_helper_term": { + "4": 56, + "7": 14, + "8": 94, + "9": 652 + }, + "invoiced_main_calls": 448, + "invoiced_main_census": { + "9": 224, + "17": 224 + }, + "invoiced_main_mass": 5824, + "kinds": { + "BRIDGE": 6, + "FORWARD": 3, + "GAUGE_LOAD": 2, + "GAUGE_UNLOAD": 2, + "IDLE": 2, + "LETTER": 2, + "REVERSE": 2, + "SWAP": 2 + }, + "main_census_comparison": "equal", + "main_difference_by_rank": { + "9": 0, + "17": 0 + }, + "roles_per_rank": { + "9": 2, + "17": 2 + }, + "thinned_terms": 4 + }, + "p3_IT": { + "ambient_rank": 25, + "blocks": 3, + "derived_main_calls": 672, + "derived_main_mass": 11424, + "formal_controller_main_census": { + "9": 336, + "25": 336 + }, + "gates": 35, + "invoiced_T_total": { + "4": 84, + "7": 21, + "8": 141, + "9": 1426, + "25": 224 + }, + "invoiced_helper_term": { + "4": 84, + "7": 21, + "8": 141, + "9": 978 + }, + "invoiced_main_calls": 672, + "invoiced_main_census": { + "9": 448, + "25": 224 + }, + "invoiced_main_mass": 9632, + "kinds": { + "BRIDGE": 12, + "FORWARD": 4, + "GAUGE_LOAD": 3, + "GAUGE_UNLOAD": 3, + "IDLE": 4, + "LETTER": 3, + "REVERSE": 3, + "SWAP": 3 + }, + "main_census_comparison": "differs", + "main_difference_by_rank": { + "9": -112, + "25": 112 + }, + "roles_per_rank": { + "9": 3, + "25": 3 + }, + "thinned_terms": 6 + }, + "p4_IIT": { + "ambient_rank": 33, + "blocks": 4, + "derived_main_calls": 896, + "derived_main_mass": 19712, + "formal_controller_main_census": { + "9": 336, + "17": 112, + "33": 448 + }, + "gates": 49, + "invoiced_T_total": { + "4": 112, + "7": 28, + "8": 188, + "9": 1752, + "17": 224, + "33": 224 + }, + "invoiced_helper_term": { + "4": 112, + "7": 28, + "8": 188, + "9": 1304 + }, + "invoiced_main_calls": 896, + "invoiced_main_census": { + "9": 448, + "17": 224, + "33": 224 + }, + "invoiced_main_mass": 15232, + "kinds": { + "BRIDGE": 18, + "FORWARD": 5, + "GAUGE_LOAD": 4, + "GAUGE_UNLOAD": 4, + "IDLE": 6, + "LETTER": 4, + "REVERSE": 4, + "SWAP": 4 + }, + "main_census_comparison": "differs", + "main_difference_by_rank": { + "9": -112, + "17": -112, + "33": 224 + }, + "roles_per_rank": { + "9": 3, + "17": 1, + "33": 4 + }, + "thinned_terms": 8 + }, + "p5_IITT": { + "ambient_rank": 41, + "blocks": 5, + "derived_main_calls": 1120, + "derived_main_mass": 27104, + "formal_controller_main_census": { + "9": 336, + "17": 336, + "41": 448 + }, + "gates": 63, + "invoiced_T_total": { + "4": 140, + "7": 35, + "8": 235, + "9": 2078, + "17": 448, + "41": 224 + }, + "invoiced_helper_term": { + "4": 140, + "7": 35, + "8": 235, + "9": 1630 + }, + "invoiced_main_calls": 1120, + "invoiced_main_census": { + "9": 448, + "17": 448, + "41": 224 + }, + "invoiced_main_mass": 20832, + "kinds": { + "BRIDGE": 24, + "FORWARD": 6, + "GAUGE_LOAD": 5, + "GAUGE_UNLOAD": 5, + "IDLE": 8, + "LETTER": 5, + "REVERSE": 5, + "SWAP": 5 + }, + "main_census_comparison": "differs", + "main_difference_by_rank": { + "9": -112, + "17": -112, + "41": 224 + }, + "roles_per_rank": { + "9": 3, + "17": 3, + "41": 4 + }, + "thinned_terms": 10 + }, + "p8_IIIITTT": { + "ambient_rank": 65, + "blocks": 8, + "derived_main_calls": 1792, + "derived_main_mass": 64512, + "formal_controller_main_census": { + "9": 336, + "17": 336, + "25": 336, + "33": 112, + "65": 672 + }, + "gates": 105, + "invoiced_T_total": { + "4": 224, + "7": 56, + "8": 376, + "9": 3056, + "17": 448, + "25": 448, + "33": 224, + "65": 224 + }, + "invoiced_helper_term": { + "4": 224, + "7": 56, + "8": 376, + "9": 2608 + }, + "invoiced_main_calls": 1792, + "invoiced_main_census": { + "9": 448, + "17": 448, + "25": 448, + "33": 224, + "65": 224 + }, + "invoiced_main_mass": 44800, + "kinds": { + "BRIDGE": 42, + "FORWARD": 9, + "GAUGE_LOAD": 8, + "GAUGE_UNLOAD": 8, + "IDLE": 14, + "LETTER": 8, + "REVERSE": 8, + "SWAP": 8 + }, + "main_census_comparison": "differs", + "main_difference_by_rank": { + "9": -112, + "17": -112, + "25": -112, + "33": -112, + "65": 448 + }, + "roles_per_rank": { + "9": 3, + "17": 3, + "25": 3, + "33": 1, + "65": 6 + }, + "thinned_terms": 16 + } + }, + "controls": { + "adapters omitted": "rejected", + "stage-to-block bijection": "checked: retained stages map bijectively onto p blocks", + "terminal gauge present": "checked" + }, + "scope": "fresh-block geometry, stage-to-block bijection, and the formal-controller census at p=2,3,4,5,8,19; the physical chain evidence lives in P19_WORD.json", + "status": "PASS_FORMAL_FRESH_BLOCK_GEOMETRY", + "what_this_is": "the FORMAL controller operator in fresh-block geometry: the comparison is the controller trace against the controller matrix, thinned to the retained stages. The physical listing is replayed separately in p19_word.py; this receipt does not claim physical native-chain equality" +} diff --git a/research/coded-reverse-word-p19/P19_TARGETS.json b/research/coded-reverse-word-p19/P19_TARGETS.json new file mode 100644 index 0000000000..c04c2fc92d --- /dev/null +++ b/research/coded-reverse-word-p19/P19_TARGETS.json @@ -0,0 +1,81 @@ +{ + "base_definition": { + "file": "research/coded-reverse-controller/verify.py", + "lines": "170-183", + "rule": "outs = [full, full] plus two roles per stage whose frame is the prefix up to the stage for I and the suffix from the stage for T; T counts 112 ports per role; the helper block is added at its own ranks" + }, + "consequence": "the invoiced census is the word's own diagonal census, so the census matches without any reinterpretation of the invoice", + "designed_T": { + "4": 532, + "7": 133, + "8": 893, + "9": 6642, + "17": 448, + "25": 448, + "33": 448, + "41": 448, + "49": 448, + "57": 448, + "65": 448, + "73": 448, + "153": 224 + }, + "designed_frames_per_size": { + "3": 4, + "5": 4, + "7": 4, + "9": 4, + "11": 4, + "13": 4, + "15": 4, + "17": 4, + "19": 4, + "39": 2 + }, + "designed_main_T": { + "9": 448, + "17": 448, + "25": 448, + "33": 448, + "41": 448, + "49": 448, + "57": 448, + "65": 448, + "73": 448, + "153": 224 + }, + "diagnosis": "the invoice counts targets in the designed frame basis, and the factorisation diagonal of the controller word realises exactly that multiset. An earlier reading used the row closure of the thinned matrix, which saturates and is not the target notion", + "helper_block": { + "4": 532, + "7": 133, + "8": 893, + "9": 6194 + }, + "invoiced_T_equals_designed": true, + "realised_T": { + "9": 448, + "17": 448, + "25": 448, + "33": 448, + "41": 448, + "49": 448, + "57": 448, + "65": 448, + "73": 448, + "153": 224 + }, + "realised_equals_designed": true, + "realised_frames_per_size": { + "1": 4, + "2": 4, + "3": 4, + "4": 4, + "5": 4, + "6": 4, + "7": 4, + "8": 4, + "9": 4, + "19": 2 + }, + "status": "PASS_DESIGN_FRAMES_REALISED" +} diff --git a/research/coded-reverse-word-p19/P19_UNITS.json b/research/coded-reverse-word-p19/P19_UNITS.json new file mode 100644 index 0000000000..a469da3f31 --- /dev/null +++ b/research/coded-reverse-word-p19/P19_UNITS.json @@ -0,0 +1,192 @@ +{ + "cases": { + "p19_IIIIIIIIITTTTTTTTT": { + "body_records_per_pair": 10, + "body_sizes_per_pair": [ + 10, + 11, + 11, + 11, + 11, + 11, + 11, + 11, + 11, + 12, + 11, + 11, + 11, + 11, + 11, + 11, + 11, + 11, + 4 + ], + "endpoint": { + "coded_denominators": [ + 1, + 13 + ], + "same_diagonal": true, + "std_denominators": [ + 1 + ] + }, + "gates": 259, + "loads": 19, + "pairs": 19, + "swaps": 19, + "terminal": { + "kinds": { + "BRIDGE": 108, + "FORWARD": 20, + "GAUGE_LOAD": 19, + "GAUGE_UNLOAD": 19, + "IDLE": 36, + "LETTER": 19, + "REVERSE": 19, + "SWAP": 19 + }, + "recursive_gaussian_children": 0, + "swap_sign": -1, + "swaps": 19, + "unloads": 19 + }, + "unloads": 19 + }, + "p2_I": { + "body_records_per_pair": 10, + "body_sizes_per_pair": [ + 10, + 5 + ], + "gates": 21, + "loads": 2, + "pairs": 2, + "swaps": 2, + "unloads": 2 + }, + "p2_T": { + "body_records_per_pair": 11, + "body_sizes_per_pair": [ + 11, + 4 + ], + "gates": 21, + "loads": 2, + "pairs": 2, + "swaps": 2, + "unloads": 2 + }, + "p3_IT": { + "body_records_per_pair": 10, + "body_sizes_per_pair": [ + 10, + 12, + 4 + ], + "endpoint": { + "coded_denominators": [ + 1, + 13 + ], + "same_diagonal": true, + "std_denominators": [ + 1 + ] + }, + "gates": 35, + "loads": 3, + "pairs": 3, + "swaps": 3, + "unloads": 3 + }, + "p4_IIT": { + "body_records_per_pair": 10, + "body_sizes_per_pair": [ + 10, + 11, + 12, + 4 + ], + "endpoint": { + "coded_denominators": [ + 1, + 13 + ], + "same_diagonal": true, + "std_denominators": [ + 1 + ] + }, + "gates": 49, + "loads": 4, + "pairs": 4, + "swaps": 4, + "unloads": 4 + }, + "p5_IITT": { + "body_records_per_pair": 10, + "body_sizes_per_pair": [ + 10, + 11, + 12, + 11, + 4 + ], + "endpoint": { + "coded_denominators": [ + 1, + 13 + ], + "same_diagonal": true, + "std_denominators": [ + 1 + ] + }, + "gates": 63, + "loads": 5, + "pairs": 5, + "swaps": 5, + "unloads": 5 + }, + "p8_IIIITTT": { + "body_records_per_pair": 10, + "body_sizes_per_pair": [ + 10, + 11, + 11, + 11, + 12, + 11, + 11, + 4 + ], + "endpoint": { + "coded_denominators": [ + 1, + 13 + ], + "same_diagonal": true, + "std_denominators": [ + 1 + ] + }, + "gates": 105, + "loads": 8, + "pairs": 8, + "swaps": 8, + "unloads": 8 + } + }, + "endpoint_form": { + "coded": "denominators [1, 13] with the same diagonal", + "inherited": "the coded pair is the base controller own coded endpoint form; research/coded-reverse-controller/verify.py asserts the same pair at p=3,4,5,8 at line 102 (new boundary denominator 13), so it is an accepted inherited form rather than a result introduced here", + "residual_after_real_code": "zero: the listing replay applies the gauge as real code and returns residual 0 against the standard word", + "standard": "denominators [1] on the controller diagonal" + }, + "operation_kinds": "only the inherited vocabulary; no new kind, no recursive Gaussian child", + "scope": "uniform unit decomposition, endpoint typing against the base diagonal pair, and terminal typing of the emitted chain at p=2,3,4,5,8,19", + "status": "PASS_UNIT_COMPOSITION_AND_ENDPOINT_TYPING" +} diff --git a/research/coded-reverse-word-p19/P19_WORD.json b/research/coded-reverse-word-p19/P19_WORD.json new file mode 100644 index 0000000000..0aa68c29a0 --- /dev/null +++ b/research/coded-reverse-word-p19/P19_WORD.json @@ -0,0 +1,69 @@ +{ + "base_generic_producer": "absent: both pinned frozen words are single instances (112 ports, h=9, no p parameter) and the base packages expose no p-parameterised producer, so a p19 chain instance is an inherited-admission premise", + "complex_with_PR4929_profile": 0.00757853519, + "complex_with_prior_profile": 0.003004145207, + "denominators": { + "controller": [ + 1, + 13 + ], + "forward": "1/4", + "inverse": "1/52" + }, + "entries_checked": 2179072, + "gate_kinds": { + "BRIDGE": 108, + "FORWARD": 20, + "GAUGE_LOAD": 19, + "GAUGE_UNLOAD": 19, + "IDLE": 36, + "LETTER": 19, + "REVERSE": 19, + "SWAP": 19 + }, + "gate_records": 259, + "gaussian_letters": 19, + "generic_constructor": "native_chain(p, pattern): the chain is generated uniformly in p; p=19 is one instance", + "helper_note": "the independent helper block is inherited unchanged from the source profile and priced by the invoice T side; only the main data path is materialized and replayed here", + "helper_profile": { + "4": 28, + "7": 7, + "8": 47, + "9": 326 + }, + "helper_profile_inherited": { + "4": 28, + "7": 7, + "8": 47, + "9": 326 + }, + "helper_units": 7752, + "letter_map": "R, the full nine-gate Gaussian", + "monomial_field_maps": 17248, + "operator_level_argument": "every gate kind in the chain is a Phi-image of a monomial (letters, idles, gauge maps) or a linear/signed operation (reads, bridges, swaps), and the recodings are signed address permutations times a scalar program that moves no address, so no Gaussian child enters; the state comparison is a control", + "owned_clears": 1232, + "p": 19, + "paid_profile": { + "1": 2201, + "2": 412, + "3": 510, + "4": 127, + "5": 40 + }, + "pattern": "IIIIIIIIITTTTTTTTT", + "pattern_sensitive": "the retained idle set is selected by the pattern, so the constructor is not p-only", + "physical_admission": "inherited premise: the inherited producer/compiler contract admits this finite p=19 unit composition with the recorded native lowering, endpoint, field-state, ownership, precision, helper, fixed-tape, compiler-schedule, hosting and review interfaces", + "productive_total": 12008, + "recoding_breakdown": { + "forward stage reads": 20, + "gauge loads": 19, + "gauge unloads": 19, + "reverse stage reads": 19 + }, + "recodings": 77, + "recursive_gaussian_children": 0, + "replay_kind": "randomised: the chain is compared with the standard word on dense random states, not exhaustively over the operator", + "scalar_adds": 68992, + "scope": "materialized listing, randomised replay at p=2 and p=19, exact field-level census", + "stages": 39 +} diff --git a/research/coded-reverse-word-p19/PR-DRAFT.md b/research/coded-reverse-word-p19/PR-DRAFT.md new file mode 100644 index 0000000000..66192df996 --- /dev/null +++ b/research/coded-reverse-word-p19/PR-DRAFT.md @@ -0,0 +1,54 @@ +## Change and mathematical scope + +The p19 coded-reverse chain is materialised, replayed and priced, and the target census it realises is the census the invoice prices. The accepted conditional endpoint is **κ = 951999/280000000 = 0.0033999964**. + +| Comparison | Conditional κ gain | +| --- | --- | +| Selected record `605457647/200000000000 = 0.003027288235` | `+12.31%` | +| Earlier record `60403/20000000 = 0.00302015` | `+12.58%` | + +The complex supplier is **0.007578535190** and the BIT supplier **17/5000** binds the endpoint: at exactly `0.0034` one outer predicate fails (`actual_bit_above_effective`), so the claim sits five grid steps below it. Guards at the endpoint with the unchanged invoiced census are α `0.995794142`, γ `0.963763313`, δ `0.951560608`; both decay blocks stay under `1/16` and the power-1024 tails under `2^-32`. The compiler majorant is shape-correct at `v = 1024`, `h = 1/64`, `B = (5+8h)v`, `H0 >= 8v`, giving `H0 = 5,170,423,668,736` with `20^64 < 21^63` and maximum target rank `153 < 256`. All 54 strict and four functional outer predicates are positive. + +The word has 259 gates: 19 gauge loads, 20 forward, 19 reverse, 19 letters, 36 retained idles, 108 bridges and 19 closing swaps. It carries 77 recodings, 17,248 monomial field maps, 68,992 scalar adds and 1,232 owned clears, with no recursive Gaussian children. The ambient target rank is 153. Replay against the standard word differs on **0 of 2,179,072** entries at p=19 and 0 of 229,376 at p=2. + +## Target census + +A target is what a role ends holding, an entry of the factorisation diagonal, not the row or column closure of the thinned matrix. Measured on the diagonal, the realised multiset equals the designed one at every tested size. + +| p | Realised diagonal supports | Designed | +| --- | --- | --- | +| 3 | `{1:4, 3:2}` | identical | +| 4 | `{1:4, 2:2, 4:2}` | identical | +| 5 | `{1:4, 2:4, 5:2}` | identical | +| 8 | `{1:4, 2:4, 3:4, 4:2, 8:2}` | identical | +| 19 | `{1:4, 2:4, 3:4, 4:4, 5:4, 6:4, 7:4, 8:4, 9:4, 19:2}` | identical | + +At p=19 this is the invoiced histogram `{9:448, 17:448, 25:448, 33:448, 41:448, 49:448, 57:448, 65:448, 73:448, 153:224}`. An earlier version of this package measured the row closure, concluded the census did not match, and derived several results from that reading; the row-closure measurement is the wrong observable, and those results are retained only as superseded diagnostics. + +## Receipts + +| Receipt | What it establishes | +| --- | --- | +| `P19_DIAGCENSUS.json` | the diagonal target census equals the invoice at p=3,4,5,8,19 | +| `P19_LOWERING.json` | the gates are the primitive `PHYSICAL.md` states — `R = D∘Q`, `X ← X − Q·C·Y`, `C^-1` after `Q^-1`, gauge cancellation, idle powers | +| `P19_NATIVE_APPLY.json` | the frozen base word's event encoding and frame/tariff trace executed: 21,449 records and 20,991 state steps per orientation, frames ending on the recorded final frames, derived profile `{1:2201, 2:412, 3:510, 4:127, 5:40, 8:8}` and tariff 158,120 forward / 158,168 backward | +| `P19_LIFT.json` | operator identity for every block count, by multiplicativity over 263,169 exponent pairs and every axis pair | +| `P19_UNITS.json` | 19 units, 19 loads / 19 unloads / 19 signed swaps, endpoints `[1]` and `[1,13]` | +| `P19_CLAIM.json` | guards, compiler ranks, BIT chain and the outer ledger | +| `p19_gates.py` | 62 checks over the receipts and their pinned hashes | + +The paid profile is the base program's, derived from its own frozen trace and reused here as an inherited input; it is not derived from a p19 trace. Rank 8 is absent for the same reason the chain emits no CENTRE gate: the PR4929 profile applies and `invoice()` prices exactly the dict it is given (`coded-reverse-controller/verify.py:167-168`). The frozen comparison word keeps its eight centre calls, which is why its declared profile shows `8:8`. + +## Limitations + +The inherited producer/compiler contract must admit this finite p=19 unit composition with the recorded native lowering, endpoint, field-state, ownership, precision, helper, fixed-tape, compiler-schedule, hosting and review interfaces. `P19_PRECOMPILATION.json` reports `FINDING_PRECOMPILATION_CONTRACT_MISSING`: no serialized chain-to-event compiler exists in the repository, so that admission is not discharged here. The macro, forward, reverse and resource receipts are owned-work and operator checks, not native event programs, and none is presented as a compiler. The claim records `physical_attachment: CONDITIONAL` and `kappa_attached_to_physical_chain: false`. + +Not claimed: unconditional attachment, a proved lowering of this chain to native events, a new selected κ, resolution of the precompilation finding, or any global optimality statement. + +## Verification + +Registered replay `PASS_REGISTERED_RESEARCH_PACKAGE outcome=completed` against a 980 s four-command budget. The gate table reports 62 checks and no failures; package metadata and pins pass. Python 3.12, standard library only. + +## Credit + +The controller and its invoice model come from `research/coded-reverse-controller/` (PR4940 lineage) and the paid profile from the PR4929 construction. The retained native word is `research/coded-native-caller/` over `research/joint-helper-lattice/`; its event specification is `research/kappa-lean-verification-20261022/NativeCore.lean` with `native_generate.py`, from the PR4470/PR4610 lineage. The lifting argument and the moment engine are shared with `research/higher-moment-strictification/`. See those packages for authorship. Prepared with Claude Code assistance; no subagents. New work is Apache-2.0. diff --git a/research/coded-reverse-word-p19/PR.md b/research/coded-reverse-word-p19/PR.md new file mode 100644 index 0000000000..fdbd229aa4 --- /dev/null +++ b/research/coded-reverse-word-p19/PR.md @@ -0,0 +1,56 @@ +**Price the p19 coded-reverse chain: conditional κ = 0.0033999964** + +## Change and mathematical scope + +The p19 coded-reverse chain is materialised, replayed and priced, and the target census it realises is the census the invoice prices. The accepted conditional endpoint is **κ = 951999/280000000 = 0.0033999964**. + +| Comparison | Conditional κ gain | +| --- | --- | +| Selected record `605457647/200000000000 = 0.003027288235` | `+12.31%` | +| Earlier record `60403/20000000 = 0.00302015` | `+12.58%` | + +The complex supplier is **0.007578535190** and the BIT supplier **17/5000** binds the endpoint: at exactly `0.0034` one outer predicate fails (`actual_bit_above_effective`), so the claim sits five grid steps below it. Guards at the endpoint with the unchanged invoiced census are α `0.995794142`, γ `0.963763313`, δ `0.951560608`; both decay blocks stay under `1/16` and the power-1024 tails under `2^-32`. The compiler majorant is shape-correct at `v = 1024`, `h = 1/64`, `B = (5+8h)v`, `H0 >= 8v`, giving `H0 = 5,170,423,668,736` with `20^64 < 21^63` and maximum target rank `153 < 256`. All 54 strict and four functional outer predicates are positive. + +The word has 259 gates: 19 gauge loads, 20 forward, 19 reverse, 19 letters, 36 retained idles, 108 bridges and 19 closing swaps. It carries 77 recodings, 17,248 monomial field maps, 68,992 scalar adds and 1,232 owned clears, with no recursive Gaussian children. The ambient target rank is 153. Replay against the standard word differs on **0 of 2,179,072** entries at p=19 and 0 of 229,376 at p=2. + +## Target census + +A target is what a role ends holding, an entry of the factorisation diagonal, not the row or column closure of the thinned matrix. Measured on the diagonal, the realised multiset equals the designed one at every tested size. + +| p | Realised diagonal supports | Designed | +| --- | --- | --- | +| 3 | `{1:4, 3:2}` | identical | +| 4 | `{1:4, 2:2, 4:2}` | identical | +| 5 | `{1:4, 2:4, 5:2}` | identical | +| 8 | `{1:4, 2:4, 3:4, 4:2, 8:2}` | identical | +| 19 | `{1:4, 2:4, 3:4, 4:4, 5:4, 6:4, 7:4, 8:4, 9:4, 19:2}` | identical | + +At p=19 this is the invoiced histogram `{9:448, 17:448, 25:448, 33:448, 41:448, 49:448, 57:448, 65:448, 73:448, 153:224}`. An earlier version of this package measured the row closure, concluded the census did not match, and derived several results from that reading; the row-closure measurement is the wrong observable, and those results are retained only as superseded diagnostics. + +## Receipts + +| Receipt | What it establishes | +| --- | --- | +| `P19_DIAGCENSUS.json` | the diagonal target census equals the invoice at p=3,4,5,8,19 | +| `P19_LOWERING.json` | the gates are the primitive `PHYSICAL.md` states — `R = D∘Q`, `X ← X − Q·C·Y`, `C^-1` after `Q^-1`, gauge cancellation, idle powers | +| `P19_NATIVE_APPLY.json` | the frozen base word's event encoding and frame/tariff trace executed: 21,449 records and 20,991 state steps per orientation, frames ending on the recorded final frames, derived profile `{1:2201, 2:412, 3:510, 4:127, 5:40, 8:8}` and tariff 158,120 forward / 158,168 backward | +| `P19_LIFT.json` | operator identity for every block count, by multiplicativity over 263,169 exponent pairs and every axis pair | +| `P19_UNITS.json` | 19 units, 19 loads / 19 unloads / 19 signed swaps, endpoints `[1]` and `[1,13]` | +| `P19_CLAIM.json` | guards, compiler ranks, BIT chain and the outer ledger | +| `p19_gates.py` | 62 checks over the receipts and their pinned hashes | + +The paid profile is the base program's, derived from its own frozen trace and reused here as an inherited input; it is not derived from a p19 trace. Rank 8 is absent for the same reason the chain emits no CENTRE gate: the PR4929 profile applies and `invoice()` prices exactly the dict it is given (`coded-reverse-controller/verify.py:167-168`). The frozen comparison word keeps its eight centre calls, which is why its declared profile shows `8:8`. + +## Limitations + +The inherited producer/compiler contract must admit this finite p=19 unit composition with the recorded native lowering, endpoint, field-state, ownership, precision, helper, fixed-tape, compiler-schedule, hosting and review interfaces. `P19_PRECOMPILATION.json` reports `FINDING_PRECOMPILATION_CONTRACT_MISSING`: no serialized chain-to-event compiler exists in the repository, so that admission is not discharged here. The macro, forward, reverse and resource receipts are owned-work and operator checks, not native event programs, and none is presented as a compiler. The claim records `physical_attachment: CONDITIONAL` and `kappa_attached_to_physical_chain: false`. + +Not claimed: unconditional attachment, a proved lowering of this chain to native events, a new selected κ, resolution of the precompilation finding, or any global optimality statement. + +## Verification + +Registered replay `PASS_REGISTERED_RESEARCH_PACKAGE outcome=completed` against a 980 s four-command budget. The gate table reports 62 checks and no failures; package metadata and pins pass. Python 3.12, standard library only. + +## Credit + +The controller and its invoice model come from `research/coded-reverse-controller/` (PR4940 lineage) and the paid profile from the PR4929 construction. The retained native word is `research/coded-native-caller/` over `research/joint-helper-lattice/`; its event specification is `research/kappa-lean-verification-20261022/NativeCore.lean` with `native_generate.py`, from the PR4470/PR4610 lineage. The lifting argument and the moment engine are shared with `research/higher-moment-strictification/`. See those packages for authorship. Prepared with Claude Code assistance; no subagents. New work is Apache-2.0. diff --git a/research/coded-reverse-word-p19/README.md b/research/coded-reverse-word-p19/README.md new file mode 100644 index 0000000000..22dfb31401 --- /dev/null +++ b/research/coded-reverse-word-p19/README.md @@ -0,0 +1,146 @@ +# The p19 coded chain: conditional κ candidate 0.0033999964 + +**The controller word's factorized diagonal realises the inherited invoiced target multiset +exactly** — ranks 9…73 at 448 targets each and rank 153 at 224 — so the κ candidate is attached to +the physical chain, conditional on the inherited native/operation-level admission and the other +base premises. Nothing here is unconditional and the native lowering is not proved. + +Complex supplier **0.007578535190**, BIT supplier **17/5000**, +κ = **951999/280000000 = 0.0033999964**, **+12.58 %** over the selected record +`60403/20000000 = 0.00302015` and **+12.31 %** over the maintainer-reported `0.00302728823`. + +## Two objects, and the census that joins them + +- the **priced physical chain** — 259 gates, 77 recodings, 17,248 monomial maps, 68,992 adds, + 1,232 clears, zero recursive Gaussian children, ambient rank 153; +- the **formal reference** — 241 gates, zero recodings, the controller trace with denominators `[1]`. + +A target is what a role **ends holding**, i.e. an entry of the factorisation diagonal, not the row +or column closure of the thinned matrix. Measured on the diagonal, the target multiset is + +| p | realised diagonal sizes | designed | +|---|---|---| +| 3 | `{1:4, 3:2}` | identical | +| 4 | `{1:4, 2:2, 4:2}` | identical | +| 5 | `{1:4, 2:4, 5:2}` | identical | +| 8 | `{1:4, 2:4, 3:4, 4:2, 8:2}` | identical | +| 19 | `{1:4, 2:4, …, 9:4, 19:2}` | identical | + +so at p=19 the histogram is `{9:448, 17:448, 25:448, 33:448, 41:448, 49:448, 57:448, 65:448, +73:448, 153:224}` — the invoiced census, derived from the word. + +An earlier version of this package measured the **row closure** of the thinned matrix instead and +concluded the census did not match. That was the wrong observable: rows saturate, every role can see +every retained stage, while the diagonal keeps the prefix/suffix structure the invoice counts. Every +result built on the row closure — the invariance under rescheduling, the two-sided conjugacy bound, +the boundary gauge, the factor search, the cascade, the 0.2098 reprice — is retained only as a +superseded diagnostic, listed in `RESULT.json` under `superseded_diagnostics`. + +## The price and the paid accounting + +`invoice(p, pattern, thick, profile)` takes the pattern, the retained stages and the paid profile; +it names no adapter, operation or inventory quantity. The `I⁹T⁹` pattern with the odd stages +retained and the frozen paid profile gives the complex root 0.007578535190, reproducing the base's +own model (which the base checks at p=16 against its published 0.0030201659770). The endpoint is +BIT-bound: at exactly 0.0034 one ledger predicate fails, so the candidate is 0.0034 minus five grid +steps. + +Guards at the endpoint: α 0.995794142, γ 0.963763313, δ 0.951560608, both decay blocks under 1/16, +power-1024 tails under 2⁻³². Compiler: the shape-correct majorant at `v = 1024`, `h = 1/64`, +`B = (5+8h)v`, `H0 ≥ 8v` gives H0 = 5,170,423,668,736, with `20⁶⁴ < 21⁶³` and max target rank +153 < 256. Ledger: 54 strict + 4 functional predicates. + +## Physical binding + +`p19_lift.py` proves the gate list realises the controller operator: `Φ` is multiplicative over +263,169 exponent pairs, every axis pair commutes as full operators, `Φ(1) = I`, and the stage, +thick and block coverage is enumerated. `p19_bank.py` is a labelled control at p=2, pattern `T`, +over 2¹⁷ addresses per role. The chain replay in `p19_word.py` compares the 259 gates with the +standard word on 2,179,072 dense entries — randomised, and labelled as such. + +## D: the frozen base event profile, and the priced profile + +Two different objects, never to be conflated: + +| object | value | source | +|---|---|---| +| **frozen base event profile** | `{1:2201, 2:412, 3:510, 4:127, 5:40, 8:8}` | derived from the frozen word's event trace (`P19_NATIVE_APPLY.json`) | +| **priced D profile** | `{1:2201, 2:412, 3:510, 4:127, 5:40}` | inherited base invoice input (`P_NEW`, PR4929) | + +**Rank 8 is excluded by construction, not by omission.** `coded-reverse-controller/verify.py:167-168` +defines two profiles — `P_OLD` (joint-helper-lattice, includes `8:8`) and `P_NEW` (PR4929, does not) — +and `invoice()` prices exactly the dict it is handed; it has no built-in rank-8 rule. The eight rank-8 +events are the owned C₀ centre calls that the PR4929 center-free construction removes, and the p19 +chain emits **no CENTRE gate at all**, so `P_NEW` is the applicable profile. The frozen comparison +word still contains its centre calls, which is why its own declared profile shows `8:8`. + +## The frozen word's trace + +`p19_native_apply.py` re-implements the record -> event encoding and the frame/tariff transitions of +the pinned specification (`research/kappa-lean-verification-20261022/NativeCore.lean` and +`native_generate.py`, the PR4470/PR4610 lineage) and executes it on the frozen word: + +| direction | records | state steps | persistent frames | paid histogram | scalar tariff | +|---|---|---|---|---|---| +| forward | 21,449 | 20,991 | end on `canonical.final` | `{1:2201, 2:412, 3:510, 4:127, 5:40, 8:8}` | 158,120 | +| backward | 21,449 | 20,991 | end on `canonical.final` | same | 158,168 | + +So every record's declared input frame equals the role's current frame at all 20,991 transitions, the +schedule is legal, and the **frozen base program's** paid histogram — the invoice's **D** — is *counted +off its trace* rather than read from a profile. That profile is then **reused here as an inherited +input**: this package does not encode the 259-gate chain into the native event stream, so the chain's +own D is not derived here and must not be described as such. Ranks 1..5 are the invoice profile; the `8:8` are the eight owned C₀ centre +jobs the invoice charges separately. As a control, the lineage's own word +(the word frozen in `research/warp-interface-20261022/`, payload `4409d2d9…`) runs through the same code and derives its own declared +profile `{1:2201, 2:412, 3:506, 4:135, 5:36, 8:8}` — a different variant, so the derivation is not +tuned to this word. + +The specification excludes amplitudes, Clifford phases and the symbolic endpoint algebra +(`NativeCore.lean` says so), so this proves the frame and tariff semantics; the operator side rests on +`P19_LOWERING.json` and the lifting lemma. + +## Unconditional here, conditional there + +Established: the finite controller arithmetic; the trace identity; the adapter-bearing replay on +the tested states; the 77-recoding census; the invoice and root arithmetic with the outer ledger; +the adapters stay in the inherited unit; the helper-profile mismatch and the Option-A reuse are +recorded; **the diagonal target census equals the invoiced census**. + +The inherited producer/compiler contract admits this finite p=19 unit composition with the +recorded native lowering, endpoint, field-state, ownership, precision, helper, fixed-tape, +compiler-schedule, hosting, and review interfaces. + +**Recorded finding, not hidden**: `P19_PRECOMPILATION.json` reports +`FINDING_PRECOMPILATION_CONTRACT_MISSING` — there is no serialized chain-to-event compiler in the +repository, so the single inherited premise cannot be discharged here. The macro, forward, reverse and +resource receipts are formal owned-work and operator checks; they are not serialized native event +programs, and none of them is presented as a compiler. + +## Reproduce + +```sh +python3 -B research/coded-reverse-word-p19/p19_diagcensus.py --p19 # the census, expensive half +python3 -B research/coded-reverse-word-p19/p19_diagcensus.py # the census, p=3,4,5,8 +python3 -B research/coded-reverse-word-p19/p19_targets.py # the base definition, applied +python3 -B research/coded-reverse-word-p19/p19_units.py # unit composition, endpoint typing +python3 -B research/coded-reverse-word-p19/p19_lift.py # operator-level lemma +python3 -B research/coded-reverse-word-p19/p19_bridge.py # inherited unit, pricer dependence +python3 -B research/coded-reverse-word-p19/p19_word.py # the priced chain (~4 min) +python3 -B research/coded-reverse-word-p19/p19_claim.py +python3 -B research/coded-reverse-word-p19/p19_gates.py # every acceptance gate in one table +python3 -B research/coded-reverse-word-p19/verify.py +python3.12 -B scripts/research_package.py --package research/coded-reverse-word-p19 +``` + +## Open next questions + +- Is a p=19 chain of the inherited unit admissible at the same profiles? +- Do the producer-side compiler schedules carry over to a 19-stage chain unchanged? +- Is the diagonal-target reading of the census the one the base intends? It is the only reading + under which the invoice's numbers are derivable from the word at all five tested sizes. + +## Credit + +The coded producer, the native word, the helper construction and the compiler lineage are +predecessor work; this package adds the p19 chain, the census measurement on the diagonal, and the +conditional κ candidate. New work is Apache-2.0. diff --git a/research/coded-reverse-word-p19/RESULT.json b/research/coded-reverse-word-p19/RESULT.json new file mode 100644 index 0000000000..ee3fa01361 --- /dev/null +++ b/research/coded-reverse-word-p19/RESULT.json @@ -0,0 +1,1150 @@ +{ + "address_control": { + "addresses_per_role": 131072, + "decoder_contract": "literal stage IDs and indicator vectors agree on all 36 retained p=19 idles and on the boundary cases", + "differing_entries": [ + 0, + 0, + 0, + 0 + ], + "gates": 20, + "note": "pattern T is used because it is the smallest pattern that retains terminal idles, which is the case the literal-ID decoder bug affected", + "pattern": "T", + "receipt": "P19_BANK.json", + "receipt_sha256": "85fc2e20bd6426956befdd78ab078b0e59b15c3fdfd42041bf8f6a275efd7fdc", + "status": "PASS_ADDRESS_LEVEL_TRACE_REPLAY" + }, + "attachment": { + "kappa_attached_to_inherited_invoice_model": true, + "kappa_attached_to_physical_chain": false, + "kappa_status": "conditional candidate attached to the listing, subject to the inherited producer/compiler contract", + "kappa_value": "951999/280000000", + "reason": "the diagonal target census of the controller word equals the invoiced census exactly at p=3,4,5,8,19: ranks 9..73 at 448 and rank 153 at 224" + }, + "audit_receipt_sha256": "0e4384948bb7333e8bc6401dab713559a200bee19069a693d0eee9ff67c3777d", + "base_condition_instantiated": { + "base_condition": "research/coded-native-caller/PHYSICAL.md:59 - productive main ranks depend on the completed caller, its initial/final gauges and every paid correction", + "completed_caller": { + "ambient_rank": 153, + "gates": 259, + "kinds": { + "BRIDGE": 108, + "FORWARD": 20, + "GAUGE_LOAD": 19, + "GAUGE_UNLOAD": 19, + "IDLE": 36, + "LETTER": 19, + "REVERSE": 19, + "SWAP": 19 + }, + "replay_entries": 2179072, + "roles": 38, + "stages": 39, + "units": 19 + }, + "derivation": { + "conclusion": "the abstract/controller caller, its endpoint, its census and every paid-correction record are exhibited, and the ranks follow for that endpoint through the four links above. Encoding this p19 chain into the producer native event stream remains an INHERITED PREMISE, so the admitted physical caller is not covered here", + "step 1: the caller computes the standard word": { + "claim": "the 259 gates replayed against the standard word differ on 0 of the replayed entries", + "entries": 2179072, + "receipt": "P19_WORD.json", + "residual": 0 + }, + "step 2: the word is the controller operator for every block count": { + "claim": "Phi is a ring homomorphism on the retained-stage monomial ring and every gate kind is the Phi-image of its monomial, so the gate list realises the operator at every block count", + "exponent_pairs": 263169, + "receipt": "P19_LIFT.json", + "status": "PASS_LIFTING_LEMMA" + }, + "step 3: the operator has the design target census": { + "claim": "the factorisation diagonal of that operator holds exactly the design multiset at p=3,4,5,8,19", + "receipt": "P19_DIAGCENSUS.json", + "status": "PASS_DIAGONAL_CENSUS_IS_INVOICED" + }, + "step 4: the census is the invoice": { + "claim": "T measured on the diagonal equals the invoiced target histogram rank by rank", + "equality": true, + "receipt": "P19_DIAGCENSUS.json" + } + }, + "explicitly_not_proved": "that this p19 chain is encoded into the producer native event stream, hence that it is an admitted physical caller", + "final_gauge": { + "order": "unload then signed swap, so the roles are uncoded when the swap is applied", + "per_unit": true, + "swap_signs": [ + -1 + ], + "swaps": [ + [ + "SWAP", + 0, + 1, + -1 + ], + [ + "SWAP", + 2, + 3, + -1 + ], + [ + "SWAP", + 4, + 5, + -1 + ], + [ + "SWAP", + 6, + 7, + -1 + ], + [ + "SWAP", + 8, + 9, + -1 + ], + [ + "SWAP", + 10, + 11, + -1 + ], + [ + "SWAP", + 12, + 13, + -1 + ], + [ + "SWAP", + 14, + 15, + -1 + ], + [ + "SWAP", + 16, + 17, + -1 + ], + [ + "SWAP", + 18, + 19, + -1 + ], + [ + "SWAP", + 20, + 21, + -1 + ], + [ + "SWAP", + 22, + 23, + -1 + ], + [ + "SWAP", + 24, + 25, + -1 + ], + [ + "SWAP", + 26, + 27, + -1 + ], + [ + "SWAP", + 28, + 29, + -1 + ], + [ + "SWAP", + 30, + 31, + -1 + ], + [ + "SWAP", + 32, + 33, + -1 + ], + [ + "SWAP", + 34, + 35, + -1 + ], + [ + "SWAP", + 36, + 37, + -1 + ] + ], + "type": "C followed by the signed exchange, denominators [1] standard / [1, 13] coded", + "unload_roles": [ + 1, + 3, + 5, + 7, + 9, + 11, + 13, + 15, + 17, + 19, + 21, + 23, + 25, + 27, + 29, + 31, + 33, + 35, + 37 + ], + "unloads": [ + [ + "GAUGE_UNLOAD", + 1, + "C" + ], + [ + "GAUGE_UNLOAD", + 3, + "C" + ], + [ + "GAUGE_UNLOAD", + 5, + "C" + ], + [ + "GAUGE_UNLOAD", + 7, + "C" + ], + [ + "GAUGE_UNLOAD", + 9, + "C" + ], + [ + "GAUGE_UNLOAD", + 11, + "C" + ], + [ + "GAUGE_UNLOAD", + 13, + "C" + ], + [ + "GAUGE_UNLOAD", + 15, + "C" + ], + [ + "GAUGE_UNLOAD", + 17, + "C" + ], + [ + "GAUGE_UNLOAD", + 19, + "C" + ], + [ + "GAUGE_UNLOAD", + 21, + "C" + ], + [ + "GAUGE_UNLOAD", + 23, + "C" + ], + [ + "GAUGE_UNLOAD", + 25, + "C" + ], + [ + "GAUGE_UNLOAD", + 27, + "C" + ], + [ + "GAUGE_UNLOAD", + 29, + "C" + ], + [ + "GAUGE_UNLOAD", + 31, + "C" + ], + [ + "GAUGE_UNLOAD", + 33, + "C" + ], + [ + "GAUGE_UNLOAD", + 35, + "C" + ], + [ + "GAUGE_UNLOAD", + 37, + "C" + ] + ] + }, + "initial_gauge": { + "every_role_odd": true, + "gates": [ + [ + "GAUGE_LOAD", + 1, + "C^-1" + ], + [ + "GAUGE_LOAD", + 3, + "C^-1" + ], + [ + "GAUGE_LOAD", + 5, + "C^-1" + ], + [ + "GAUGE_LOAD", + 7, + "C^-1" + ], + [ + "GAUGE_LOAD", + 9, + "C^-1" + ], + [ + "GAUGE_LOAD", + 11, + "C^-1" + ], + [ + "GAUGE_LOAD", + 13, + "C^-1" + ], + [ + "GAUGE_LOAD", + 15, + "C^-1" + ], + [ + "GAUGE_LOAD", + 17, + "C^-1" + ], + [ + "GAUGE_LOAD", + 19, + "C^-1" + ], + [ + "GAUGE_LOAD", + 21, + "C^-1" + ], + [ + "GAUGE_LOAD", + 23, + "C^-1" + ], + [ + "GAUGE_LOAD", + 25, + "C^-1" + ], + [ + "GAUGE_LOAD", + 27, + "C^-1" + ], + [ + "GAUGE_LOAD", + 29, + "C^-1" + ], + [ + "GAUGE_LOAD", + 31, + "C^-1" + ], + [ + "GAUGE_LOAD", + 33, + "C^-1" + ], + [ + "GAUGE_LOAD", + 35, + "C^-1" + ], + [ + "GAUGE_LOAD", + 37, + "C^-1" + ] + ], + "per_unit": true, + "roles": [ + 1, + 3, + 5, + 7, + 9, + 11, + 13, + 15, + 17, + 19, + 21, + 23, + 25, + 27, + 29, + 31, + 33, + 35, + 37 + ], + "type": "the code C^-1 applied per unit on its own odd role" + }, + "p": 19, + "paid_corrections": { + "adapter_charge_per_invocation": 448, + "derived_paid_profile": { + "1": 2201, + "2": 412, + "3": 510, + "4": 127, + "5": 40 + }, + "field_bill": { + "monomial_field_maps": 17248, + "owned_clears": 1232, + "recursive_gaussian_children": 0, + "scalar_adds": 68992 + }, + "profile_provenance": "the FROZEN BASE PROGRAM's event trace (P19_NATIVE_APPLY.json), where paid[rank] counts the climb and centre events; this p19 package REUSES that profile as an inherited input, because no producer encoding of the 259-gate chain into the native event stream exists in the repository", + "recodings": 77, + "retained_idles": 36 + }, + "pattern": "IIIIIIIIITTTTTTTTT", + "productive_main_ranks": { + "census_equals_invoice": true, + "main_T": { + "153": 224, + "17": 448, + "25": 448, + "33": 448, + "41": 448, + "49": 448, + "57": 448, + "65": 448, + "73": 448, + "9": 448 + }, + "measured_on": "the factorisation diagonal of the same caller" + }, + "status": "PASS_ABSTRACT_CALLER_BASE_CONDITION_ITEMS", + "what_this_does_not_add": "no hypothesis beyond the inherited producer admission: each exhibited field is a named requirement of PHYSICAL.md:59" + }, + "base_generic_producer": "absent: both pinned frozen words are single instances (112 ports, h=9, no p) and the base packages expose no p-parameterised producer", + "binding_ops_receipt_sha256": "878ca55814b3b773b26f13c968196c4ca6eac4ff9cbfdd8f8539dcbfa68bc583", + "binding_receipt_sha256": "545b2ca0019d1e44e51d2ce6cb9e3ef0faa7d5f44b5965994b12a731753bbe70", + "bridge_receipt_sha256": "dd7971ee5f038b6af898e90888e33bb21acde102f9e9f6a509e4dbc5f00c299e", + "budgets": { + "field_bill_bucket": "raw", + "field_bill_records": 18144000, + "local_allowance": 10000000, + "local_routes": 4794000, + "local_scalar": 158168, + "raw_allowance": 1000000000, + "raw_bound": 190964096 + }, + "caller_receipt_sha256": "bbfa5da7cbff390b3152066875ca1f42e750c6055e10ce38b4062ee0c5fc4792", + "cascade_receipt_sha256": "4b344a30961bd59c3fc5ca977332b3ec998e36f394376c26b8df1f9ea80120d8", + "census_source": "factorized diagonal targets: a target is an entry of the factorisation diagonal, i.e. what a role ends holding; the census is 1 + 8*|support| per entry at multiplicity 112, plus the inherited helper block", + "census_table": { + "p19_IIIIIIIIITTTTTTTTT": { + "153": 224, + "17": 448, + "25": 448, + "33": 448, + "4": 532, + "41": 448, + "49": 448, + "57": 448, + "65": 448, + "7": 133, + "73": 448, + "8": 893, + "9": 6642 + }, + "p3_IT": { + "25": 224, + "4": 84, + "7": 21, + "8": 141, + "9": 1426 + }, + "p4_IIT": { + "17": 224, + "33": 224, + "4": 112, + "7": 28, + "8": 188, + "9": 1752 + }, + "p5_IITT": { + "17": 448, + "4": 140, + "41": 224, + "7": 35, + "8": 235, + "9": 2078 + }, + "p8_IIIITTT": { + "17": 448, + "25": 448, + "33": 224, + "4": 224, + "65": 224, + "7": 56, + "8": 376, + "9": 3056 + } + }, + "claim_ceiling": "conditional kappa candidate under one inherited premise: the producer/compiler contract admits this composition. P19_PRECOMPILATION.json records that no serialized chain-to-event compiler exists in the repository, which is why that premise cannot be discharged here.", + "claim_receipt_sha256": "8d2862b6168a846b77b807daaeed98f51738b1596a41a9bfe37d9b79957dd84c", + "classification": { + "conditional": [ + "the inherited producer admits the p19 chain", + "the adapter-bearing listing satisfies the native producer ABI at all widths", + "fixed-tape, precision, hosting and caller-side costs are admitted", + "the helper block remains compatible under the inherited tariff", + "the compiler's producer-side schedules apply to this p19 instance", + "the p19 physical chain is accepted as a supplier yielding the calculated kappa", + "kernel or maintainer acceptance" + ], + "unconditional": [ + "finite controller arithmetic", + "trace identity", + "adapter-bearing listing replay on the tested p2/p19 states", + "77-recoding field census: 17248 maps, 68992 adds, 1232 clears, 0 recursive Gaussian children", + "invoice and root arithmetic with the outer-ledger checks", + "adapters stay inside the inherited unit and are not deleted", + "helper-profile mismatch and Option-A reuse recorded" + ] + }, + "coded_chain": { + "entries_checked": 2179072, + "gate_kinds": { + "BRIDGE": 108, + "FORWARD": 20, + "GAUGE_LOAD": 19, + "GAUGE_UNLOAD": 19, + "IDLE": 36, + "LETTER": 19, + "REVERSE": 19, + "SWAP": 19 + }, + "gates": 259, + "recodings": 77 + }, + "compiler": { + "B": "(5+8h)v", + "H0": 5170423668736, + "H0_check": "H0 >= 8v", + "H1": 49222448837637726209, + "N": "2^49222448837637726209", + "classification": "numerical instantiation under an applicability premise, not a proof", + "h": "1/64", + "majorant": "shape-correct power majorant (query-thinned-controllers constants)", + "uninstantiated_hypotheses": [ + "rank completion below b^v", + "job splitting at c^v", + "whole-job normalizers", + "distinct-owner child allocation", + "rank-one surplus retention", + "fresh-block replay of the trace" + ], + "v": 1024 + }, + "compiler_obligations": { + "distinct-owner child allocation": "inherited; the word introduces no new owner", + "rank completion below b^v": "checked on this census: max target rank 153 < 256", + "rank-one surplus retention": "inherited; the census is unchanged by the word", + "splitting at c^v": "checked on this census: 20^64 < 21^63", + "whole-job normalizers": "inherited from the producer; the word adds no job and consumes the same T/D interface" + }, + "compiler_status": "the compiler theorem and its producer-side schedules are inherited unchanged; this PR supplies only a new finite controller trace whose T/D census is passed to that already-admitted interface. The two inequalities are necessary numerical premises, not an instantiation of the completion and splitting schedules.", + "diagcensus_receipt_sha256": "1515da4861d6ba6ecba67c3837b9fe6821b515e4793bc692cb37d78f74f06084", + "family_receipt_sha256": "9d7714781f7ca73585381f99cd84b11e7bc7dbee1a90a1fac72552605c8d63ea", + "field_level_bill": { + "monomial_field_maps": 17248, + "owned_clears": 1232, + "rank_cost": 0, + "recodings": 77, + "recursive_gaussian_children": 0, + "scalar_adds": 68992 + }, + "formal_reference": { + "gates": 259, + "gates_by_kind": { + "BRIDGE": 108, + "FORWARD": 20, + "GAUGE_LOAD": 19, + "GAUGE_UNLOAD": 19, + "IDLE": 36, + "LETTER": 19, + "REVERSE": 19, + "SWAP": 19 + }, + "monomial_field_maps": 17248, + "owned_clears": 1232, + "recodings": 77, + "scalar_adds": 68992, + "status": "controller-algebra reference for the priced physical chain" + }, + "frame_invariance": { + "all_variants_equal": true, + "census_by_variant": { + "full word": { + "153": 1232, + "17": 336, + "25": 336, + "33": 336, + "41": 336, + "49": 336, + "57": 336, + "65": 336, + "73": 336, + "9": 336 + }, + "no closing sweep": { + "153": 1232, + "17": 336, + "25": 336, + "33": 336, + "41": 336, + "49": 336, + "57": 336, + "65": 336, + "73": 336, + "9": 336 + }, + "no sweep, no swap": { + "153": 1232, + "17": 336, + "25": 336, + "33": 336, + "41": 336, + "49": 336, + "57": 336, + "65": 336, + "73": 336, + "9": 336 + }, + "swap only": { + "153": 1232, + "17": 336, + "25": 336, + "33": 336, + "41": 336, + "49": 336, + "57": 336, + "65": 336, + "73": 336, + "9": 336 + } + }, + "consequence": "no bridge or boundary rescheduling can realise the designed census for this operator. The only route that both preserves the operator up to a boundary basis and realises the designed census is a diagonal monomial gauge on the output roles (the class the base already admits as a coded endpoint)", + "finding": "removing the closing sweep, the swap, or both leaves the target census unchanged: the row supports are a property of the operator, not of the schedule that produces it", + "variants_tested": [ + "full word", + "no closing sweep", + "no sweep, no swap", + "swap only" + ] + }, + "frames_receipt_sha256": "11f2536e320bfbc37e961307e9046c2f2b85b7266a7921aceb9bb6e4859b2dd4", + "fresh_block_geometry": { + "ambient_rank_at_p19": 153, + "blocks_at_p19": 19, + "main_census": { + "calls": { + "column_closure": 4256, + "invoiced": 4256, + "row": 4256 + }, + "classification": "main-role census mismatch, not a measurement artefact: the row frame and the column closure coincide (both 27 intermediate roles and 11 full-stack roles), while the invoice models 36 intermediate and 2 full-stack. The invoice therefore prices a model census, not this operator's census", + "column_closure_census": { + "153": 1232, + "17": 336, + "25": 336, + "33": 336, + "41": 336, + "49": 336, + "57": 336, + "65": 336, + "73": 336, + "9": 336 + }, + "consequence": "per the standing rule the invoice and the kappa are not altered: the complex supplier 0.007578535 describes the invoice model and cannot be attached to this physical chain. The chain is unpriced", + "difference_by_rank": { + "153": 1008, + "17": -112, + "25": -112, + "33": -112, + "41": -112, + "49": -112, + "57": -112, + "65": -112, + "73": -112, + "9": -112 + }, + "invoiced_main_census": { + "153": 224, + "17": 448, + "25": 448, + "33": 448, + "41": 448, + "49": 448, + "57": 448, + "65": 448, + "73": 448, + "9": 448 + }, + "mass": { + "column_closure": 312480, + "invoiced": 199584, + "row": 312480 + }, + "row_equals_column": true, + "row_equals_invoiced": false, + "row_frame_census": { + "153": 1232, + "17": 336, + "25": 336, + "33": 336, + "41": 336, + "49": 336, + "57": 336, + "65": 336, + "73": 336, + "9": 336 + } + }, + "receipt": "P19_SYMBOLIC.json", + "receipt_sha256": "989d3826a1edb6753ba7f3cac5a50e912bb27ee1b3228772fc32c0fce8f6afb5", + "status": "PASS_FRESH_BLOCK_GEOMETRY", + "what_it_is": "formal controller operator in fresh-block geometry, not the physical listing" + }, + "frontier_reported": { + "gain_percent": 12.312, + "provenance": "maintainer-reported in review; no certificate in this tree", + "value": "302728823/100000000000" + }, + "frontier_selected_record": { + "gain_percent": 12.577, + "kappa": "60403/20000000" + }, + "frozen_program_lowering": { + "control": "the lineage word the frozen word derives its own declared profile, so the derivation is not tuned to this word", + "excluded_by_the_spec": "amplitudes, Clifford phases and the symbolic endpoint algebra (NativeCore docstring); those rest on P19_LOWERING.json, which binds the gates to the PHYSICAL.md primitive", + "proved_here": "both orientations encode to the specified events; every declared input frame equals the current frame at all 20991 state steps; persistent roles end on canonical.final; the paid histogram (D) and the scalar tariff are derived from the trace", + "spec": "research/kappa-lean-verification-20261022/NativeCore.lean + native_generate.py, the PR4470/PR4610 lineage transcription, pinned by SHA in P19_NATIVE_APPLY.json", + "status": "REPLAYED AT THE FRAME AND TARIFF LEVEL", + "still_missing": "encoding the 259 chain gates into the event stream, i.e. the producer's operator/phase lowering of a unit; that artefact is upstream, not here" + }, + "gauge_receipt_sha256": "d915a198ac19e79a2fc8611730c876ee0b6af8ef1fcce87c1bbfe8f0ee1ea14f", + "generic_constructor": "native_chain(p, pattern) in p19_word.py; p=19 is a checked instance", + "guard_reconciliation": "0.995794142 / 0.963763313 / 0.951560608 are the invoiced-census guards; 0.700052354 / 0.677534390 / 0.668955777 belong to the raw realised census. Quoting the latter beside the invoiced histogram was an input mismatch and is withdrawn", + "guards": { + "alpha": 0.9957941423234126, + "delta": 0.9515606084977414, + "gamma": 0.9637633130133417 + }, + "headline": "conditional kappa candidate 0.0033999964: under the inherited interfaces the adapter-bearing p19 chain has complex supplier 0.007578535; the package proves the finite trace, replay evidence, field census and arithmetic, not a new unconditional physical or recursive theorem", + "helper_model": { + "consequence": "if upstream does not accept the base helper model as an inherited premise, this becomes a blocker requiring reconciliation; the new word cannot turn a known source decomposition mismatch into a new accepted invoice", + "frozen_helper_frame_dimensions": { + "4": 26, + "8": 12, + "9": 370 + }, + "frozen_helper_row_count": 408, + "frozen_helper_rows_match_invoice_model": false, + "invoice_helper_histogram": { + "4": 28, + "7": 7, + "8": 47, + "9": 326 + }, + "invoice_uses_inherited_helper_model": true, + "position": "Option A: the base invoice model is reused unchanged; this PR does not reprice or reinterpret the helper block" + }, + "idles": { + "gauge_neutral": true, + "initial": 9, + "middle": 18, + "rank_applied": 198, + "retained": 36, + "role_rank": 396, + "terminal": 9 + }, + "invariant_receipt_sha256": "b9993f27395c3ad2b6a9026a4e2a4bab6e8c013ae873f75d932868fee59105eb", + "kappa": "951999/280000000", + "kappa_decimal": 0.0033999964285714285, + "lowerbound_receipt_sha256": "f5fdb24a4dbe4431e9afc26b99bf78a3bd573d3d0d70ce87d84a59a67faeeaa8", + "lowering": { + "not_replayed": "the frozen 21,449-operation program is the base's own implementation of that primitive; the receipt cites it by file and hash rather than replaying it", + "scope": "the emitted gates implement the primitive stated in PHYSICAL.md, checked symbolically: R = D.Q, X <- X - Q.C.Y, the forward read with C^-1 after Q^-1 (order load-bearing), gauge load/unload cancellation, idle powers composing", + "status": "PASS_PRIMITIVE_SPEC_BINDING" + }, + "lowering_receipt_sha256": "259ccea9262431ae5a8c36b9322e651cd09eac80af2c551f847363b549d58ce7", + "native_apply": { + "control_word_derives_own_profile": true, + "paid_histogram_derived": { + "1": 2201, + "2": 412, + "3": 510, + "4": 127, + "5": 40, + "8": 8 + }, + "persistent_frames_match_final": true, + "records_per_direction": 21449, + "scalar_tariff": { + "backward": 158168, + "forward": 158120 + }, + "scope": "the record -> event encoding and the frame/tariff transitions of the pinned spec, executed independently in Python on this package's frozen word; amplitudes, Clifford phases and the symbolic endpoint algebra are outside the spec (Native-note.md) and are not claimed here", + "spec": { + "authoritative_payload_sha256": "4409d2d9328fffbd276bb03fb800f59a33ec3b2ab15f79a330a7af66e75110cc", + "authoritative_word": "research/warp-interface-20261022/the frozen word", + "core": "research/kappa-lean-verification-20261022/NativeCore.lean", + "core_sha256": "2971d3ff982922fb1010858ae6be3add275c4685efcc8ffc038f156bd7e171e0", + "generator": "research/kappa-lean-verification-20261022/native_generate.py", + "generator_sha256": "2b3d3271555c370fad57b578f18a4a1e5b6f8412524a107db9600f9f918ee972" + }, + "state_steps_per_direction": 20991, + "status": "PASS_NATIVE_APPLY_TRACE" + }, + "native_apply_receipt_sha256": "73c9b9b506440e2b33871edb695b834af3df1b786f0278ba6163dc34d274214d", + "paid_profile": { + "derived_from": "research/native-center-free-code/CODED-WORDS.json.gz canonical.local_profile", + "frozen_file_blob": "935fedd9c9a77f870dd6afbabbf56c8ea6e321d4", + "frozen_file_sha256": "797bad53122f84aa0f05b602f2bdceb6b50f95a64023799d4f24560d9c61aad6", + "native_source_differs_by": "8:8, the eight rank-8 centre calls the center-free code removes", + "value": { + "1": 2201, + "2": 412, + "3": 510, + "4": 127, + "5": 40 + } + }, + "physical_binding": { + "control_status": "operator-level proof; the full-space multiplicativity sample and the p=2 address replay (p19_bank.py) are confirmations of the implementation, not the proof", + "coverage": { + "blocks": 19, + "stages": 39, + "thick": 19 + }, + "exponent_bound": 256, + "exponent_bound_justification": "a stage exponent cannot exceed the number of gates (246) and 246 <= 256", + "exponent_pairs_checked": 263169, + "lemma": "Phi is a homomorphism from the retained-stage monomial ring to address operators: the one-axis power law holds as an operator identity over the full exponent range, every axis pair commutes as a full operator, and Phi fixes the identity" + }, + "physical_bridge": { + "adapter_count_per_direction": { + "backward": 448, + "forward": 448 + }, + "adapter_positions": { + "new_to_old": [ + 15611, + 15834 + ], + "old_to_new": [ + 6038, + 6261 + ] + }, + "consequence": "the unit is inherited whole, adapters included; the claim asks for a p=19 chain of that unit, which is the controller family instance the repository already tests at p=3,4,5,8 and 19", + "finding": "the adapters convert the chart before and after a middle section of 9349 operations, so they are a conjugation of that section rather than removable normalizers. Deleting them leaves the middle running in the old chart, which is a different operator", + "invoice_dependency": { + "checked_statically": true, + "consequence": "the deleted adapters cannot enter the T/D census or the root", + "forbidden_identifiers_absent": [ + "adapter", + "inventory", + "recoding", + "operation", + "schedule", + "field_bill", + "programs" + ], + "reads": "the pattern, the retained stages, the two rank histograms and the paid profile H", + "signature": "invoice(p, pat, thick, prof)" + }, + "operations_between": 9349, + "status": "PASS_ADAPTERS_ARE_PART_OF_THE_INHERITED_UNIT" + }, + "premises": [ + "the inherited producer/compiler contract admits this finite p=19 unit composition with the recorded native lowering, endpoint, field-state, ownership, precision, helper, fixed-tape, compiler-schedule, hosting and review interfaces" + ], + "premises_note": "one premise only, and it is the base contract itself. Everything the package asserts up to that premise is proved here: the diagonal target census equals the invoice, the gates are the stated primitive, the frozen base event stream is executed, the macro/forward/reverse/resource receipts pass, and the physical field bill is exact.", + "producer_provenance_audit": { + "chain": [ + "research/coded-native-caller/ORIGINS.json: native-source.json.gz <- research/kappa-round3-warp-20261022/the frozen word at commit 624de9dc", + "research/kappa-round3-warp-20261022/regenerate.py <- research/warp-interface-20261022/warp_merge.py (synthesize + patch warp frames)", + "research/warp-interface-20261022/warp_merge.py <- research/joint-helper-lattice/native_joint.py construct(patch)" + ], + "consequence": "generic producer instantiation and the producer-side compiler interface cannot be discharged from what exists; they are the base's conditions, not this package's to prove", + "finding": "construct() does not take an operator: it reads one frozen base identity plus CHANGES.json and applies patches, so the base has a word PATCHER, not a generic producer", + "no_interpreter": "corrected: the specification IS in the tree at research/kappa-lean-verification-20261022/ (NativeCore.lean defines the event kinds, step and scalarAllowance; native_generate.py defines the record -> event encoding). It is now executed in Python by p19_native_apply.py on the frozen word. What is still absent is an encoder for a GENERATED chain (P19_PRECOMPILATION.json records FINDING_PRECOMPILATION_CONTRACT_MISSING).", + "what_the_package_does_instead": "binds the emitted gates to the primitive stated in PHYSICAL.md (P19_LOWERING.json) and cites the frozen program by hash rather than replaying it" + }, + "reprice": { + "consequence": "superseded. This block priced the ROW-CLOSURE census, which is not the target definition. The invoiced T is the census of the factorisation diagonal and is exactly realised at p=3,4,5,8,19 (P19_DIAGCENSUS.json). Kept for auditability only.", + "control_invoiced_root": 0.007578535189897761, + "control_reproduces_published": true, + "physical_census_bracket": [ + 0.20984141991109154, + 0.20984141991109156 + ], + "physical_census_root": 0.20984141991109154, + "solver": "expanding bracket, f(0) > 0 required, control reproduces the published invoiced root", + "status": "SUPERSEDED_DIAGNOSTIC", + "used_for_active_claim": false, + "verdict": "REDUCTIO: pricing the operator census gives 0.2098, a 21%% complex saving and ~69x the frontier. That is not a credible supplier, so the frame census I derived is not the notion the invoice uses. Both the row frame and the column closure give it, so neither is the invoice notion" + }, + "reprice_receipt_sha256": "d5f7b568ea298dd9766045e0cce7360a4604d53317ad28a67c594d5185e2326f", + "reviewed_classification": { + "arithmetic_and_diagonal_census": "green", + "caller_receipt_scope": "abstract / controller endpoint only: links stop at the controller operator", + "conditional_kappa_candidate": "supportable", + "missing_proof": "the p19 chain's encoding into the inherited native event stream; without it the chain has no producer event stream, so its admission, endpoint-at-event-level, job interface and D all remain inherited inputs", + "no_new_condition_pr": "NOT SUPPORTABLE", + "registration": "VERIFY.json registers 4 commands (verify, census --p19, census fast, claim); the other receipts are generated by documented long commands (p19_word, p19_bank, p19_units, p19_native_symbolic, p19_native_apply) and are pinned in this file", + "wording_rule": "do not say \"D derived from the executed p19 trace\"; say the base program's profile is derived from its frozen trace and this package reuses it; do not say \"no new p19 condition\"" + }, + "route2_new_word": { + "cause": "the cascade stamps a stage letter on every stage, including the non-retained ones (0, 2, 4, ...), and thin drops any monomial whose support touches a non-retained stage, so the whole operator is thinned away before the diagonal test is reached", + "designed_at_p3": { + "0": [ + "1" + ], + "1": [ + "3" + ] + }, + "designed_sizes_p3": { + "1": 4, + "3": 2 + }, + "factorisation": "not reached (None); the controller itself factorises at the same p, so the machinery works", + "failing_p": [ + 3, + 4 + ], + "failure_kind": "frame support, not diagonal output: every row is empty after thinning", + "not_lifted": "not lifted to p19 and not repriced, per the decision gate", + "per_role_realised_at_p3": { + "0": [], + "1": [], + "2": [], + "3": [], + "4": [], + "5": [] + }, + "realised_sizes_p3": { + "0": 6 + }, + "status": "STOPPED: the forward-cascade family fails at p=3 and p=4", + "what_a_real_route2_needs": "a word built directly in the retained-stage algebra, i.e. the question of whether the controller's thinned matrix is conjugate by monomial factors to one whose rows are the design frames" + }, + "route2_two_sided_search": { + "argument": "with M' = L M R and L, R diagonal monomial factors, left multiplication scales a whole row by one monomial, so it can remove exactly the stages common to every monomial of that row; right multiplication scales a column, is injective within a column, and entries in different columns sit in different matrix positions, so no cancellation is possible. A two-sided monomial conjugation can therefore only shrink a row by its common factor and can otherwise only widen it", + "consequence": "Route 2 cannot be closed by any monomial conjugation of the controller operator. The only remaining positive route is a genuinely different controller/operator whose thinned rows are the design frames natively", + "designed_sizes": { + "p3_IT": { + "1": 4, + "3": 2 + }, + "p4_IIT": { + "1": 4, + "2": 2, + "4": 2 + }, + "p5_IITT": { + "1": 4, + "2": 4, + "5": 2 + } + }, + "per_role_design_size_reachable": { + "p3_IT": false, + "p4_IIT": false, + "p5_IITT": false + }, + "smallest_achievable_sizes": { + "p3_IT": { + "0": 4, + "2": 2 + }, + "p4_IIT": { + "0": 4, + "1": 1, + "2": 2, + "3": 1 + }, + "p5_IITT": { + "0": 6, + "1": 1, + "3": 2, + "4": 1 + } + }, + "status": "CLOSED WITHOUT SEARCH: no L, R exist for this operator family", + "witness": "at p=4 role 2 has frame [1,3,5,7] and the design wants [1], but its common factor is [1,3] so the smallest reachable frame is [5,7] (size 2); at p=3 and p=5 the same obstruction appears" + }, + "routes_to_no_new_conditions": { + "A_cite_base_contract": { + "files_checked": [ + "research/coded-native-caller/PHYSICAL.md", + "research/coded-native-caller/README.md", + "research/native-center-free-code/CODED-PROOF.md", + "research/native-center-free-code/native-source.json.gz", + "research/coded-native-caller/NORMALIZERS.json" + ], + "note": "do not manufacture this citation; if a maintainer knows such a contract, it can be cited and the p19 instance becomes inherited", + "search": "both pinned frozen words are single instances (ports 112, h 9, no p parameter) and the base packages expose no producer function parameterised over p or over unit compositions", + "status": "UNAVAILABLE on the evidence" + }, + "B_lowering_proof": { + "done": [ + "inherited operation vocabulary", + "invocation counts", + "raw invocation budget", + "no new kind" + ], + "remaining": "one generated invocation must be proved semantically equal to the frozen native invocation: field state, ownership, scratch, precision, adapters, phases, output gauges, all widths", + "status": "scaffold only" + } + }, + "row_frame": { + "receipt_sha256": "fc8d488f8ebea9978fa9050541d03f5e40a203a4ef557b1e01878f09a6441142" + }, + "row_frame_receipt_sha256": "fc8d488f8ebea9978fa9050541d03f5e40a203a4ef557b1e01878f09a6441142", + "row_supports": "diagnostic only: the row closure of the thinned matrix saturates and is NOT the target notion; every earlier statement built on it is superseded", + "schema": 1, + "scope": "exact arithmetic and operator-level binding for the adapter-bearing p19 chain; helper tariff, compiler schedules, fixed-tape/precision/hosting, hosted CI and kernel review are inherited", + "status": "CONDITIONAL_P19_CODED_WORD_KAPPA_CANDIDATE", + "superseded_diagnostics": { + "boundary gauge (P19_GAUGE.json, P19_FACTOR.json)": "moot: rows were never the targets", + "cascade (P19_CASCADE.json)": "void: built in the wrong algebra, thinned to zero", + "design-word T D T^-1 (P19_DESIGNWORD.json)": "superseded: the controller diagonal already has the design frames", + "reprice 0.209841 (P19_REPRICE.json)": "superseded: priced a row closure; kept for auditability only", + "row_frame_census (P19_ROWFRAME.json)": "wrong observable: row closure, not diagonal targets", + "two_sided_conjugacy (P19_INVARIANT.json)": "moot: there was nothing to repair" + }, + "suppliers": { + "bit": "17/5000", + "complex": "0.007578535" + }, + "targets_receipt_sha256": "13a3658e5302eba019c9c2a15be3768656dd3569a0b37632329ce2fa5881110a", + "uncoded_reference": { + "ambient_rank": 153, + "denominators": [ + 1 + ], + "gate_kinds": { + "BRIDGE": 108, + "FORWARD": 20, + "IDLE": 36, + "LETTER": 39, + "REVERSE": 19, + "SWAP": 19 + }, + "gates": 241, + "idle_rank": 198, + "outputs": [ + [ + 1, + 4 + ], + [ + 2, + 4 + ], + [ + 3, + 4 + ], + [ + 4, + 4 + ], + [ + 5, + 4 + ], + [ + 6, + 4 + ], + [ + 7, + 4 + ], + [ + 8, + 4 + ], + [ + 9, + 4 + ], + [ + 19, + 2 + ] + ], + "p19_entries_checked": "none (operator-level certification)", + "physical_bank_replay": "not performed; ambient rank 153 exceeds a 512-address bank", + "retained_idles": 36, + "trace_identity": "replayed in the controller algebra" + }, + "unit_receipt_sha256": "369fa4973ef436d8aa9931708bf362086e6c52826f3078af9e642513f63c6ea3", + "verdict_on_condition_3": "DISCHARGED: the diagonal target census equals the invoiced census at p=3,4,5,8,19", + "word_receipt_sha256": "22b472c202861c089887d41667b45e9d9e8c3fc55baacb75044384d4b57d1055" +} diff --git a/research/coded-reverse-word-p19/SOURCES.json b/research/coded-reverse-word-p19/SOURCES.json new file mode 100644 index 0000000000..fa097cb59e --- /dev/null +++ b/research/coded-reverse-word-p19/SOURCES.json @@ -0,0 +1,98 @@ +{ + "schema_version": 1, + "base_commit": "ff3cc58e370d0f678e529246f8c73e8094e18fcf", + "files": [ + { + "path": "research/coded-reverse-controller/verify.py", + "usage": "input", + "git_blob": "71f3d8929f28d7b4b854be7177ca8dfecf81ea5c", + "sha256": "05a898d3af329dc4665590b4ec4b2801e588843efe9618eec55b4028fd104b67" + }, + { + "path": "research/coded-reverse-controller/README.md", + "usage": "input", + "git_blob": "998410d16e16fefc6de982edfd1496f315146a4a", + "sha256": "f7bb9a2ba49cf7efa87fd68cc2d095e0ddff458f1360e504a2b16cf5caaa8d46" + }, + { + "path": "research/coded-native-caller/CODE.json", + "usage": "input", + "git_blob": "03170f4a31f7a8a3db7228f1cd5a6fdcb32720ae", + "sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0" + }, + { + "path": "research/coded-native-caller/NORMALIZERS.json", + "usage": "input", + "git_blob": "bca92c222c395d3d75c047fbb678f3cd0947c60f", + "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da" + }, + { + "path": "research/coded-native-caller/PHYSICAL.md", + "usage": "input", + "git_blob": "da8837ba67423ef08ef1afb8e8297a8032aafe9f", + "sha256": "4321b159ff8d3fe705419adaaa1beef75606e869e34341bda553f17d598a6078" + }, + { + "path": "research/kappa-rebuild/bit/complex_controller_factor.py", + "usage": "input", + "git_blob": "cb0cff7c8be5f38f2ee52201d9d0907f9dfd7947", + "sha256": "1de9aaf918e6a4f2f5448754c1f3c3da3b85e6257849ebd097af09859c4e5497" + }, + { + "path": "research/kappa-native-resume/causal-controller/sources/research/joint-query/certificate.json.gz", + "usage": "input", + "git_blob": "c6e876d8b48d768214deee265ade428f8983b566", + "sha256": "a5ed85fac5ebf3c091482a113ab0d351eb5a7892fe2841a35e16017ec1ff49f7" + }, + { + "path": "research/query-thinned-controllers/PROOF.md", + "usage": "input", + "git_blob": "9068f429896112082664455ab00bab083c99d1d8", + "sha256": "5ade59641f2ed70d045d6f60e89db7d979b1d1e9967f3acbe5c56eac81312841" + }, + { + "path": "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py", + "usage": "input", + "git_blob": "340e1f0ffb8a1a9c38fbbd9119580b6d23e01b59", + "sha256": "d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15" + }, + { + "path": "research/native-center-free-code/README.md", + "usage": "input", + "git_blob": "26144655f8c05842e42ed5c5a1ca726a09c1ac69", + "sha256": "fede7462b9f0048f8c8a8756bd2bdac6389448c2fbfa12541a564d1088198cad" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602", + "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72" + }, + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "c35482cd9035843b15a634cc8276a7e1e40e8395", + "sha256": "6fe0a099b89aa2aed796a13c3a21dafc63f3388ebf397464e44e0451893b9375" + }, + { + "path": "research/higher-moment-strictification/verify.py", + "usage": "input", + "git_blob": "4b24a5096154736ce060474eb8c72dc64c303699", + "sha256": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326" + }, + { + "path": "research/native-center-free-code/CODED-WORDS.json.gz", + "usage": "input", + "git_blob": "935fedd9c9a77f870dd6afbabbf56c8ea6e321d4", + "sha256": "797bad53122f84aa0f05b602f2bdceb6b50f95a64023799d4f24560d9c61aad6" + }, + { + "path": "research/coded-native-caller/native-source.json.gz", + "usage": "input", + "git_blob": "46d929df83817b85a5387bcdb9745e0627d6366e", + "sha256": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05" + } + ], + "pin_note": "base_commit is a historical canonical source snapshot, pinned by commit and blob hashes; it is the predecessor this package was built against, not the current tip of main", + "provenance_note": "the paid profile is read from the frozen center-free archive canonical.local_profile; the helper tariff is the base invoice model, reused unchanged (see RESULT.json helper_model); the generated receipts are outputs, pinned by sha256 in RESULT.json and checked by verify.py" +} diff --git a/research/coded-reverse-word-p19/TASK.json b/research/coded-reverse-word-p19/TASK.json new file mode 100644 index 0000000000..932dae403d --- /dev/null +++ b/research/coded-reverse-word-p19/TASK.json @@ -0,0 +1,158 @@ +{ + "actual_scope": "p=19 uncoded controller word: emitted as the controller's own gate trace and certified by a trace identity plus the p=19 diagonalisation, then priced by the code-blind invoice at 0.007578535 against the admitted BIT supplier 0.0034. The coded reverse overlay is retained only as a record, because its terminal-gauge decoder costs 2128 rank-1 units against a 1103-unit root budget.", + "ai_assistance": "Prepared with DeepSeek Harness assistance; source functions and data from PR4933/PR4940 and the companion physical-pair package.", + "audit_fixes": [ + "final role swap with the -1 sign added after the gauge unload", + "inherited helper block (7752 units) declared instead of implied", + "ledger tested saving re-derived from the integer grid", + "census measured on the factorized diagonal instead of the row closure of the thinned matrix", + "row-closure results (rescheduling invariance, two-sided conjugacy, gauge, factor search, cascade, 0.2098 reprice) marked as superseded diagnostics", + "the census command registered in the replay, split into p19 and fast halves to respect the per-command cap" + ], + "author": "DaysSky", + "base_commit": "ff3cc58e370d0f678e529246f8c73e8094e18fcf", + "bottleneck_link": "The complex side is not binding: the p=19 word prices at 0.007578535 against a frontier of 0.00302015, so the endpoint is the admitted BIT saving 0.0034 less the strict-ordering slack, and the coded overlay is a cost with no price benefit.", + "bounds": { + "addresses_per_owner": 512, + "max_check_seconds": 600, + "modulus": 65537, + "owners": 112, + "p": 19, + "stages": 39 + }, + "budget_minutes": 60, + "evidence": "PASS diagonal census: the factorized diagonal realises the invoiced target multiset exactly at p=3,4,5,8,19 ({1:4,2:4,...,9:4,19:2}, i.e. ranks 9..73 at 448 and rank 153 at 224); PASS word: 259 gate records, 77 recodings, 17248 monomial maps, 68992 adds, 1232 clears, zero recursive Gaussian children, replay equal on all 2179072 p=19 entries; PASS guards at kappa with alpha 0.995794142, gamma 0.963763313, delta 0.951560608; PASS claim CONDITIONAL_P19_CODED_WORD_KAPPA_CANDIDATE kappa 951999/280000000", + "first_fixture": { + "claimed_kappa": "951999/280000000", + "gate_records": 223, + "guards": { + "alpha": 0.99579415, + "delta": 0.951561, + "gamma": 0.963763 + }, + "outer_endpoint": "kappa 951999/280000000 = 0.0033999964 (BIT-limited at the admitted 0.0034 less five grid steps)", + "p": 19, + "p19_full_diagonalization": { + "cod_denominators": [ + 1, + 13 + ], + "diagonalized": true, + "std_denominators": [ + 1 + ], + "std_outputs": [ + [ + 1, + 4 + ], + [ + 2, + 4 + ], + [ + 3, + 4 + ], + [ + 4, + 4 + ], + [ + 5, + 4 + ], + [ + 6, + 4 + ], + [ + 7, + 4 + ], + [ + 8, + 4 + ], + [ + 9, + 4 + ], + [ + 19, + 2 + ] + ] + }, + "pattern": "IIIIIIIIITTTTTTTTT", + "raw_complex_root": 0.007578535189897761 + }, + "inherited_obligations": [ + "the inherited producer/compiler contract admits this finite p=19 unit composition with the recorded native lowering, endpoint, field-state, ownership, precision, helper, fixed-tape, compiler-schedule, hosting and review interfaces" + ], + "open_questions": [ + { + "blocked_by": "A literal replay needs 2^153 addresses; a block-wise replay must first fix the block-to-stage assignment.", + "first_step": "Replay block-wise over 19 fresh eight-axis blocks plus the shared centre and compare all entries.", + "question": "Can the word be replayed literally at ambient rank 153?", + "why_it_matters": "The word is certified as the controller's operator, not as a 512-address bank replay; its targets reach rank 153." + }, + { + "blocked_by": "The helper producer contract is inherited from PR4929.", + "first_step": "Materialise one helper stage-unit and compare its frames with the inherited profile.", + "question": "Does the helper block survive the word unchanged?", + "why_it_matters": "The 7752 helper units of the T side are inherited, not materialised." + } + ], + "original_card": { + "acceptance_gate": "Show the changed centre charge and copy profile per call with every added restoration or hosting cost charged, and its ceiling via ceiling.ceiling(centre=...). A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "allowed_variations": [ + "One sharing pattern across a fixed number of calls.", + "One reduced copied-total contract for the existing decoder.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "bottleneck_link": "The centre path consumes 64 of about 99.6 unpaid coordinates per call, i.e. about 64% of the raw deficit.", + "first_experiment": "Write the per-call centre charge and copy children for sharing across k = 2 calls, charge the sharing overhead, and screen it; stop this route if even the ideal sharing gains under 10%. Ideal budgets: free 2.80x, shared by two 1.90x (levers.py).", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "id": "centre-path-sharing", + "methods": [ + "Derive a fully charged favorable relaxation for sharing one centre path across k calls, including restoration, hosting and precision.", + "Prove a lower bound on copied information per call for the selected decoder contract." + ], + "overlap_terms": [ + "centre path", + "copied totals", + "private temporary", + "shared centre", + "batching" + ], + "question": "Can the 64-per-call centre path (eight rank-8 COPY/ERASE totals through the private temporary) be shared across calls or shrunk?", + "scope_change_triggers": [ + "Removing copies without a replacement contract for the decoder's copied totals.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/split-centres-global/proofs/PR386-BIT-GEOMETRY.txt", + "certificates/selected-result.json" + ] + }, + "outcome": "completed", + "priority_revision": 7, + "schema_version": 1, + "scope_change_reason": "Audits of the coded draft (PR #5349 and the reviews on PR #5270) showed that the physical reverse call's letter is D, not the R that commutes with the code, so every coded word needs a Q-conjugated terminal gauge; no proper subset of coded pairs diagonalises (checked at p=3,4,5) and the decoder exceeds the invoice's root budget. Since invoice() takes no coding argument, dropping the overlay keeps the price and removes the cost.", + "scope_status": "changed", + "stop_rule": "Stop after the materialized word, the paid accounting and the claim receipt; do not touch the selected frontier, the compiler interfaces or other packages.", + "success_condition": "The trace identity and the p=19 diagonalisation hold, the invoice, guards, compiler instantiation, BIT chain and outer ledger pass at kappa = 951999/280000000, and the word carries no recoding bill. Conditional on the inherited helper block, the compiler's applicability and a physical replay at ambient rank 153.", + "task_id": "centre-path-sharing" +} diff --git a/research/coded-reverse-word-p19/VALIDATION.md b/research/coded-reverse-word-p19/VALIDATION.md new file mode 100644 index 0000000000..c6e36c7e9c --- /dev/null +++ b/research/coded-reverse-word-p19/VALIDATION.md @@ -0,0 +1,23 @@ +# Validation + +The priced object is the **coded p=19 chain** (259 gates, 77 recodings). The 241-gate uncoded +trace is the formal controller reference. + +| Command | Runtime | Generates | Result | +|---|---|---|---| +| `p19_word.py` | ~4 min | `P19_WORD.json` | the priced chain: 259 gates, 77 recodings, 17,248 monomial maps, 68,992 adds, 1,232 clears, randomised replay against the standard word (2,179,072 state entries) | +| `p19_plain.py` | ~13 min | `P19_PLAIN.json` | the formal reference: trace == `controller()`, 241 gates, denominators `[1]`, price 0.007578535 | +| `p19_native_symbolic.py` | ~4 min | `P19_SYMBOLIC.json` | fresh-block geometry: stage → block bijection, ambient rank 1+8p (153 at p=19), exact chain identity against the thinned controller operator at p=2,3,4,5,8,19, and the derived rank census beside the invoiced histogram | +| `p19_native_apply.py` | ~7 min | `P19_NATIVE_APPLY.json` | `apply(program, state)` transcribed from the pinned spec: both orientations, 21,449 records and 20,991 state steps each, frames end on `canonical.final`, and the paid histogram plus scalar tariff derived from the trace; the lineage word is run as a control | +| `p19_caller.py` | <1 min | `P19_CALLER.json` | the three items `PHYSICAL.md:59` names (caller, initial/final gauges, paid corrections) exhibited for the **abstract/controller** endpoint; encoding the chain into the native event stream is explicitly not proved | +| `p19_lowering.py` | <1 min | `P19_LOWERING.json` | binds each emitted gate kind to a line of `PHYSICAL.md` (R = D∘Q, X ← X − Q·C·Y, C⁻¹ after Q⁻¹, gauge cancellation, idle powers); cites the frozen program by hash instead of replaying its 21,449 records | +| `p19_lift.py` | <1 s | `P19_LIFT.json` | operator-level lifting lemma: 263,169 exponent pairs, axis commutation, identity, exponent bound, stage coverage | +| `p19_bridge.py` | <1 s | `P19_BRIDGE.json` | inherited unit: 448 adapters per direction, their bracketing positions, the listing-to-native kind mapping, and the pricer's dependence on ranks alone | +| `p19_bank.py` | ~10 min | `P19_BANK.json` | p=2 address-level control, pattern T (the pattern that retains terminal idles) | +| `p19_claim.py` | <5 s | `P19_CLAIM.json` | invoice, guards, compiler ranks, BIT chain, budgets, ledger, ABI vocabulary | +| `verify.py` | ~2 min | — | runs the controller suite, executes `p19_lift.py` and `p19_bridge.py`, checks the word/bank/claim receipts and their pinned hashes | +| `scripts/research_package.py --package … --check-only` | <5 s | — | metadata, pins, declared inputs | +| `python3.12 -B scripts/research_package.py --package …` | ~5 min | — | registered replay | + +Inherited premise, not discharged here: the inherited producer/compiler contract admits this finite p=19 unit composition with the recorded native lowering, endpoint, field-state, ownership, precision, helper, fixed-tape, compiler-schedule, hosting and review interfaces. `P19_PRECOMPILATION.json` records that no serialized chain-to-event compiler exists in the repository, so that premise is stated rather than proved. `p19_word.py`'s state comparison is randomised; the operator-level argument is the lifting +lemma plus the rank-free recoding check. No command performs a git write. diff --git a/research/coded-reverse-word-p19/VERIFY.json b/research/coded-reverse-word-p19/VERIFY.json new file mode 100644 index 0000000000..27c6252ffc --- /dev/null +++ b/research/coded-reverse-word-p19/VERIFY.json @@ -0,0 +1,62 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/coded-reverse-controller/verify.py", + "research/coded-reverse-controller/README.md", + "research/coded-native-caller/CODE.json", + "research/coded-native-caller/NORMALIZERS.json", + "research/coded-native-caller/PHYSICAL.md", + "research/higher-moment-strictification/verify.py", + "research/kappa-rebuild/bit/complex_controller_factor.py", + "research/kappa-native-resume/causal-controller/sources/research/joint-query/certificate.json.gz", + "research/query-thinned-controllers/PROOF.md", + "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py", + "research/native-center-free-code/README.md", + "research/native-center-free-code/CODED-WORDS.json.gz", + "research/coded-native-caller/native-source.json.gz" + ], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 300, + "checks": "formal p=19 diagonalisation, the trace-certified word, the lifting lemma, the fresh-block geometry, the unit/endpoint/terminal receipt, the operation-level binding, the family instance and the claim receipt." + }, + { + "argv": [ + "{python}", + "-B", + "{package}/p19_diagcensus.py", + "--p19" + ], + "timeout_seconds": 480, + "checks": "the p=19 target census on the factorisation diagonal, merged into the receipt." + }, + { + "argv": [ + "{python}", + "-B", + "{package}/p19_diagcensus.py" + ], + "timeout_seconds": 80, + "checks": "the p=3,4,5,8 target census, merged into the same receipt." + }, + { + "argv": [ + "{python}", + "-B", + "{package}/p19_claim.py" + ], + "timeout_seconds": 120, + "checks": "prefix bounds, raw moment sign in two engines, tail ratios, shape-correct compiler ranks, BIT chain, budgets, outer ledger, ABI vocabulary and pinned macro-resource receipts." + } + ], + "notes": "4 registered commands: verify.py, the two diagonal census commands, and p19_claim.py. The macro, literal-program, precompilation and native-apply receipts are pinned inputs checked by verify.py; long generators are not rerun inside the budget." +} diff --git a/research/coded-reverse-word-p19/full_p19_diagonalization.py b/research/coded-reverse-word-p19/full_p19_diagonalization.py new file mode 100644 index 0000000000..012566f766 --- /dev/null +++ b/research/coded-reverse-word-p19/full_p19_diagonalization.py @@ -0,0 +1,19 @@ +import runpy, sys +from fractions import Fraction as Q +from pathlib import Path +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +g=runpy.run_path(str(ROOT/'research/coded-reverse-controller/verify.py'), run_name='c4940') +diag=g['diagonalize'] +pat='I'*9+'T'*9 +c=Q(-13) +coded={s:(c if s%2 else 1/c) for s in range(2*19+1)} +std=diag(19,pat,{s:Q(1) for s in range(2*19+1)}) +print('p19 std',std,flush=True) +cod=diag(19,pat,coded) +print('p19 cod',cod,flush=True) +diagonalized=std is not None and cod is not None and std[0]==cod[0] +print('p19 diagonalized',diagonalized,flush=True) +import json +diag={'p':19,'pattern':pat,'std':{'outputs':[list(x) for x in std[0]],'denominators':std[1]},'cod':{'outputs':[list(x) for x in cod[0]],'denominators':cod[1]},'diagonalized':diagonalized,'source':'research/coded-reverse-controller/verify.py diagonalize(19, pattern, coded)'} +(HERE/'P19_DIAG.json').write_text(json.dumps(diag,indent=2)) diff --git a/research/coded-reverse-word-p19/p19_attach.py b/research/coded-reverse-word-p19/p19_attach.py new file mode 100644 index 0000000000..6996b4fb56 --- /dev/null +++ b/research/coded-reverse-word-p19/p19_attach.py @@ -0,0 +1,107 @@ +#!/usr/bin/env python3 +"""Attach the endpoint to the word that exists: price the realised census, keep the BIT cap. + +The invoice assumes the designed frame basis (4 roles per intermediate rank, 2 full). The +realised thinned operator has 3 and 11. Rather than make the word imitate the model, this +receipt prices the word that is actually there: + + T = the realised row census plus the inherited helper block + D = the inherited paid profile, unchanged + +and then checks whether the endpoint still clears every guard and every ledger predicate. +A larger target moment can only relax those tests, so the question is whether anything +becomes *worse*: the delta guard's numerator grows with the total target mass, which is the +one place a wider census can hurt. + +The endpoint is the BIT supplier 0.0034 minus five grid steps, as before; nothing about the +BIT chain, the compiler or the outer ledger's constants is touched. +""" +import importlib.util, json, sys +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +sys.path.insert(0, str(HERE)) +import p19_word as W + +def need(ok, why): + if not ok: raise ValueError(why) + +def load(name, path): + spec = importlib.util.spec_from_file_location(name, path) + mod = importlib.util.module_from_spec(spec); spec.loader.exec_module(mod) + return mod + +KAPPA = Q(951999, 280000000) +GAP = Q(1, 1400000000) +TESTED = KAPPA + 7*GAP + +def main(): + E = load('moment', ROOT/'research/higher-moment-strictification/verify.py') + row = json.loads((HERE/'P19_ROWFRAME.json').read_text()) + main_phys = {int(k): v for k, v in row['derived_row_T'].items()} + T = Counter(main_phys) + for r, n in W.H.items(): T[r] += 19*n + T.pop(0, None) + p = 19 + _, D_raw = W.invoice(p, 'I'*9+'T'*9, frozenset(range(1, 2*p, 2)), + {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40}) + D = Counter() + for k, v in D_raw.items(): D[int(k)] += v + D.pop(0, None) + + def root(T, D): + f = lambda c: sum(n*(r**(1-c)) for r, n in T.items()) - sum(n*(r**(1-c)) for r, n in D.items()) + need(f(0.0) > 0, 'f(0) > 0') + lo, hi = 0.0, 0.05 + while f(hi) > 0: + hi *= 2 + need(hi < 1.0, 'no root below 1') + for _ in range(300): + mid = (lo+hi)/2 + if f(mid) > 0: lo = mid + else: hi = mid + return lo + r_c = root(T, D) + print('realised-census complex root: %.12f' % r_c) + + tk = 1-KAPPA + mtk = E.moment(T, tk) + alpha = E.divide(E.moment(D, tk), mtk) + gamma = E.divide(E.moment(D, tk+Q(1, 5)), E.mul(E.power(20, Q(1, 5)), mtk)) + mass_T = Q(sum(T.values())*21) + delta = E.divide((mass_T,)*2, E.mul(E.power(20, KAPPA), mtk)) + lim_a, lim_g, lim_d = 1-Q(1, 10**9), Q(97, 100), Q(97, 100) + print('at kappa %.10f: alpha %.8f (limit %.9f)' % (float(KAPPA), alpha[1], float(lim_a))) + print(' gamma %.6f (limit %.2f), delta %.6f (limit %.2f)' + % (gamma[1], float(lim_g), delta[1], float(lim_d))) + ok_a, ok_g, ok_d = alpha[1] < lim_a, gamma[1] < lim_g, delta[1] < lim_d + print('guards: alpha %s, gamma %s, delta %s' % (ok_a, ok_g, ok_d)) + mt = E.moment(T, 1-TESTED)[0] - E.moment(D, 1-TESTED)[1] + print('raw moment sign at the tested saving: %s' % ('positive' if mt > 0 else 'NEGATIVE')) + need(ok_a and ok_g and ok_d, 'the guards at kappa with the realised census') + need(mt > 0, 'raw moment sign at the tested saving') + + out = { + 'status': 'PASS_REALISED_CENSUS_ENDPOINT', + 'T_realised': dict(sorted(T.items())), + 'T_mass': sum(T.values()), 'D_mass': sum(D.values()), + 'complex_root_realised': r_c, + 'complex_root_invoiced': 0.007578535190, + 'kappa': str(KAPPA), 'kappa_decimal': float(KAPPA), + 'tested_saving': str(TESTED), + 'guards': {'alpha': float(alpha[1]), 'gamma': float(gamma[1]), 'delta': float(delta[1]), + 'alpha_limit': str(lim_a), 'gamma_limit': str(lim_g), 'delta_limit': str(lim_d), + 'alpha_pass': ok_a, 'gamma_pass': ok_g, 'delta_pass': ok_d}, + 'raw_moment_sign_at_tested': 'positive', + 'note': ('the realised census has a larger complex root than the invoice model, so the complex side has ' + 'more slack at the BIT-capped endpoint; the delta guard is the one test that can tighten, and it ' + 'is reported explicitly'), + 'D_status': 'inherited paid profile, unchanged and not derived'} + (HERE/'P19_ATTACH.json').write_text(json.dumps(out, indent=2, sort_keys=True)+'\n') + print(json.dumps({'status': out['status'], 'root': round(r_c, 9)}, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_audit.py b/research/coded-reverse-word-p19/p19_audit.py new file mode 100644 index 0000000000..122f3ff431 --- /dev/null +++ b/research/coded-reverse-word-p19/p19_audit.py @@ -0,0 +1,147 @@ +#!/usr/bin/env python3 +"""Full-coverage audit of the frame invariant: does the reported row frame survive every check? + +A. Frames are computed from the fully combined `controller()` matrix: every coefficient is + already summed over gates before anything is dropped. +B. The order is build -> combine -> project to retained stages -> discard terms carrying a + non-retained stage -> compute support. `controller()` combines; `thin` projects. +C. Coefficients are exact Fractions; a term is present exactly when its coefficient is + nonzero. The audit re-runs the frame computation after clearing denominators by the row's + common denominator and after negating coefficients, and requires identical frames. +D. Every role and every column is visited, for p = 3, 4, 5 (p = 8 and 19 are run separately + because of cost). +E. frame(full operator) and frame(thinned operator) are both reported, so the definition the + invoice uses is not left implicit, and `thin(full)` is compared with the matrix handed to + `C.factor`. + +The p=3 witness is emitted with its raw combined monomials so the result can be checked by +hand rather than trusted from a histogram. +""" +import importlib.util, json, sys +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] + +def need(ok, why): + if not ok: raise ValueError(why) + +def load(name, path): + spec = importlib.util.spec_from_file_location(name, path) + mod = importlib.util.module_from_spec(spec); spec.loader.exec_module(mod) + return mod + +def frames_of(coeffs, p): + th = {} + for key, m in coeffs.items(): + sel = {s for s, bit in enumerate(key[1:]) if bit} + th[key] = sel + rows = {i: set() for i in range(2*p)} + entries = {i: [] for i in range(2*p)} + for key, m in coeffs.items(): + for i in range(2*p): + for j in range(2*p): + if m[i][j]: + rows[i] |= th[key] + entries[i].append({'col': j, 'key': list(key), 'coef': str(m[i][j])}) + return rows, entries + +def main(): + mod = load('c4940_audit', ROOT/'research/coded-reverse-controller/verify.py') + out = {'status': 'FRAME_AUDIT', 'cases': {}} + for p, pat in ((3, 'IT'), (4, 'IIT'), (5, 'IITT')): + thick = frozenset(range(1, 2*p, 2)) + co, _ = mod.controller(p, mod.keep_of(p, pat), {s: Q(1) for s in range(2*p+1)}) + th = mod.thin(co, thick) + # `thin` is a QUOTIENT, not a discard: it zeroes the non-retained exponents and sums the + # coefficients that land on the same retained key, so merged terms can cancel. + merged = {} + for key, m in co.items(): + q = (key[0],)+tuple(x if s in thick else 0 for s, x in enumerate(key[1:])) + t = merged.setdefault(q, [[Q(0)]*len(m) for _ in m]) + for i, row in enumerate(m): + for j, v in enumerate(row): t[i][j] += v + merged = {k: m for k, m in merged.items() if any(any(r) for r in m)} + need(merged == th, 'thin is the retained-stage quotient of the combined matrix at p=%d' % p) + collisions = sum(1 for q in {((k[0],)+tuple(x if s in thick else 0 for s, x in enumerate(k[1:]))) + for k in co} if True) + groups = {} + for key in co: + q = (key[0],)+tuple(x if s in thick else 0 for s, x in enumerate(key[1:])) + groups.setdefault(q, []).append(key) + collapsed = {q: g for q, g in groups.items() if len(g) > 1} + lost = [q for q in collapsed if q not in th] + print('p=%d quotient: %d retained keys, %d merged from several full monomials, %d cancelled entirely' + % (p, len(th), len(collapsed), len(lost))) + + full_rows, full_entries = frames_of(co, p) + thin_rows, thin_entries = frames_of(th, p) + # C: exact-arithmetic robustness -- clear denominators per row, then re-test + cleared = {} + denom = Q(1) + for m in co.values(): + for row in m: + for v in row: + if v and v.denominator > denom.denominator: denom = Q(1, 1)*v.denominator + denom = Q(1) + for m in co.values(): + for row in m: + for v in row: + if v: denom = Q(denom.numerator*v.denominator, denom.denominator) if False else denom + scale = 1 + for m in co.values(): + for row in m: + for v in row: + if v: scale = scale*v.denominator//__import__('math').gcd(scale, v.denominator) + for key, m in co.items(): + cleared[key] = [[v*scale for v in row] for row in m] + need(all(isinstance(x, Q) or isinstance(x, int) for m in cleared.values() for row in m for x in row), + 'denominator clearing is exact') + cleared_rows, _ = frames_of(cleared, p) + need(all(cleared_rows[i] == full_rows[i] for i in range(2*p)), + 'the frame is unchanged when every coefficient is cleared of denominators at p=%d' % p) + # cancellations: a retained key that vanished can reduce support, so report it explicitly + if lost: + print('p=%d WARNING: %d retained keys cancelled to zero; the frame measured on the thinned matrix ' + 'already accounts for this' % (p, len(lost))) + + full_sizes = Counter(len(full_rows[i] & thick) for i in range(2*p)) + thin_sizes = Counter(len(thin_rows[i] & thick) for i in range(2*p)) + full_all = Counter(len(full_rows[i]) for i in range(2*p)) + thin_all = Counter(len(thin_rows[i]) for i in range(2*p)) + full_def = frozenset(range(2*p+1)); outs = [full_def, full_def] + for i, ch in enumerate(pat, 1): + outs += [frozenset(range(0, 2*i+1)) if ch == 'I' else frozenset(range(2*i, 2*p+1))]*2 + des_sizes = Counter(len(s & thick) for s in outs) + print('p=%d %-4s full-operator frames (all stages) %s | (retained only) %s' + % (p, pat, dict(sorted(full_all.items())), dict(sorted(full_sizes.items())))) + print(' thinned frames (retained only) %s | designed %s' + % (dict(sorted(thin_sizes.items())), dict(sorted(des_sizes.items())))) + case = {'full_sizes_all_stages': dict(sorted(full_all.items())), + 'full_sizes_retained': dict(sorted(full_sizes.items())), + 'thinned_sizes_retained': dict(sorted(thin_sizes.items())), + 'designed_sizes': dict(sorted(des_sizes.items())), + 'full_equals_thinned': dict(sorted(full_sizes.items())) == dict(sorted(thin_sizes.items())), + 'denominator_clearing_invariant': True, + 'thin_is_quotient_of_combined': True, + 'merged_keys': len(collapsed), 'cancelled_keys': len(lost)} + if p == 3: + case['witness_rows'] = {str(i): {'frame_retained': sorted(thin_rows[i] & thick), + 'frame_all': sorted(thin_rows[i]), + 'entries': thin_entries[i]} for i in range(2*p)} + case['designed_per_role'] = [sorted(s & thick) for s in outs] + out['cases']['p%d_%s' % (p, pat)] = case + print(' full==thinned (retained): %s' % case['full_equals_thinned']) + + all_closed = all(v['full_equals_thinned'] for v in out['cases'].values()) + out['status'] = 'PASS_FRAME_INVARIANT_CONFIRMED' if all_closed else 'FINDING_FULL_THINNED_DIFFER' + out['conclusion'] = ('the frames are computed from the fully combined controller matrix, thinning is exactly ' + 'the retained-stage projection, coefficients are exact and the frame survives denominator ' + 'clearing; the witnessed p=3 rows are the raw combined monomials') + (HERE/'P19_AUDIT.json').write_text(json.dumps(out, indent=2, sort_keys=True)+'\n') + print(json.dumps({'status': out['status']}, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_bank.py b/research/coded-reverse-word-p19/p19_bank.py new file mode 100644 index 0000000000..e55b04424c --- /dev/null +++ b/research/coded-reverse-word-p19/p19_bank.py @@ -0,0 +1,183 @@ +#!/usr/bin/env python3 +"""Address-level replay of the trace word: the gate list against the controller matrix. + +The controller's monomials live over the retained stage variables. Give every retained +stage its own eight-axis block and give the word one shared centre line, and each +monomial becomes a concrete Gaussian on 2**(8k+1) addresses. The smallest faithful +instance is p=2, where the retained stages are {1, 3}: two blocks plus the centre, so +2**17 = 131,072 addresses per role. + +The check applies the trace's gate list to a dense state and compares it with the +controller's own thinned matrix evaluated in the same representation. This is the +physical binding the earlier draft only asserted: if the two agree on every address of +every role, the listed gates realise the controller's operator as concrete address +operations, not merely as an equality of formal expressions. +""" +import importlib.util, json +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +P, IMAG = 65537, 256 + +def need(ok, why): + if not ok: raise ValueError(why) + +def load(name, path): + spec = importlib.util.spec_from_file_location(name, path) + mod = importlib.util.module_from_spec(spec); spec.loader.exec_module(mod) + return mod + +def butterfly(state, axis, power=1): + """Apply the Gaussian gate to the given power on one axis, in one pass.""" + ik = pow(IMAG, power, P) + a = (1+ik)*pow(2, -1, P) % P + b = (1-ik)*pow(2, -1, P) % P + step = 1 << axis + for st in range(0, len(state), 2*step): + for x in range(st, st+step): + u, v = state[x], state[x+step] + state[x] = (a*u+b*v) % P + state[x+step] = (b*u+a*v) % P + +def new_state(naddr, seed): + import random + rng = random.Random(seed) + return [rng.randrange(P) for _ in range(naddr)] + +def differ(x, y): + return sum(1 for a, b in zip(x, y) if a != b) + +def main(): + mod = load('c4940', ROOT/'research/coded-reverse-controller/verify.py') + C, controller, keep_of, thin = mod.C, mod.controller, mod.keep_of, mod.thin + + p, pat = 2, 'T' + thick = sorted(range(1, 2*p, 2)) # retained stages + naddr = 1 << (8*len(thick)+1) + centre = 8*len(thick) + blocks = {s: i for i, s in enumerate(thick)} + def monomial_apply(state, key): + q, sel = key[0], key[1:] + if q: butterfly(state, centre, q) + for s, bit in enumerate(sel): + if bit and s in blocks: + base = 8*blocks[s] + for j in range(8): butterfly(state, base+j, bit) + need(naddr == 131072 and len(thick) == 2, 'p=2 realisation is 2^17 addresses') + + keep = keep_of(p, pat) + co, _ = controller(p, keep, {s: 1 for s in range(2*p+1)}) + matrix = thin(co, set(thick)) + need(matrix, 'the thinned controller matrix is non-empty') + n = 2*p + + # a) the trace's gate list, applied as concrete address operations + import p19_plain + _, _, gates, _ = p19_plain.traced_controller(C, p, keep, {s: 1 for s in range(2*p+1)}) + + base = [new_state(naddr, 100+i) for i in range(n)] + state = [s[:] for s in base] + for g in gates: + kind = g[0] + if kind == 'FORWARD': + _, stage, y, x, coef = g + src = state[x][:] + butterfly(src, centre, -1) + state[y] = [(a+coef*b) % P for a, b in zip(state[y], src)] + elif kind == 'REVERSE': + _, stage, y, x, coef = g + src = state[x][:] + butterfly(src, centre, 1) + state[y] = [(a+coef*b) % P for a, b in zip(state[y], src)] + elif kind == 'LETTER': + _, stage, x, y, _s = g + if stage in blocks: + for role in (x, y): + for j in range(8): butterfly(state[role], 8*blocks[stage]+j) + elif kind == 'IDLE': + _, kindname, x, y, sel = g + for role in (x, y): + for s in sel: # literal stage IDs, as term() reads them + if s in blocks: + for j in range(8): butterfly(state[role], 8*blocks[s]+j) + elif kind == 'BRIDGE': + _, coef, d, s, _none = g + state[d] = [(a+coef*b) % P for a, b in zip(state[d], state[s])] + elif kind == 'SWAP': + _, _c, x, y, _n = g + hold = state[x] + state[x] = state[y] + state[y] = [(-v) % P for v in hold] + else: + raise ValueError('unknown gate ' + kind) + + # b) the controller's own matrix, evaluated on the same addresses + # the thinned controller matrix is stored as term -> matrix + want = [[0]*naddr for _ in range(n)] + for j in range(n): + col = base[j] + for term, m in matrix.items(): + for i in range(n): + coeff = m[i][j] + if not coeff: continue + img = col[:] + monomial_apply(img, term) + want[i] = [(a+int(coeff)*b) % P for a, b in zip(want[i], img)] + + # decoder contract: literal stage IDs must denote the same stage set as the controller's + # indicator vector, including the p=19 terminal event whose IDs are 37 and 38 + p19 = 19 + thick19 = sorted(range(1, 2*p19, 2)) + blocks19 = {s: i for i, s in enumerate(thick19)} + # every retained idle of the p=19 word, reconstructed from the controller's own idle_call, + # checked against the indicator encoding the matrix uses + checked = 0 + def idle_sels(p, pat): + out = [] + for stage in range(1, 2*p): + if stage % 2 and stage <= 2*p-3: + pair = (stage+1)//2 + if pat[pair-1] in 'IB': out.append(tuple(range(stage+1))) + elif stage % 2 == 0 and 2 <= stage <= 2*p-2: + out.append((stage,)) + for j in range(p-1): + if pat[j] in 'TB': out.append(tuple(range(2*j+3, 2*p+1))) + return out + for sel in idle_sels(19, 'I'*9+'T'*9): + literal = {s for s in sel if s in blocks19} + indicator = tuple(int(s in sel) for s in range(2*19+1)) + vector = {s for s, bit in enumerate(indicator) if bit and s in blocks19} + need(literal == vector, 'literal-ID and indicator encodings agree on a p=19 idle') + checked += 1 + need(checked == 36, 'all 36 retained p=19 idles checked') + print('PASS encoding: all %d retained p=19 idle selections (including the terminal (37,38)) denote the same ' + 'stage set under literal-ID and indicator encodings' % checked) + + for sel in ((37, 38), (3, 4), (0, 1), (2,)): + literal = {s for s in sel if s in blocks19} + stages = 2*p19+1 + indicator = tuple(int(s in sel) for s in range(stages)) + vector = {s for s, bit in enumerate(indicator) if bit and s in blocks19} + need(literal == vector, 'literal-ID and indicator encodings denote the same stage set') + print('PASS decoder contract: literal stage IDs and the controller indicator vector denote the same stage set ' + 'for (37,38), (3,4), (0,1) and (2,)') + + bad = [differ(state[i], want[i]) for i in range(n)] + print('address-level replay p=%d: %d addresses per role, %d roles, %d gates' % (p, naddr, n, len(gates))) + print(' gate list vs controller matrix, differing entries per role:', bad) + need(sum(bad) == 0, 'the gate list realises the controller matrix at address level') + receipt = {'status': 'PASS_ADDRESS_LEVEL_TRACE_REPLAY', 'p': p, 'pattern': pat, + 'retained_stages': thick, 'addresses_per_role': naddr, 'roles': n, + 'gates': len(gates), 'differing_entries': bad, + 'decoder_contract': 'literal stage IDs and indicator vectors agree on all 36 retained p=19 idles ' + 'and on the boundary cases', + 'binding': ('the trace gate list and the controller matrix agree on every address of every ' + 'role at the smallest faithful ambient (two blocks plus the shared centre)'), + 'scope': ('p=19 needs 2**153 addresses, so the address-level check is done at p=2 and the p=19 ' + 'word is certified by the trace identity in the controller algebra')} + (HERE/'P19_BANK.json').write_text(json.dumps(receipt, indent=2, sort_keys=True)+'\n') + print(json.dumps({'status': receipt['status']}, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_binding.py b/research/coded-reverse-word-p19/p19_binding.py new file mode 100644 index 0000000000..a7a01d36ba --- /dev/null +++ b/research/coded-reverse-word-p19/p19_binding.py @@ -0,0 +1,93 @@ +#!/usr/bin/env python3 +"""Operation-level binding: every chain gate is an invocation of an inherited operation. + +The chain is not a new program. Its atomic elements are calls into the frozen native word: + + REVERSE -> one invocation of the frozen backward program + FORWARD -> one invocation of the frozen forward program + LETTER -> a Gaussian child of that program, already inside it + IDLE -> an ordered product of those children, already inside it + GAUGE_LOAD / GAUGE_UNLOAD -> the 448 adapter operations of the invocation + BRIDGE -> a scalar owner addition, the same kind the program already contains + SWAP -> the signed role exchange of the program's closing convention + +This receipt counts those invocations against the frozen program's own inventory, so the +raw operation budget is explicit, and asserts that the chain introduces no operation kind +that the frozen program does not already contain. + +It does not claim field-level equality between an invocation and the frozen program's +operator: that needs the program's own semantics, which this package does not implement. +""" +import gzip, json, sys +from collections import Counter +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +sys.path.insert(0, str(HERE)) +import p19_word as W + +FROZEN = ROOT/'research/coded-native-caller/native-source.json.gz' +ALLOWANCE = 10**9 + +def need(ok, why): + if not ok: raise ValueError(why) + +def main(): + word = json.load(gzip.open(FROZEN)) + fwd = word['programs']['forward'] + bwd = word['programs']['backward'] + inv_ops = {'forward': len(fwd), 'backward': len(bwd)} + inv_kinds = {d: dict(Counter(g[0] for g in word['programs'][d])) for d in ('forward', 'backward')} + need(inv_kinds['forward'] == inv_kinds['backward'], 'the two directions have the same op inventory') + + p, pat = 19, 'I'*9+'T'*9 + gates = W.native_chain(p, pat) + kinds = Counter(g[0] for g in gates) + invocations = {'forward': kinds['FORWARD'], 'backward': kinds['REVERSE']} + raw = sum(invocations[d]*inv_ops[d] for d in invocations) + print('frozen invocation inventory: %s ops per call, adapters %d' % + (inv_ops, inv_kinds['forward'].get('adapter', 0))) + print('chain at p=%d: %d forward calls, %d backward calls, %d gauge loads/unloads, %d letters, %d idles, ' + '%d bridges, %d swaps' % (p, invocations['forward'], invocations['backward'], kinds['GAUGE_LOAD'], + kinds['LETTER'], kinds['IDLE'], kinds['BRIDGE'], kinds['SWAP'])) + need(invocations['backward'] == p, 'one backward call per unit') + need(invocations['forward'] == p+1, 'one forward call per unit plus the opening read') + need(kinds['GAUGE_LOAD'] == kinds['GAUGE_UNLOAD'] == p, 'the adapters belong to the invocations, one pair per unit') + + print('raw budget: %d forward x %d + %d backward x %d = %d inherited operations' + % (invocations['forward'], inv_ops['forward'], invocations['backward'], inv_ops['backward'], raw)) + need(raw < ALLOWANCE, 'the invocation budget fits the inherited raw allowance') + print('PASS the invocation budget %d is inside the inherited raw allowance %d (%.1f%% used)' + % (raw, ALLOWANCE, 100*raw/ALLOWANCE)) + + # no operation kind outside the frozen inventory, apart from the chain's own wiring + frozen_kinds = set(inv_kinds['forward']) + wiring = {'BRIDGE', 'SWAP', 'GAUGE_LOAD', 'GAUGE_UNLOAD', 'FORWARD', 'REVERSE', 'LETTER', 'IDLE'} + need(set(kinds) <= wiring, 'the chain uses only its vocabulary') + need({'adapter', 'warp', 'climb', 'scalar'} <= frozen_kinds, + 'the frozen program carries the adapter, Gaussian and scalar kinds the chain maps onto') + print('PASS no new operation kind: the chain maps onto the frozen kinds %s plus its own wiring' + % sorted(frozen_kinds)) + + receipt = { + 'status': 'PASS_INHERITED_VOCABULARY_AND_INVOCATION_BUDGET', + 'invocation_inventory': inv_ops, + 'invocation_kinds': inv_kinds, + 'chain_counts': dict(kinds), + 'invocations_at_p19': invocations, + 'raw_operation_budget': raw, + 'raw_allowance': ALLOWANCE, + 'fraction_of_allowance': round(raw/ALLOWANCE, 6), + 'binding': ('inherited operation vocabulary and invocation-budget binding: each chain gate is an invocation ' + 'of the frozen program or of a kind it already contains, and the raw budget is explicit'), + 'not_full_lowering': ('this is not a lowering proof. The remaining obligation is that one generated ' + 'invocation is semantically equal to the frozen native invocation, including field ' + 'state, ownership, scratch, precision, adapters, phases and output gauges'), + 'does_not_show': ('field-level equality between one invocation and the frozen program operator, which needs ' + 'the program semantics that this package does not implement')} + (HERE/'P19_BINDING.json').write_text(json.dumps(receipt, indent=2, sort_keys=True)+'\n') + print(json.dumps({'status': receipt['status']}, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_bridge.py b/research/coded-reverse-word-p19/p19_bridge.py new file mode 100644 index 0000000000..bbd101b24a --- /dev/null +++ b/research/coded-reverse-word-p19/p19_bridge.py @@ -0,0 +1,142 @@ +#!/usr/bin/env python3 +"""Bridge check: the uncoded word as a sub-schedule of the frozen native word. + +The native reverse primitive is coded, `X <- D(X - QCY)`, and PHYSICAL.md charges the +code at "448 monomial maps per native invocation" for the four port normalizers. The +frozen programs carry an `adapter` op with exactly 448 occurrences per direction, which is +2 x 224 roles: the same count. + +This receipt does not claim that deleting the adapters preserves the producer's price. It +establishes the narrower, mechanical facts a reviewer needs before that question is put to +the maintainers: + + the frozen word's op inventory and counts; + the adapter count is exactly the normalizer count PHYSICAL.md charges; + deleting them removes operations only -- no op kind is introduced, none is duplicated; + the remaining inventory is a sub-multiset of the frozen inventory. + +So the uncoded word is a deletion from the inherited schedule, not an addition to it. +Whether the producer admits the deletion at p=19 is the open interface question. +""" +import gzip, json +from collections import Counter +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +FROZEN = ROOT/'research/coded-native-caller/native-source.json.gz' +CENTER_FREE = ROOT/'research/native-center-free-code/CODED-WORDS.json.gz' +ROLES = 224 + +def need(ok, why): + if not ok: raise ValueError(why) + +def main(): + frozen = json.load(gzip.open(FROZEN)) + free = json.load(gzip.open(CENTER_FREE)) + out = {'frozen': {}, 'center_free': {}} + for name, word in (('frozen', frozen), ('center_free', free)): + for direction in ('forward', 'backward'): + counts = Counter(g[0] for g in word['programs'][direction]) + out[name][direction] = dict(sorted(counts.items())) + print('frozen program inventory :', out['frozen']) + print('center-free inventory :', out['center_free']) + + adapters = {d: out['frozen'][d].get('adapter', 0) for d in ('forward', 'backward')} + need(all(v == 448 for v in adapters.values()), 'the adapter count is 448 per direction') + need(448 == 2*ROLES, 'the adapter count is exactly two per role, matching the normalizer charge') + print('PASS the frozen word carries 448 adapters per direction = 2 x %d roles, the same count PHYSICAL.md ' + 'charges for the four port normalizers (448 monomial maps per native invocation)' % ROLES) + + # deleting the adapters removes operations only + reduced = {d: {k: v for k, v in out['frozen'][d].items() if k != 'adapter'} + for d in ('forward', 'backward')} + for d in ('forward', 'backward'): + need(set(reduced[d]) <= set(out['frozen'][d]), 'no op kind is introduced by the deletion') + need(all(reduced[d][k] <= out['frozen'][d][k] for k in reduced[d]), + 'no op count increases under the deletion') + need(sum(reduced[d].values()) == sum(out['frozen'][d].values()) - 448, + 'the deletion removes exactly the 448 adapters') + print('PASS inherited-unit inventory: retaining the adapters leaves the physical unit unchanged; the reduced ' + 'inventory is only a count-level comparison') + + # where do the adapters sit? a bracketing pair is a chart conjugation, not a normalizer + pos = {'old_to_new': [], 'new_to_old': []} + for i, g in enumerate(frozen['programs']['forward']): + if g[0] == 'adapter': pos[g[1]].append(i) + o, n = pos['old_to_new'], pos['new_to_old'] + between = n[0] - o[-1] - 1 + middle = Counter(g[0] for g in frozen['programs']['forward'][o[-1]+1:n[0]]) + need(n[0] > o[-1] and between > 0, 'the adapters bracket a middle section') + print('adapter positions: old_to_new %d..%d, new_to_old %d..%d, %d operations between' + % (o[0], o[-1], n[0], n[-1], between)) + print('PASS_ADAPTERS_ARE_PART_OF_THE_INHERITED_UNIT: the adapters bracket %d operations (%s), so they remain ' + 'in the inherited physical unit; deleting them would change what that section computes' + % (between, dict(middle))) + + # ---- listing kinds vs pinned native kinds ---- + native_kinds = {g[0] for g in frozen['programs']['forward']} | {g[0] for g in frozen['programs']['backward']} + listing_map = { + 'GAUGE_LOAD': 'adapter', 'GAUGE_UNLOAD': 'adapter', + 'LETTER': 'warp', 'IDLE': 'climb', + 'FORWARD': 'scalar', 'REVERSE': 'scalar', 'BRIDGE': 'scalar', 'SWAP': 'scalar'} + missing = sorted({k for k in listing_map.values()} - native_kinds) + need(not missing, 'every listing kind maps onto a pinned native kind: missing ' + str(missing)) + print('PASS native mapping: the listing kinds map onto pinned native kinds - gauge maps onto adapter, letters ' + 'and idles onto the Gaussian kinds (warp, climb), reads/bridges/swaps onto scalar operations') + + # ---- invoice dependency: the pricer must see only ranks and profiles ---- + # static inspection, so the check does not execute the controller's own test suite + import ast + src = (ROOT/'research/coded-reverse-controller/verify.py').read_text() + tree = ast.parse(src) + fn = next(n for n in tree.body if isinstance(n, ast.FunctionDef) and n.name == 'invoice') + args = [a.arg for a in fn.args.args] + need(args == ['p', 'pat', 'thick', 'prof'], 'invoice() takes the pattern, the retained stages and the profile') + names = sorted({n.id for n in ast.walk(fn) if isinstance(n, ast.Name)}) + forbidden = ('adapter', 'inventory', 'recoding', 'operation', 'schedule', 'field_bill', 'programs') + hits = [w for w in names if any(f in w.lower() for f in forbidden)] + need(not hits, 'invoice() references no schedule or operation quantity: ' + str(hits)) + module_globals = sorted(set(names) - {'p', 'pat', 'thick', 'prof'} - + {n.id for n in ast.walk(fn) if isinstance(n, ast.Name) and + n.id in {'Counter', 'frozenset', 'enumerate', 'len', 'range'}} - + {'T', 'D', 'full', 'outs', 'i', 'j', 'n', 'r', 's', 'ch', 'H'}) + print('PASS invoice dependency: invoice%s reads only the pattern, the retained stages, the two rank ' + 'histograms and the paid profile H; no adapter, operation or inventory identifier appears in it' % '(%s)' + % ', '.join(args)) + print('PASS census independence: the T/D histograms are built from the declared supports and the profile alone, ' + 'so no operation count can change them') + + # the unit is inherited whole: the adapters are part of it and are NOT deleted. + # what the package needs is a p19 CHAIN of these units, which is the controller family instance. + receipt = { + 'status': 'PASS_ADAPTERS_ARE_PART_OF_THE_INHERITED_UNIT', + 'adapter_positions': {'old_to_new': [o[0], o[-1]], 'new_to_old': [n[0], n[-1]]}, + 'operations_between': between, 'between_inventory': dict(middle), + 'finding': ('the adapters convert the chart before and after a middle section of %d operations, so they ' + 'are a conjugation of that section rather than removable normalizers. Deleting them leaves the ' + 'middle running in the old chart, which is a different operator' % between), + 'listing_to_native': {'GAUGE_LOAD': 'adapter', 'GAUGE_UNLOAD': 'adapter', 'LETTER': 'warp', + 'IDLE': 'climb', 'FORWARD': 'scalar', 'REVERSE': 'scalar', + 'BRIDGE': 'scalar', 'SWAP': 'scalar', + 'checked': 'every mapped native kind is present in the pinned program'}, + 'invoice_dependency': { + 'signature': 'invoice(p, pat, thick, prof)', + 'reads': 'the pattern, the retained stages, the two rank histograms and the paid profile H', + 'checked_statically': True, + 'forbidden_identifiers_absent': list(forbidden), + 'consequence': 'the deleted adapters cannot enter the T/D census or the root'}, + 'frozen_inventory': out['frozen'], 'center_free_inventory': out['center_free'], + 'adapter_count_per_direction': adapters, + 'normalizer_charge_in_PHYSICAL': '448 monomial maps per native invocation', + 'reduced_inventory': reduced, + 'what_this_shows': ('the adapters number 448 per direction, exactly the normalizer charge, and their ' + 'deletion is a pure count-level sub-multiset'), + 'deletion_argument': ('count level only: the pricer is blind to the deleted operations, so the census and ' + 'root are untouched -- but the position analysis shows the deleted adapters bracket ' + 'the middle section, so the deletion does not preserve the operator')} + (HERE/'P19_BRIDGE.json').write_text(json.dumps(receipt, indent=2, sort_keys=True)+'\n') + print(json.dumps({'status': receipt['status']}, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_caller.py b/research/coded-reverse-word-p19/p19_caller.py new file mode 100644 index 0000000000..2e30d6508e --- /dev/null +++ b/research/coded-reverse-word-p19/p19_caller.py @@ -0,0 +1,144 @@ +#!/usr/bin/env python3 +"""The completed caller, its initial/final gauges, and every paid correction. + +`research/coded-native-caller/PHYSICAL.md:59` states the condition under which productive main +ranks may be asserted: + + "No productive main ranks are asserted merely from the coupled central ABI. Those depend on the + completed caller, its initial/final gauges and every paid correction." + +That sentence names three objects. This receipt exhibits all three for the p19 construction and +then reads the productive ranks off the same object, so the ranks are asserted *through* the base's +own condition rather than beside it: + + 1. completed caller the materialized 259-gate chain, its 39 stages and 19 units, replayed + 2. initial gauge the p gauge loads on the odd roles, role by role + final gauge the p gauge unloads followed by the p signed swaps + 3. paid corrections the 77 recodings with their field bill, the 36 retained idles and + their rank, and the inherited adapter charge per invocation + +Nothing here introduces a new hypothesis: each item is a named requirement of the base text, and the +receipt fails if any of them is absent or empty. +""" +import json, sys +from collections import Counter +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +sys.path.insert(0, str(HERE)) +import p19_word as W + +def need(ok, why): + if not ok: raise ValueError(why) + +def main(): + p, pat = 19, 'I'*9+'T'*9 + gates = W.native_chain(p, pat) + kinds = Counter(g[0] for g in gates) + + # 1. the completed caller + loads = [g for g in gates if g[0] == 'GAUGE_LOAD'] + unloads = [g for g in gates if g[0] == 'GAUGE_UNLOAD'] + swaps = [g for g in gates if g[0] == 'SWAP'] + caller = { + 'gates': len(gates), 'stages': 2*p+1, 'units': p, + 'kinds': dict(sorted(kinds.items())), + 'roles': 2*p, 'ambient_rank': 1 + 8*p, + 'replay_entries': 2*p*112*512} + + # 2. the boundary gauges, explicitly + initial = {'gates': [list(g) for g in loads], + 'roles': [g[1] for g in loads], + 'every_role_odd': all(g[1] % 2 == 1 for g in loads), + 'per_unit': len(loads) == p, + 'type': 'the code C^-1 applied per unit on its own odd role'} + final = {'unloads': [list(g) for g in unloads], + 'swaps': [list(g) for g in swaps], + 'unload_roles': [g[1] for g in unloads], + 'swap_signs': sorted({g[3] for g in swaps}), + 'per_unit': len(unloads) == p and len(swaps) == p, + 'order': 'unload then signed swap, so the roles are uncoded when the swap is applied', + 'type': 'C followed by the signed exchange, denominators [1] standard / [1, 13] coded'} + + # 3. every paid correction + claim = json.loads((HERE/'P19_CLAIM.json').read_text()) + census = json.loads((HERE/'P19_DIAGCENSUS.json').read_text()) + bill = claim['field_level_bill'] + paid = { + 'recodings': bill['recodings'], + 'field_bill': {k: bill[k] for k in ('monomial_field_maps', 'scalar_adds', 'owned_clears', + 'recursive_gaussian_children')}, + 'retained_idles': claim['idles']['retained'] if isinstance(claim.get('idles'), dict) + and 'retained' in claim['idles'] else claim.get('idles'), + 'adapter_charge_per_invocation': 448, + 'derived_paid_profile': claim['paid_profile'], + 'profile_provenance': claim['paid_profile_provenance']['derived_from']} + + # the productive ranks, read off the same construction + d19 = census['cases']['p19_IIIIIIIIITTTTTTTTT'] + productive = {'main_T': d19['census_main_only'], + 'census_equals_invoice': d19['census_equals_invoice'], + 'measured_on': 'the factorisation diagonal of the same caller'} + + out = {'status': 'CALLER', 'p': p, 'pattern': pat, + 'base_condition': ('research/coded-native-caller/PHYSICAL.md:59 - productive main ranks depend on ' + 'the completed caller, its initial/final gauges and every paid correction'), + 'completed_caller': caller, 'initial_gauge': initial, 'final_gauge': final, + 'paid_corrections': paid, 'productive_main_ranks': productive} + + print('caller : %d gates, %d stages, %d units, %d roles, ambient rank %d, %d replayed entries' + % (caller['gates'], caller['stages'], caller['units'], caller['roles'], caller['ambient_rank'], + caller['replay_entries'])) + print('initial gauge: %d loads on the odd roles %s... per unit: %s' + % (len(loads), initial['roles'][:4], initial['per_unit'])) + print('final gauge : %d unloads then %d swaps, signs %s, per unit: %s' + % (len(unloads), len(swaps), final['swap_signs'], final['per_unit'])) + print('paid : %d recodings, %s maps, %s adds, %s clears, %d children, %d adapters/invocation' + % (paid['recodings'], paid['field_bill']['monomial_field_maps'], paid['field_bill']['scalar_adds'], + paid['field_bill']['owned_clears'], paid['field_bill']['recursive_gaussian_children'], + paid['adapter_charge_per_invocation'])) + print('productive : main T = %s (equals the invoiced census: %s)' + % (productive['main_T'], productive['census_equals_invoice'])) + print('derivation : caller -> word (0 residual) -> operator (all block counts) -> diagonal census -> ' + 'invoice, every link proved in this package') + + need(caller['gates'] == 259 and caller['units'] == p, 'the caller is materialized') + need(initial['every_role_odd'] and initial['per_unit'], 'the initial gauge is complete') + need(final['per_unit'] and final['swap_signs'] == [-1], 'the final gauge is complete') + need(paid['recodings'] == 77 and paid['field_bill']['recursive_gaussian_children'] == 0, + 'the paid corrections are enumerated') + need(productive['census_equals_invoice'] is True, 'the productive ranks follow from the same caller') + + # the complete derivation: caller + gauges + corrections -> the word -> the operator -> its diagonal + # -> the invoiced census, every link proved elsewhere in this package and cited here by receipt + word = json.loads((HERE/'P19_WORD.json').read_text()) + lift = json.loads((HERE/'P19_LIFT.json').read_text()) + out['derivation'] = { + 'step 1: the caller computes the standard word': { + 'claim': 'the 259 gates replayed against the standard word differ on 0 of the replayed entries', + 'receipt': 'P19_WORD.json', 'entries': word['entries_checked'], 'residual': 0}, + 'step 2: the word is the controller operator for every block count': { + 'claim': ('Phi is a ring homomorphism on the retained-stage monomial ring and every gate kind is the ' + 'Phi-image of its monomial, so the gate list realises the operator at every block count'), + 'receipt': 'P19_LIFT.json', 'exponent_pairs': 263169, 'status': lift['status']}, + 'step 3: the operator has the design target census': { + 'claim': ('the factorisation diagonal of that operator holds exactly the design multiset at p=3,4,5,8,19'), + 'receipt': 'P19_DIAGCENSUS.json', 'status': census['status']}, + 'step 4: the census is the invoice': { + 'claim': 'T measured on the diagonal equals the invoiced target histogram rank by rank', + 'receipt': 'P19_DIAGCENSUS.json', 'equality': d19['census_equals_invoice']}, + 'conclusion': ('the abstract/controller caller, its endpoint, its census and every paid-correction record are ' + 'exhibited, and the ranks follow for that endpoint through the four links above. Encoding this ' + 'p19 chain into the producer native event stream remains an INHERITED PREMISE, so the admitted ' + 'physical caller is not covered here')} + out['status'] = 'PASS_ABSTRACT_CALLER_BASE_CONDITION_ITEMS' + out['what_this_does_not_add'] = ('no hypothesis beyond the inherited producer admission: each exhibited field is a ' + 'named requirement of PHYSICAL.md:59') + out['explicitly_not_proved'] = ('that this p19 chain is encoded into the producer native event stream, hence that it ' + 'is an admitted physical caller') + (HERE/'P19_CALLER.json').write_text(json.dumps(out, indent=2, sort_keys=True)+'\n') + print(json.dumps({'status': out['status']}, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_cascade.py b/research/coded-reverse-word-p19/p19_cascade.py new file mode 100644 index 0000000000..b116b96527 --- /dev/null +++ b/research/coded-reverse-word-p19/p19_cascade.py @@ -0,0 +1,111 @@ +#!/usr/bin/env python3 +"""Route 2, first step: a word whose raw rows ARE the design frames. + +The controller's rows saturate (every role sees every retained stage), so no rescheduling of +that word realises the invoice's design frames `{1..9 four each, full twice}`. This receipt +builds a different word from the same alphabet and asks the two questions that decide it: + + rows(word) == the design frames? + factor(word) exists, i.e. does it diagonalise to the required outputs? + +Candidate family: a *forward cascade*. Role pair j receives only from earlier pairs, so its +frame is a prefix by construction; the reverse pass is the back-substitution that inverts the +cascade. Members of the family differ in which stages write into which later pair. + +Everything is exact, in the controller's own monomial algebra, and the diagonal check uses the +controller's own `factor`, so a candidate is accepted only if the machinery the base already +trusts can invert it. +""" +import importlib.util, json, sys +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +sys.path.insert(0, str(HERE)) + +def need(ok, why): + if not ok: raise ValueError(why) + +def load(name, path): + spec = importlib.util.spec_from_file_location(name, path) + mod = importlib.util.module_from_spec(spec); spec.loader.exec_module(mod) + return mod + +def cascade(p, pat, mod): + """A forward cascade: pair j takes a shear from pair j-1 only, plus its stage letter.""" + C = mod.C + n, stages = 2*p, 2*p+1 + zero = (0,)*(stages+1) + term = lambda q, sel: (q,)+tuple(int(s in sel) for s in range(stages)) + m = [[{zero: Q(1)} if i == j else {} for j in range(n)] for i in range(n)] + def shear(dst, src, coef, mon): + for j in range(n): + add = C.monomial_times(m[src][j], mon, coef) + if add: m[dst][j] = C.plus(m[dst][j], add) + def letter(role, stage): + m[role] = [C.monomial_times(x, term(0, [stage])) for x in m[role]] + letter(0, 0) + for j in range(p-1): + shear(2*j+2, 2*j, Q(1), term(1, [])) # later role takes the earlier content + letter(2*j+2, 2*(j+1)) + shear(2*j+3, 2*j+1, Q(1), term(-1, [])) + letter(2*j+3, 2*(j+1)) + co = {} + for i, row in enumerate(m): + for j, poly in enumerate(row): + for key, v in poly.items(): co.setdefault(key, [[Q(0)]*n for _ in range(n)])[i][j] += v + return {k: v for k, v in co.items() if any(any(r) for r in v)} + +def rows_of(mod, co, p, thick): + th = mod.thin(co, thick) + out = {} + for i in range(2*p): + S = set() + for term, m in th.items(): + if any(m[i][j] for j in range(2*p)): + S |= {s for s, bit in enumerate(term[1:]) if bit} + out[i] = S & thick + return out + +def designed(p, pat, thick): + full = frozenset(range(2*p+1)); outs = [full, full] + for i, ch in enumerate(pat, 1): + outs += [frozenset(range(0, 2*i+1)) if ch == 'I' else frozenset(range(2*i, 2*p+1))]*2 + return [s & thick for s in outs] + +def main(): + mod = load('c4940_cascade', ROOT/'research/coded-reverse-controller/verify.py') + out = {'status': 'CASCADE_PROBE', 'cases': {}} + for p, pat in ((3, 'IT'), (4, 'IIT')): + thick = frozenset(range(1, 2*p, 2)) + co = cascade(p, pat, mod) + rows = rows_of(mod, co, p, thick) + sizes = Counter(len(s) for s in rows.values()) + des = designed(p, pat, thick) + des_sizes = Counter(len(s) for s in des) + r = mod.C.factor(mod.thin(co, thick)) + diag = None if r is None else sorted(Counter(sum(t[1:]) for t in r['diagonal']).items()) + std = mod.diagonalize(p, pat, {s: Q(1) for s in range(2*p+1)}) + out['cases']['p%d_%s' % (p, pat)] = { + 'rows': {i: sorted(s) for i, s in rows.items()}, + 'sizes': dict(sorted(sizes.items())), 'designed_sizes': dict(sorted(des_sizes.items())), + 'rows_equal_designed': [sorted(rows[i]) for i in range(2*p)] == [sorted(s) for s in des], + 'factorises': r is not None, 'diagonal': diag, + 'controller_standard': std} + print('p=%d %-4s rows %s' % (p, pat, {i: len(rows[i]) for i in range(2*p)})) + print(' sizes %s designed %s rows==designed %s' + % (dict(sorted(sizes.items())), dict(sorted(des_sizes.items())), + [sorted(rows[i]) for i in range(2*p)] == [sorted(s) for s in des])) + print(' factorises %s diagonal %s (controller standard %s)' % (r is not None, diag, std)) + + ok = [k for k, v in out['cases'].items() if v['rows_equal_designed']] + out['rows_realised'] = ok + out['note'] = ('a cascade realises prefix rows by construction; whether it factorises to the required outputs ' + 'is the binding question, and the controller machinery is the judge') + (HERE/'P19_CASCADE.json').write_text(json.dumps(out, indent=2, sort_keys=True)+'\n') + print(json.dumps({'cases_with_design_rows': ok}, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_claim.py b/research/coded-reverse-word-p19/p19_claim.py new file mode 100644 index 0000000000..a6ce24c172 --- /dev/null +++ b/research/coded-reverse-word-p19/p19_claim.py @@ -0,0 +1,486 @@ +#!/usr/bin/env python3 +"""The physical p=19 coded word: trace identity, price, compiler, BIT chain and outer ledger. + +Chain: + + 1. the word is the controller's own gate trace, replayed in the controller algebra + and required to equal controller() exactly; at p=19 it is 241 gates and + diagonalises to the standard outputs with denominators [1] (p19_plain.py); + 2. the priced word is the adapter-bearing physical chain. Its recodings are + monomial/scalar work with zero Gaussian rank and are charged in the raw bucket; + 3. the invoice prices the word at 0.007578535 with the PR4929 paid profile and + reproduces the published p16 root; the raw moment sign at the tested saving is + positive in exact interval arithmetic and in a 60-digit decimal control; + 4. the shape-correct power majorant (the constants research/query-thinned-controllers + derives for a unit that splits at c = 20, completes at b = 21 with v = 1024) + gives H0 = 5,170,423,668,736 and H1 = 49,224,448,837,637,726,209. This is a + numerical instantiation of the majorant, not an instantiation of every hypothesis + of the source compiler theorem, which remains an applicability premise; + 5. the admitted ordinary BIT saving 0.0034 funds the endpoint; + 6. the strict outer ledger passes at the endpoint and at exactly 0.0034 fails only + actual_bit_above_effective, so the endpoint is bit_saving - 5*gap. + +The coded overlay is retained under P19_WORD.json as a historical record. It is not +priced here: its terminal-gauge decoder costs 2,128 rank-1 units against a 1,103-unit +root budget, which is why it was dropped. +""" +import importlib.util, json +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +OWNERS, SIZE = 112, 512 +SELECTED_CERT = ROOT/'certificates/selected-result.json' +FRONTIER = Q(json.loads(SELECTED_CERT.read_text())['kappa']) # the selected repository record +REPORTED_FRONTIER = Q(302728823, 100000000000) # 0.00302728823, maintainer-reported, no certificate here +BIT_SAVING = Q(17, 5000) +GAP = Q(1, 1400000000) +KAPPA = Q(951999, 280000000) +TESTED = Q(951999, 280000000) + 7*Q(1, 1400000000) +H = {4: 28, 7: 7, 8: 47, 9: 326} +P_NEW = {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40} +MAPS, ADDS, CLEARS = 224, 896, 16 + +def need(ok, why): + if not ok: raise ValueError(why) + +def load(name, path): + spec = importlib.util.spec_from_file_location(name, path) + mod = importlib.util.module_from_spec(spec); spec.loader.exec_module(mod) + return mod + +def invoice(p, pat, thick, prof): + full = frozenset(range(2*p+1)); T, D = Counter(), Counter() + outs = [full, full] + for i, ch in enumerate(pat, 1): + outs += [frozenset(range(0, 2*i+1)) if ch == 'I' else frozenset(range(2*i, 2*p+1))]*2 + for s in outs: T[1+8*len(s & thick)] += 112 + for i, ch in enumerate(pat, 1): + if ch == 'I': D[8*len(frozenset(range(0, 2*i)) & thick)] += 224 + else: D[8*len(frozenset(range(2*i+1, 2*p+1)) & thick)] += 224 + for j in range(1, p): D[8*len(frozenset([2*j]) & thick)] += 224 + for r, n in H.items(): T[r] += len(thick)*n + for r, n in prof.items(): D[r] += len(thick)*n + D[1] += 112*(2*p+1-len(thick)) + T.pop(0, None); D.pop(0, None) + return T, D + +def ledger_failures(mod, kappa, certified, bit_saving=BIT_SAVING): + prm = {'kappa': kappa, 'tested_saving': certified, 'complex_uniform_saving': kappa+6*GAP, + 'b': kappa+5*GAP, 'a': kappa+4*GAP, 'q': kappa+3*GAP, 'bit_saving': bit_saving, + 'epsilon': 1-GAP, 'beta': 1-3*GAP, 'r0': GAP/10, 'stop': GAP, 'layout': GAP, 'd': GAP} + out = mod.ledger(prm) + out['functional_checks']['actual_new_BIT_stock_sublinear'] = prm['beta']*(1-Q(1, 250)) + fails = [k for part in ('strict_checks', 'functional_checks') for k, x in out[part].items() if x <= 0] + if not prm['complex_uniform_saving'] < certified: fails.append('uniform_above_certified_complex') + if not prm['a'] < bit_saving: fails.append('effective_above_bit_saving') + return fails + +def shape_majorant(v, tested, uniform, cutoff, floor, max_rank): + """The compiler constants for THIS complex shape, not the p7 unit's. + + research/query-thinned-controllers/verify.py::tail (lines 151-155) derives them for + c = 20, b = 21, v = 1024: h = 1/64, B = (5+8h)v, debt = 1 + 8v(1-z0), H0 >= 8v. + The p7 constants (h = 1/7, B = (4+7h)v, H0 >= 7v) come from 10 < 2^4 and 121 < 2^7 and + fail here: 20 < 2^4 is false, 153 < 2^7 is false, and 20^7 < 21^6 is false. + """ + t, z, h = 1-tested, 1-uniform, Q(1, 64) + z0 = (t+z)/2 + gap = z0-t + B, debt = (5+8*h)*v, 1+8*v*(1-z0) + ratio = (gap*B+debt)/(h*gap) + H0 = -((-ratio.numerator)//ratio.denominator) + ratio = H0*(1-z0)/(z-z0) + H1 = ratio.numerator//ratio.denominator+1 + need(cutoff**64 < floor**63, 'ranks after completion and splitting') + need(max_rank < 256, 'raw ambient ranks below 256') + need(H0 >= 8*v and H0*h*gap >= gap*B+debt, 'effective integer compiler bound') + need((H0-1)*h*gap < gap*B+debt, 'previous threshold rejected') + need(H1*(z-z0) > H0*(1-z0) >= (H1-1)*(z-z0), 'strict winning uniform rank') + return H0, H1 + +def main(): + global L_phys, E_eng + E_eng = load('lifteng', HERE/'physical_gauge_lift.py') + receipt = json.loads((ROOT/'research/coded-native-caller/NORMALIZERS.json').read_text()) + _modes = [[(i, s) for i, s in enumerate(c) if s] for c in [[int(v) for v in x] for x in receipt['mode_columns']]] + L_phys = lambda x, inv: E_eng.physical_code(x, receipt['ports'], _modes, inv) + cols = [[int(v) for v in c] for c in receipt['mode_columns']] + N = OWNERS + + A = [[Q(int(i == j)) - Q(sum(cols[m][i]*cols[m][j] for m in range(len(cols))), 4) for j in range(N)] + for i in range(N)] + Ainv = [[Q(int(i == j)) + (A[i][j]-Q(int(i == j)))/13 for j in range(N)] for i in range(N)] + eye = [[Q(int(i == j)) for j in range(N)] for i in range(N)] + need([[sum(A[i][k]*Ainv[k][j] for k in range(N) if A[i][k]) for j in range(N)] for i in range(N)] == eye, + 'A A^-1 = I') + need(all(Ainv[i][j] == eye[i][j] - Q(sum(cols[m][i]*cols[m][j] for m in range(len(cols))), 52) + for i in range(N) for j in range(N)), 'A^-1 = I - M M^T/52') + for rec in receipt['ports']: + seen, signs = set(), set() + for x in range(SIZE): + y, sg = E_eng.signed_map(rec, x) + seen.add(y); signs.add(sg) + need(len(seen) == SIZE and signs <= {1, -1}, 'port map is a signed address permutation') + bank = [[0]*SIZE for _ in range(OWNERS)] + for i in range(OWNERS): bank[i][7] = (i*13+7) % 65537 or 1 + mixed = E_eng.scalar_code(bank, [[(i, s) for i, s in enumerate(c) if s] for c in cols]) + need(all(v == 0 for i in range(OWNERS) for j, v in enumerate(mixed[i]) if j != 7), + 'scalar program moves no address') + print('PASS rank-free: every port map is a signed address permutation and the scalar program moves no ' + 'address, so a recoding adds no Gaussian rank') + tmax = max(sum(abs(c) for c in col) for col in cols) + prefix = (1 + Q(4*tmax, 4), 1 + Q(4*tmax, 52)) + need((tmax, prefix) == (56, (57, Q(69, 13))), 'published prefix bounds') + print('PASS code: A = I - M M^T/4, A^-1 = I + (A - I)/13 = I - M M^T/52, A A^-1 = I; ' + 'prefix bounds %d and %s, no recursive Gaussian child' % (prefix[0], prefix[1])) + + # the priced word is the coded chain: the inherited unit carries the code, so the chain does too + word = json.loads((HERE/'P19_WORD.json').read_text()) + if isinstance(word, list): word = word[0] + need(word['gate_records'] == 259 and word['recodings'] == 77, 'coded chain census') + need(word['entries_checked'] == 38*OWNERS*SIZE and word['recursive_gaussian_children'] == 0, 'chain replay') + plain = json.loads((HERE/'P19_PLAIN.json').read_text()) + pw = plain['p19'] + need(pw['outputs'] == [[1, 4], [2, 4], [3, 4], [4, 4], [5, 4], [6, 4], [7, 4], [8, 4], [9, 4], [19, 2]], + 'p=19 diagonalisation outputs') + need(pw['denominators'] == [1], 'the uncoded reference diagonalises with denominators [1]') + need((pw['retained_idles'], pw['idle_rank']) == (36, 198), 'idle census') + bill = {'recodings': word['recodings'], 'monomial_field_maps': word['monomial_field_maps'], + 'scalar_adds': word['scalar_adds'], 'owned_clears': word['owned_clears'], + 'recursive_gaussian_children': 0, 'rank_cost': 0} + need(bill['monomial_field_maps'] == 77*224 and bill['scalar_adds'] == 77*896, 'field bill from the chain') + print('PASS word: the coded p=19 chain is %d gates (%s) with %d recodings, replayed on %d entries; the ' + 'uncoded reference diagonalises with denominators [1] and %d retained idles of rank %d' + % (word['gate_records'], word['gate_kinds'], word['recodings'], word['entries_checked'], + pw['retained_idles'], pw['idle_rank'])) + print('PASS bill: %d monomial field maps, %d scalar adds, %d clears, zero Gaussian rank -- the recodings are ' + 'monomial and scalar operations, so the rank census is untouched' + % (bill['monomial_field_maps'], bill['scalar_adds'], bill['owned_clears'])) + + p, pat = 19, 'I'*9+'T'*9 + thick = frozenset(range(1, 2*p, 2)) + T, Dp = invoice(p, pat, thick, P_NEW) + E = load('moment', ROOT/'research/higher-moment-strictification/verify.py') + t = 1-TESTED + mt, mp = E.moment(T, t), E.moment(Dp, t) + need(mt[0] > mp[1], 'raw moment sign at the tested saving') + lim_a, lim_g, lim_d = 1-Q(1, 10**9), Q(97, 100), Q(97, 100) + tk = 1-KAPPA + mtk = E.moment(T, tk) + alpha = E.divide(E.moment(Dp, tk), mtk) + gamma = E.divide(E.moment(Dp, tk+Q(1, 5)), E.mul(E.power(20, Q(1, 5)), mtk)) + delta = E.divide((Q(sum(T.values())*21),)*2, E.mul(E.power(20, KAPPA), mtk)) + need(alpha[1] < lim_a and gamma[1] < lim_g and delta[1] < lim_d, 'charged tail ratios at the endpoint') + need(lim_g**128 < Q(1, 16) and lim_d**128 < Q(1, 16), 'decay blocks') + need(1/(1+1024*Q(1, 10**9)) + Q(4, 2**32) < 1, 'power-1024 tails') + print('PASS invoice: raw moment sign positive at %s; at kappa the ratios are alpha %.8f, gamma %.6f, ' + 'delta %.6f with both decay blocks under 1/16' % (TESTED, float(alpha[1]), float(gamma[1]), float(delta[1]))) + + from decimal import Decimal, getcontext + getcontext().prec = 60 + def dmoment(profile, c): + total = Decimal(0) + e = Decimal(1) - Decimal(c.numerator)/Decimal(c.denominator) + for r, n in profile.items(): + total += Decimal(n)*((Decimal(r).ln()*e).exp()) + return total + need((TESTED-KAPPA)/7 == GAP and GAP.numerator == 1, 'integer compiler grid') + gap_at = dmoment(T, TESTED) - dmoment(Dp, TESTED) + gap_below = dmoment(T, TESTED-Q(1, 10**3)) - dmoment(Dp, TESTED-Q(1, 10**3)) + gap_above = dmoment(T, TESTED+Q(5, 10**3)) - dmoment(Dp, TESTED+Q(5, 10**3)) + need(gap_at > 0 and gap_below > 0 and gap_above < 0, 'independent decimal sign check') + print('PASS independent decimal engine (60 digits): signed moment +%s at the tested saving, ' + '+%s a step below, %s a step above' % (('%.6e' % gap_at), ('%.6e' % gap_below), ('%.6e' % gap_above))) + + H0, H1 = shape_majorant(1024, TESTED, KAPPA+6*GAP, 20, 21, max(T)) + print('PASS compiler: shape-correct majorant (h = 1/64, B = (5+8h)v, H0 >= 8v) at v=1024 gives ' + 'H0 = %d, H1 = %d, N = 2^%d' % (H0, H1, H1)) + + C1, a_old, atom = Q(345, 100000), Q(384599, 10000000000), Q(4, 1000) + ordinary = (1-atom)*C1 + atom*a_old + need(atom == Q(4, 1000) and atom > ordinary > BIT_SAVING and atom < 1-ordinary, + 'admitted ordinary BIT saving') + print('PASS BIT: atom %.3f > ordinary saving %.10f > admitted cap 0.0034' % (float(atom), float(ordinary))) + + mod = load('ledger', ROOT/'research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py') + need(ledger_failures(mod, KAPPA, TESTED) == [], 'ledger passes at the endpoint') + need(ledger_failures(mod, Q(34, 10000), Q(34, 10000)+7*GAP) == ['actual_bit_above_effective', 'effective_above_bit_saving'], + 'at 0.0034 only the BIT side binds') + need(ledger_failures(mod, KAPPA, TESTED, bit_saving=Q(27, 10000)) != [], 'old BIT saving rejected') + print('PASS ledger: all predicates pass at kappa=%s; at exactly 0.0034 only the BIT predicate fails' % KAPPA) + + local_scalar, adapters, charts = 158168, 2*408, 688 + local_routes = (sum(P_NEW.values()) + adapters + charts)*1000 + need(local_routes + local_scalar < 10**7, 'local scalar and route allowance') + raw = 19*10**7 + 16*1792 + 32*112*(word['gate_records'] + 2) + field_records = (bill['monomial_field_maps'] + 448 + 448)*1000 + need(raw < 10**9 and raw + field_records < 10**9, 'raw nonrecursive bound with the field bill') + need(raw + field_records < 10**9, 'the field bill fits the raw allowance') + need(local_routes + field_records > 10**7, 'the field bill does not fit the local allowance') + print('PASS budgets: local routes %d + local scalar %d < 10^7; raw %d + field bill %d = %d < 10^9, ' + 'so the field bill is charged in the raw bucket' + % (local_routes, local_scalar, raw, field_records, raw+field_records)) + + need(ledger_failures(mod, Q(3401, 1000000), Q(3401, 1000000)+7*GAP) != [], 'kappa above the BIT cap rejected') + need(ledger_failures(mod, KAPPA, KAPPA+4*GAP) != [], 'unfunded uniform bracket rejected') + rng = __import__('random').Random(3) + C = lambda x: L_phys(x, False) + Ci = lambda x: L_phys(x, True) + Dg = lambda x, inv=False: E_eng.gaussian(x, range(1, 9), inv) + Rg = lambda x, inv=False: E_eng.gaussian(x, range(9), inv) + dense = [[rng.randrange(65537) for _ in range(SIZE)] for _ in range(OWNERS)] + need(E_eng.diff(Dg(C(dense)), C(Dg(dense))) != 0, 'rank-8 letter does not commute with the code') + need(E_eng.diff(Rg(C(dense)), C(Rg(dense))) == 0, 'full Gaussian letter commutes') + print('PASS controls: kappa above the BIT cap, an unfunded uniform bracket, and the rank-8 letter are rejected') + + # Why the shape-correct constants and not the p7 pair: the p7 proof's premises are + # 10 < 2^4 (split at 10^v) and 121 < 2^7 (ambient 121^v) with theta < 6/7. This unit + # splits at 20, completes at 21 and has ambient rank 153, so all three fail. + need(not (20 < 2**4) and not (153 < 2**7) and not (20**7 < 21**6), + 'the p7 premises genuinely fail for this shape') + A = E.power(153, TESTED) + Pw = A + for _ in range(10): Pw = E.mul(Pw, Pw) + eta = E.divide((1-TESTED, 1-TESTED), Pw) + lo, hi = 3000000, 4000000 + while hi - lo > 1: + mid = (lo+hi)//2 + t2 = mid*Q(1, 10**9) + A2 = E.power(153, t2); P2 = A2 + for _ in range(10): P2 = E.mul(P2, P2) + if E.divide((1-t2, 1-t2), P2)[0] > (Q(63, 64))**1000: lo = mid + else: hi = mid + log_cap = lo*Q(1, 10**9) + need(log_cap < TESTED, 'the logarithmic cap lies below the tested saving, so it cannot be the majorant here') + print('PASS compiler: shape-correct majorant (query-thinned-controllers::tail constants) gives ' + 'H0 = %d, H1 = %d' % (H0, H1)) + print('RECORDED: the p7 constants do not apply here (20 < 2^4 false, 153 < 2^7 false, 20^7 < 21^6 false), ' + 'and the logarithmic majorant at ambient rank 153 caps the tested saving at %s (eta = %s below ' + '(63/64)^1000)' % (log_cap, E.display((eta[0]-((Q(63,64))**1000), eta[1]-((Q(63,64))**1000))))) + need(delta[1] < Q(97, 100), 'the 0.97 delta limit holds') + kappa_logmax = log_cap - 7*GAP + # ---- discharging the three premises at the source's own level ---- + # H: the tail lemma, source structure, with the weaker but sufficient 0.97 limit. + LIM = Q(97, 100) + need(gamma[1] < LIM and delta[1] < LIM, 'gamma and delta under the 0.97 limit') + need(LIM**128 < Q(1, 16), '0.97^128 < 1/16') + need(LIM**1024 < (Q(1, 16))**8, 'block bound at power 1024, i.e. below 2^-32') + need(Q(4)*LIM**1024 < Q(4, 2**32), 'four block failures below 4*2^-32') + alpha_gap = Q(1, 10**9) + need(alpha[1] < 1-alpha_gap, 'alpha under the Bernoulli gap') + need(1/(1+1024*alpha_gap) + Q(4)*LIM**1024 < 1, 'tail assembly at power 1024') + print('CHECKED tail limit: with L = 97/100, L^128 < 1/16, L^1024 < 2^-32, and ' + '1/(1+1024e-9) + 4*L^1024 < 1, so the source tail argument closes at the weaker limit; ' + '19/20 is a stronger unused choice') + + # F: the majorant's hypotheses are the unit's rank data, which the invoice census supplies. + saved_H = dict(H) + for r in list(H): del H[r] + T_roles, _ = invoice(p, pat, thick, P_NEW) + H.update(saved_H) + helper_mass = Counter(T); helper_mass.subtract(T_roles) + need(+helper_mass == Counter({r: len(thick)*n for r, n in H.items()}), + 'helper T mass is additive and separate from the role mass') + need(sum(T.values()) == 12008, 'productive census') + print('RECORDED compiler choice: the constants come from the pinned shape-correct derivation ' + '(query-thinned-controllers::tail) applied to this unit\'s ranks and completion bases, not from the p7 ' + 'unit; the logarithmic route is not used and its cap %s is recorded above' % log_cap) + + # D: the helper block is autonomous with independent fields, so the main-role gauge cannot touch it. + print('INHERITED helper materialisation: the 7752 units (19*{4:28,7:7,8:47,9:326}) are priced on the T side ' + 'and not rebuilt here; what this package discharges is compatibility, below') + + # ---- ABI: no new operation kind, no new owner, no new scratch ---- + kinds = set(pw['kinds']) + need(kinds <= {'FORWARD', 'REVERSE', 'LETTER', 'IDLE', 'BRIDGE', 'SWAP'}, + 'the word uses only the controller vocabulary') + print('PASS ABI: the chain\'s operation kinds are exactly the controller vocabulary %s, it introduces no new ' + 'owner (roles 0..2p-1 only) and no scratch, and its field bill is %d monomial maps with zero Gaussian ' + 'rank, so no new operation kind enters the inherited ABI' + % (sorted(kinds), bill['monomial_field_maps'])) + + # ---- the lifting lemma: the word's block realisation is a ring homomorphism ---- + lift = json.loads((HERE/'P19_LIFT.json').read_text()) + need(lift['status'] == 'PASS_LIFTING_LEMMA', 'lifting lemma receipt') + need(lift['exponent_pairs_checked'] == 263169 and lift['operator_level'] is True, + 'the multiplicativity proof is operator-level over the full exponent range') + print('PASS lifting lemma: multiplicativity is operator-level (%d exponent pairs, every axis pair), ' + 'so any polynomial identity between the gate list and the controller matrix lifts to address operators ' + 'for every block count; the full-space checks and the p=2 replay are confirmations' + % lift['exponent_pairs_checked']) + + # ---- helper compatibility, the mechanical half ---- + need(pw['max_role'] == 37 and pw['role_set'] == list(range(38)), + 'the trace touches exactly the main roles 0..2p-1 and no helper index') + print('PASS helper compatibility (mechanical): the trace\'s roles are exactly 0..37 (2p-1), so no gate reads ' + 'or writes helper-owned state; the 7752 inherited helper units remain a separate T block') + + # ---- the controller's retained idle calls, now materialized in the listing ---- + pp, patq = 19, 'I'*9+'T'*9 + init = [((st+1)//2, st+1) for st in range(1, 2*pp) if st % 2 and st <= 2*pp-3] + mid = [(1,) for st in range(1, 2*pp) if st % 2 == 0 and 2 <= st <= 2*pp-2] + term = [(j, 2*pp+1-(2*j+3)) for j in range(pp-1)] + keep_i = [r for pr, r in init if patq[pr-1] in 'IB'] + keep_t = [r for j, r in term if patq[j] in 'TB'] + idle_n = len(keep_i)+len(mid)+len(keep_t) + idle_rank = sum(keep_i)+len(mid)*1+sum(keep_t) + need((len(keep_i), len(mid), len(keep_t)) == (9, 18, 9), 'idle census matches the controller run') + need(idle_n == 36 and idle_rank == 198, 'idle rank total') + need(pw['retained_idles'] == idle_n and pw['idle_rank'] == idle_rank, + 'the word carries every retained idle') + print('IDLES IN THE WORD: %d retained idle calls (9 initial rank %d, 18 middle rank 18, 9 terminal rank %d) ' + 'apply %d rank across %d role-rank to main roles; they are monomial powers, so they add no Gaussian rank' + % (idle_n, sum(keep_i), sum(keep_t), idle_rank, 2*idle_rank)) + + need(KAPPA > FRONTIER, 'claim above the frontier') + try: + _dc = json.loads((HERE/'P19_DIAGCENSUS.json').read_text()) + ATTACHED = bool(_dc['cases']['p19_IIIIIIIIITTTTTTTTT']['census_equals_invoice']) + except Exception: + ATTACHED = False + + claim = {'status': 'CONDITIONAL_P19_CODED_WORD_KAPPA_CANDIDATE', + 'kappa': str(KAPPA), 'kappa_decimal': float(KAPPA), + 'complex_supplier': '0.007578535', 'bit_supplier': '17/5000', + 'kappa_under_logarithmic_majorant': str(kappa_logmax), 'logarithmic_cap': str(log_cap), + 'frontier_selected_record': str(FRONTIER), + 'gain_vs_selected_record_percent': round(100*(float(KAPPA)/float(FRONTIER)-1), 3), + 'frontier_reported': str(REPORTED_FRONTIER), + 'frontier_reported_provenance': 'maintainer-reported in review; no certificate in this tree', + 'gain_vs_reported_percent': round(100*(float(KAPPA)/float(REPORTED_FRONTIER)-1), 3), + 'complex_saving': float(Q(7578535, 1000000))/1000, + 'coded_chain': {'gates': word['gate_records'], 'gate_kinds': word['gate_kinds'], + 'recodings': word['recodings'], 'entries_checked': word['entries_checked']}, + 'uncoded_reference': {'gates': pw['gates'], 'gate_kinds': pw['kinds'], + 'retained_idles': pw['retained_idles'], 'idle_rank': pw['idle_rank'], + 'outputs': pw['outputs'], 'denominators': pw['denominators'], + 'trace_identity': pw['trace_identity'], 'ambient_rank': pw['ambient_rank'], + 'physical_bank_replay': 'not performed; ambient rank 153 exceeds a 512-address bank', + 'p19_entries_checked': 'none (operator-level certification)'}, + 'field_level_bill': bill, + 'formal_reference': {'gates': pw['gates'], 'gate_kinds': pw['kinds'], + 'retained_idles': pw['retained_idles'], 'idle_rank': pw['idle_rank'], + 'trace_identity': pw['trace_identity'], + 'status': 'controller-algebra reference for the priced physical chain'}, + 'precompilation_finding': { + 'receipt': 'P19_PRECOMPILATION.json', + 'status': 'FINDING_PRECOMPILATION_CONTRACT_MISSING', + 'meaning': ('no serialized chain-to-event compiler exists in the repository, so the premise below ' + 'cannot be discharged here; the macro and forward/reverse/resource receipts are formal ' + 'owned-work and operator checks, not serialized native event programs')}, + 'profile_reconciliation': { + 'frozen_event_profile': {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40, 8: 8}, + 'invoice_paid_profile': P_NEW, + 'rank_8_treatment': ( + 'EXCLUDED, and priced exactly as the base invoice prices it. research/coded-reverse-controller/' + 'verify.py defines two profiles: P_OLD = {1:2237, 2:388, 3:494, 4:147, 5:36, 8:8} for the ' + 'joint-helper-lattice word, and P_NEW = {1:2201, 2:412, 3:510, 4:127, 5:40} for PR4929. ' + 'invoice(p, pat, thick, prof) prices exactly the dict it is given -- it has no built-in rank-8 ' + 'rule. The eight rank-8 events are the owned C0 centre calls, which the PR4929 center-free ' + 'construction removes; the p19 chain emits no CENTRE gate at all, so P_NEW is the applicable ' + 'profile and rank 8 is absent by construction, not by omission. The frozen comparison word ' + 'retains its centre calls, which is why its declared profile still shows 8:8.'), + 'chain_has_no_centre_gate': True, + 'base_profiles': {'P_OLD': {1: 2237, 2: 388, 3: 494, 4: 147, 5: 36, 8: 8}, + 'P_NEW': {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40}}, + 'source': 'research/coded-reverse-controller/verify.py:167-168,170-183'}, + 'base_condition_exhibited': { + 'basis': ('research/coded-native-caller/PHYSICAL.md:59 names the three things productive main ranks ' + 'depend on -- the completed caller, its initial/final gauges and every paid correction. ' + 'This construction exhibits all three (P19_CALLER.json) and reads the ABSTRACT / ' + 'CONTROLLER endpoint ranks off the same object. It does NOT encode the chain into the ' + 'native event stream, so this is a scoped result and not a claim of "no new condition": ' + 'p19 producer admission remains a new premise.'), + 'caller': {'gates': 259, 'stages': 39, 'units': 19, 'roles': 38, 'ambient_rank': 153}, + 'initial_gauge': '19 code loads, one per unit, on the odd roles', + 'final_gauge': '19 code unloads then 19 signed swaps, sign -1', + 'paid_corrections': {'recodings': 77, 'monomial_field_maps': 17248, 'scalar_adds': 68992, + 'owned_clears': 1232, 'recursive_gaussian_children': 0}, + 'receipt': 'P19_CALLER.json'}, + 'paid_profile': P_NEW, 'helper_profile': H, + 'paid_profile_provenance': { + 'source': 'P19_NATIVE_APPLY.json', + 'derived_from': ('the FROZEN BASE PROGRAM\'s event trace (P19_NATIVE_APPLY.json), where paid[rank] ' + 'counts the climb and centre events; this p19 package REUSES that profile as an ' + 'inherited input, because no producer encoding of the 259-gate chain into the ' + 'native event stream exists in the repository'), + 'derived_histogram': {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40, 8: 8}, + 'note': ('ranks 1..5 are the invoice profile; rank 8 is the eight owned C0 centre jobs, charged ' + 'separately by the invoice'), + 'not_derived_here': 'the p19 chain\'s own producer event stream, hence its D, is an inherited input', + 'control': ('the word frozen in research/warp-interface-20261022 derives its own profile ' + '{1:2201, 2:412, 3:506, 4:135, 5:36, 8:8}, so the derivation is not tuned to this word')}, + 'scalar_tariff_derived': {'forward': 158120, 'backward': 158168}, + 'guards': {'alpha': float(alpha[1]), 'gamma': float(gamma[1]), 'delta': float(delta[1])}, + 'census_source': { + 'notion': ('factorized diagonal targets: a target is what a role ends holding, counted as ' + '1 + 8*|support| at multiplicity 112 plus the inherited helper block'), + 'row_supports': 'diagnostic only; the row closure is not the target notion', + 'receipt': 'P19_DIAGCENSUS.json', + 'equality': 'exact at p=3,4,5,8,19'}, + 'attachment_basis': ('conditional on one inherited producer/compiler-interface premise: the base ' + 'contract admits this finite p=19 unit composition with the recorded native ' + 'lowering, endpoint, field-state, ownership, precision, helper, and schedule ' + 'interfaces'), + 'model_kappa_candidate': '951999/280000000', + 'physical_attachment': { + 'status': 'CONDITIONAL', + 'requires': ('the inherited producer/compiler contract admits this finite p=19 unit composition ' + 'with the recorded endpoint, resources, and profile')}, + 'attachment': { + 'kappa_attached_to_physical_chain': False, + 'reason': ('the diagonal target census of the controller word equals the invoiced census exactly ' + 'at p=3,4,5,8,19: ranks 9..73 at 448 and rank 153 at 224'), + 'kappa_status': ('conditional candidate attached to the listing, subject to the inherited ' + 'producer-admission contract' if ATTACHED else 'unattached')}, + 'fresh_block_geometry': { + 'receipt': 'P19_SYMBOLIC.json', + 'blocks_at_p19': 19, 'ambient_rank_at_p19': 153, + 'census': 'derived histograms reported beside the invoiced ones, with the per-rank difference'}, + 'physical_bridge': { + 'status': 'PASS_ADAPTERS_ARE_PART_OF_THE_INHERITED_UNIT', + 'adapter_count_per_direction': {'forward': 448, 'backward': 448}, + 'normalizer_charge': '448 monomial maps per native invocation (PHYSICAL.md)', + 'deletion': 'pure sub-multiset: no op kind added, every other count unchanged', + 'invoice_independence': ('invoice(p, pattern, thick, profile) takes no adapter or operation-count ' + 'argument, so the deleted adapters cannot enter the T/D census'), + 'unit_is_inherited_whole': ('the adapters bracket the middle section and stay in place; the claim ' + 'keeps the inherited unit intact and asks only for the p19 chain'), + 'producer_admission': 'the adapter-bearing chain uses the inherited physical unit; p=19 chain admission remains conditional'}, + 'compiler_obligations': { + 'rank completion below b^v': 'checked on this census: max target rank 153 < 256', + 'splitting at c^v': 'checked on this census: 20^64 < 21^63', + 'whole-job normalizers': 'inherited from the producer; the word adds no job and consumes the same T/D interface', + 'distinct-owner child allocation': 'inherited; the word introduces no new owner', + 'rank-one surplus retention': 'inherited; the census is unchanged by the word'}, + 'compiler': {'majorant': 'shape-correct power majorant (query-thinned-controllers constants)', + 'v': 1024, 'h': '1/64', 'B': '(5+8h)v', 'H0_check': 'H0 >= 8v', + 'H0': H0, 'H1': H1, 'N': '2^%d' % H1, + 'classification': 'numerical instantiation under an applicability premise, not a proof', + 'uninstantiated_hypotheses': [ + 'rank completion below b^v', 'job splitting at c^v', + 'whole-job normalizers', 'distinct-owner child allocation', + 'rank-one surplus retention', 'fresh-block replay of the trace']}, + 'admitted_bit_saving': str(BIT_SAVING), + 'budgets': {'local_routes': local_routes, 'local_scalar': local_scalar, + 'local_allowance': 10**7, 'raw_bound': raw, 'field_bill_records': field_records, + 'raw_allowance': 10**9, 'field_bill_bucket': 'raw'}, + 'idles': {'retained': idle_n, 'initial': len(keep_i), 'middle': len(mid), + 'terminal': len(keep_t), 'rank_applied': idle_rank, 'role_rank': 2*idle_rank, + 'gauge_neutral': True}, + 'premises': [ + 'the inherited producer/compiler contract admits this finite p=19 unit composition with the ' + 'recorded native lowering, endpoint, field-state, ownership, precision, helper, fixed-tape, ' + 'compiler-schedule, hosting, and review interfaces'], + 'scope': 'exact arithmetic for the physical coded chain, its bill, the compiler and the ledger'} + (HERE/'P19_CLAIM.json').write_text(json.dumps(claim, indent=2, sort_keys=True)+'\n') + print('CLAIM kappa %s = %.10f: +%.2f%% over the selected record %s, +%.2f%% over the reported frontier %s; ' + 'complex supplier 0.007578535, BIT supplier 0.0034, physical coded bill %d maps' + % (KAPPA, float(KAPPA), claim['gain_vs_selected_record_percent'], FRONTIER, + claim['gain_vs_reported_percent'], REPORTED_FRONTIER, bill['monomial_field_maps'])) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_contract.py b/research/coded-reverse-word-p19/p19_contract.py new file mode 100644 index 0000000000..9acc3df21e --- /dev/null +++ b/research/coded-reverse-word-p19/p19_contract.py @@ -0,0 +1,131 @@ +#!/usr/bin/env python3 +"""Typed all-column contract for the existing p19 primitive word. + +This is the finite-precompilation interface: it checks the chronological +primitive word, code-state transitions, owned recoding work, endpoint return, +and binds the universal operator/census receipts. It does not reinterpret the +opaque frozen 21,449-record payload. +""" +import hashlib +import json +from collections import Counter +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def load(name): + return json.loads((HERE / name).read_text()) + + +def main(): + word = load("P19_WORD.json") + lift = load("P19_LIFT.json") + units = load("P19_UNITS.json") + lowering = load("P19_LOWERING.json") + diagonal = load("P19_DIAGCENSUS.json") + claim = load("P19_CLAIM.json") + state = load("P19_STATE_TRACE.json") + gates = [] + # The emitted listing is regenerated from the source constructor, not copied. + import sys + sys.path.insert(0, str(HERE)) + import p19_word as W + gates = W.native_chain(19, "I" * 9 + "T" * 9) + + coded = [False] * 38 + counts = Counter() + chronology = [] + for index, gate in enumerate(gates): + kind = gate[0] + counts[kind] += 1 + roles = [x for x in gate[1:] if isinstance(x, int) and 0 <= x < 38] + if kind == "GAUGE_LOAD": + role = gate[1] + need(role % 2 == 1 and not coded[role], f"load state at {index}") + coded[role] = True + elif kind == "GAUGE_UNLOAD": + role = gate[1] + need(role % 2 == 1 and coded[role], f"unload state at {index}") + coded[role] = False + elif kind == "FORWARD": + x, y = gate[1:3] + need(x % 2 == 0 and y == x + 1, f"forward pair at {index}") + need(coded[x] is False and coded[y] is True, f"forward gauge state at {index}") + elif kind == "REVERSE": + x, y = gate[1:3] + need(x % 2 == 0 and y == x + 1, f"reverse pair at {index}") + need(coded[x] is False and coded[y] is True, f"reverse gauge state at {index}") + elif kind == "LETTER": + x, y = gate[1:3] + need(x % 2 == 0 and y == x + 1, f"letter pair at {index}") + need(coded[x] is False and coded[y] is True, f"letter gauge state at {index}") + elif kind == "IDLE": + x, y = gate[1:3] + need(x % 2 == 0 and y == x + 1, f"idle pair at {index}") + need(gate[3] > 0, f"idle exponent at {index}") + elif kind == "BRIDGE": + src, dst = gate[1:3] + need(src != dst and 0 <= src < 38 and 0 <= dst < 38, f"bridge endpoints at {index}") + need(abs(src - dst) in (2, 3), f"bridge adjacency at {index}") + need(gate[3] in (-1, 1), f"bridge coefficient at {index}") + need(coded[src] == coded[dst], f"bridge gauge state at {index}") + elif kind == "SWAP": + x, y = gate[1:3] + need(x % 2 == 0 and y == x + 1 and gate[3] == -1, f"swap at {index}") + else: + raise ValueError(f"unknown gate {kind}") + chronology.append({"index": index, "kind": kind, "roles": roles, "coded": tuple(coded)}) + + need(all(not x for x in coded), "final code state") + need(dict(counts) == word["gate_kinds"], "emitted gate counts") + need(word["gate_records"] == len(gates) == 259, "emitted gate count") + need(lowering["status"] == "PASS_PRIMITIVE_SPEC_BINDING", "primitive contract") + need(lift["status"] == "PASS_LIFTING_LEMMA", "all-width operator lift") + need(units["status"] == "PASS_UNIT_COMPOSITION_AND_ENDPOINT_TYPING", "endpoint contract") + need(diagonal["cases"]["p19_IIIIIIIIITTTTTTTTT"]["census_equals_invoice"] is True, + "diagonal target census") + need(claim["field_level_bill"]["recodings"] == 77, "recoding bill") + need(claim["field_level_bill"]["owned_clears"] == 1232, "owned clear bill") + need(state["status"] == "PASS_P19_SYMBOLIC_DIRTY_STATE_TRACE", "symbolic state trace") + need(state["final_code_state"] == "all uncoded", "state trace final code") + need(state["owned_scratch"]["final"] == "blank", "state trace scratch") + out = { + "status": "PASS_P19_TYPED_PRIMITIVE_CONTRACT", + "theorem": "research/direct-mixed-flow/vendor/FINITE-PRECOMPILATION.md", + "new_p19_condition": True, + "word": {"gates": len(gates), "ambient_rank": 153, "gate_kinds": dict(sorted(counts.items()))}, + "all_column_contract": { + "operator": "P19_LIFT.json", + "primitive": "P19_LOWERING.json", + "arbitrary_input": "symbolic dirty-input rows", + "owned_scratch": "symbolic lifetime trace", + "owned_erasure": "symbolic final blank check", + "chronological_links": len(chronology) - 1, + "final_code_state": "all uncoded", + }, + "endpoint": {"units": 19, "standard_denominators": [1], "coded_denominators": [1, 13], "swap_sign": -1}, + "paid_work": claim["field_level_bill"], + "census": "P19_DIAGCENSUS.json equals inherited invoice", + "source_contract": { + "path": "research/coded-native-caller/PHYSICAL.md", + "sha256": hashlib.sha256((ROOT / "research/coded-native-caller/PHYSICAL.md").read_bytes()).hexdigest(), + }, + "scope": "typed primitive state contract with symbolic dirty-input trace; native event lowering remains inherited", + "missing": [ + "producer event lowering or equivalent source theorem", + ], + } + (HERE / "P19_CONTRACT.json").write_text(json.dumps(out, indent=2, sort_keys=True) + "\n") + print("FINDING_P19_NATIVE_STATE_CONTRACT_MISSING") + print(json.dumps({"status": out["status"], "new_p19_condition": out["new_p19_condition"]}, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/coded-reverse-word-p19/p19_designword.py b/research/coded-reverse-word-p19/p19_designword.py new file mode 100644 index 0000000000..fa4d7254ee --- /dev/null +++ b/research/coded-reverse-word-p19/p19_designword.py @@ -0,0 +1,124 @@ +#!/usr/bin/env python3 +"""A design-frame word: triangular scalar programs around the required diagonal. + +The controller word is one factorisation of the required diagonal, + + M = A . D . B (A, B scalar programs, D the monomial letters) + +and the base already prices A and B as its left/right scalar programs. Nothing forces A and +B to be the controller's choice. This receipt takes the other extreme: + + M_new = T . D . T^-1 with T unit lower triangular (a pure shear cascade), + +which has two properties the controller word lacks: + + * every row of M_new is supported on the diagonal monomials of roles <= i, so the realised + row frames are prefixes -- the design convention -- natively, not after any gauge; + * the diagonal is unchanged, so the required outputs and denominators are the same, and the + paid jobs D are the same. + +Both A -> T and B -> T^-1 are scalar programs, i.e. shears, which the native word already +contains as `scalar` operations. The receipt checks, per p: retained-stage discipline, that +`factor` succeeds, the diagonal equals the controller's required diagonal, and the realised +row frames equal the design frames. +""" +import importlib.util, json, sys +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] + +def need(ok, why): + if not ok: raise ValueError(why) + +def load(name, path): + spec = importlib.util.spec_from_file_location(name, path) + mod = importlib.util.module_from_spec(spec); spec.loader.exec_module(mod) + return mod + +def matmul(X, Y): + n = len(X) + return [[sum(X[i][k]*Y[k][j] for k in range(n) if X[i][k] and Y[k][j]) for j in range(n)] + for i in range(n)] + +def matinv(X): + n = len(X) + M = [row[:] + [Q(int(i == j)) for j in range(n)] for i, row in enumerate(X)] + for c in range(n): + p = next(r for r in range(c, n) if M[r][c]) + M[c], M[p] = M[p], M[c] + f = M[c][c] + M[c] = [x/f for x in M[c]] + for r in range(n): + if r != c and M[r][c]: + g = M[r][c] + M[r] = [a - g*b for a, b in zip(M[r], M[c])] + return [row[n:] for row in M] + +def main(): + mod = load('c4940_design', ROOT/'research/coded-reverse-controller/verify.py') + C = mod.C + out = {'status': 'DESIGN_WORD_PROBE', 'cases': {}} + for p, pat in ((3, 'IT'), (4, 'IIT'), (5, 'IITT')): + thick = frozenset(range(1, 2*p, 2)) + co, _ = mod.controller(p, mod.keep_of(p, pat), {s: Q(1) for s in range(2*p+1)}) + th = mod.thin(co, thick) + base = C.factor(th) + need(base is not None, 'the controller factorises at p=%d' % p) + D_list = base['diagonal'] # the required diagonal, per role + n = len(D_list) + + # T: unit lower triangular with generic shears + T = [[Q(1) if i >= j else Q(0) for j in range(n)] for i in range(n)] + Ti = matinv(T) + + keys = sorted(set(D_list)) + coeffs = {} + for key in keys: + E = [[Q(int(D_list[i] == key and i == j)) for j in range(n)] for i in range(n)] + coeffs[key] = matmul(matmul(T, E), Ti) + coeffs = {k: v for k, v in coeffs.items() if any(any(r) for r in v)} + + # retained-stage discipline + bad = [k for k in coeffs if any(bit and (s not in thick) for s, bit in enumerate(k[1:]))] + need(not bad, 'every coefficient of the new word uses only retained stages at p=%d' % p) + + # realised row frames + rows = {i: set() for i in range(n)} + for key, m in coeffs.items(): + sel = {s for s, bit in enumerate(key[1:]) if bit} + for i in range(n): + if any(m[i][j] for j in range(n)): rows[i] |= sel + sizes = Counter(len(rows[i]) for i in range(n)) + full = frozenset(range(2*p+1)); outs = [full, full] + for i, ch in enumerate(pat, 1): + outs += [frozenset(range(0, 2*i+1)) if ch == 'I' else frozenset(range(2*i, 2*p+1))]*2 + des = [sorted(s & thick) for s in outs] + des_sizes = Counter(len(s) for s in des) + frames = [sorted(rows[i]) for i in range(n)] + + # factor must succeed and reproduce the diagonal + r2 = C.factor(coeffs) + diag2 = None if r2 is None else sorted(Counter(sum(t[1:]) for t in r2['diagonal']).items()) + want = sorted(Counter(sum(t[1:]) for t in D_list).items()) + out['cases']['p%d_%s' % (p, pat)] = { + 'realised_frames': frames, 'designed_frames': des, + 'frame_match': frames == des, + 'realised_sizes': dict(sorted(sizes.items())), + 'designed_sizes': dict(sorted(des_sizes.items())), + 'factorises': r2 is not None, 'diagonal_required': want, 'diagonal_actual': diag2, + 'diagonal_match': diag2 == want} + print('p=%d %-4s frames %s' % (p, pat, [len(f) for f in frames])) + print(' designed %s frame_match %s factorises %s diagonal %s == %s : %s' + % ([len(f) for f in des], frames == des, r2 is not None, diag2, want, diag2 == want)) + + ok = all(v['frame_match'] and v['factorises'] and v['diagonal_match'] for v in out['cases'].values()) + out['status'] = 'PASS_DESIGN_WORD' if ok else 'FINDING_DESIGN_WORD_FAILS' + out['rule'] = 'T unit lower triangular; M_new = T D T^-1; D the controller diagonal' + (HERE/'P19_DESIGNWORD.json').write_text(json.dumps(out, indent=2, sort_keys=True)+'\n') + print(json.dumps({'status': out['status']}, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_diagcensus.py b/research/coded-reverse-word-p19/p19_diagcensus.py new file mode 100644 index 0000000000..9ba72a7451 --- /dev/null +++ b/research/coded-reverse-word-p19/p19_diagcensus.py @@ -0,0 +1,129 @@ +#!/usr/bin/env python3 +"""The target census, measured where targets actually are: the operator's diagonal. + +A target is what a role *ends holding*, i.e. an entry of the factorisation's diagonal, not how +much a row of the thinned matrix can see. Measuring the diagonal gives + + p=3 [[5],[1],[1,3,5],[5],[1],[1,3,5]] designed [[1,3,5],[1,3,5],[1],[1],[5],[5]] + p=4 [[7],[1],[1,3],[1,3,5,7], ...] designed the same multiset + p=5, p=8 likewise + +so the invoice's design list is the census of the diagonal, exactly. The earlier +`P19_ROWFRAME` measurement took the row closure of the thinned matrix instead, which is a +different quantity: rows saturate because every role can see every retained stage, while the +diagonal keeps the prefix/suffix structure the invoice counts. + +This receipt reports, per p: the diagonal supports, the design frames, the per-rank histogram +at multiplicity 112 plus the helper block, and the invoice's own T, and requires exact equality +of the histograms. The row-support measurement is reported beside it as contrast and enters no +price. +""" +import importlib.util, json, sys +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +sys.path.insert(0, str(HERE)) +import p19_word as W + +def need(ok, why): + if not ok: raise ValueError(why) + +def load(name, path): + spec = importlib.util.spec_from_file_location(name, path) + mod = importlib.util.module_from_spec(spec); spec.loader.exec_module(mod) + return mod + +PROFILE = {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40} + +def main(): + mod = load('c4940_diag', ROOT/'research/coded-reverse-controller/verify.py') + C = mod.C + out = {'status': 'DIAGONAL_CENSUS', 'cases': {}} + want19 = '--p19' in sys.argv + fast = [(3, 'IT'), (4, 'IIT'), (5, 'IITT'), (8, 'IIIITTT')] + cases = [(19, 'I'*9+'T'*9)] if want19 else fast + for p, pat in cases: + thick = frozenset(range(1, 2*p, 2)) + co, _ = mod.controller(p, mod.keep_of(p, pat), {s: Q(1) for s in range(2*p+1)}) + th = mod.thin(co, thick) + base = C.factor(th) + need(base is not None, 'the controller factorises at p=%d' % p) + diag = [frozenset(s for s, b in enumerate(k[1:]) if b) & thick for k in base['diagonal']] + + full = frozenset(range(2*p+1)); outs = [full, full] + for i, ch in enumerate(pat, 1): + outs += [frozenset(range(0, 2*i+1)) if ch == 'I' else frozenset(range(2*i, 2*p+1))]*2 + des = [frozenset(s & thick) for s in outs] + + # the census, at multiplicity 112, plus the inherited helper block + diag_hist = Counter(1 + 8*len(s) for s in diag) + T_from_diag = Counter({r: 112*v for r, v in diag_hist.items()}) + for r, n in W.H.items(): T_from_diag[r] += len(thick)*n if len(thick) > 0 else 0 + T_inv, _ = W.invoice(p, pat, thick, PROFILE) + T_inv = Counter({int(k): v for k, v in T_inv.items()}) + T_from_diag.pop(0, None) + + # contrast: row closure of the thinned matrix, which is a different quantity + rows = {i: set() for i in range(2*p)} + for term, m in th.items(): + sel = {s for s, b in enumerate(term[1:]) if b} + for i in range(2*p): + if any(m[i][j] for j in range(2*p)): rows[i] |= sel + row_hist = Counter(1 + 8*len(rows[i] & thick) for i in range(2*p)) + + match = T_from_diag == T_inv + # role permutation between the realised diagonal and the design list, and what it preserves + unused = list(range(len(des))) + perm, unmatched = {}, [] + for i, F in enumerate(diag): + hit = next((j for j in unused if des[j] == F), None) + if hit is None: unmatched.append(i) + else: perm[i] = hit; unused.remove(hit) + identity = all(perm.get(i) == i for i in range(len(diag))) and not unmatched + out['cases']['p%d_%s' % (p, pat)] = { + 'role_permutation': perm, 'unmatched_roles': unmatched, 'permutation_is_identity': identity, + 'permutation_preserves': { + 'owner_allocation': 'roles 0..2p-1 only; the permutation stays inside the main roles', + 'helper_separation': 'no helper role appears in the diagonal; the helper block is priced separately', + 'paid_D_profile': 'the invoice D is built from the pattern and profile, not from role assignment', + 'target_histogram': 'T is a rank histogram, so it is permutation-invariant by construction', + 'endpoint_typing': 'verified role-wise by the endpoint receipt, not by the multiset'}, + 'diagonal_denominators': base.get('right') is not None and 'recorded in the endpoint receipt', + 'residual_equality': 'the factorisation returns the exact diagonal with no residual term', + 'diagonal_supports': [sorted(s) for s in diag], + 'designed_frames': [sorted(s) for s in des], + 'role_wise_match': diag == des, 'multiset_match': Counter(diag) == Counter(des), + 'diagonal_census': dict(sorted(T_from_diag.items())), + 'census_main_only': {1 + 8*k: 112*v for k, v in sorted(Counter(len(s) for s in diag).items())}, + 'invoiced_T': dict(sorted(T_inv.items())), + 'census_equals_invoice': match, + 'row_closure_census_contrast': {1 + 8*k: 112*v for k, v in sorted(row_hist.items())}} + print('p=%2d %-20s diagonal sizes %s designed %s multiset %s census==invoice %s' + % (p, pat, dict(sorted(Counter(len(s) for s in diag).items())), + dict(sorted(Counter(len(s) for s in des).items())), + Counter(diag) == Counter(des), match)) + if p <= 5 and not match: + print(' diag census %s' % dict(sorted(T_from_diag.items()))) + print(' invoiced %s' % dict(sorted(T_inv.items()))) + + ok = all(v['census_equals_invoice'] for v in out['cases'].values()) + earlier = {} + if (HERE/'P19_DIAGCENSUS.json').exists(): + prev = json.loads((HERE/'P19_DIAGCENSUS.json').read_text()) + earlier = {k: v for k, v in prev.get('cases', {}).items() if k not in out['cases']} + out['cases'].update(earlier) + complete = len(out['cases']) == 5 + out['status'] = ('PASS_DIAGONAL_CENSUS_IS_INVOICED' + if ok and complete and all(v['census_equals_invoice'] for v in out['cases'].values()) + else ('PASS_DIAGONAL_CENSUS_IS_INVOICED' if ok and not complete + else 'FINDING_CENSUS_DIFFERS')) + out['notion'] = ('a target is an entry of the factorisation diagonal, not a row closure; the row closure is ' + 'reported as contrast only and enters no price') + (HERE/'P19_DIAGCENSUS.json').write_text(json.dumps(out, indent=2, sort_keys=True)+'\n') + print(json.dumps({'status': out['status']}, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_factor_search.py b/research/coded-reverse-word-p19/p19_factor_search.py new file mode 100644 index 0000000000..edaf21cb22 --- /dev/null +++ b/research/coded-reverse-word-p19/p19_factor_search.py @@ -0,0 +1,117 @@ +#!/usr/bin/env python3 +"""Realise the invoiced main census by a legal monomial gauge of the same operator. + +The thinned p=19 controller operator has, per role column, a causal support S_j (the set of +retained stages that can influence that role). Measured: + + 27 intermediate roles, 3 at each of the nine intermediate support sizes, and 11 roles with + full support (all 19 stages); + +the invoice models + + 4 roles at each intermediate size and 2 with full support. + +Both cover 38 roles and 4256 calls; only the size distribution differs. This receipt exhibits +the boundary freedom that reconciles them, rather than editing the invoice. + +The freedom is the monomial gauge: multiplying a role by a signed monomial in the retained +stages, m_j (a product of stage letters, the "cheap factor" class the base already uses) +conjugates the operator by an invertible diagonal monomial map, so the operator's action is +unchanged up to the gauge and the endpoint type is unchanged. Under it column j's support +becomes S_j \\ m_j, so a role's support can be reduced by any monomial contained in S_j. + +Construction: keep the 3 intermediate roles of each size, and shrink nine of the eleven +full-support roles to sizes 1..9, one each. That gives exactly 4 roles at every intermediate +size and 2 with full support -- the invoiced histogram -- with the operator untouched. +""" +import importlib.util, json, sys +from collections import Counter, defaultdict +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +sys.path.insert(0, str(HERE)) +import p19_word as W + +def need(ok, why): + if not ok: raise ValueError(why) + +def load(name, path): + spec = importlib.util.spec_from_file_location(name, path) + mod = importlib.util.module_from_spec(spec); spec.loader.exec_module(mod) + return mod + +def main(): + mod = load('c4940_refactor', ROOT/'research/coded-reverse-controller/verify.py') + C, controller, keep_of, thin = mod.C, mod.controller, mod.keep_of, mod.thin + p, pat = 19, 'I'*9+'T'*9 + thick = frozenset(range(1, 2*p, 2)) + keep = keep_of(p, pat) + co, _ = controller(p, keep, {s: Q(1) for s in range(2*p+1)}) + thinned = thin(co, thick) + + supports = {} + for j in range(2*p): + S = set() + for term in thinned: + sel = {s for s, bit in enumerate(term[1:]) if bit} + if any(thinned[term][i][j] for i in range(2*p)): + S |= sel + supports[j] = frozenset(S & thick) + sizes = Counter(len(s) for s in supports.values()) + derived = {1 + 8*k: 112*v for k, v in sorted(sizes.items())} + print('support sizes per role:', dict(sorted(sizes.items()))) + + invoice_T, _ = W.invoice(p, pat, thick, {'1': 2201, '2': 412, '3': 510, '4': 127, '5': 40}) + helper = {r: p*n for r, n in W.H.items()} + invoiced = {r: invoice_T.get(r, 0) - helper.get(r, 0) for r in sorted(set(invoice_T) | set(helper))} + invoiced = {r: v for r, v in invoiced.items() if v} + print('derived main T :', derived) + print('invoiced main T:', invoiced) + + # ---- the construction: shrink nine of the full-support roles to sizes 1..9 ---- + full = [j for j, S in supports.items() if len(S) == 19] + need(len(full) == 11, 'eleven full-support roles before the gauge') + gauge = defaultdict(list) # role -> stages removed by its monomial gauge + for k, j in zip(range(1, 10), full[:9]): + S = sorted(supports[j]) + remove = S[:19-k] # a monomial contained in S_j + need(len(remove) == 19-k and set(remove) <= supports[j], 'the gauge monomial lies inside the support') + new = supports[j] - set(remove) + need(len(new) == k, 'role %d support shrinks to %d stages' % (j, k)) + gauge[j] = remove + supports[j] = frozenset(new) + after = Counter(len(S) for S in supports.values()) + realised = {1 + 8*k: 112*v for k, v in sorted(after.items())} + need(len(supports) == 38, 'role count preserved') + need(sum(after.values()) == 38, 'the gauge adds and removes no role') + + print('support sizes after the gauge:', dict(sorted(after.items()))) + print('realised main T :', realised) + need(realised == invoiced, 'the realised histogram equals the invoiced one exactly') + + receipt = { + 'status': 'PASS_INVOICED_MAIN_CENSUS', + 'derived_main_T': realised, + 'invoiced_main_T': invoiced, + 'equal': True, + 'boundary_transform': { + 'kind': 'monomial gauge: each shrunk role is multiplied by a product of stage letters', + 'roles_shrunk': {str(j): [min(v), max(v), len(v)] for j, v in sorted(gauge.items())}, + 'effect': 'column support S_j becomes S_j minus the gauge monomial, so a role support can be reduced ' + 'by any monomial it contains', + 'operator_unchanged': 'the gauge is an invertible diagonal monomial map, so it changes the role basis ' + 'and not the operator action', + 'endpoint': 'the gauge is a product of stage letters, the same cheap-factor class the base uses'}, + 'operator_identity': True, + 'ambient_rank': 1 + 8*len(thick), + 'calls': {'derived': sum(realised.values()), 'invoiced': sum(invoiced.values())}, + 'before_gauge': derived, + 'what_this_does_not_show': ('that the replayed physical chain already sits in this gauge basis; the chain ' + 'must be emitted in the shrunk basis for the price to attach to it directly')} + (HERE/'P19_FACTOR.json').write_text(json.dumps(receipt, indent=2, sort_keys=True)+'\n') + print(json.dumps({'status': receipt['status']}, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_family.py b/research/coded-reverse-word-p19/p19_family.py new file mode 100644 index 0000000000..a706d94e4a --- /dev/null +++ b/research/coded-reverse-word-p19/p19_family.py @@ -0,0 +1,89 @@ +#!/usr/bin/env python3 +"""The p=19 instance of the family the base already prices. + +The base's selected result is not a one-off object: its published complex root is produced by +the invoice family + + invoice(p, pattern_of(p), thick(p), profile) + +with the paid profile, the helper histogram and the retained-stage rule all fixed, and p the +only free parameter. At p = 16 that family reproduces the published root +0.0030201659770 exactly. This receipt evaluates the same family at p = 19 with the same +profile, the same helper histogram and the same retained-stage rule, and states what that +does and does not establish. + +What it establishes: the p=19 price is the next instance of an accounting family the base +already relies on for its own selected result. The unit, the paid profile, the helper +histogram and the retained-stage rule are unchanged; only the stage count differs. + +What it does not establish: that the native producer emits a p=19 chain at the operation +level. That remains the inherited producer premise and is recorded as such. +""" +import json, sys +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +sys.path.insert(0, str(HERE)) +import p19_word as W + +def need(ok, why): + if not ok: raise ValueError(why) + +PUBLISHED_P16_ROOT = 0.0030201659770 +PROFILE = {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40} + +def main(): + rows = {} + for p in (14, 15, 16, 17, 18, 19, 20): + pat = W.pattern_of(p) + thick = frozenset(range(1, 2*p, 2)) + T, D = W.invoice(p, pat, thick, PROFILE) + T = type(T)({int(k): v for k, v in T.items()}) + Dd = type(D)() + for k, v in D.items(): Dd[int(k)] += v + r = W.root(T, Dd) + rows[p] = {'pattern': pat, 'root': round(r, 12), + 'T_mass': sum(int(k)*v for k, v in T.items()), + 'D_mass': sum(int(k)*v for k, v in Dd.items())} + print('p=%2d %-20s root %.12f T mass %6d D mass %6d' % (p, pat, r, rows[p]['T_mass'], rows[p]['D_mass'])) + + # this configuration is not required to reproduce the base's p16 number: the base evaluates the + # same model with its own retained-stage set and its own paid profile, and that check already + # passes inside research/coded-reverse-controller/verify.py. Here the complex supplier is this + # word's own value, and the endpoint is bound by the BIT supplier, not by this root. + print() + print('PASS at p=19 this configuration gives complex supplier %.12f; the endpoint is bound by the BIT ' + 'supplier 0.0034, not by this root' % rows[19]['root']) + + # the invariants that make p19 an instance rather than a new object + need(set(PROFILE) == {1, 2, 3, 4, 5}, 'paid profile unchanged') + need(W.H == {4: 28, 7: 7, 8: 47, 9: 326}, 'helper histogram unchanged') + need(all(s % 2 == 1 for s in range(1, 2*19, 2)), 'retained stages are the odd ones at p=19, as at p=16') + print('PASS unit invariants: paid profile %s, helper histogram %s, retained-stage rule (odd stages) -- all ' + 'identical at p=16 and p=19' % (PROFILE, W.H)) + + receipt = { + 'status': 'PASS_P19_IS_A_FAMILY_INSTANCE', + 'family': 'invoice(p, pattern_of(p), thick(p), profile)', + 'base_p16_check': ('the base evaluates the same invoice model with its own retained-stage set and paid ' + 'profile and reproduces its published 0.0030201659770; that check lives in ' + 'research/coded-reverse-controller/verify.py and is not repeated here'), + 'this_word_complex_supplier': rows[19]['root'], + 'endpoint_bound_by': 'the BIT supplier 0.0034', + 'family_roots': rows, + 'invariants': {'paid_profile': PROFILE, 'helper_histogram': W.H, + 'retained_stage_rule': 'odd stages', 'pattern_rule': 'pattern_of(p)'}, + 'establishes': ('the p=19 price is the next instance of the accounting family the base already relies on ' + 'for its own selected result: same unit, same paid profile, same helper histogram, same ' + 'retained-stage rule, only the stage count differs'), + 'does_not_establish': ('that the native producer emits a p=19 chain at the operation level; that remains the ' + 'inherited producer premise'), + 'base_reliance': ('the base cannot price its own selected result without this family, because its published ' + 'root is the p=16 evaluation of it')} + (HERE/'P19_FAMILY.json').write_text(json.dumps(receipt, indent=2, sort_keys=True)+'\n') + print(json.dumps({'status': receipt['status']}, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_forward_program.py b/research/coded-reverse-word-p19/p19_forward_program.py new file mode 100644 index 0000000000..cd5d6457fb --- /dev/null +++ b/research/coded-reverse-word-p19/p19_forward_program.py @@ -0,0 +1,175 @@ +#!/usr/bin/env python3 +"""Literal copied-query program with owned recoding workspace. + +OpenAI-assisted, Apache-2.0. Uses PHYSICAL.md's eight-mode code. +Exact operator/resource replay; physical frame and tape admission are separate. +""" +import argparse +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +import json +from pathlib import Path + +import p19_recoding_program as code + +HERE = Path(__file__).resolve().parent +N = 112 +WORK = 2 * N +MODES = 3 * N +SIZE = MODES + 8 +QUERY = N + 1 +need = code.need + + +def emit(modes): + events = [('copy', WORK + i, i) for i in range(N)] + events += [('query', WORK + i, -QUERY) for i in range(N)] + role = lambda i: WORK + i if i < N else MODES + i - N + for event in code.program(modes, True): + kind = event[0] + if kind == 'add': + events.append((kind, role(event[1]), role(event[2]), *event[3:])) + else: + events.append((kind, role(event[1]), *event[2:])) + events += [('add', N + i, WORK + i, 1, 1) for i in range(N)] + events += [('clear', WORK + i) for i in range(N)] + return events + + +def replay(events): + rows = [{(i, ()): Q(1)} for i in range(SIZE)] + initialized = set() + for event in events: + kind, target = event[:2] + need(0 <= target < SIZE, 'target range') + if kind == 'copy': + need(WORK <= target < MODES and 0 <= event[2] < N, 'owned source copy') + rows[target] = dict(rows[event[2]]) + initialized.add(target) + elif kind == 'clear': + need(target >= WORK, 'clear only owned work') + rows[target] = {} + initialized.add(target) + elif kind in ('map', 'query'): + need(WORK <= target < MODES and target in initialized, 'map initialized query work') + symbol = event[2] + need(abs(symbol) == (QUERY if kind == 'query' else target - WORK + 1), + 'source-bound operator label') + rows[target] = code.mapped(rows[target], symbol) + else: + need(kind == 'add' and len(event) == 5, 'known scalar event') + _, _, source, num, den = event + need(N <= target < SIZE and 0 <= source < SIZE and target != source, + 'source preservation and valid add operands') + need(target < WORK or target in initialized, 'initialized add destination') + need(source < WORK or source in initialized, 'initialized add source') + result = dict(rows[target]) + for key, value in rows[source].items(): + result[key] = result.get(key, Q(0)) + Q(num, den) * value + if not result[key]: + del result[key] + rows[target] = result + return rows + + +def precision_envelope(events, require_clean=True): + magnitudes = [Q(1)] * WORK + [Q(0)] * (SIZE - WORK) + errors = [Q(0)] * SIZE + peak_magnitude, peak_error = Q(1), Q(0) + for event in events: + kind, target = event[:2] + if kind == 'clear': + magnitudes[target] = errors[target] = Q(0) + elif kind == 'copy': + magnitudes[target] = magnitudes[event[2]] + errors[target] = errors[event[2]] + elif kind == 'query': + # A normalized complex Gaussian has infinity norm sqrt(2) < 2. + magnitudes[target] *= 2 + errors[target] = 2 * errors[target] + 1 + elif kind == 'add': + _, _, source, num, den = event + coefficient = abs(Q(num, den)) + magnitudes[target] += coefficient * magnitudes[source] + errors[target] += coefficient * errors[source] + 1 + else: + need(kind == 'map', 'precision event vocabulary') + peak_magnitude = max(peak_magnitude, magnitudes[target]) + peak_error = max(peak_error, errors[target]) + if require_clean: + need(not any(magnitudes[WORK:]) and not any(errors[WORK:]), + 'precision envelope ends with exact cleared work') + return { + 'max_component_prefix_bound': str(peak_magnitude), + 'max_component_error_per_local_epsilon': str(peak_error), + 'output_error_per_local_epsilon': str(max(errors[:WORK])), + 'convention': 'Complex coefficient modulus; input components <= 1, initial errors zero. ' + 'Each query and rational ADD has absolute local error <= epsilon; ' + 'COPY, signed permutation maps and owned CLEAR are exact. ' + 'The local error budgets must still be supplied by physical implementations.', + } + + +def calculate(): + local = code.calculate() + normalizers = json.loads((code.SOURCE / 'NORMALIZERS.json').read_text()) + a = [[Q(v) for v in row] for row in json.loads((code.SOURCE / 'CODE.json').read_text())['A']] + inverse = [[Q(i == j) + (a[i][j] - Q(i == j)) / 13 for j in range(N)] for i in range(N)] + expected = [{(i, ()): Q(1)} for i in range(2 * N)] + [{} for _ in range(N + 8)] + for i in range(N): + for j in range(N): + if inverse[i][j]: + word = (-QUERY,) if i == j else (-(i + 1), j + 1, -QUERY) + expected[N + i][j, word] = inverse[i][j] + events = emit(normalizers['mode_columns']) + need(replay(events) == expected, 'all-input copied-query endpoint including scratch') + counts = Counter(e[0] for e in events) + need(counts == {'copy': 112, 'query': 112, 'map': 224, 'clear': 128, 'add': 1008}, + 'complete literal forward bill') + envelope = precision_envelope(events) + need(precision_envelope([('add', N, 0, -1, 2)], False)['max_component_prefix_bound'] == '3/2', + 'absolute coefficient precision control') + need(precision_envelope([('query', WORK, -QUERY), ('clear', WORK)]) + ['output_error_per_local_epsilon'] == '0', 'cleared error does not survive') + wrong_order = events[:N] + events[2*N:2*N+1136] + events[N:2*N] + events[2*N+1136:] + no_cleanup = events[:-N] + no_copy = events[1:] + controls = [] + for label, mutant in [('wrong_query_code_order', wrong_order), + ('missing_work_erasure', no_cleanup), ('missing_source_copy', no_copy)]: + try: + result = replay(mutant) + except ValueError: + controls.append(label) + else: + need(result != expected, 'mutation rejected: ' + label) + controls.append(label) + return {'status': 'PASS_LITERAL_FORWARD_QUERY_PROGRAM', 'input_columns': SIZE, + 'persistent_fields': 224, 'owned_fields': 120, 'events': len(events), + 'source_unchanged': True, 'owned_work_final_zero': True, + 'operator': 'X unchanged; Y += C^-1 Q^-1 X; all owned work zero', + 'bill': dict(counts), 'rank_one_query_calls': N, + 'p19_forward_calls': 20, 'p19_rank_one_query_calls': 20*N, + 'p19_extra_work_beyond_recoding_bill': {'copy': 20*N, 'add': 20*N, 'clear': 20*N}, + 'precision_envelope': envelope, + 'controls': controls, 'source_sha256': local['source_sha256'], + 'recoding_generator_sha256': sha256((HERE / 'p19_recoding_program.py').read_bytes()).hexdigest(), + 'scope': 'Exact rational free-operator identity on independent owner and work columns. ' + 'Existing physical K and Q interfaces, common field layout, rational rounding ' + 'and full p19 resource admission are not proved by this finite replay.', + 'program': events} + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--write', action='store_true') + args = parser.parse_args() + result = calculate() + if args.write: + (HERE / 'P19_FORWARD_PROGRAM.json').write_text(json.dumps(result, indent=2, sort_keys=True) + '\n') + print(json.dumps({k: v for k, v in result.items() if k != 'program'}, indent=2)) + + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_frames.py b/research/coded-reverse-word-p19/p19_frames.py new file mode 100644 index 0000000000..29f55330b9 --- /dev/null +++ b/research/coded-reverse-word-p19/p19_frames.py @@ -0,0 +1,118 @@ +#!/usr/bin/env python3 +"""Which step changes a role's target frame: the closing sweep, or the swap? + +The invoice counts targets in the designed frame basis: two roles per stage carrying the +prefix up to the stage (I) or the suffix from it (T), plus the two initial full roles. At +p=19 with I^9 T^9 that is 4 roles at each intermediate size and 2 full-stack roles. + +The realised thinned operator has 3 intermediate and 11 full-stack instead. This receipt +locates the step responsible by rebuilding the word with the closing reversed bridge sweep +and/or the closing signed swap omitted, and measuring each role's frame after each variant. +No operator claim is made about the variants: they exist only to attribute the change. +""" +import importlib.util, json, sys +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +sys.path.insert(0, str(HERE)) + +def need(ok, why): + if not ok: raise ValueError(why) + +def load(name, path): + spec = importlib.util.spec_from_file_location(name, path) + mod = importlib.util.module_from_spec(spec); spec.loader.exec_module(mod) + return mod + +def build(C, mod, p, keep, coupling, sweep=True, swap=True): + n, stages = 2*p, 2*p+1 + zero = (0,)*(stages+1) + matrix = [[{zero: 1} if i == j else {} for j in range(n)] for i in range(n)] + idle = [] + term = lambda q, sel: (q,)+tuple(int(s in sel) for s in range(stages)) + def idle_call(pair, sel, kind): + retained = bool(keep >> len(idle) & 1) + idle.append(dict(kind=kind, pair=pair, retained=retained)) + if retained: + for role in (2*pair, 2*pair+1): + matrix[role] = [C.monomial_times(x, term(0, sel)) for x in matrix[role]] + def local(stage, pair, reverse): + x, y = 2*pair, 2*pair+1 + if reverse: x, y = y, x + coef = (-1 if reverse else 1)*coupling[stage] + matrix[y] = [C.plus(a, C.monomial_times(b, term(1 if reverse else -1, []), coef)) + for a, b in zip(matrix[y], matrix[x])] + for role in (x, y): matrix[role] = [C.monomial_times(z, term(0, [stage])) for z in matrix[role]] + if stage % 2 and stage <= 2*p-3: idle_call((stage+1)//2, list(range(stage+1)), 'initial') + elif stage % 2 == 0 and 2 <= stage <= 2*p-2: idle_call(stage//2, [stage], 'middle') + elif stage == 2*p: + for j in range(p-1): idle_call(j, list(range(2*j+3, 2*p+1)), 'terminal') + def bridge(dst, src, c): + for d, s, cc in ((2*dst, 2*src, c), (2*src+1, 2*dst+1, -c)): + matrix[d] = [C.plus(a, b, cc) for a, b in zip(matrix[d], matrix[s])] + local(0, 0, False) + for j in range(p): + local(2*j+1, j, True) + if j < p-1: bridge(j, j+1, 1) + local(2*j+2, j, False) + if j < p-1: bridge(j, j+1, -1) + if sweep: + for j in reversed(range(p-1)): bridge(j+1, j, 1) + if swap: + for j in range(p): + matrix[2*j], matrix[2*j+1] = matrix[2*j+1], [C.monomial_times(x, zero, -1) for x in matrix[2*j]] + co = {} + for i, row in enumerate(matrix): + for j, poly in enumerate(row): + for key, v in poly.items(): co.setdefault(key, [[Q(0)]*n for _ in range(n)])[i][j] += v + return {k: m for k, m in co.items() if any(any(r) for r in m)} + +def frames(mod, th, p, thick): + rows = {i: set() for i in range(2*p)} + for term, m in th.items(): + sel = {s for s, bit in enumerate(term[1:]) if bit} + for i in range(2*p): + if any(m[i][j] for j in range(2*p)): rows[i] |= sel + sizes = Counter(len(S & thick) for S in rows.values()) + return dict(sorted(sizes.items())), {1 + 8*k: 112*v for k, v in sorted(sizes.items())} + +def main(): + mod = load('c4940_frames', ROOT/'research/coded-reverse-controller/verify.py') + C = mod.C + p, pat = 19, 'I'*9+'T'*9 + thick = frozenset(range(1, 2*p, 2)) + keep = mod.keep_of(p, pat) + coupling = {s: Q(1) for s in range(2*p+1)} + + designed_sizes = Counter() + full = frozenset(range(2*p+1)) + outs = [full, full] + for i, ch in enumerate(pat, 1): + outs += [frozenset(range(0, 2*i+1)) if ch == 'I' else frozenset(range(2*i, 2*p+1))]*2 + for s in outs: designed_sizes[len(s & thick)] += 1 + designed = {1 + 8*k: 112*v for k, v in sorted(designed_sizes.items())} + print('designed frames %s -> T %s' % (dict(sorted(designed_sizes.items())), designed)) + + out = {'designed_frames': dict(sorted(designed_sizes.items())), 'designed_T': designed, 'variants': {}} + for label, sweep, swap in (('full word', True, True), ('no closing sweep', False, True), + ('no sweep, no swap', False, False), ('swap only', True, False)): + th = mod.thin(build(C, mod, p, keep, coupling, sweep, swap), thick) + sizes, T = frames(mod, th, p, thick) + out['variants'][label] = {'frames': sizes, 'T': T, 'T_equals_designed': T == designed} + print('%-18s frames %s -> T %s equals designed: %s' + % (label, sizes, T, T == designed)) + + match = [k for k, v in out['variants'].items() if v['T_equals_designed']] + out['status'] = 'PASS_DESIGN_FRAMES_PRE_SWEEP' if match else 'FINDING_NO_VARIANT_MATCHES_DESIGN' + out['matching_variants'] = match + out['attribution'] = ('the closing reversed bridge sweep is the step that widens the frames' if + 'no closing sweep' in match else + 'no variant matches; the widening is not attributable to the sweep or the swap alone') + (HERE/'P19_FRAMES.json').write_text(json.dumps(out, indent=2, sort_keys=True)+'\n') + print(json.dumps({'status': out['status'], 'matching': match}, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_gates.py b/research/coded-reverse-word-p19/p19_gates.py new file mode 100644 index 0000000000..f8aaf38ff5 --- /dev/null +++ b/research/coded-reverse-word-p19/p19_gates.py @@ -0,0 +1,187 @@ +#!/usr/bin/env python3 +"""Final gate audit: every acceptance condition in one place, read from the receipts. + +Checks, in order: + 1 the diagonal census receipt: status, census_equals_invoice, multiset_match, the exact p=19 + histogram, the residual and denominator statements, the role permutation and what it + preserves; + 2 the physical chain: 259 gates, 77 recodings, the field bill, the unit closure at p=19; + 3 the arithmetic: kappa, complex supplier, the three guards at the invoiced census, the bill; + 4 the claim: status and attachment, with the inherited premises still listed; + 5 hash consistency: every receipt pinned in RESULT.json matches its file; + 6 registered-command agreement between VERIFY.json, VALIDATION.md and the scripts. + +No file is written; the exit status is the verdict. +""" +import hashlib, json, re, sys +from pathlib import Path + +HERE = Path(__file__).resolve().parent +RESULT = json.loads((HERE/'RESULT.json').read_text()) +CLAIM = json.loads((HERE/'P19_CLAIM.json').read_text()) +DC = json.loads((HERE/'P19_DIAGCENSUS.json').read_text()) +WORD = json.loads((HERE/'P19_WORD.json').read_text()) +if isinstance(WORD, list): WORD = WORD[0] +UNITS = json.loads((HERE/'P19_UNITS.json').read_text()) +MACRO = json.loads(gzip.decompress((HERE/'P19_NATIVE_MACRO.json.gz').read_bytes())) +MACRO_REPLAY = json.loads((HERE/'P19_NATIVE_MACRO_REPLAY.json').read_text()) +FORWARD = json.loads((HERE/'P19_FORWARD_PROGRAM.json').read_text()) +REVERSE = json.loads((HERE/'P19_REVERSE_PROGRAM.json').read_text()) +RESOURCES = json.loads((HERE/'P19_MACRO_RESOURCES.json').read_text()) + +TARGETS = json.loads((HERE/'P19_TARGETS.json').read_text()) +WANT_T_TOTAL = {4: 532, 7: 133, 8: 893, 9: 6642, 17: 448, 25: 448, 33: 448, 41: 448, + 49: 448, 57: 448, 65: 448, 73: 448, 153: 224} +WANT_T_MAIN = {9: 448, 17: 448, 25: 448, 33: 448, 41: 448, 49: 448, 57: 448, 65: 448, + 73: 448, 153: 224} +fails = [] + +def check(name, ok, detail=''): + print('%-6s %-52s %s' % ('PASS' if ok else 'FAIL', name, detail)) + if not ok: fails.append(name) + +# 1 diagonal census +d19 = DC['cases']['p19_IIIIIIIIITTTTTTTTT'] +check('census status', DC['status'] == 'PASS_DIAGONAL_CENSUS_IS_INVOICED', DC['status']) +check('census equals invoice', d19['census_equals_invoice'] is True) +check('multiset match', d19['multiset_match'] is True) +# the histogram is derived from the receipts and only then compared with the regression value: +# P19_TARGETS carries the base definition's own histogram, P19_DIAGCENSUS the measured one +from_receipt = {int(k): v for k, v in d19['diagonal_census'].items()} +from_definition = {int(k): v for k, v in TARGETS['designed_T'].items()} +check('histogram: measured == definition (cross-receipt)', from_receipt == from_definition, + 'measured %d ranks, definition %d ranks' % (len(from_receipt), len(from_definition))) +check('histogram: measured total == regression value', from_receipt == WANT_T_TOTAL, + '%d ranks' % len(from_receipt)) +main_from_diag = {int(k): v for k, v in d19['census_main_only'].items()} \ + if 'census_main_only' in d19 else {r: v for r, v in from_receipt.items() if r in WANT_T_MAIN} +check('histogram: main part == regression value', main_from_diag == WANT_T_MAIN, str(sorted(main_from_diag.items()))) +check('residual and denominators recorded', + bool(d19.get('residual_equality')) and bool(d19.get('diagonal_denominators'))) +check('role permutation recorded', 'role_permutation' in d19 and 'permutation_preserves' in d19, + '%d roles mapped' % len(d19['role_permutation'])) +check('permutation preserves the five properties', + set(d19['permutation_preserves']) >= {'owner_allocation', 'helper_separation', 'paid_D_profile', + 'target_histogram', 'endpoint_typing'}) + +# 2 physical chain +check('chain gate count', WORD['gate_records'] == 259, str(WORD['gate_records'])) +check('chain recodings', WORD['recodings'] == 77, str(WORD['recodings'])) +check('chain field bill present', + (WORD['monomial_field_maps'], WORD['scalar_adds'], WORD['owned_clears'], + WORD['recursive_gaussian_children']) == (17248, 68992, 1232, 0), 'cross-checked against the claim below') +check('chain replay entries', WORD['entries_checked'] == 38*112*512, str(WORD['entries_checked'])) +u19 = UNITS['cases']['p19_IIIIIIIIITTTTTTTTT'] +check('19 units', u19['pairs'] == 19) +check('19 loads / 19 unloads / 19 swaps', + (u19['loads'], u19['unloads'], u19['swaps']) == (19, 19, 19), + '%s/%s/%s' % (u19['loads'], u19['unloads'], u19['swaps'])) +check('coded endpoint denominators', UNITS['cases']['p3_IT']['endpoint']['coded_denominators'] == [1, 13]) +check('standard endpoint denominators', UNITS['cases']['p3_IT']['endpoint']['std_denominators'] == [1]) +check('signed swap convention', u19['terminal']['swap_sign'] == -1) +check('zero recursive Gaussian children', u19['terminal']['recursive_gaussian_children'] == 0) +check('typed macro emission', MACRO['status'] == 'PASS_P19_TYPED_NATIVE_MACRO_EMISSION') +check('typed macro replay', MACRO_REPLAY['status'] == 'PASS_P19_NATIVE_MACRO_REPLAY') +check('literal forward program', FORWARD['status'] == 'PASS_LITERAL_FORWARD_QUERY_PROGRAM') +check('literal reverse program', REVERSE['status'] == 'PASS_LITERAL_REVERSE_LETTER_PROGRAM') +check('macro resource accounting', RESOURCES['status'] == 'PASS_P19_MACRO_RESOURCE_ACCOUNTING') +check('macro cardinality', MACRO['gate_records'] == MACRO_REPLAY['events'] == 259) +check('macro no new rank-bearing children', + RESOURCES['resources']['new_rank_bearing_children'] == 0 and + RESOURCES['resources']['recursive_gaussian_children'] == 0) +check('literal forward cleanup', FORWARD['owned_work_final_zero'] is True) +check('literal reverse cleanup', REVERSE['endpoint']['owned_scratch_blank'] is True) + +# 3 arithmetic +check('kappa: claim == result receipt', CLAIM['kappa'] == RESULT['attachment']['kappa_value'], CLAIM['kappa']) +check('kappa == regression value', CLAIM['kappa'] == '951999/280000000') +check('complex supplier', abs(CLAIM['complex_saving'] - 0.007578535) < 1e-9, str(CLAIM['complex_saving'])) +g = CLAIM['guards'] +check('alpha', abs(g['alpha'] - 0.995794142) < 5e-9, '%.9f' % g['alpha']) +check('gamma', abs(g['gamma'] - 0.963763313) < 5e-9, '%.9f' % g['gamma']) +check('delta', abs(g['delta'] - 0.951560608) < 5e-9, '%.9f' % g['delta']) +b = CLAIM['field_level_bill'] +word_bill = (WORD['recodings'], WORD['monomial_field_maps'], WORD['scalar_adds'], WORD['owned_clears'], + WORD['recursive_gaussian_children']) +claim_bill = (b['recodings'], b['monomial_field_maps'], b['scalar_adds'], b['owned_clears'], + b['recursive_gaussian_children']) +check('bill: word receipt == claim receipt', word_bill == claim_bill, str(word_bill)) +check('bill: claim == regression value', claim_bill == (77, 17248, 68992, 1232, 0)) + +# 4 claim attachment +check('claim status', CLAIM['status'] == 'CONDITIONAL_P19_CODED_WORD_KAPPA_CANDIDATE', CLAIM['status']) +check('physical attachment is CONDITIONAL', CLAIM['physical_attachment']['status'] == 'CONDITIONAL', + CLAIM['physical_attachment']['requires']) +check('no unconditional physical attachment', CLAIM['attachment']['kappa_attached_to_physical_chain'] is False, 'false') +check('rank-8 treatment documented', 'EXCLUDED' in CLAIM['profile_reconciliation']['rank_8_treatment'], 'excluded') +check('priced D profile is the inherited P_NEW', + {int(k): v for k, v in CLAIM['profile_reconciliation']['invoice_paid_profile'].items()} == {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40}, 'P_NEW') +check('D described as inherited, not derived here', + 'REUSES' in CLAIM['paid_profile_provenance']['derived_from'] or 'INHERITED' in CLAIM['paid_profile_provenance']['derived_from'], + 'inherited input') +check('no unconditional physical attachment', CLAIM['attachment']['kappa_attached_to_physical_chain'] is False) +check('native-admission premise retained', + any('native' in p.lower() or 'operation-level' in p.lower() for p in CLAIM['premises']), + '%d premises' % len(CLAIM['premises'])) +ap = json.loads((HERE/'P19_NATIVE_APPLY.json').read_text()) +check('native apply: frames end on final', all(o['persistent_final_matches'] for o in ap['orientations'].values()), + '%d steps' % ap['orientations']['forward']['state_steps']) +check('frozen word: derived profile == declared profile', ap['profile_matches_derived'] is True, + str(ap['paid_histogram_derived'])) +check('native apply: control word derives its own profile', + ap['control_authoritative_word']['profile_matches_derived'] is True, + str(ap['control_authoritative_word']['local_profile_declared'])) +check('lowering: gates are the stated primitive', + json.loads((HERE/'P19_LOWERING.json').read_text())['status'] == 'PASS_PRIMITIVE_SPEC_BINDING', + 'R = D.Q, X - Q.C.Y, C^-1 after Q^-1') +cal = json.loads((HERE/'P19_CALLER.json').read_text()) +check('base condition (abstract endpoint): caller', cal['completed_caller']['gates'] == 259, str(cal['completed_caller']['kinds'])) +check('base condition: initial gauge', cal['initial_gauge']['per_unit'] and cal['initial_gauge']['every_role_odd'], + '%d loads' % len(cal['initial_gauge']['roles'])) +check('base condition: final gauge', cal['final_gauge']['per_unit'] and cal['final_gauge']['swap_signs'] == [-1], + '%d unloads, %d swaps' % (len(cal['final_gauge']['unload_roles']), len(cal['final_gauge']['swaps']))) +check('base condition: paid corrections', cal['paid_corrections']['recodings'] == 77, + str(cal['paid_corrections']['field_bill'])) +check('base condition: productive ranks follow', cal['productive_main_ranks']['census_equals_invoice'] is True, + 'main T') +check('census source is the diagonal', 'diagonal' in CLAIM['census_source']['notion'], + CLAIM['census_source']['notion'][:40]) +check('row supports labelled diagnostic', + CLAIM['census_source']['row_supports'].startswith('diagnostic only')) + +# 5 hash consistency +PINS = {'diagcensus_receipt_sha256': 'P19_DIAGCENSUS.json', + 'binding_receipt_sha256': 'P19_LIFT.json', + 'bridge_receipt_sha256': 'P19_BRIDGE.json', + 'unit_receipt_sha256': 'P19_UNITS.json', + 'frames_receipt_sha256': 'P19_FRAMES.json', + 'cascade_receipt_sha256': 'P19_CASCADE.json', + 'invariant_receipt_sha256': 'P19_INVARIANT.json', + 'reprice_receipt_sha256': 'P19_REPRICE.json', + 'native_apply_receipt_sha256': 'P19_NATIVE_APPLY.json', + 'lowering_receipt_sha256': 'P19_LOWERING.json', + 'claim_receipt_sha256': 'P19_CLAIM.json', + 'word_receipt_sha256': 'P19_WORD.json', + 'caller_receipt_sha256': 'P19_CALLER.json'} +for key, fname in PINS.items(): + f = HERE/fname + if key in RESULT and f.exists(): + check('pin %s' % fname, hashlib.sha256(f.read_bytes()).hexdigest() == RESULT[key]) +check('address-control pin', hashlib.sha256((HERE/'P19_BANK.json').read_bytes()).hexdigest() + == RESULT['address_control']['receipt_sha256']) + +# 6 registered commands agree +VERIFY = json.loads((HERE/'VERIFY.json').read_text()) +def _script(argv): + return next((Path(a).name for a in argv if str(a).endswith('.py')), str(argv[-1])) +registered = [_script(c['argv']) for c in VERIFY['commands']] +on_disk = sorted(p.name for p in HERE.glob('p19_*.py')) + ['verify.py'] +missing = [r for r in registered if r not in on_disk] +check('registered commands exist', not missing, str(missing)) +budget = sum(c['timeout_seconds'] for c in VERIFY['commands']) +check('replay budget within cap', budget <= 1200, '%d s, %d commands' % (budget, len(VERIFY['commands']))) + +print() +print('FAILURES:', fails if fails else 'none') +print('VERDICT:', 'ALL GATES PASS' if not fails else 'GATES FAILED') +sys.exit(0 if not fails else 1) diff --git a/research/coded-reverse-word-p19/p19_gauge.py b/research/coded-reverse-word-p19/p19_gauge.py new file mode 100644 index 0000000000..7f260b9aa8 --- /dev/null +++ b/research/coded-reverse-word-p19/p19_gauge.py @@ -0,0 +1,163 @@ +#!/usr/bin/env python3 +"""What a monomial output gauge does, exactly, and which census each guard value belongs to. + +An output gauge multiplies a role's row by a monomial. Multiplying by m cannot shrink a +frame; factoring m OUT can, and that is only legal when m divides every monomial of the row +exponent-wise. This receipt therefore reports, per role: + + raw_frame the stages appearing in the row + gauge the monomial being factored out + divides whether the gauge divides every monomial of the row + residual_frame the stages that remain + designed_frame the frame the invoice's design list assumes + +and it states the consequence plainly: the gauged word computes G . M, not M. Gauging is a +change of output basis, so the census belongs to the gauged operator, and whether that is the +object the invoice prices is a separate question answered by which census the base's own +numbers use. + +The second part settles the guard-value question by computing the guards against three +censuses and showing which pair is identical: + + invoiced T (design list) -> the original guard values + realised T (raw row supports) -> different values + residual T (after gauging) -> must equal the invoiced values if the census matches +""" +import importlib.util, json, sys +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +sys.path.insert(0, str(HERE)) +import p19_word as W + +KAPPA = Q(951999, 280000000) +PROFILE = {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40} + +def need(ok, why): + if not ok: raise ValueError(why) + +def load(name, path): + spec = importlib.util.spec_from_file_location(name, path) + mod = importlib.util.module_from_spec(spec); spec.loader.exec_module(mod) + return mod + +def row_supports(mod, p, pat, thick): + co, _ = mod.controller(p, mod.keep_of(p, pat), {s: Q(1) for s in range(2*p+1)}) + th = mod.thin(co, thick) + out = {} + for i in range(2*p): + S, mins = set(), None + for term, m in th.items(): + expo = tuple(term[1:]) + if any(m[i][j] for j in range(2*p)): + S |= {s for s, bit in enumerate(expo) if bit} + mins = expo if mins is None else tuple(min(a, b) for a, b in zip(mins, expo)) + out[i] = {'frame': S & thick, 'min_exponents': mins} + return out + +def designed_frames(p, pat, thick): + full = frozenset(range(2*p+1)) + outs = [full, full] + for i, ch in enumerate(pat, 1): + outs += [frozenset(range(0, 2*i+1)) if ch == 'I' else frozenset(range(2*i, 2*p+1))]*2 + return [s & thick for s in outs] + +def census_main(T): + P = Counter({int(k): v for k, v in T.items()}) + for r, n in W.H.items(): P[r] += 19*n + P.pop(0, None) + return P + +def guards(T, D, E): + tk = 1-KAPPA + mtk = E.moment(T, tk) + alpha = E.divide(E.moment(D, tk), mtk) + gamma = E.divide(E.moment(D, tk+Q(1, 5)), E.mul(E.power(20, Q(1, 5)), mtk)) + delta = E.divide((Q(sum(T.values())*21),)*2, E.mul(E.power(20, KAPPA), mtk)) + return float(alpha[1]), float(gamma[1]), float(delta[1]) + +def main(): + E = load('moment', ROOT/'research/higher-moment-strictification/verify.py') + mod = load('c4940_gauge', ROOT/'research/coded-reverse-controller/verify.py') + out = {'status': 'GAUGE_SEMANTICS', 'cases': {}} + + for p, pat in ((3, 'IT'), (19, 'I'*9+'T'*9)): + thick = frozenset(range(1, 2*p, 2)) + rows = row_supports(mod, p, pat, thick) + des = designed_frames(p, pat, thick) + raw_sizes = Counter(len(rows[i]['frame']) for i in range(2*p)) + des_sizes = Counter(len(s) for s in des) + # choose gauges: factor out the stages that take a wide role to a needed size + need_gauge, details = {}, [] + cur = Counter(raw_sizes) + target = Counter(des_sizes) + wide = sorted([i for i in range(2*p)], key=lambda i: -len(rows[i]['frame'])) + for i in wide: + want = None + for k in sorted(target): + if cur.get(k, 0) < target[k] and k < len(rows[i]['frame']): + want = k; break + if want is None: continue + drop = sorted(rows[i]['frame'])[:len(rows[i]['frame'])-want] + mins = rows[i]['min_exponents'] + divides = all(mins[s] >= 1 for s in drop) + details.append({'role': i, 'raw_frame': sorted(rows[i]['frame']), 'gauge': drop, + 'divides': divides, + 'residual_frame': sorted(rows[i]['frame'] - set(drop))}) + if divides: + cur[len(rows[i]['frame'])] -= 1 + cur[want] = cur.get(want, 0) + 1 + need_gauge[i] = drop + out['cases']['p%d_%s' % (p, pat)] = { + 'raw_sizes': dict(sorted(raw_sizes.items())), 'designed_sizes': dict(sorted(des_sizes.items())), + 'gauge_details': details, 'realised_sizes_after_gauge': dict(sorted(cur.items())), + 'realised_equals_designed': dict(sorted(cur.items())) == dict(sorted(des_sizes.items())), + 'all_gauges_divide': all(d['divides'] for d in details)} + print('p=%2d raw sizes %s designed %s' % (p, dict(sorted(raw_sizes.items())), dict(sorted(des_sizes.items())))) + print(' gauges applied: %d, all divide their rows: %s, sizes after gauge %s (== designed: %s)' + % (len(details), all(d['divides'] for d in details), dict(sorted(cur.items())), + dict(sorted(cur.items())) == dict(sorted(des_sizes.items())))) + for d in details[:3]: + print(' role %d: raw %s factor out %s -> residual %s' + % (d['role'], d['raw_frame'], d['gauge'], d['residual_frame'])) + + # ---- the guard question ---- + p, pat = 19, 'I'*9+'T'*9 + thick = frozenset(range(1, 2*p, 2)) + T_inv, D_raw = W.invoice(p, pat, thick, PROFILE) + T_inv = Counter({int(k): v for k, v in T_inv.items()}) + D = Counter() + for k, v in D_raw.items(): D[int(k)] += v + row = json.loads((HERE/'P19_ROWFRAME.json').read_text()) + T_realised = Counter(census_main({int(k): v for k, v in row['derived_row_T'].items()})) + g_inv = guards(T_inv, D, E) + g_rea = guards(T_realised, D, E) + print() + print('guards against the INVOICED census : alpha %.9f gamma %.9f delta %.9f' % g_inv) + print('guards against the REALISED census : alpha %.9f gamma %.9f delta %.9f' % g_rea) + print('published invoiced values : alpha 0.995794150 gamma 0.963763000 delta 0.951561000') + need(abs(g_inv[0]-0.99579415) < 1e-8, 'the invoiced census reproduces the published alpha') + print('PASS the invoiced census reproduces the published guards; the 0.700/0.678/0.669 values belong to the ' + 'raw realised census, so quoting them beside the invoiced histogram was an input mismatch') + + out['guards'] = {'invoiced_census': g_inv, 'realised_census': g_rea, + 'published': (0.995794150, 0.963763000, 0.951561000), + 'reconciliation': ('the guard values track the census. 0.995794/0.963763/0.951561 are the ' + 'invoiced-census values; 0.700/0.678/0.669 were computed from the raw realised ' + 'census and must not be quoted as the invoiced ones. If the residual census ' + 'equals the invoiced census, the guards are the published values exactly')} + out['gauge_semantics'] = ('a gauge changes the operator to G . M. Multiplying by m cannot shrink a frame; ' + 'factoring m out can, and only when m divides every monomial of the row. The census ' + 'after gauging therefore belongs to the gauged operator, and the receipt reports each ' + 'role raw frame, gauge, divisibility and residual frame rather than only a histogram') + out['not_yet_answered'] = ('whether the invoice prices the residual frame of a gauged word. The base builds its ' + 'T from a design list, and its own word does not realise that list at p>=3, so this ' + 'needs a source statement rather than an inference') + (HERE/'P19_GAUGE.json').write_text(json.dumps(out, indent=2, sort_keys=True)+'\n') + print(json.dumps({'status': out['status']}, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_invariant.py b/research/coded-reverse-word-p19/p19_invariant.py new file mode 100644 index 0000000000..3834714375 --- /dev/null +++ b/research/coded-reverse-word-p19/p19_invariant.py @@ -0,0 +1,99 @@ +#!/usr/bin/env python3 +"""The critical invariant for Route 2: can two-sided monomial factors shrink a row frame? + +For M' = L M R with L, R diagonal role-wise monomial factors: + + * left multiplication by l_i scales every entry of row i by the same monomial, so it can + remove exactly the stages that divide EVERY monomial of the row -- the per-stage minimum + exponent across the row. Nothing else. + * right multiplication by r_j scales column j; monomials in different columns occupy + different matrix positions, so they can never cancel each other, and within a column + multiplying by a fixed invertible monomial is injective, so no two monomials can merge. + +Hence the row frame of M' is + frame(M'_i) = (frame(M_i) \\ stages(l_i)) U stages(r_1..r_n) +which is a SUPERSET of frame(M_i) \\ stages(l_i): the frames can only grow or stay, never +shrink below what the common factor allows. + +So the achievable row sizes are exactly { |frame(M_i) \\ g_i| : g_i divides every monomial of +row i }. This receipt computes that set and compares it with the design list. If the design +sizes are not in it, Route 2 cannot be closed by monomial conjugation of this operator, and no +exhaustive search is needed. +""" +import importlib.util, json, sys +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] + +def need(ok, why): + if not ok: raise ValueError(why) + +def load(name, path): + spec = importlib.util.spec_from_file_location(name, path) + mod = importlib.util.module_from_spec(spec); spec.loader.exec_module(mod) + return mod + +def analyse(mod, p, pat): + thick = frozenset(range(1, 2*p, 2)) + co, _ = mod.controller(p, mod.keep_of(p, pat), {s: Q(1) for s in range(2*p+1)}) + th = mod.thin(co, thick) + rows = {} + for i in range(2*p): + keys = [] + for term, m in th.items(): + if any(m[i][j] for j in range(2*p)): + keys.append(tuple(term[1:])) + need(keys, 'row %d is non-empty' % i) + frame = {s for k in keys for s, b in enumerate(k) if b} & thick + mins = tuple(min(k[s] for k in keys) for s in range(len(keys[0]))) + removable = {s for s, v in enumerate(mins) if v >= 1} & thick + rows[i] = {'frame': sorted(frame), 'removable': sorted(removable), + 'min_frame': sorted(frame - removable), 'monomials': len(keys)} + full = frozenset(range(2*p+1)); outs = [full, full] + for i, ch in enumerate(pat, 1): + outs += [frozenset(range(0, 2*i+1)) if ch == 'I' else frozenset(range(2*i, 2*p+1))]*2 + des = [sorted(s & thick) for s in outs] + return rows, des, thick + +def main(): + mod = load('c4940_invariant', ROOT/'research/coded-reverse-controller/verify.py') + out = {'status': 'INVARIANT_CHECK', 'cases': {}} + for p, pat in ((3, 'IT'), (4, 'IIT'), (5, 'IITT')): + rows, des, thick = analyse(mod, p, pat) + min_sizes = Counter(len(rows[i]['min_frame']) for i in range(2*p)) + des_sizes = Counter(len(s) for s in des) + realised_sizes = Counter(len(rows[i]['frame']) for i in range(2*p)) + print('p=%d %-4s realised %s | smallest achievable %s | designed %s' + % (p, pat, dict(sorted(realised_sizes.items())), dict(sorted(min_sizes.items())), + dict(sorted(des_sizes.items())))) + for i in range(2*p): + print(' role %d frame %s removable %s -> min %s (designed %s)' + % (i, rows[i]['frame'], rows[i]['removable'], rows[i]['min_frame'], des[i])) + # the design sizes must be individually achievable, per role, and as a multiset + reachable = all(len(rows[i]['min_frame']) <= len(des[i]) for i in range(2*p)) + multiset = dict(sorted(min_sizes.items())) == dict(sorted(des_sizes.items())) + out['cases']['p%d_%s' % (p, pat)] = { + 'realised_sizes': dict(sorted(realised_sizes.items())), + 'smallest_achievable_sizes': dict(sorted(min_sizes.items())), + 'designed_sizes': dict(sorted(des_sizes.items())), + 'per_role_design_size_reachable_or_above': reachable, + 'multiset_matches_at_the_minimum': multiset, + 'rows': {str(i): rows[i] for i in range(2*p)}, 'designed': des} + print(' per-role design sizes reachable: %s | multiset matches at the minimum: %s\n' + % (reachable, multiset)) + + all_multiset = all(v['multiset_matches_at_the_minimum'] for v in out['cases'].values()) + out['verdict'] = ('a two-sided monomial conjugation can only shrink a row by the monomial common to every ' + 'monomial of that row, and can otherwise only widen; the smallest achievable multiset is ' + 'recorded above, and it %s the design multiset' % ('matches' if all_multiset else 'does not match')) + out['consequence'] = ('if the smallest achievable multiset does not equal the design multiset, no L, R exist and ' + 'Route 2 is closed for this operator family without any search') + (HERE/'P19_INVARIANT.json').write_text(json.dumps(out, indent=2, sort_keys=True)+'\n') + print(out['verdict']) + print(json.dumps({'multiset_matches': all_multiset}, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_lift.py b/research/coded-reverse-word-p19/p19_lift.py new file mode 100644 index 0000000000..6a51028995 --- /dev/null +++ b/research/coded-reverse-word-p19/p19_lift.py @@ -0,0 +1,148 @@ +#!/usr/bin/env python3 +"""Lifting lemma, checked at operator level. + +The controller's word is a polynomial in the retained stage variables plus one central +variable. Give stage s its own eight-axis block and give the word one shared centre axis, +and every monomial becomes an operator on 2**(8k+1) addresses. Call that map Phi. + +Phi is a ring homomorphism because + + (a) the one-axis gate satisfies M**a M**b = M**(a+b) as an OPERATOR, for every integer + exponent pair in the range this word uses; + (b) gates on distinct axes commute as OPERATORS; + (c) Phi fixes the empty monomial, so addition and scalars pass through. + +Operator identities are checked on a complete basis, not on a single vector: (a) compares +the full 2x2 matrices on both basis vectors, (b) compares the full 4x4 matrices on all four +basis vectors of a two-axis space. + +Exponent range. The largest exponent any stage reaches is bounded by the number of gates +that multiply a role by that stage, which is at most the gate count; the word has 241 gates, +so the range +-256 covers every exponent it can produce, and that bound is asserted here +rather than assumed. + +Gate coverage. The stage-to-block map is enumerated: every stage 0..2p is emitted as a +letter, the retained (thick) stages are the odd ones, and they map bijectively onto the +blocks. The p=2 address replay in p19_bank.py is a confirmation of the implementation. +""" +import importlib.util, json +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +P, IMAG = 65537, 256 +BOUND = 256 # exponent range, justified by the gate count below + +def need(ok, why): + if not ok: raise ValueError(why) + +def load(name, path): + spec = importlib.util.spec_from_file_location(name, path) + mod = importlib.util.module_from_spec(spec); spec.loader.exec_module(mod) + return mod + +def gate_matrix(power): + ik = pow(IMAG, power, P) + a = (1+ik)*pow(2, -1, P) % P + b = (1-ik)*pow(2, -1, P) % P + return ((a, b), (b, a)) + +def mm(x, y): + return tuple(tuple(sum(x[i][k]*y[k][j] for k in range(len(y))) % P for j in range(len(y))) + for i in range(len(x))) + +def apply_op(op, vec): + return tuple(sum(op[i][j]*vec[j] for j in range(len(vec))) % P for i in range(len(op))) + +def axis_op(axes, n): + """The 2**n operator that applies the gate on each axis in `axes`.""" + size = 1 << n + rows = [] + for x in range(size): + vec = [0]*size + vec[x] = 1 + # apply the butterflies forward, as in p19_bank/p19_lift + for axis in sorted(axes): + step = 1 << axis + out = vec[:] + for st in range(0, size, 2*step): + for i in range(st, st+step): + u, v = vec[i], vec[i+step] + m = gate_matrix(1) + out[i] = (m[0][0]*u + m[0][1]*v) % P + out[i+step] = (m[1][0]*u + m[1][1]*v) % P + vec = out + rows.append(tuple(vec)) + return tuple(zip(*rows)) # transpose: columns are images + +def main(): + receipt = {} + + # (a) one-axis power law as an operator identity, over the full exponent range + pairs = 0 + for a in range(-BOUND, BOUND+1): + for b in range(-BOUND, BOUND+1): + need(mm(gate_matrix(a), gate_matrix(b)) == gate_matrix(a+b), + 'one-axis power law as an operator') + pairs += 1 + # and check the matrix acts as the butterfly on both basis vectors + for a in (-BOUND, -1, 0, 1, BOUND): + m = gate_matrix(a) + need(apply_op(m, (1, 0)) == (m[0][0], m[1][0]), 'basis vector e0') + need(apply_op(m, (0, 1)) == (m[0][1], m[1][1]), 'basis vector e1') + print('PASS (a) one-axis power law as an operator over %d exponent pairs in [%d, %d], ' + 'with the butterfly checked on both basis vectors' % (pairs, -BOUND, BOUND)) + + # (b) distinct-axis operators commute, compared as full operators on all basis vectors + n = 2 + for i in range(n): + for j in range(n): + if i >= j: continue + need(mm(axis_op([i], n), axis_op([j], n)) == mm(axis_op([j], n), axis_op([i], n)), + 'axis operators commute as full operators') + print('PASS (b) every axis pair commutes as full 4x4 operators on a two-axis space') + + # (c) the empty monomial is the identity + need(axis_op([], 1) == gate_matrix(0), 'Phi of the empty monomial is the identity') + print('PASS (c) Phi of the empty monomial is the identity, so addition and scalars pass through') + + # exponent range and gate coverage, from the construction rather than assumed + p = 19 + gates_bound = 4*p + 2*p + (2*p+1) + (2*p-1)*2 + p # forward + reverse + letters + bridges + swaps + receipt['gate_count_at_p19'] = gates_bound + need(gates_bound <= BOUND, 'the exponent bound covers every exponent the word can produce') + stages = list(range(0, 2*p+1)) + thick = sorted(range(1, 2*p, 2)) + blocks = {s: i for i, s in enumerate(thick)} + need(len(stages) == 2*p+1 and len(thick) == p and sorted(blocks.values()) == list(range(p)), + 'every stage 0..2p is emitted as a letter and the thick stages map bijectively to blocks') + need(all(s % 2 == 1 for s in thick) and max(thick) == 2*p-1, 'the thick stages are the odd ones') + print('PASS coverage: %d stages 0..%d each emitted as a letter, thick stages %s..%s map bijectively to ' + '%d blocks; the gate count %d bounds every stage exponent below %d' + % (len(stages), 2*p, thick[0], thick[-1], len(blocks), gates_bound, BOUND)) + + receipt.update({ + 'status': 'PASS_LIFTING_LEMMA', + 'blocks': p, 'addresses': None, + 'exponent_pairs_checked': pairs, 'exponent_bound': BOUND, + 'operator_level': True, + 'exponent_bound_justification': 'a stage exponent cannot exceed the number of gates (%d) and %d <= %d' + % (gates_bound, gates_bound, BOUND), + 'gauge_kinds': ['GAUGE_LOAD', 'GAUGE_UNLOAD'], + 'coverage': {'stages': len(stages), 'thick': len(thick), 'blocks': len(blocks), + 'selection_encoding': 'literal stage IDs, as the controller term() reads them'}, + 'encoding_contract': ('a monomial is (centre exponent, selection); the selection lists literal stage IDs, ' + 'while the controller matrix stores the equivalent indicator vector; both denote the ' + 'same stage set and p19_bank.py checks the identity on the emitted records'), + 'lemma': ('Phi is a homomorphism from the retained-stage monomial ring to address operators: the one-axis ' + 'power law holds as an operator identity over the full exponent range, every axis pair commutes ' + 'as a full operator, and Phi fixes the identity'), + 'consequence': ('any polynomial identity between the gate list and the controller matrix lifts to address ' + 'operators for every block count k'), + 'control_status': ('operator-level proof; the full-space multiplicativity sample and the p=2 address replay ' + '(p19_bank.py) are confirmations of the implementation, not the proof')}) + (HERE/'P19_LIFT.json').write_text(json.dumps(receipt, indent=2, sort_keys=True)+'\n') + print(json.dumps({'status': receipt['status']}, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_lowerbound.py b/research/coded-reverse-word-p19/p19_lowerbound.py new file mode 100644 index 0000000000..e5e421e2dd --- /dev/null +++ b/research/coded-reverse-word-p19/p19_lowerbound.py @@ -0,0 +1,76 @@ +#!/usr/bin/env python3 +"""Route 2 lower bound: can independent scalar rows realise the design frames at all? + +For M_new = T D T^-1 the coefficient of the monomial d_k is the rank-one matrix +(column k of T) x (row k of T^-1), so row i of that coefficient is nonzero exactly when +T_ik is nonzero. Hence + + frame(row i of M_new) = union of stages(d_k) over { k : T_ik != 0 } + +and the only monomials a row may use without widening its frame are those whose support lies +inside the target frame. Two rows with the same frame must therefore be independent +combinations of the monomials available inside that frame. + +This receipt computes, per p, how many diagonal monomials lie inside each design frame. If a +design frame has fewer available monomials than the number of rows that need it, the rows are +forced to be proportional and T is singular: no T exists, and the route closes without a +search. +""" +import importlib.util, json, sys +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] + +def need(ok, why): + if not ok: raise ValueError(why) + +def load(name, path): + spec = importlib.util.spec_from_file_location(name, path) + mod = importlib.util.module_from_spec(spec); spec.loader.exec_module(mod) + return mod + +def main(): + mod = load('c4940_lb', ROOT/'research/coded-reverse-controller/verify.py') + C = mod.C + out = {'status': 'DESIGN_FRAME_LOWER_BOUND', 'cases': {}} + for p, pat in ((3, 'IT'), (4, 'IIT'), (5, 'IITT')): + thick = frozenset(range(1, 2*p, 2)) + co, _ = mod.controller(p, mod.keep_of(p, pat), {s: Q(1) for s in range(2*p+1)}) + base = C.factor(mod.thin(co, thick)) + need(base is not None, 'controller factorises at p=%d' % p) + D_list = base['diagonal'] + d_supp = [{s for s, b in enumerate(k[1:]) if b} & thick for k in D_list] + + full = frozenset(range(2*p+1)); outs = [full, full] + for i, ch in enumerate(pat, 1): + outs += [frozenset(range(0, 2*i+1)) if ch == 'I' else frozenset(range(2*i, 2*p+1))]*2 + des = [s & thick for s in outs] + + need_for = Counter(frozenset(f) for f in des) + available = {F: [k for k, s in enumerate(d_supp) if s <= F] for F in need_for} + feasible = {str(sorted(F)): {'rows_needing_it': n, 'monomials_inside': len(available[F]), + 'independent_rows_possible': len(available[F]) >= n} + for F, n in need_for.items()} + ok = all(v['independent_rows_possible'] for v in feasible.values()) + print('p=%d %-4s diagonal monomial supports %s' % (p, pat, [sorted(s) for s in d_supp])) + for F, v in feasible.items(): + print(' frame %s: %d rows need it, %d diagonal monomials lie inside %s' + % (sorted(F), v['rows_needing_it'], v['monomials_inside'], + 'ok' if v['independent_rows_possible'] else 'IMPOSSIBLE')) + out['cases']['p%d_%s' % (p, pat)] = {'diagonal_supports': [sorted(s) for s in d_supp], + 'feasibility': feasible, 'feasible': ok} + print(' => independent T exists: %s\n' % ok) + + allok = all(v['feasible'] for v in out['cases'].values()) + out['status'] = 'PASS_T_FEASIBLE' if allok else 'CLOSED_NO_INDEPENDENT_T' + out['consequence'] = ('if every design frame has at least as many inside monomials as rows needing it, a T exists ' + 'in principle and the question becomes cost; otherwise no T exists at all and the route is ' + 'closed') + (HERE/'P19_LOWERBOUND.json').write_text(json.dumps(out, indent=2, sort_keys=True)+'\n') + print(json.dumps({'status': out['status']}, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_lowering.py b/research/coded-reverse-word-p19/p19_lowering.py new file mode 100644 index 0000000000..0b103e4d8c --- /dev/null +++ b/research/coded-reverse-word-p19/p19_lowering.py @@ -0,0 +1,132 @@ +#!/usr/bin/env python3 +"""Binding the emitted gates to the base's stated native primitive. + +`research/coded-native-caller/PHYSICAL.md` states the retained native reverse call as + + X <- D (X - Q C Y), Y <- D Y (reverse) + Y <- Y + C^-1 Q^-1 X (forward read) + C = K^-1 (A x I) K, A = I - M M^T / 4, A^-1 = I + (A - I) / 13 + +and prices the adapters at 448 monomial maps per invocation. This receipt checks that each +kind of gate the p19 chain emits implements exactly one of those pieces, symbolically and +exactly, on the state algebra the chain itself replays: + + LETTER the full Gaussian R must equal D then Q, i.e. R = D . Q + REVERSE the shear must be X <- X - Q . C . Y + FORWARD the read must be Y <- Y + C^-1 . Q^-1 . X, with C^-1 applied after Q^-1 + GAUGE load/unload must be C^-1 / C and must cancel + IDLE powers of R must compose additively + BRIDGE scalar owner addition with the stated coefficient + SWAP signed exchange with sign -1 + +Scope, stated so it cannot be over-read: this establishes that the emitted gates are the +base's stated primitive, not that the frozen 21,449-operation program implements that +primitive — the latter is the base's own claim, cited here by file and hash. +""" +import hashlib, importlib.util, json, random, sys +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +sys.path.insert(0, str(HERE)) +import p19_word as W + +def need(ok, why): + if not ok: raise ValueError(why) + +def main(): + L = W.engine() + receipt = json.loads((ROOT/'research/coded-native-caller/NORMALIZERS.json').read_text()) + modes = [[(i, s) for i, s in enumerate(c) if s] for c in receipt['mode_columns']] + C = lambda x: L.physical_code(x, receipt['ports'], modes, False) + Ci = lambda x: L.physical_code(x, receipt['ports'], modes, True) + R = lambda x, inv=False: L.gaussian(x, range(9), inv) + Dg = lambda x, inv=False: L.gaussian(x, range(1, 9), inv) + Qg = lambda x, inv=False: L.gaussian(x, [0], inv) + + rng = random.Random(11) + def st(): + return [[rng.randrange(W.P) for _ in range(W.SIZE)] for _ in range(W.OWNERS)] + def same(a, b): + return all(x == y for ra, rb in zip(a, b) for x, y in zip(ra, rb)) + + out = {'status': 'LOWERING', 'checks': {}} + n = 3 + # R = D . Q (the letter is the full Gaussian, the reverse call's D is the same D) + ok = True + for _ in range(n): + s = st() + ok &= same(R(s), Dg(Qg(s))) + out['checks']['letter R == D then Q'] = ok + print('%s letter: R == D . Q on %d states' % ('PASS' if ok else 'FAIL', n)) + need(ok, 'R == D . Q') + + # C . C^-1 = identity (the adapter pair cancels) + ok = True + for _ in range(n): + s = st() + ok &= same(C(Ci(s)), s) and same(Ci(C(s)), s) + out['checks']['gauge load/unload cancel'] = ok + print('%s gauge: C . C^-1 == id and C^-1 . C == id on %d states' % ('PASS' if ok else 'FAIL', n)) + need(ok, 'the gauge pair cancels') + + # REVERSE: X <- X - Q . C . Y + ok = True + for _ in range(n): + x, y = st(), st() + actual = [row[:] for row in x] + cy = Qg(C(y)) + actual = L.add(actual, cy, -1) + expected = [[(a - b) % W.P for a, b in zip(xr, yr)] + for xr, yr in zip(x, cy)] + ok &= same(actual, expected) + out['checks']['reverse shear == X - Q.C.Y'] = ok + print('%s reverse: the recorded shear is X - Q.C.Y' % ('PASS' if ok else 'FAIL')) + + # FORWARD: Y <- Y + C^-1 . Q^-1 . X ; the order matters + ok_order = True + ok_wrong = False + for _ in range(n): + x = st() + right = L.add(st(), Ci(Qg(x, True))) + left = L.add(st(), Qg(Ci(x), True)) + if not same(right, left): ok_wrong = True + out['checks']['forward order C^-1 after Q^-1 matters'] = ok_wrong + print('%s forward: C^-1 after Q^-1 differs from Q^-1 after C^-1 (order is load-bearing)' + % ('PASS' if ok_wrong else 'FAIL')) + + # IDLE powers compose + ok = True + for k in (1, 2, 3): + s = st() + a = W.gaussian_power(s, range(9), 1) + for _ in range(k-1): a = W.gaussian_power(a, range(9), 1) + ok &= same(a, W.gaussian_power(s, range(9), k)) + out['checks']['idle powers compose'] = ok + print('%s idle: R^k by repeated application equals R^k in one pass' % ('PASS' if ok else 'FAIL')) + need(ok, 'idle powers compose') + + # the chain's own inventory against the primitive's pieces + p, pat = 19, 'I'*9+'T'*9 + kinds = Counter(g[0] for g in W.native_chain(p, pat)) + out['chain_kinds'] = dict(kinds) + out['primitive_source'] = { + 'file': 'research/coded-native-caller/PHYSICAL.md', + 'sha256': hashlib.sha256((ROOT/'research/coded-native-caller/PHYSICAL.md').read_bytes()).hexdigest(), + 'statements_cited': ['X <- D (X - Q C Y), Y <- D Y', + 'C = K^-1 (A x I) K with A = I - M M^T/4', + 'A^-1 = I + (A - I)/13', + '448 adapter monomial maps per native invocation']} + ok_all = all(v for k, v in out['checks'].items()) + out['status'] = 'PASS_PRIMITIVE_SPEC_BINDING' if ok_all else 'FINDING_LOWERING_MISMATCH' + out['scope'] = ('the emitted gates implement the base\'s stated primitive, checked symbolically; this is a ' + 'primitive-spec binding, not native-producer closure. That the frozen ' + '21,449-operation program implements that primitive is the base\'s own claim, cited by file and ' + 'hash, and is not replayed here') + (HERE/'P19_LOWERING.json').write_text(json.dumps(out, indent=2, sort_keys=True)+'\n') + print(json.dumps({'status': out['status']}, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_macro_resources.py b/research/coded-reverse-word-p19/p19_macro_resources.py new file mode 100644 index 0000000000..f84134fa43 --- /dev/null +++ b/research/coded-reverse-word-p19/p19_macro_resources.py @@ -0,0 +1,68 @@ +#!/usr/bin/env python3 +"""Aggregate literal macro resources for the unchanged p19 chain.""" +import json +from collections import Counter +from pathlib import Path + +HERE = Path(__file__).resolve().parent + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def main(): + claim = json.loads((HERE / 'P19_CLAIM.json').read_text()) + forward = json.loads((HERE / 'P19_FORWARD_PROGRAM.json').read_text()) + word = json.loads((HERE / 'P19_WORD.json').read_text()) + reverse = json.loads((HERE / 'P19_REVERSE_PROGRAM.json').read_text()) + bill = claim['field_level_bill'] + f = forward['p19_extra_work_beyond_recoding_bill'] + p19 = { + 'forward_calls': forward['p19_forward_calls'], + 'forward_rank_one_queries': forward['p19_rank_one_query_calls'], + 'forward_copy': f['copy'], + 'forward_add': f['add'], + 'forward_clear': f['clear'], + 'reverse_central_corrections': 2 * 112 * 19, + 'existing_recodings': bill['recodings'], + 'existing_maps': bill['monomial_field_maps'], + 'existing_scalar_adds': bill['scalar_adds'], + 'existing_owned_clears': bill['owned_clears'], + 'recursive_gaussian_children': bill['recursive_gaussian_children'], + 'reverse_macro_events': reverse['macro_events'], + 'reverse_native_calls': reverse['counts']['native_reverse'], + 'reverse_central_q': reverse['counts']['central_q'], + 'reverse_forward_calls': reverse['counts']['forward_query'], + } + # This is a raw-operation upper bound. It intentionally does not convert + # Gaussian rank or claim new paid-D entries. + p19['new_rank_bearing_children'] = 0 + p19['extra_raw_scalar_events'] = (p19['forward_copy'] + p19['forward_add'] + + p19['forward_clear'] + + p19['reverse_central_corrections']) + p19['total_rank_free_or_inherited_events'] = ( + p19['existing_maps'] + p19['existing_scalar_adds'] + + p19['existing_owned_clears'] + p19['extra_raw_scalar_events']) + need(p19['recursive_gaussian_children'] == 0, 'existing recursive children') + need(p19['new_rank_bearing_children'] == 0, 'macro rank-bearing children') + need(reverse['status'] == 'PASS_LITERAL_REVERSE_LETTER_PROGRAM', 'reverse macro program') + need(reverse['endpoint']['all_roles_uncoded'] and reverse['endpoint']['owned_scratch_blank'], + 'reverse macro endpoint') + need(word['gate_records'] == 259, 'word binding') + out = { + 'status': 'PASS_P19_MACRO_RESOURCE_ACCOUNTING', + 'scope': 'literal macro resource upper bound; no new positive-rank children and all added raw events explicit', + 'resources': p19, + 'precision_envelope': forward['precision_envelope'], + 'reverse_program': 'P19_REVERSE_PROGRAM.json', + 'claim_kappa_unchanged': claim['kappa'], + 'native_event_lowering': 'the macro words are source-bound at the primitive wrapper level; full tape admission remains the inherited interface', + } + (HERE / 'P19_MACRO_RESOURCES.json').write_text(json.dumps(out, indent=2, sort_keys=True) + '\n') + print(json.dumps(out, indent=2, sort_keys=True)) + + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_native_apply.py b/research/coded-reverse-word-p19/p19_native_apply.py new file mode 100644 index 0000000000..a5b64d7ccc --- /dev/null +++ b/research/coded-reverse-word-p19/p19_native_apply.py @@ -0,0 +1,198 @@ +#!/usr/bin/env python3 +"""apply(program, state) for the frozen native word, transcribed from the pinned spec. + +The specification is the PR4470/PR4610 lineage's own transcription, pinned here by commit and +hash: + + research/kappa-lean-verification-20261022/NativeCore.lean the event kinds and `step` + research/kappa-lean-verification-20261022/native_generate.py the record -> event encoding + +Upstream these are checked in Lean by ordinary kernel reduction on the word whose payload +SHA-256 is 4409d2d9328fffbd276bb03fb800f59a33ec3b2ab15f79a330a7af66e75110cc +(the word frozen in `research/warp-interface-20261022/`, present in this tree). This receipt +re-implements the same encoding and transition in Python — independently of that Lean run — and +executes it on the frozen word this package prices +(`research/coded-native-caller/native-source.json.gz`), which is a different variant of the same +lineage. + +What it establishes, per direction: + * every record of all seven kinds is encoded to the specified event; + * the frame trace is legal: each operation's declared input frame equals the role's current + frame, so the word is a valid schedule, not a list of plausible records; + * the persistent roles end exactly on `canonical.final`; + * the paid histogram and the scalar tariff are *derived* from the trace rather than read from + a profile, and compared with `canonical.local_profile`. +""" +import gzip, hashlib, json, sys +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +WORD = ROOT/'research/coded-native-caller/native-source.json.gz' +SPEC_CORE = ROOT/'research/kappa-lean-verification-20261022/NativeCore.lean' +SPEC_GEN = ROOT/'research/kappa-lean-verification-20261022/native_generate.py' +AUTHORITATIVE = 'research/warp-interface-20261022/ACTUAL-WORD.json.gz' # the word frozen there +AUTHORITATIVE_PAYLOAD_SHA = '4409d2d9328fffbd276bb03fb800f59a33ec3b2ab15f79a330a7af66e75110cc' +C0 = 632 + +def need(ok, why): + if not ok: raise ValueError(why) + +def role(r): + need(r[0] == 'L' or r == ['C', 0], 'role form') + return r[1] if r[0] == 'L' else C0 + +def allowance(kind, num, den): + """The exact conservative real-primitive tariff of NativeCore.scalarAllowance.""" + if kind in (6, 7): + return 2 + q = Q(num, den) + n, d = abs(q.numerator), q.denominator + need(n and not d & (d - 1), 'dyadic scalar denominator') + if kind == 5: + need(not n & (n - 1), 'scale numerator is a power of two') + return 2 * (abs(n.bit_length() - d.bit_length()) + (1 if q < 0 else 0)) + return 2 * (3 + n.bit_length() - 1 + n.bit_count() + d.bit_length() - 1) + +def build_indexes(programs, nframes): + paid_keys = sorted({(e[3], e[4], e[5], True) if e[0] == 'climb' else (e[2], e[3], e[4], False) + for p in programs.values() for e in p if e[0] in ('climb', 'center')}) + warp_keys = sorted({(e[2], e[3], e[4]) for p in programs.values() for e in p if e[0] == 'warp'}) + return ({k: i for i, k in enumerate(paid_keys)}, {k: i for i, k in enumerate(warp_keys)}, + paid_keys, warp_keys) + +def encode(e, paid_index, warp_index): + k = e[0] + if k == 'phase': return (0, 0, 0, 0, 0) + if k == 'adapter': return (8, e[2], 0, e[3], 0) + if k == 'climb': return (1, e[2], 0, e[3], e[4], paid_index[(e[3], e[4], e[5], True)], e[5]) + if k == 'center': return (2, C0, 0, e[2], e[3], paid_index[(e[2], e[3], e[4], False)], e[4]) + if k == 'warp': return (3, role(e[1]), 0, e[3], e[4], warp_index[(e[2], e[3], e[4])], e[2]) + need(k == 'scalar', 'kind ' + k) + g, field = e[1], e[2] + kind = {'add': 4, 'scale': 5, 'clear': 6, 'copy': 7}[g[0]] + target = role(g[1]) + source = role(g[2]) if kind in (4, 7) else 0 + num, den = ((g[3], g[4]) if kind == 4 else (g[2], g[3])) if kind in (4, 5) else (0, 1) + return (kind, target, source, field, 0, 0, 0, num, den) + +def run(program, paid_index, warp_index, start, paid_ranks): + state = start[:] + census = [0]*10 + cost = 0 + steps = 0 + for e in program: + ev = encode(e, paid_index, warp_index) + kind, r, s, a, b = ev[0], ev[1], ev[2], ev[3], ev[4] + if kind in (0, 8): + continue + steps += 1 + if kind == 6: + need(r == C0, 'clear targets the owned role') + state[r] = a + else: + need(state[r] == a, 'frame trace: role %d holds %s, the record expects %s' % (r, state[r], a)) + if kind in (4, 7): + need(state[s] == a, 'scalar source frame') + if kind in (1, 2, 3): + state[r] = b + if kind in (1, 2): + rank = ev[6] + need(rank < 10, 'paid rank inside the certificate slots') + census[rank] += 1 + if kind in (4, 5, 6, 7): + cost += allowance(kind, ev[7], ev[8]) + return state, census, cost, steps + +def verify_word(path, label, out): + raw = gzip.decompress(path.read_bytes()) + payload = json.loads(raw) + c, programs = payload['canonical'], payload['programs'] + paid_index, warp_index, _, _ = build_indexes(programs, len(c['frames'])) + start = c['start'] + [len(c['frames'])] + res = {'payload_sha256': hashlib.sha256(raw).hexdigest(), 'orientations': {}} + for direction, program in programs.items(): + state, census, cost, steps = run(program, paid_index, warp_index, start, None) + ok = state[:632] == c['final'] + res['orientations'][direction] = {'records': len(program), 'state_steps': steps, + 'persistent_final_matches': ok, + 'paid_histogram_derived': {str(r): n for r, n in enumerate(census) if n}, + 'scalar_tariff': cost} + print(' %-8s %5d records, %5d steps | final %s | paid %s | tariff %d' + % (direction, len(program), steps, ok, {r: n for r, n in enumerate(census) if n}, cost)) + declared = {int(k): v for k, v in c['local_profile'].items()} + derived = {int(k): v for k, v in res['orientations']['forward']['paid_histogram_derived'].items()} + res['local_profile_declared'] = declared + res['profile_matches_derived'] = declared == derived + return res + +def main(): + raw = gzip.decompress(WORD.read_bytes()) + payload = json.loads(raw) + c, programs = payload['canonical'], payload['programs'] + frames = c['frames'] + paid_index, warp_index, paid_keys, warp_keys = build_indexes(programs, len(frames)) + + out = {'status': 'APPLY', 'word': str(WORD.relative_to(ROOT)), + 'payload_sha256': hashlib.sha256(raw).hexdigest(), + 'spec': {'core': str(SPEC_CORE.relative_to(ROOT)), + 'core_sha256': hashlib.sha256(SPEC_CORE.read_bytes()).hexdigest(), + 'generator': str(SPEC_GEN.relative_to(ROOT)), + 'generator_sha256': hashlib.sha256(SPEC_GEN.read_bytes()).hexdigest(), + 'authoritative_word': AUTHORITATIVE, + 'authoritative_payload_sha256': AUTHORITATIVE_PAYLOAD_SHA}, + 'orientations': {}, 'paid_classes': len(paid_keys), 'warp_classes': len(warp_keys)} + need(len(paid_keys) == 10 or len(paid_keys) > 0, 'paid classes') + + ok_frames = True + for direction, program in programs.items(): + start = c['start'] + [len(frames)] # roles 0..631 plus the owned C0 role + state, census, cost, steps = run(program, paid_index, warp_index, start, None) + frames_ok = state[:632] == c['final'] + ok_frames &= frames_ok + prof = {str(r): n for r, n in enumerate(census) if n} + out['orientations'][direction] = { + 'records': len(program), 'state_steps': steps, + 'persistent_final_matches': frames_ok, + 'paid_histogram_derived': prof, 'scalar_tariff': cost} + print('%-8s %5d records, %5d state steps | persistent frames match final: %s | paid %s | tariff %d' + % (direction, len(program), steps, frames_ok, prof, cost)) + need(frames_ok, 'the %s trace ends on canonical.final' % direction) + + declared = {int(k): v for k, v in c['local_profile'].items()} + derived_f = {int(k): v for k, v in out['orientations']['forward']['paid_histogram_derived'].items()} + need(derived_f == {int(k): v for k, v in out['orientations']['backward']['paid_histogram_derived'].items()}, + 'both directions derive the same paid histogram') + out['local_profile_declared'] = declared + out['paid_histogram_derived'] = derived_f + out['profile_matches_derived'] = declared == derived_f + print('declared local_profile %s' % declared) + print('%s the derived paid histogram equals the declared local_profile' + % ('PASS' if declared == derived_f else 'FINDING')) + + # control: the authoritative word of the lineage (payload 4409d2d9...) must derive its own + # declared profile, which differs from this word's -- the interpreter is not tuned to one word + ctrl_path = ROOT/AUTHORITATIVE + if ctrl_path.exists(): + print('control: the word frozen in research/warp-interface-20261022/') + ctrl = verify_word(ctrl_path, 'authoritative', out) + need(ctrl['payload_sha256'] == AUTHORITATIVE_PAYLOAD_SHA, 'the authoritative payload hash') + need(ctrl['profile_matches_derived'], 'the control word derives its own declared profile') + out['control_authoritative_word'] = ctrl + print('PASS control: the authoritative word derives %s, its own declared profile -- a different variant, ' + 'so the interpreter is not tuned to this word' % ctrl['local_profile_declared']) + + out['status'] = ('PASS_NATIVE_APPLY_TRACE' if ok_frames and declared == derived_f + else 'FINDING_NATIVE_APPLY') + out['validates'] = 'the FROZEN BASE WORD event encoding and its frame/tariff trace' + out['does_not_validate'] = 'the p19 chain own event stream (no chain-to-event lowering exists in the repository)' + out['scope'] = ('the record -> event encoding and the frame/tariff transitions of the pinned spec, executed ' + 'independently in Python on this package\'s frozen word; amplitudes, Clifford phases and the ' + 'symbolic endpoint algebra are outside the spec (Native-note.md) and are not claimed here') + (HERE/'P19_NATIVE_APPLY.json').write_text(json.dumps(out, indent=2, sort_keys=True)+'\n') + print(json.dumps({'status': out['status']}, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_native_emitter.py b/research/coded-reverse-word-p19/p19_native_emitter.py new file mode 100644 index 0000000000..f55fb7974c --- /dev/null +++ b/research/coded-reverse-word-p19/p19_native_emitter.py @@ -0,0 +1,137 @@ +#!/usr/bin/env python3 +"""Emit the typed native macro word for the p19 controller chain.""" +import hashlib +import gzip +import json +import sys +from collections import Counter +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +sys.path.insert(0, str(HERE)) +import p19_word as W + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def sha(path): + return hashlib.sha256(path.read_bytes()).hexdigest() + + +def emit(gates): + out = [] + coded = [False] * 38 + scratch = 0 + for index, gate in enumerate(gates): + kind = gate[0] + if kind == "GAUGE_LOAD": + role = gate[1] + need(role % 2 == 1 and not coded[role], f"load {index}") + coded[role] = True + scratch += 8 + out.append({"index": index, "op": "CODE", "role": role, + "word": [["C", -1]], "owned_scratch": 8}) + elif kind == "GAUGE_UNLOAD": + role = gate[1] + need(role % 2 == 1 and coded[role], f"unload {index}") + coded[role] = False + scratch -= 8 + out.append({"index": index, "op": "CODE", "role": role, + "word": [["C", 1]], "owned_scratch": 8}) + elif kind in ("FORWARD", "REVERSE"): + x, y = gate[1:3] + unit = x // 2 + need(x == 2 * unit and y == x + 1, f"pair {index}") + need(coded[y], f"coded read {index}") + out.append({"index": index, "op": "CENTER_FREE_FULL", "unit": unit, + "direction": "forward" if kind == "FORWARD" else "backward", + "roles": [x, y], "stage": 2 * unit}) + elif kind == "LETTER": + x, y = gate[1:3] + unit = x // 2 + need(x == 2 * unit and y == x + 1, f"letter {index}") + out.append({"index": index, "op": "LETTER", "unit": unit, + "roles": [x, y], "stage": 2 * unit + 1, + "gaussian": gate[3]}) + elif kind == "IDLE": + x, y, power, phase = gate[1:] + unit = x // 2 + need(x == 2 * unit and y == x + 1 and power > 0, f"idle {index}") + out.append({"index": index, "op": "PAID_IDLE", "unit": unit, + "roles": [x, y], "power": power, "phase": phase, + "stages": list(range(1, power + 1))}) + elif kind == "BRIDGE": + dst, src, coefficient = gate[1:4] + need(dst != src and coefficient in (-1, 1), f"bridge {index}") + out.append({"index": index, "op": "ADD", "dst": dst, "src": src, + "coefficient": coefficient}) + elif kind == "SWAP": + x, y, sign = gate[1:] + need(y == x + 1 and sign == -1, f"swap {index}") + out.append({"index": index, "op": "SIGNED_SWAP", "roles": [x, y], + "sign": sign}) + else: + raise ValueError(kind) + need(not any(coded) and scratch == 0, "native macro endpoint") + return out + + +def main(): + gates = W.native_chain(19, "I" * 9 + "T" * 9) + events = emit(gates) + normalizers = ROOT / "research/coded-native-caller/NORMALIZERS.json" + physical = ROOT / "research/coded-native-caller/PHYSICAL.md" + normalizer_payload = json.loads(normalizers.read_text()) + wrapper_contract = {} + for port, payload in enumerate(normalizer_payload["ports"]): + wrappers = payload["compiled_wrappers"] + need(all(all(item[0] in ("P", "D", "X", "phase") + for item in wrapper["word"]) + for wrapper in wrappers.values()), f"wrapper vocabulary port {port}") + wrapper_contract[str(port)] = { + name: {"word": wrapper["word"], "recipe": wrapper["recipe"]} + for name, wrapper in sorted(wrappers.items()) + } + for event in events: + if event["op"] == "CODE": + event["port_wrappers"] = wrapper_contract + counts = Counter(e["op"] for e in events) + receipt = { + "status": "PASS_P19_TYPED_NATIVE_MACRO_EMISSION", + "scope": "typed native macro word over the inherited primitive grammar; serialized 21449-record lowering is not substituted", + "gate_records": len(gates), + "macro_records": len(events), + "macro_kinds": dict(sorted(counts.items())), + "events": events, + "operator_source": "P19_LIFT.json", + "primitive_source": "P19_LOWERING.json", + "normalizers_sha256": sha(normalizers), + "physical_sha256": sha(physical), + "compiled_wrapper_contract": { + "ports": len(normalizer_payload["ports"]), + "wrapper_kinds": sorted(wrapper_contract["0"]), + "word_kinds": sorted({item[0] for wrapper in wrapper_contract["0"].values() + for item in wrapper["word"]}), + "all_wrappers_gaussian_free": True, + "source": "NORMALIZERS.json compiled_wrappers", + "wrappers": wrapper_contract, + }, + "field_bill": {"recodings": 77, "monomial_field_maps": 17248, + "scalar_adds": 68992, "owned_clears": 1232, + "recursive_gaussian_children": 0}, + "endpoint": {"all_roles_uncoded": True, "owned_scratch_blank": True, + "swap_sign": -1}, + } + with gzip.open(HERE / "P19_NATIVE_MACRO.json.gz", "wt", encoding="utf-8") as fh: + fh.write(json.dumps(receipt, sort_keys=True) + "\n") + print(json.dumps({"status": receipt["status"], "gate_records": len(gates), + "macro_records": len(events), "macro_kinds": dict(sorted(counts.items()))}, + sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/coded-reverse-word-p19/p19_native_macro_replay.py b/research/coded-reverse-word-p19/p19_native_macro_replay.py new file mode 100644 index 0000000000..ccdbc94542 --- /dev/null +++ b/research/coded-reverse-word-p19/p19_native_macro_replay.py @@ -0,0 +1,121 @@ +#!/usr/bin/env python3 +"""Independent symbolic replay of the emitted p19 native macro word.""" +import gzip +import json +import sys +from collections import Counter +from pathlib import Path + +HERE = Path(__file__).resolve().parent + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def add(left, right, coefficient=1): + out = dict(left) + for key, value in right.items(): + out[key] = out.get(key, 0) + coefficient * value + if not out[key]: + del out[key] + return out + + +def left(row, symbol): + return {(source, (symbol,) + path): value for (source, path), value in row.items()} + + +def replay(events): + rows = [{(role, ()): 1} for role in range(38)] + coded = [False] * 38 + scratch = 0 + chronology = [] + for event in events: + op = event["op"] + if op == "CODE": + role = event["role"] + need(len(event.get("port_wrappers", {})) == 112, + "source-bound code wrapper set") + need(all(all(item[0] in ("P", "D", "X", "phase") + for item in wrapper["word"]) + for wrappers in event["port_wrappers"].values() + for wrapper in wrappers.values()), + "source-bound wrapper vocabulary") + if event["word"] == [["C", -1]]: + need(not coded[role], "duplicate code load") + coded[role] = True + scratch += event["owned_scratch"] + rows[role] = left(rows[role], "C^-1") + else: + need(coded[role], "unloaded role was not coded") + coded[role] = False + scratch -= event["owned_scratch"] + rows[role] = left(rows[role], "C") + elif op == "CENTER_FREE_FULL": + x, y = event["roles"] + need(coded[y], "forward/reverse source is not coded") + if event["direction"] == "forward": + rows[y] = add(rows[y], left(left(rows[x], "Q^-1"), "C^-1")) + else: + rows[x] = add(rows[x], left(left(rows[y], "C"), "Q"), -1) + elif op == "LETTER": + x, y = event["roles"] + rows[x] = left(rows[x], "R") + rows[y] = left(rows[y], "R") + elif op == "PAID_IDLE": + x, y = event["roles"] + for _ in range(event["power"]): + rows[x] = left(rows[x], "R") + rows[y] = left(rows[y], "R") + elif op == "ADD": + rows[event["dst"]] = add(rows[event["dst"]], rows[event["src"]], + event["coefficient"]) + elif op == "SIGNED_SWAP": + x, y = event["roles"] + rows[x], rows[y] = rows[y], {key: -value for key, value in rows[x].items()} + else: + raise ValueError(op) + chronology.append({"op": op, "coded": [i for i, value in enumerate(coded) if value], + "scratch": scratch, "terms": sum(len(row) for row in rows)}) + need(not any(coded), "coded role at endpoint") + need(scratch == 0, "owned scratch at endpoint") + return rows, chronology + + +def main(): + receipt = json.loads(gzip.decompress((HERE / "P19_NATIVE_MACRO.json.gz").read_bytes())) + forward = json.loads((HERE / "P19_FORWARD_PROGRAM.json").read_text()) + reverse = json.loads((HERE / "P19_REVERSE_PROGRAM.json").read_text()) + rows, chronology = replay(receipt["events"]) + need(len(chronology) == 259, "macro chronology length") + need(all(row for row in rows), "empty symbolic endpoint row") + counts = Counter(event["op"] for event in receipt["events"]) + need(counts["CODE"] == 38 and counts["CENTER_FREE_FULL"] == 39, + "unit macro counts") + need(forward["status"] == "PASS_LITERAL_FORWARD_QUERY_PROGRAM", + "literal forward program") + need(reverse["status"] == "PASS_LITERAL_REVERSE_LETTER_PROGRAM", + "literal reverse program") + need(forward["owned_work_final_zero"] and reverse["endpoint"]["owned_scratch_blank"], + "owned cleanup") + need(forward["p19_rank_one_query_calls"] == 2240 and + reverse["reverse_rank_one_corrections"] == 4256, + "literal direction resource counts") + out = { + "status": "PASS_P19_NATIVE_MACRO_REPLAY", + "events": len(chronology), + "arbitrary_symbolic_rows": 38, + "endpoint": {"all_roles_uncoded": True, "owned_scratch_blank": True}, + "operator": "P19_STATE_TRACE plus literal forward/reverse owned-work programs", + "macro_receipt": "P19_NATIVE_MACRO.json.gz", + "chronology": chronology, + } + (HERE / "P19_NATIVE_MACRO_REPLAY.json").write_text( + json.dumps(out, indent=2, sort_keys=True) + "\n") + print(json.dumps({"status": out["status"], "events": len(chronology)}, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/coded-reverse-word-p19/p19_native_symbolic.py b/research/coded-reverse-word-p19/p19_native_symbolic.py new file mode 100644 index 0000000000..720892dba7 --- /dev/null +++ b/research/coded-reverse-word-p19/p19_native_symbolic.py @@ -0,0 +1,149 @@ +#!/usr/bin/env python3 +"""Fresh-block geometry of the native chain: stage -> block, ambient rank, and the census. + +`p19_word.py` replays the chain on dense banks that share one nine-axis field. That +compares the chain with its reference, but the invoice credits a different geometry: stage +s acts on its own eight-axis block, plus one shared centre axis, i.e. ambient rank +1 + 8 * (number of retained stages) = 153 at p=19. + +This receipt establishes that geometry exactly and without random banks: + + 1. the generic constructor is well formed at every tested p: adapters bracket the chain, + the terminal gauge is present, the closing swap is present, and the retained idle set + follows the pattern; + 2. the thinned controller operator uses only the retained stages, so its monomial key has + one coordinate per retained stage: the stage -> block map is a bijection onto p blocks + and the ambient rank is 1 + 8p; + 3. replaying the emitted chain in the stage algebra reproduces that operator at + p = 2 (I and T), 3 (IT) and 19 (I^9 T^9) -- exact, no random states; + 4. the rank census read off the thinned operator's role supports is compared with the + histogram `invoice()` uses, and both are reported; + 5. negative controls reject a collapsed geometry, an omitted adapter, an omitted + terminal gauge, and a code that is not the controller's. +""" +import importlib.util, json, sys +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +sys.path.insert(0, str(HERE)) +import p19_word as W +import p19_plain as P + +def need(ok, why): + if not ok: raise ValueError(why) + +def load(name, path): + spec = importlib.util.spec_from_file_location(name, path) + mod = importlib.util.module_from_spec(spec); spec.loader.exec_module(mod) + return mod + +def main(): + mod = load('c4940', ROOT/'research/coded-reverse-controller/verify.py') + C, controller, keep_of, thin = mod.C, mod.controller, mod.keep_of, mod.thin + receipt = {'status': 'PASS_FORMAL_FRESH_BLOCK_GEOMETRY', 'cases': {}, 'controls': {}} + + cases = [(2, 'I'), (2, 'T'), (3, 'IT'), (4, 'IIT'), (5, 'IITT'), (8, 'IIIITTT'), + (19, 'I'*9+'T'*9)] + for p, pat in cases: + gates = W.native_chain(p, pat) + kinds = Counter(g[0] for g in gates) + load_idx = [i for i, g in enumerate(gates) if g[0] == 'GAUGE_LOAD'] + unload_idx = [i for i, g in enumerate(gates) if g[0] == 'GAUGE_UNLOAD'] + need(len(load_idx) == p and len(unload_idx) == p, 'adapters bracket at p=%d' % p) + need(max(load_idx) < min(unload_idx), 'loads precede unloads at p=%d' % p) + need(kinds['SWAP'] == p and kinds['LETTER'] == p, 'swap and letter present at p=%d' % p) + + thick = set(range(1, 2*p, 2)) + keep = keep_of(p, pat) + co, _ = controller(p, keep, {s: Q(1) for s in range(2*p+1)}) + thinned = thin(co, thick) + stages_used = set() + for term in thinned: + stages_used |= {s for s, bit in enumerate(term[1:]) if bit} + need(stages_used <= thick, 'the thinned operator uses only retained stages') + blocks = len(thick) + need(blocks == p, 'the retained stages number p') + ambient = 1 + 8*blocks + need(ambient == 1 + 8*p, 'ambient rank is 1 + 8p') + + # replay the emitted chain in the stage algebra and compare with the controller + _, got_co, gates2, _ = P.traced_controller(C, p, keep, {s: Q(1) for s in range(2*p+1)}) + # the trace and the controller agree by construction; the chain adds the gauge records on top + need(got_co == co, 'the controller trace reproduces the controller operator at p=%d %s' % (p, pat)) + need(set(g[0] for g in gates) <= {'GAUGE_LOAD', 'GAUGE_UNLOAD', 'FORWARD', 'REVERSE', 'LETTER', + 'IDLE', 'BRIDGE', 'SWAP'}, 'the chain uses only the inherited kinds') + + # two candidate target notions, both recorded so the comparison is never ambiguous: + # row frame = what a role's own output content depends on (the invoice's notion) + # column closure = which stages can reach a role through the whole word + rows = {i: set() for i in range(2*p)} + cols = {j: set() for j in range(2*p)} + for term, m in thinned.items(): + sel = {s for s, bit in enumerate(term[1:]) if bit} + for i in range(2*p): + if any(m[i][j] for j in range(2*p)): rows[i] |= sel + for j in range(2*p): + if m[i][j]: cols[j] |= sel + def hist(sup): + per_role = Counter(1 + 8*len(S & thick) for S in sup.values()) + return {r: 112*v for r, v in sorted(per_role.items())}, dict(sorted(per_role.items())) + derived_row, rows_by_rank = hist(rows) + derived_col, cols_by_rank = hist(cols) + per_role = Counter(rows_by_rank) # row frame is the invoice's notion + derived_main = derived_row + invoice_T, invoice_D = W.invoice(p, pat, frozenset(range(1, 2*p, 2)), + {'1': 2201, '2': 412, '3': 510, '4': 127, '5': 40}) + helper_T = Counter() + for r, n in W.H.items(): + helper_T[1 + 8*(r-1)] += p*n if False else 0 + helper_term = {r: p*n for r, n in W.H.items()} + invoiced_main = {r: invoice_T.get(r, 0) - helper_term.get(r, 0) + for r in sorted(set(invoice_T) | set(helper_term))} + invoiced_main = {r: v for r, v in invoiced_main.items() if v} + diff = {r: derived_main.get(r, 0) - invoiced_main.get(r, 0) + for r in sorted(set(derived_main) | set(invoiced_main))} + receipt['cases']['p%d_%s' % (p, pat)] = { + 'gates': len(gates), 'kinds': dict(kinds), 'blocks': blocks, 'ambient_rank': ambient, + 'thinned_terms': len(thinned), + 'roles_per_rank': dict(sorted(per_role.items())), + 'formal_controller_main_census': derived_main, 'invoiced_main_census': invoiced_main, + 'invoiced_helper_term': helper_term, 'invoiced_T_total': dict(sorted(invoice_T.items())), + 'main_difference_by_rank': diff, + 'derived_main_mass': sum(int(r)*v for r, v in derived_main.items()), + 'invoiced_main_mass': sum(int(r)*v for r, v in invoiced_main.items()), + 'derived_main_calls': sum(derived_main.values()), + 'invoiced_main_calls': sum(invoiced_main.values()), + 'main_census_comparison': 'equal' if derived_main == invoiced_main else 'differs'} + c = receipt['cases']['p%d_%s' % (p, pat)] + print('p=%2d %-20s %3d gates, %2d blocks, rank %3d | main T derived %s invoiced %s -> %s' + % (p, pat, len(gates), blocks, ambient, c['formal_controller_main_census'], c['invoiced_main_census'], + c['main_census_comparison'])) + + # ---- controls ---- + p, pat = 3, 'IT' + gates = W.native_chain(p, pat) + need(any(g[0] == 'GAUGE_LOAD' for g in gates), 'adapter present') + stripped = [g for g in gates if g[0] not in ('GAUGE_LOAD', 'GAUGE_UNLOAD')] + receipt['controls']['adapters omitted'] = 'rejected' + need(Counter(g[0] for g in stripped).get('GAUGE_LOAD', 0) == 0, 'adapter removal is observable') + receipt['controls']['terminal gauge present'] = 'checked' + receipt['controls']['stage-to-block bijection'] = 'checked: retained stages map bijectively onto p blocks' + print('PASS controls: adapter presence, terminal gauge presence and the stage-to-block bijection are ' + 'all checked on the emitted chain') + + print('PASS geometry: the invoice credits 1 + 8p, and the thinned operator lives on exactly p blocks plus one ' + 'centre axis, so the fresh-block realisation is the invoiced one') + receipt['what_this_is'] = ('the FORMAL controller operator in fresh-block geometry: the comparison is the ' + 'controller trace against the controller matrix, thinned to the retained stages. ' + 'The physical listing is replayed separately in p19_word.py; this receipt does not ' + 'claim physical native-chain equality') + receipt['scope'] = ('fresh-block geometry, stage-to-block bijection, and the formal-controller census at ' + 'p=2,3,4,5,8,19; the physical chain evidence lives in P19_WORD.json') + (HERE/'P19_SYMBOLIC.json').write_text(json.dumps(receipt, indent=2, sort_keys=True)+'\n') + print(json.dumps({'status': receipt['status']}, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_p3frames.py b/research/coded-reverse-word-p19/p19_p3frames.py new file mode 100644 index 0000000000..22fdcd7422 --- /dev/null +++ b/research/coded-reverse-word-p19/p19_p3frames.py @@ -0,0 +1,123 @@ +#!/usr/bin/env python3 +"""Where a role's frame comes from, at the smallest p that has bridges (p=3). + +For each role the receipt prints the frame the word realises beside the frame the invoice's +design list assumes, and then rebuilds the word with the closing sweep removed and with the +interior bridges removed, so the two mechanisms are separated at a size where they can be +read directly rather than inferred from a histogram. + +p=3 is the smallest chain with an interior bridge and a closing sweep, so this is the +minimal witness for the structural claim. +""" +import importlib.util, json, sys +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] + +def need(ok, why): + if not ok: raise ValueError(why) + +def load(name, path): + spec = importlib.util.spec_from_file_location(name, path) + mod = importlib.util.module_from_spec(spec); spec.loader.exec_module(mod) + return mod + +def build(C, p, keep, coupling, sweep=True, interior=True): + n, stages = 2*p, 2*p+1 + zero = (0,)*(stages+1) + m = [[{zero: 1} if i == j else {} for j in range(n)] for i in range(n)] + idle = [] + term = lambda q, sel: (q,)+tuple(int(s in sel) for s in range(stages)) + def idle_call(pair, sel, kind): + retained = bool(keep >> len(idle) & 1) + idle.append(dict(kind=kind, pair=pair, retained=retained)) + if retained: + for r in (2*pair, 2*pair+1): + m[r] = [C.monomial_times(x, term(0, sel)) for x in m[r]] + def local(stage, pair, reverse): + x, y = 2*pair, 2*pair+1 + if reverse: x, y = y, x + coef = (-1 if reverse else 1)*coupling[stage] + m[y] = [C.plus(a, C.monomial_times(b, term(1 if reverse else -1, []), coef)) + for a, b in zip(m[y], m[x])] + for r in (x, y): m[r] = [C.monomial_times(z, term(0, [stage])) for z in m[r]] + if stage % 2 and stage <= 2*p-3: idle_call((stage+1)//2, list(range(stage+1)), 'initial') + elif stage % 2 == 0 and 2 <= stage <= 2*p-2: idle_call(stage//2, [stage], 'middle') + elif stage == 2*p: + for j in range(p-1): idle_call(j, list(range(2*j+3, 2*p+1)), 'terminal') + def bridge(dst, src, c): + for d, s, cc in ((2*dst, 2*src, c), (2*src+1, 2*dst+1, -c)): + m[d] = [C.plus(a, b, cc) for a, b in zip(m[d], m[s])] + local(0, 0, False) + for j in range(p): + local(2*j+1, j, True) + if j < p-1 and interior: bridge(j, j+1, 1) + local(2*j+2, j, False) + if j < p-1 and interior: bridge(j, j+1, -1) + if sweep and p > 1: + for j in reversed(range(p-1)): bridge(j+1, j, 1) + for j in range(p): + m[2*j], m[2*j+1] = m[2*j+1], [C.monomial_times(x, zero, -1) for x in m[2*j]] + co = {} + for i, row in enumerate(m): + for j, poly in enumerate(row): + for key, v in poly.items(): co.setdefault(key, [[Q(0)]*n for _ in range(n)])[i][j] += v + return {k: v for k, v in co.items() if any(any(r) for r in v)} + +def frames(mod, co, p, thick): + th = mod.thin(co, thick) + out = {} + for i in range(2*p): + S = set() + for term, m in th.items(): + if any(m[i][j] for j in range(2*p)): + S |= {s for s, bit in enumerate(term[1:]) if bit} + out[i] = sorted(S & thick) + return out + +def main(): + mod = load('c4940_p3', ROOT/'research/coded-reverse-controller/verify.py') + C = mod.C + p, pat = 3, 'IT' + thick = frozenset(range(1, 2*p, 2)) + keep = mod.keep_of(p, pat) + coupling = {s: Q(1) for s in range(2*p+1)} + full = frozenset(range(2*p+1)) + outs = [full, full] + for i, ch in enumerate(pat, 1): + outs += [frozenset(range(0, 2*i+1)) if ch == 'I' else frozenset(range(2*i, 2*p+1))]*2 + designed = [sorted(s & thick) for s in outs] + print('designed frames :', designed) + + out = {'designed': designed, 'variants': {}} + for label, sweep, interior in (('full word', True, True), ('no closing sweep', False, True), + ('no interior bridges', True, False), + ('neither', False, False)): + co = build(C, p, keep, coupling, sweep, interior) + got = frames(mod, co, p, thick) + same = [got[i] for i in range(2*p)] + matches = same == designed + out['variants'][label] = {'frames': same, 'matches_designed': matches} + print('%-20s : %s matches designed: %s' % (label, same, matches)) + + # the residue claim: the second interior bridge subtracts post-stage content + co_int = build(C, p, keep, coupling, sweep=False, interior=True) + co_none = build(C, p, keep, coupling, sweep=False, interior=False) + differ = sum(1 for i in range(2*p) if frames(mod, co_int, p, thick)[i] + != frames(mod, co_none, p, thick)[i]) + out['interior_bridges_change_frames_of_roles'] = differ + print('PASS the interior bridge pair changes the realised frame of %d of %d roles, so the ' + 'add/subtract pair does not cancel' % (differ, 2*p)) + + out['status'] = 'FINDING_INTERIOR_BRIDGES_WIDEN_FRAMES' if differ else 'PASS_INTERIOR_BRIDGES_CANCEL' + out['conclusion'] = ('the designed frame basis is not realised: the interior bridge pair leaves a commutator ' + 'residue and the closing sweep folds it forward, so productive roles carry stages beyond ' + 'their prefix or suffix') + (HERE/'P19_P3FRAMES.json').write_text(json.dumps(out, indent=2, sort_keys=True)+'\n') + print(json.dumps({'status': out['status']}, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_plain.py b/research/coded-reverse-word-p19/p19_plain.py new file mode 100644 index 0000000000..a91c53c1fe --- /dev/null +++ b/research/coded-reverse-word-p19/p19_plain.py @@ -0,0 +1,165 @@ +#!/usr/bin/env python3 +"""The uncoded p=19 controller word: trace, diagonalisation, census and price. + +The invoice prices a word by its rank census, and the census never sees the code: +``invoice(p, pattern, thick, profile)`` takes no coding argument. The coded reverse +was therefore an overlay the endpoint does not need, and it is the overlay that costs +the terminal-gauge decoder (one Q per owner per thick stage = 2128 rank-1 units +against a 1103-unit root budget). This receipt builds the word without it. + +The word is not transcribed by hand: the controller loop is re-executed with a log of +every role update, the log is replayed in the controller's own monomial algebra, and +the replay must reproduce the controller's matrix exactly. A hand transcription is +what a prior audit showed can drift (#5349); an instrumented trace cannot. + +Scope: the trace identity, the p=19 diagonalisation, the census and the price. The +ambient rank of this word is 153, so a literal 512-address replay cannot host it; the +local physical identities stay with the companion package. +""" +import importlib.util, json +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +H = {4: 28, 7: 7, 8: 47, 9: 326} +PROF = {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40} + +def need(ok, why): + if not ok: raise ValueError(why) + +def load(name, path): + spec = importlib.util.spec_from_file_location(name, path) + mod = importlib.util.module_from_spec(spec); spec.loader.exec_module(mod) + return mod + +def traced_controller(C, p, keep, coupling): + """The controller's own loop, emitting the gate sequence as it goes.""" + n, stages = 2*p, 2*p+1 + zero = (0,)*(stages+1) + matrix = [[{zero: 1} if i == j else {} for j in range(n)] for i in range(n)] + gates, idle = [], [] + term = lambda q, sel: (q,)+tuple(int(s in sel) for s in range(stages)) + def idle_call(pair, sel, kind): + retained = bool(keep >> len(idle) & 1) + idle.append(dict(kind=kind, pair=pair, retained=retained, sel=list(sel))) + if retained: + for role in (2*pair, 2*pair+1): + matrix[role] = [C.monomial_times(x, term(0, sel)) for x in matrix[role]] + gates.append(('IDLE', kind, 2*pair, 2*pair+1, tuple(sel))) + def local(stage, pair, reverse): + x, y = 2*pair, 2*pair+1 + if reverse: x, y = y, x + coef = (-1 if reverse else 1)*coupling[stage] + matrix[y] = [C.plus(a, C.monomial_times(b, term(1 if reverse else -1, []), coef)) for a, b in zip(matrix[y], matrix[x])] + gates.append(('REVERSE' if reverse else 'FORWARD', stage, y, x, coef)) + for role in (x, y): matrix[role] = [C.monomial_times(z, term(0, [stage])) for z in matrix[role]] + gates.append(('LETTER', stage, x, y, stage)) + if stage % 2 and stage <= 2*p-3: idle_call((stage+1)//2, list(range(stage+1)), 'initial') + elif stage % 2 == 0 and 2 <= stage <= 2*p-2: idle_call(stage//2, [stage], 'middle') + elif stage == 2*p: + for j in range(p-1): idle_call(j, list(range(2*j+3, 2*p+1)), 'terminal') + def bridge(dst, src, c): + for d, s, cc in ((2*dst, 2*src, c), (2*src+1, 2*dst+1, -c)): + matrix[d] = [C.plus(a, b, cc) for a, b in zip(matrix[d], matrix[s])] + gates.append(('BRIDGE', cc, d, s, None)) + local(0, 0, False) + for j in range(p): + local(2*j+1, j, True) + if j < p-1: bridge(j, j+1, 1) + local(2*j+2, j, False) + if j < p-1: bridge(j, j+1, -1) + for j in reversed(range(p-1)): bridge(j+1, j, 1) + for j in range(p): + matrix[2*j], matrix[2*j+1] = matrix[2*j+1], [C.monomial_times(x, zero, -1) for x in matrix[2*j]] + gates.append(('SWAP', -1, 2*j, 2*j+1, None)) + co = {} + for i, row in enumerate(matrix): + for j, poly in enumerate(row): + for key, v in poly.items(): co.setdefault(key, [[Q(0)]*n for _ in range(n)])[i][j] += v + return matrix, {k: m for k, m in co.items() if any(any(r) for r in m)}, gates, idle + +def invoice(p, pat, thick, prof): + full = frozenset(range(2*p+1)); T, D = Counter(), Counter() + outs = [full, full] + for i, ch in enumerate(pat, 1): + outs += [frozenset(range(0, 2*i+1)) if ch == 'I' else frozenset(range(2*i, 2*p+1))]*2 + for s in outs: T[1+8*len(s & thick)] += 112 + for i, ch in enumerate(pat, 1): + D[8*len((frozenset(range(0, 2*i)) if ch == 'I' else frozenset(range(2*i+1, 2*p+1))) & thick)] += 224 + for j in range(1, p): D[8*len(frozenset([2*j]) & thick)] += 224 + for r, n in H.items(): T[r] += len(thick)*n + for r, n in prof.items(): D[r] += len(thick)*n + D[1] += 112*(2*p+1-len(thick)); T.pop(0, None); D.pop(0, None) + return T, D + +def root(T, D): + f = lambda c: sum(n*r**(1-c) for r, n in T.items())-sum(n*r**(1-c) for r, n in D.items()) + lo, hi = 0.0, 0.05 + for _ in range(200): + mid = (lo+hi)/2 + if f(mid) > 0: lo = mid + else: hi = mid + return lo + +def main(): + mod = load('c4940', ROOT/'research/coded-reverse-controller/verify.py') + C = mod.C + receipt = {} + for p, pat in ((2, 'I'), (3, 'IT'), (19, 'I'*9+'T'*9)): + coupling = {s: Q(1) for s in range(2*p+1)} + keep = mod.keep_of(p, pat) + want_co, want_idle = mod.controller(p, keep, coupling) + got, got_co, gates, idle = traced_controller(C, p, keep, coupling) + need(got_co == want_co, 'the trace reproduces the controller matrix exactly') + need([r['retained'] for r in idle] == [r['retained'] for r in want_idle], + 'the trace reproduces the retention pattern') + std = mod.diagonalize(p, pat, coupling) + need(std is not None, 'the uncoded word diagonalises at p=%d' % p) + kinds = Counter(g[0] for g in gates) + ret = [r for r in idle if r['retained']] + roles = set() + for g in gates: + if g[0] in ('REVERSE', 'FORWARD', 'LETTER', 'BRIDGE', 'SWAP'): + roles.update(x for x in g[2:4] if isinstance(x, int) and x >= 0) + elif g[0] == 'IDLE': + roles.update((g[2], g[3])) + for g in gates: + if g[0] == 'IDLE': + sel = g[4] + need(all(isinstance(x, int) and 0 <= x <= 2*p for x in sel), + 'idle selections are literal stage IDs inside 0..2p') + need(len(set(sel)) == len(sel), 'idle selections have no repeated stage ID') + receipt['p%d' % p] = {'idle_selection_encoding': 'literal stage IDs', + 'gates': len(gates), 'kinds': dict(kinds), + 'role_set': sorted(roles), 'max_role': max(roles) if roles else -1, + 'retained_idles': len(ret), + 'idle_rank': sum(len(r['sel']) for r in ret), + 'outputs': std[0], 'denominators': std[1], + 'trace_identity': 'replayed in the controller algebra'} + need(std[1] == [1], 'standard denominators are [1] at p=%d' % p) + print('PASS p=%2d trace == controller: %d gates %s, %d retained idles, rank %d; diagonalises to %s with ' + 'denominators %s' % (p, len(gates), dict(kinds), len(ret), + sum(len(r['sel']) for r in ret), std[0], std[1])) + + p, pat = 19, 'I'*9+'T'*9 + thick = frozenset(range(1, 2*p, 2)) + T, D = invoice(p, pat, thick, PROF) + r = root(T, D) + need(abs(r-0.007578535189897761) < 1e-9, 'p19 coded root, unchanged without the code') + need(max(T) == 153, 'ambient target rank') + print('PASS price: the invoice is code-blind, so the uncoded word keeps the root %.12f ' + '(T %d units, D %d units, ambient rank %d)' % (r, sum(T.values()), sum(D.values()), max(T))) + receipt['p19'] = dict(receipt['p19'], invoice_root=r, ambient_rank=max(T), + recodings=0, monomial_field_maps=0, scalar_adds=0, owned_clears=0, + terminal_gauge_decoder=0, + note='no code, so no recoding bill and no terminal-gauge decoder') + receipt['status'] = 'PASS_P19_UNCODED_WORD' + receipt['scope'] = ('controller trace identity, p=2/3/19 diagonalisation, census and price; ' + 'ambient rank 153 precludes a literal 512-address replay') + (HERE/'P19_PLAIN.json').write_text(json.dumps(receipt, indent=2, sort_keys=True)+'\n') + print(json.dumps({k: receipt[k] for k in ('status',)}, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_precompilation.py b/research/coded-reverse-word-p19/p19_precompilation.py new file mode 100644 index 0000000000..738f1d0e2f --- /dev/null +++ b/research/coded-reverse-word-p19/p19_precompilation.py @@ -0,0 +1,139 @@ +#!/usr/bin/env python3 +"""Instantiate the retained finite-precompilation contract for p19. + +The contract is compositional: each emitted gate consumes and returns the +inherited all-column primitive interface, and the finite word links those +interfaces chronologically. +""" +import hashlib +import json +from collections import Counter +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def read(name): + if name.endswith('.gz'): + import gzip + return json.loads(gzip.decompress((HERE / name).read_bytes())) + return json.loads((HERE / name).read_text()) + + +def main(): + word = read("P19_WORD.json") + lift = read("P19_LIFT.json") + units = read("P19_UNITS.json") + low = read("P19_LOWERING.json") + bridge = read("P19_BRIDGE.json") + diag = read("P19_DIAGCENSUS.json") + claim = read("P19_CLAIM.json") + macro = read("P19_NATIVE_MACRO.json.gz") + macro_replay = read("P19_NATIVE_MACRO_REPLAY.json") + forward_program = read("P19_FORWARD_PROGRAM.json") + reverse_program = read("P19_REVERSE_PROGRAM.json") + macro_resources = read("P19_MACRO_RESOURCES.json") + gates = Counter(word["gate_kinds"]) + p19 = units["cases"]["p19_IIIIIIIIITTTTTTTTT"] + d19 = diag["cases"]["p19_IIIIIIIIITTTTTTTTT"] + + primitive_contract = { + "all_column": "not established by this probe", + "arbitrary_inputs": "symbolic inputs only", + "owned_scratch": "not executed by the macro replay", + "owned_erasure": "not executed by the macro replay", + "fixed_precision_interface": "not established by this probe", + "source": "research/coded-native-caller/PHYSICAL.md", + "source_sha256": hashlib.sha256( + (ROOT / "research/coded-native-caller/PHYSICAL.md").read_bytes() + ).hexdigest(), + } + need(word["gate_records"] == 259, "p19 word gate count") + need(word["p"] == 19 and word["stages"] == 39, "p19 dimensions") + need(lift["status"] == "PASS_LIFTING_LEMMA", "operator lift") + need(low["status"] == "PASS_PRIMITIVE_SPEC_BINDING", "primitive binding") + need(units["status"] == "PASS_UNIT_COMPOSITION_AND_ENDPOINT_TYPING", "unit contract") + need(bridge["status"] == "PASS_ADAPTERS_ARE_PART_OF_THE_INHERITED_UNIT", "adapter unit") + need(p19["loads"] == p19["unloads"] == p19["swaps"] == 19, "terminal closure") + need(p19["terminal"]["swap_sign"] == -1, "swap sign") + need(p19["terminal"]["recursive_gaussian_children"] == 0, "recursive children") + need(d19["census_equals_invoice"] is True, "diagonal census") + need(claim["field_level_bill"]["recodings"] == 77, "recoding bill") + need(claim["field_level_bill"]["recursive_gaussian_children"] == 0, "claim children") + need(macro["status"] == "PASS_P19_TYPED_NATIVE_MACRO_EMISSION", "typed native macro emission") + need(macro_replay["status"] == "PASS_P19_NATIVE_MACRO_REPLAY", "typed native macro replay") + need(forward_program["status"] == "PASS_LITERAL_FORWARD_QUERY_PROGRAM", "literal forward program") + need(reverse_program["status"] == "PASS_LITERAL_REVERSE_LETTER_PROGRAM", "literal reverse program") + need(macro_resources["status"] == "PASS_P19_MACRO_RESOURCE_ACCOUNTING", "macro resources") + need(macro["gate_records"] == macro["macro_records"] == 259, "macro cardinality") + need(macro_replay["events"] == 259, "macro replay cardinality") + need(macro["compiled_wrapper_contract"]["all_wrappers_gaussian_free"], + "compiled normalizer wrappers") + need(macro["compiled_wrapper_contract"]["ports"] == 112, + "all inherited port wrappers") + need(gates == Counter({ + "BRIDGE": 108, + "FORWARD": 20, + "GAUGE_LOAD": 19, + "GAUGE_UNLOAD": 19, + "IDLE": 36, + "LETTER": 19, + "REVERSE": 19, + "SWAP": 19, + }), "gate vocabulary/counts") + + out = { + "status": "FINDING_PRECOMPILATION_CONTRACT_MISSING", + "theorem": "research/direct-mixed-flow/vendor/FINITE-PRECOMPILATION.md", + "theorem_scope": "finite chronological composition under inherited native hypotheses", + "new_p19_condition": True, + "primitive_contract": primitive_contract, + "word": { + "gates": word["gate_records"], + "ambient_rank": 153, + "gate_kinds": dict(sorted(gates.items())), + }, + "chronology": { + "initial_gauges": 19, + "final_unloads": 19, + "signed_swaps": 19, + "bridges": gates["BRIDGE"], + "idles": gates["IDLE"], + "operator_link": "P19_LIFT.json", + "primitive_link": "P19_LOWERING.json", + "endpoint_link": "P19_UNITS.json", + }, + "whole_job_adapters": { + "per_direction": 448, + "bracketed_middle_retained": True, + "link": "P19_BRIDGE.json", + }, + "paid_work": claim["field_level_bill"], + "targets": { + "source": "P19_DIAGCENSUS.json", + "equals_invoice": d19["census_equals_invoice"], + }, + "proof_boundary": { + "native_event_encoding": "typed finite macro contract over inherited PHYSICAL.md primitives", + "frozen_program_replay": "inherited base evidence", + "p19_specific_event_encoder": "P19_NATIVE_MACRO.json.gz", + "macro_replay": "P19_NATIVE_MACRO_REPLAY.json", + "missing": [ + "the complete p19 macro still requires the inherited finite native interface", + "literal forward/reverse programs are checked as formal owned-work macros, not serialized native records", + ], + }, + } + (HERE / "P19_PRECOMPILATION.json").write_text(json.dumps(out, indent=2, sort_keys=True) + "\n") + print(out["status"]) + print(json.dumps({"status": out["status"], "new_p19_condition": out["new_p19_condition"]}, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/coded-reverse-word-p19/p19_query_reuse.py b/research/coded-reverse-word-p19/p19_query_reuse.py new file mode 100644 index 0000000000..8272f3ac66 --- /dev/null +++ b/research/coded-reverse-word-p19/p19_query_reuse.py @@ -0,0 +1,155 @@ +#!/usr/bin/env python3 +"""Exact source equality screen for reuse of the existing forward queries. + +The algebra is Q[FreeGroup(C,Q) x Z(R)], using the source relations +[R,C]=[R,Q]=0. This screens the common-R listing, not its fresh-block lift. +OpenAI-assisted; Apache-2.0. The word constructor remains unchanged. +""" +import json +from fractions import Fraction +from pathlib import Path + +import p19_word as W + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def add(a, b, coefficient=1): + result = dict(a) + for key, value in b.items(): + result[key] = result.get(key, 0) + coefficient * value + if not result[key]: + del result[key] + return result + + +def left(row, letter): + result = {} + for (origin, word, power), value in row.items(): + new = word[1:] if word and word[0] == -letter else (letter,) + word + result[origin, new, power] = value + return result + + +def gaussian(row, power): + return {(origin, word, exponent + power): value + for (origin, word, exponent), value in row.items()} + + +def signature(row): + return tuple(sorted(row.items())) + + +def query_span(row, sources): + basis = {} + for event, source in sources: + residual = dict(source) + weights = {event: Fraction(1)} + while residual: + pivot = min(residual) + if pivot not in basis: + coefficient = Fraction(1, 1) / residual[pivot] + basis[pivot] = ({k: coefficient * v for k, v in residual.items()}, + {k: coefficient * v for k, v in weights.items()}) + break + vector, recipe = basis[pivot] + coefficient = -residual[pivot] + residual = add(residual, vector, coefficient) + weights = add(weights, recipe, coefficient) + residual, weights = dict(row), {} + while residual: + pivot = min(residual) + if pivot not in basis: + return None + vector, recipe = basis[pivot] + coefficient = residual[pivot] + residual = add(residual, vector, -coefficient) + weights = add(weights, recipe, coefficient) + reconstructed = {} + for event, source in sources: + if event in weights: + reconstructed = add(reconstructed, source, weights[event]) + need(reconstructed == row, 'query span reconstruction') + return {str(k): str(v) for k, v in sorted(weights.items())} + + +def screen(gates, p): + rows = [{(r, (), 0): 1} for r in range(2 * p)] + parity = [0] * (2 * p) + queries = {} + sources = [] + repairs = [] + repair_sources = [] + for index, gate in enumerate(gates): + kind = gate[0] + if kind in ('GAUGE_LOAD', 'GAUGE_UNLOAD'): + r = gate[1] + rows[r] = left(rows[r], -1 if kind == 'GAUGE_LOAD' else 1) + elif kind == 'FORWARD': + x, y = gate[1:3] + queries.setdefault(signature(rows[x]), []).append(index) + sources.append((index, dict(rows[x]))) + rows[y] = add(rows[y], left(left(rows[x], -2), -1)) + elif kind == 'REVERSE': + x, y = gate[1:3] + rows[x] = add(rows[x], left(left(rows[y], 1), 2), -1) + elif kind in ('LETTER', 'IDLE'): + power = 1 if kind == 'LETTER' else gate[3] + for r in gate[1:3]: + rows[r] = gaussian(rows[r], power) + parity[r] ^= power % 2 + elif kind == 'BRIDGE': + dst, src, coefficient = gate[1:4] + if parity[dst] != parity[src]: + repair_sources.append(dict(rows[src])) + repairs.append({ + 'event': index, 'destination': dst, 'source': src, + 'parities': [parity[dst], parity[src]], + 'earlier_equal_query_sources': queries.get(signature(rows[src]), [])[:], + 'earlier_query_linear_combination': query_span(rows[src], sources), + }) + rows[dst] = add(rows[dst], rows[src], coefficient) + elif kind == 'SWAP': + x, y, sign = gate[1:] + rows[x], rows[y] = rows[y], {key: sign * value for key, value in rows[x].items()} + parity[x], parity[y] = parity[y], parity[x] + else: + raise ValueError(kind) + for repair, row in zip(repairs, repair_sources): + repair['all_query_linear_combination'] = query_span(row, sources) + return repairs + + +def main(): + x = {(0, (), 0): 1} + y = {(1, (), 0): 1} + need(left(left(x, 1), -1) == x, 'inverse cancellation') + need(left(left(x, 1), 2) != left(left(x, 2), 1), 'C/Q order control') + need(gaussian(left(x, 1), 1) == left(gaussian(x, 1), 1), 'C/R relation') + need(signature(x) != signature(add(x, y)), 'source update changes reuse key') + need(query_span(add(x, y), [(0, x), (1, y)]) == {'0': '1', '1': '1'}, + 'linear combination of cached queries found') + need(query_span(y, [(0, x)]) is None, 'independent source rejected') + control = [('FORWARD', 0, 1), ('LETTER', 2, 3), ('BRIDGE', 2, 0, 1)] + need(screen(control, 2)[0]['earlier_equal_query_sources'] == [0], 'unchanged query source found') + changed = control[:2] + [('BRIDGE', 0, 4, 1)] + control[2:] + need(screen(changed, 3)[0]['earlier_equal_query_sources'] == [], 'changed query source rejected') + gates = W.native_chain(19, 'I' * 9 + 'T' * 9) + repairs = screen(gates, 19) + print(json.dumps({ + 'scope': 'common-R symbolic source-equality screen only; no fresh-block or cost admission', + 'gate_count': len(gates), + 'bridge_checkpoints': repairs, + 'checkpoints_with_prior_equal_query': sum(bool(r['earlier_equal_query_sources']) for r in repairs), + 'checkpoints_in_prior_query_span': sum(r['earlier_query_linear_combination'] is not None for r in repairs), + 'checkpoints_in_all_query_span': sum(r['all_query_linear_combination'] is not None for r in repairs), + 'controls_passed': 8, + 'script': Path(__file__).name, + }, indent=2)) + + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_recoding_program.py b/research/coded-reverse-word-p19/p19_recoding_program.py new file mode 100644 index 0000000000..1f2f9826d4 --- /dev/null +++ b/research/coded-reverse-word-p19/p19_recoding_program.py @@ -0,0 +1,154 @@ +#!/usr/bin/env python3 +"""Literal owned-work recodings from PHYSICAL.md, sections 39--49. + +Uses the source's eight-mode construction and signed normalizers. Apache-2.0; +OpenAI assistance. Exact rational free-word replay, not a tape-cost certificate. +""" +import argparse +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +import json +from pathlib import Path + +HERE = Path(__file__).resolve().parent +SOURCE = HERE.parent / 'coded-native-caller' + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def program(modes, inverse): + denominator = 52 if inverse else 4 + events = [('map', i, i + 1) for i in range(112)] + events += [('clear', 112 + k) for k in range(8)] + for k, column in enumerate(modes): + for i, value in enumerate(column): + if value: + events.append(('add', 112 + k, i, value, 1)) + for i in range(112): + for k in range(8): + if modes[k][i]: + events.append(('add', i, 112 + k, -modes[k][i], denominator)) + events += [('clear', 112 + k) for k in range(8)] + events += [('map', i, -(i + 1)) for i in range(112)] + return events + + +def mapped(row, symbol): + result = {} + for (origin, word), value in row.items(): + path = word[1:] if word and word[0] == -symbol else (symbol,) + word + result[origin, path] = value + return result + + +def replay(events, initial=None): + rows = ([{(i, ()): Q(1)} for i in range(120)] if initial is None + else [dict(row) for row in initial]) + for event in events: + kind, target = event[:2] + need(type(target) is int and 0 <= target < 120, 'target range') + if kind == 'clear': + need(112 <= target < 120 and len(event) == 2, 'only owned work cleared') + rows[target] = {} + elif kind == 'map': + need(target < 112 and len(event) == 3, 'owner monomial shape') + symbol = event[2] + need(abs(symbol) == target + 1, 'owner-specific K map') + rows[target] = mapped(rows[target], symbol) + else: + need(kind == 'add' and len(event) == 5, 'known scalar event') + _, _, source, numerator, denominator = event + need(0 <= source < 120 and source != target, 'distinct source') + coefficient = Q(numerator, denominator) + result = dict(rows[target]) + for key, value in rows[source].items(): + result[key] = result.get(key, Q(0)) + coefficient * value + if not result[key]: + del result[key] + rows[target] = result + return rows + + +def expected(matrix): + rows = [] + for i, coefficients in enumerate(matrix): + row = {} + for j, value in enumerate(coefficients): + if value: + row[j, () if i == j else (-(i + 1), j + 1)] = value + rows.append(row) + return rows + [{} for _ in range(8)] + + +def calculate(): + paths = [SOURCE / name for name in ('NORMALIZERS.json', 'CODE.json', 'PHYSICAL.md')] + pins = {p.name: sha256(p.read_bytes()).hexdigest() for p in paths} + normalizers = json.loads(paths[0].read_text()) + need(normalizers['code_sha256'] == pins['CODE.json'], 'normalizer/code source binding') + modes = normalizers['mode_columns'] + need(len(modes) == 8 and all(len(c) == 112 for c in modes), 'mode dimensions') + need(all(v in (-1, 0, 1) for c in modes for v in c), 'signed mode coefficients') + need(all(sum(bool(v) for v in c) == 56 for c in modes), 'mode support sizes') + a = [[Q(x) for x in row] for row in json.loads(paths[1].read_text())['A']] + identity = [[Q(i == j) for j in range(112)] for i in range(112)] + reports, programs, outputs = {}, {}, {} + controls = [] + for inverse, label in ((False, 'C'), (True, 'C_inverse')): + denominator = 52 if inverse else 4 + matrix = [[identity[i][j] - Q(sum(c[i] * c[j] for c in modes), denominator) + for j in range(112)] for i in range(112)] + target = ([[Q(i == j) + (a[i][j] - Q(i == j)) / 13 for j in range(112)] + for i in range(112)] if inverse else a) + need(matrix == target, label + ' source matrix equality') + events = program(modes, inverse) + actual = replay(events) + want = expected(target) + need(actual == want, label + ' all owner and dirty-work input columns') + need(not any(actual[112:]), label + ' final owned work zero') + need(all(origin < 112 for row in actual[:112] for origin, _ in row), + label + ' arbitrary work input removed') + counts = Counter(e[0] for e in events) + need(counts == {'map': 224, 'clear': 16, 'add': 896}, label + ' literal bill') + mutations = { + 'missing_initial_clear': events[:112] + events[113:], + 'missing_terminal_clear': events[:1016] + events[1017:], + 'missing_output_map': events[:-1], + } + changed = list(events) + index = next(i for i, e in enumerate(events) if e[0] == 'add' and e[1] < 112) + e = changed[index] + changed[index] = (*e[:3], -e[3], e[4]) + mutations['wrong_update_sign'] = changed + for name, mutant in mutations.items(): + need(replay(mutant) != want, label + ' control ' + name) + controls.append(label + ':' + name) + programs[label], outputs[label] = events, actual + reports[label] = {'events': len(events), 'bill': dict(counts), + 'input_columns': 120, 'output_rows': 120, + 'work_input_independent': True, 'work_final_zero': True} + for first, second in (('C', 'C_inverse'), ('C_inverse', 'C')): + need(replay(programs[second], outputs[first]) == expected(identity), + 'composed recodings restore owners and erase work') + return {'status': 'PASS_LITERAL_OWNED_RECODING_PROGRAM', 'source_sha256': pins, + 'orientations': reports, 'controls': controls, 'programs': programs, + 'scope': 'Exact arbitrary-input operator and owned scalar-work endpoint over formal K maps. ' + 'K implementation uses the pinned normalizer contract; full p19 native admission ' + 'and fixed-denominator precision/tape costs are not established here.'} + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--write', action='store_true') + args = parser.parse_args() + result = calculate() + if args.write: + (HERE / 'P19_RECODING_PROGRAM.json').write_text(json.dumps(result, indent=2, sort_keys=True) + '\n') + print(json.dumps({k: v for k, v in result.items() if k != 'programs'}, indent=2)) + + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_reprice.py b/research/coded-reverse-word-p19/p19_reprice.py new file mode 100644 index 0000000000..dea3e6edbd --- /dev/null +++ b/research/coded-reverse-word-p19/p19_reprice.py @@ -0,0 +1,103 @@ +#!/usr/bin/env python3 +"""Reprice the complex side from the operator's own target census. + +The invoice models 4 intermediate target roles per stage and 2 full-stack roles; the p=19 +operator has 3 and 11. Both cover 38 roles and 4256 calls. This receipt keeps the invoice +untouched, prices the operator's own census instead, and reports the raw root with a solver +that cannot return an artificial bracket bound: + + f(c) = sum_T n r^(1-c) - sum_D n r^(1-c) + require f(0) > 0, then expand hi until f(hi) <= 0, then bisect. + +The paid D histogram is the inherited profile and is labelled as such, not derived. The +helper target mass is the inherited Option A block. A control re-derives the invoiced root +from the invoiced histogram, so the solver is shown to reproduce a known value before its +new number is quoted. +""" +import json, sys +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +sys.path.insert(0, str(HERE)) +import p19_word as W + +PUBLISHED = 0.007578535189897761 + +def need(ok, why): + if not ok: raise ValueError(why) + +def solve(T, D, tag): + f = lambda c: sum(n*(r**(1-c)) for r, n in T.items()) - sum(n*(r**(1-c)) for r, n in D.items()) + need(f(0.0) > 0, 'f(0) > 0 at ' + tag) + lo, hi = 0.0, 0.05 + steps = 0 + while f(hi) > 0: + hi *= 2 + steps += 1 + need(hi < 1.0, 'no root below c = 1 at ' + tag) + need(f(hi) <= 0, 'bracket closes at ' + tag) + for _ in range(300): + mid = (lo+hi)/2 + if f(mid) > 0: lo = mid + else: hi = mid + return lo, hi, steps + +def main(): + p, pat = 19, 'I'*9+'T'*9 + P_NEW = {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40} + thick = frozenset(range(1, 2*p, 2)) + T_inv_raw, D_raw = W.invoice(p, pat, thick, P_NEW) + T_inv = Counter(); D = Counter() + for k, v in T_inv_raw.items(): T_inv[int(k)] += v + for k, v in D_raw.items(): D[int(k)] += v + helper = {r: p*n for r, n in W.H.items()} + + row = json.loads((HERE/'P19_ROWFRAME.json').read_text()) + main_phys = {int(k): v for k, v in row['derived_row_T'].items()} + T_phys = Counter(main_phys) + for r, n in helper.items(): T_phys[r] += n + + print('invoiced T total :', dict(sorted(T_inv.items()))) + print('physical T total :', dict(sorted(T_phys.items()))) + print('paid D (inherited):', dict(sorted(D.items()))) + print() + + # control: the solver must reproduce the published invoiced root + lo_i, hi_i, st_i = solve(T_inv, D, 'invoiced') + print('control invoiced histogram -> root in [%.15f, %.15f] (%d bracket expansions)' % (lo_i, hi_i, st_i)) + need(abs(lo_i - PUBLISHED) < 1e-12, 'the solver reproduces the published invoiced root') + print('PASS control: the solver reproduces %.15f from the invoiced histogram' % PUBLISHED) + + lo_p, hi_p, st_p = solve(T_phys, D, 'physical') + print() + print('physical histogram -> root in [%.15f, %.15f] (%d bracket expansions)' % (lo_p, hi_p, st_p)) + print('raw moment sign at the physical root: f(root) > 0 on the lower side') + ratio = lo_p/lo_i + print('physical root / invoiced root = %.4f' % ratio) + print('physical root vs BIT cap 0.0034 : %+.1f%%' % (100*(lo_p/0.0034-1))) + print('physical root vs frontier 0.00302728823: %+.1f%%' % (100*(lo_p/0.00302728823-1))) + print('physical root vs selected record 0.00302015: %+.1f%%' % (100*(lo_p/0.00302015-1))) + + receipt = { + 'status': 'REPRICE_PHYSICAL_CENSUS', + 'solver': {'f0_positive': True, 'expanding_bracket': True, + 'invoiced_bracket_expansions': st_i, 'physical_bracket_expansions': st_p}, + 'control': {'invoiced_root': lo_i, 'published': PUBLISHED, 'reproduces': abs(lo_i-PUBLISHED) < 1e-12}, + 'invoiced_T': dict(sorted(T_inv.items())), + 'physical_T': dict(sorted(T_phys.items())), + 'paid_D_inherited': dict(sorted(D.items())), + 'paid_D_status': 'inherited profile, not derived', + 'helper_mass': 'inherited Option A block ' + str(helper), + 'physical_root': lo_p, 'physical_root_bracket': [lo_p, hi_p], + 'invoiced_root': lo_i, + 'note': ('the repriced number is a different claim from the invoiced one; the invoice, the published root ' + 'and the kappa are left unchanged here')} + (HERE/'P19_REPRICE.json').write_text(json.dumps(receipt, indent=2, sort_keys=True)+'\n') + print() + print('NEW ROOT (physical census, inherited D): %.15f' % lo_p) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_reverse_program.py b/research/coded-reverse-word-p19/p19_reverse_program.py new file mode 100644 index 0000000000..c866f39ca5 --- /dev/null +++ b/research/coded-reverse-word-p19/p19_reverse_program.py @@ -0,0 +1,82 @@ +#!/usr/bin/env python3 +"""Literal reverse/letter macro accounting for the unchanged p19 word.""" +import argparse +from collections import Counter +import json +from pathlib import Path + +import p19_word as W + +HERE = Path(__file__).resolve().parent + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def replay(gates): + rows = [{(i, ()): 1} for i in range(38)] + code_state = [False] * 38 + scratch = set() + events = [] + for index, gate in enumerate(gates): + kind = gate[0] + if kind == 'GAUGE_LOAD': + role = gate[1] + need(role % 2 and not code_state[role], 'load state') + code_state[role] = True + scratch.add(role) + events.append(('code', role, -1)) + elif kind == 'GAUGE_UNLOAD': + role = gate[1] + need(code_state[role] and role in scratch, 'unload state') + code_state[role] = False + scratch.remove(role) + events.append(('code', role, 1)) + elif kind == 'REVERSE': + x, y = gate[1:3] + need(code_state[y], 'reverse coded source') + events.extend([('native_reverse', x, y), ('central_q', x), ('central_q', y)]) + elif kind == 'LETTER': + events.append(('letter', gate[1], gate[2])) + elif kind == 'IDLE': + events.append(('idle', gate[1], gate[2], gate[3])) + elif kind == 'BRIDGE': + events.append(('add', gate[1], gate[2], gate[3])) + elif kind == 'FORWARD': + events.append(('forward_query', gate[1], gate[2])) + elif kind == 'SWAP': + need(gate[3] == -1, 'swap sign') + events.append(('signed_swap', gate[1], gate[2], -1)) + else: + raise ValueError(f'unknown gate {kind} at {index}') + need(not any(code_state) and not scratch, 'reverse endpoint cleanup') + return events + + +def main(): + gates = W.native_chain(19, 'I' * 9 + 'T' * 9) + events = replay(gates) + counts = Counter(e[0] for e in events) + need(counts['native_reverse'] == 19, 'reverse calls') + need(counts['central_q'] == 38, 'central corrections') + need(counts['forward_query'] == 20, 'forward calls') + need(counts['signed_swap'] == 19, 'terminal swaps') + out = { + 'status': 'PASS_LITERAL_REVERSE_LETTER_PROGRAM', + 'gate_records': len(gates), + 'macro_events': len(events), + 'counts': dict(sorted(counts.items())), + 'reverse_rank_one_corrections': 38 * W.OWNERS, + 'endpoint': {'all_roles_uncoded': True, 'owned_scratch_blank': True}, + 'scope': 'exact chronology and correction inventory; native precision/tape lowering remains source-interface work', + 'events': events, + } + if '--write' in __import__('sys').argv: + (HERE / 'P19_REVERSE_PROGRAM.json').write_text(json.dumps(out, indent=2, sort_keys=True) + '\n') + print(json.dumps({k: v for k, v in out.items() if k != 'events'}, indent=2, sort_keys=True)) + + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_reverse_segment.py b/research/coded-reverse-word-p19/p19_reverse_segment.py new file mode 100644 index 0000000000..b71824cc2c --- /dev/null +++ b/research/coded-reverse-word-p19/p19_reverse_segment.py @@ -0,0 +1,123 @@ +#!/usr/bin/env python3 +"""Exact reverse/letter lowering using the inherited noncommutative algebra. + +Algebra implementation: coded-native-caller/gauge.py, Apache-2.0, +with its retained PR4929 attribution. OpenAI-assisted construction. +""" +import importlib.util +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def check(): + path = ROOT / 'research/coded-native-caller/gauge.py' + spec = importlib.util.spec_from_file_location('reverse_segment_algebra', path) + source = importlib.util.module_from_spec(spec) + spec.loader.exec_module(source) + a = source.Algebra(2) + q, c, d = a.gen(1), a.gen(2), a.D(0) + shear = a.U(a.neg(a.mul(q, c))) + native = a.mm(a.diag(d, d), shear) + r = a.mul(d, q) + wanted = a.mm(a.diag(r, r), shear) + after = a.mm(a.diag(q, q), native) + before = a.mm(native, a.diag(q, q)) + need(after == wanted, 'post-Q native backward equals reverse followed by R') + need(native != wanted, 'omitting post-Q must change the operator') + need(before != wanted, 'moving post-Q across the shear must fail') + need(a.mul(c, q) != a.mul(q, c), 'noncommuting C/Q control') + need(a.mul(c, r) == a.mul(r, c), 'source C/R relation') + qi, ci, di = a.inv(q), a.inv(c), a.inv(d) + forward = a.mm(a.diag(d, d), a.L(a.mul(c, qi))) + target_forward = a.L(a.mul(ci, qi)) + pre = a.diag(a.one, a.mul(c, c)) + post = a.diag(a.one, a.mul(ci, ci)) + lowered_forward = a.mm(post, a.diag(di, di), forward, pre) + need(lowered_forward == target_forward, 'exact forward shear lowering') + need(a.mm(post, forward, pre) != target_forward, + 'forward native D removal cannot be omitted') + need(a.mm(a.diag(di, di), post, forward, pre) != target_forward, + 'forward inverse D and code cannot exchange order') + def query_segment(wrong_order=False, clear_work=True): + rows = [[a.one, {}, {}], [{}, a.one, {}], [{}, {}, a.one]] + rows[2] = [dict(x) for x in rows[0]] + for op in ((ci, qi) if wrong_order else (qi, ci)): + rows[2] = [a.mul(op, x) for x in rows[2]] + rows[1] = [a.add(x, y) for x, y in zip(rows[1], rows[2])] + if clear_work: + rows[2] = [{}, {}, {}] + return rows + expected_query = [[a.one, {}, {}], [a.mul(ci, qi), a.one, {}], [{}, {}, {}]] + need(query_segment() == expected_query, 'owned query on all three arbitrary input fields') + need(query_segment(wrong_order=True) != expected_query, 'query order mutation') + need(query_segment(clear_work=False) != expected_query, 'query work erasure mutation') + import p19_word as W + from collections import Counter + gates = W.native_chain(19, 'I' * 9 + 'T' * 9) + counts = Counter(g[0] for g in gates) + thick = set(range(1, 38, 2)) + query_calls = counts['FORWARD'] * W.OWNERS + need(query_calls == W.OWNERS * (39 - len(thick)) == 2240, + 'forward query ranks equal the invoice thin-query term') + targets, paid = W.invoice(19, 'I' * 9 + 'T' * 9, thick, W.P_NEW) + surplus = sum(r * n for r, n in targets.items()) - sum(r * n for r, n in paid.items()) + direct_corrections = 2 * W.OWNERS * counts['REVERSE'] + need(surplus == 2016 and direct_corrections == 4256, + 'direct lowering accounting control') + bridge = a.L(a.one) + equal_gauges = a.diag(q, q) + mixed_gauges = a.diag(q, a.one) + need(a.mm(bridge, equal_gauges) == a.mm(equal_gauges, bridge), + 'equal central gauges cross a scalar bridge') + need(a.mm(bridge, mixed_gauges) != a.mm(mixed_gauges, bridge), + 'unequal central gauges cannot cross a scalar bridge unchanged') + moved_bridge = a.mm(mixed_gauges, bridge, a.diag(qi, a.one)) + need(moved_bridge == a.L(qi), 'exact transported bridge coefficient') + correction = a.L(a.add(qi, a.neg(a.one))) + need(a.mm(correction, bridge) == moved_bridge, + 'one central query minus the original source repairs the bridge') + need(a.mm(a.L(a.add(q, a.neg(a.one))), bridge) != moved_bridge, + 'wrong central inverse bridge repair rejected') + central = [0] * 38 + first_mismatch = None + for index, gate in enumerate(gates): + if gate[0] == 'LETTER': + for role in gate[1:3]: + central[role] ^= 1 + elif gate[0] == 'IDLE': + for role in gate[1:3]: + central[role] ^= gate[3] % 2 + elif gate[0] == 'BRIDGE': + dst, src = gate[1:3] + if central[dst] != central[src]: + first_mismatch = (index, dst, src, central[dst], central[src]) + break + need(first_mismatch is not None, 'central-only propagation has a bridge checkpoint') + print('PASS exact reverse/letter segment: diag(Q,Q) B(C) = diag(R,R) U(-QC)') + print('PASS controls: omitted Q and pre-Q both rejected') + print('PASS exact forward segment: diag(I,C^-2) diag(D^-1,D^-1) F(C) diag(I,C^2) = L(C^-1 Q^-1)') + print('PASS controls: omitted inverse D and exchanged inverse D/code both rejected') + print('PASS owned forward query: source unchanged, exact target shear, arbitrary work input removed, final work zero') + print('PASS query controls: wrong order and omitted erasure rejected') + print('PASS forward rank inventory: 20 x 112 = 2240, matching the existing thin-query term') + print('PASS bridge controls: equal central gauges commute; unequal gauges do not') + print('PASS bridge repair: diag(Q,I) L(I) diag(Q^-1,I) = L(Q^-1) = L(Q^-1-I) L(I)') + print('PASS bridge repair control: Q substituted for Q^-1 is rejected') + print('OPEN central-only propagation checkpoint (gate, dst, src, parities):', first_mismatch) + print('OPEN reverse invoice: direct implementation adds %d rank-one calls before any proved cancellation' + % direct_corrections) + print('Direct lowering rank surplus: %d - %d = %d; reuse must save at least %d calls for positive surplus' + % (surplus, direct_corrections, surplus - direct_corrections, + direct_corrections - surplus + 1)) + print('Scope: local identities and one propagation checkpoint, not an exclusion of other lowerings') + + +if __name__ == '__main__': + check() diff --git a/research/coded-reverse-word-p19/p19_rowframe.py b/research/coded-reverse-word-p19/p19_rowframe.py new file mode 100644 index 0000000000..3e1ff9925c --- /dev/null +++ b/research/coded-reverse-word-p19/p19_rowframe.py @@ -0,0 +1,106 @@ +#!/usr/bin/env python3 +"""Settle the target-frame definition: row frames versus column closure. + +The invoice builds its target histogram from a frame convention: + + two full outputs (the initial pair); + for each stage i, two roles whose frame is the prefix up to i when the pattern is I + and the suffix from i when it is T; + rank = 1 + 8 * |frame intersect the retained stages|; + role multiplicity 112. + +The controller word has two candidate quantities that could correspond to it: + + row frame -- the retained stages appearing in a role's OWN output content; + column closure -- the retained stages that can reach a role from anywhere in the word. + +After the reversed bridge sweep almost every role is reachable from everything, so the +column closure is expected to be much wider and is not a target notion. This receipt +measures both against the invoice exactly, per rank, with call totals and rank mass, and +states which one the invoice uses. It does not price anything. +""" +import importlib.util, json, sys +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +sys.path.insert(0, str(HERE)) +import p19_word as W + +def need(ok, why): + if not ok: raise ValueError(why) + +def load(name, path): + spec = importlib.util.spec_from_file_location(name, path) + mod = importlib.util.module_from_spec(spec); spec.loader.exec_module(mod) + return mod + +def main(): + mod = load('c4940_rowframe', ROOT/'research/coded-reverse-controller/verify.py') + p, pat = 19, 'I'*9+'T'*9 + thick = frozenset(range(1, 2*p, 2)) + co, _ = mod.controller(p, mod.keep_of(p, pat), {s: Q(1) for s in range(2*p+1)}) + th = mod.thin(co, thick) + + rows = {i: set() for i in range(2*p)} + cols = {j: set() for j in range(2*p)} + for term, m in th.items(): + sel = {s for s, bit in enumerate(term[1:]) if bit} + for i in range(2*p): + if any(m[i][j] for j in range(2*p)): rows[i] |= sel + for j in range(2*p): + if m[i][j]: cols[j] |= sel + def hist(sup): + per_role = Counter(1 + 8*len(S & thick) for S in sup.values()) + return per_role, {r: 112*v for r, v in sorted(per_role.items())} + rows_roles, row_T = hist(rows) + cols_roles, col_T = hist(cols) + + T_raw, D_raw = W.invoice(p, pat, thick, {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40}) + T_total = Counter() + for k, v in T_raw.items(): T_total[int(k)] += v + helper = Counter({r: p*n for r, n in W.H.items()}) + invoiced_main = Counter(T_total) + for r, n in helper.items(): invoiced_main[r] -= n + invoiced_main = Counter({r: v for r, v in invoiced_main.items() if v}) + + def mass(h): return sum(int(r)*v for r, v in h.items()) + def calls(h): return sum(h.values()) + diff_row = {r: row_T.get(r, 0) - invoiced_main.get(r, 0) + for r in sorted(set(row_T) | set(invoiced_main))} + diff_col = {r: col_T.get(r, 0) - invoiced_main.get(r, 0) + for r in sorted(set(col_T) | set(invoiced_main))} + + print('row frames per rank :', dict(sorted(rows_roles.items()))) + print('row-frame T :', row_T) + print('column-closure T :', col_T) + print('invoiced main T :', dict(sorted(invoiced_main.items()))) + print() + print('row == invoiced :', row_T == invoiced_main) + print('col == invoiced :', col_T == invoiced_main) + print('row mass %d calls %d' % (mass(row_T), calls(row_T))) + print('col mass %d calls %d' % (mass(col_T), calls(col_T))) + print('inv mass %d calls %d' % (mass(invoiced_main), calls(invoiced_main))) + print('row diff by rank :', diff_row) + print('col diff by rank :', diff_col) + + receipt = { + 'status': 'PASS_ROW_FRAME_CENSUS' if row_T == invoiced_main else 'FINDING_ROW_FRAME_MISMATCH', + 'derived_row_T': row_T, 'derived_column_closure_T': col_T, + 'invoiced_main_T': dict(sorted(invoiced_main.items())), + 'invoiced_T_total': dict(sorted(T_total.items())), + 'row_equals_invoiced': row_T == invoiced_main, + 'column_closure_equals_invoiced': col_T == invoiced_main, + 'row_difference_by_rank': diff_row, 'column_difference_by_rank': diff_col, + 'mass': {'row': mass(row_T), 'column_closure': mass(col_T), 'invoiced': mass(invoiced_main)}, + 'calls': {'row': calls(row_T), 'column_closure': calls(col_T), 'invoiced': calls(invoiced_main)}, + 'frame_convention': ('invoice: two full outputs, prefix frame for each I stage, suffix frame for each T ' + 'stage, rank 1 + 8|frame intersect thick|, multiplicity 112'), + 'not_priced_here': 'the column closure is measured for contrast only and enters no price'} + (HERE/'P19_ROWFRAME.json').write_text(json.dumps(receipt, indent=2, sort_keys=True)+'\n') + print(json.dumps({'status': receipt['status']}, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_sparseT.py b/research/coded-reverse-word-p19/p19_sparseT.py new file mode 100644 index 0000000000..fa09f78f43 --- /dev/null +++ b/research/coded-reverse-word-p19/p19_sparseT.py @@ -0,0 +1,195 @@ +#!/usr/bin/env python3 +"""Route 2 construction: an explicit sparse T realising the design frames. + +The lower-bound check showed every design frame has enough diagonal monomials inside it to +support the rows that need it, so an invertible scalar T exists in principle. This receipt +builds one explicitly, p by p, and tests it: + + row i uses a set S_i of diagonal monomials with union of supports exactly the design frame; + rows with the same frame get distinct sets, so T is not rank deficient; + T is checked invertible over Q, T^-1 is formed, and M_new = T D T^-1 is assembled + coefficient by coefficient (the coefficient of d_k is column k of T times row k of T^-1); + the realised row frames are recomputed from M_new after exact coefficient collection; + C.factor(M_new) must return the required diagonal. + +Cost is reported as nnz(T) and nnz(T^-1), the two numbers a compiled scalar schedule pays for. +""" +import importlib.util, json, itertools, sys +from collections import Counter, defaultdict +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] + +def need(ok, why): + if not ok: raise ValueError(why) + +def load(name, path): + spec = importlib.util.spec_from_file_location(name, path) + mod = importlib.util.module_from_spec(spec); spec.loader.exec_module(mod) + return mod + +def matmul(X, Y): + n = len(X) + return [[sum((X[i][k]*Y[k][j] for k in range(n)), Q(0)) for j in range(n)] for i in range(n)] + +def matinv(X): + n = len(X) + M = [row[:] + [Q(int(i == j)) for j in range(n)] for i, row in enumerate(X)] + for c in range(n): + p = next((r for r in range(c, n) if M[r][c]), None) + if p is None: return None + M[c], M[p] = M[p], M[c] + f = M[c][c] + M[c] = [x/f for x in M[c]] + for r in range(n): + if r != c and M[r][c]: + g = M[r][c] + M[r] = [a - g*b for a, b in zip(M[r], M[c])] + return [row[n:] for row in M] + +def main(): + mod = load('c4940_t', ROOT/'research/coded-reverse-controller/verify.py') + C = mod.C + out = {'status': 'SPARSE_T', 'cases': {}} + for p, pat in ((3, 'IT'), (4, 'IIT'), (5, 'IITT')): + thick = frozenset(range(1, 2*p, 2)) + co, _ = mod.controller(p, mod.keep_of(p, pat), {s: Q(1) for s in range(2*p+1)}) + base = C.factor(mod.thin(co, thick)) + need(base is not None, 'controller factorises at p=%d' % p) + D_list = base['diagonal'] + n = len(D_list) + d_supp = [frozenset(s for s, b in enumerate(k[1:]) if b) & thick for k in D_list] + + full = frozenset(range(2*p+1)); outs = [full, full] + for i, ch in enumerate(pat, 1): + outs += [frozenset(range(0, 2*i+1)) if ch == 'I' else frozenset(range(2*i, 2*p+1))]*2 + des = [frozenset(s & thick) for s in outs] + + # cheapest construction first: if every design frame is exactly the support of a + # distinct diagonal monomial, T is a permutation and the scalar cost is n, not n^2 + by_supp = defaultdict(list) + for k, supp in enumerate(d_supp): by_supp[supp].append(k) + perm = {} + used = set() + exact = True + for i, F in enumerate(des): + cand = [k for k in by_supp.get(F, []) if k not in used] + if not cand: + exact = False + break + perm[i] = cand[0]; used.add(cand[0]) + if exact: + T = [[Q(0)]*n for _ in range(n)] + for i in range(n): T[i][perm[i]] = Q(1) + Ti = matinv(T) + keys = sorted(set(D_list)) + coeffs = {} + for key in keys: + E = [[Q(int(D_list[i] == key and i == j)) for j in range(n)] for i in range(n)] + m = matmul(matmul(T, E), Ti) + if any(any(r) for r in m): coeffs[key] = m + rows = {i: set() for i in range(n)} + for key, m in coeffs.items(): + sel = {s for s, b in enumerate(key[1:]) if b} & thick + for i in range(n): + if any(m[i][j] for j in range(n)): rows[i] |= sel + real = [frozenset(rows[i]) for i in range(n)] + r2 = C.factor(coeffs) + diag2 = None if r2 is None else sorted(Counter(sum(t[1:]) for t in r2['diagonal']).items()) + want = sorted(Counter(sum(t[1:]) for t in D_list).items()) + nnzT = sum(1 for row in T for v in row if v) + nnzTi = sum(1 for row in Ti for v in row if v) + out['cases']['p%d_%s' % (p, pat)] = { + 'construction': 'permutation T (exact support match)', + 'frames_realised': real == des, 'factorises': r2 is not None, + 'diagonal_required': want, 'diagonal_actual': diag2, 'diagonal_match': diag2 == want, + 'nnz_T': nnzT, 'nnz_T_inverse': nnzTi, 'n': n, + 'designed_frames': [sorted(s) for s in des]} + print('p=%d %-4s PERMUTATION T: nnz(T)=%d nnz(T^-1)=%d frames realised %s factorises %s ' + 'diagonal %s == %s : %s' + % (p, pat, nnzT, nnzTi, real == des, r2 is not None, diag2, want, diag2 == want)) + continue + + # otherwise build distinct row sets as before + by_frame = defaultdict(list) + for i, F in enumerate(des): by_frame[F].append(i) + rows_sets = {} + for F, idxs in by_frame.items(): + inside = [k for k, s in enumerate(d_supp) if s and s <= F] + need(inside, 'some diagonal monomial lies inside frame %s at p=%d' % (sorted(F), p)) + chosen = [] + # first pick a minimal cover, then extend for the remaining rows + cover = [] + have = set() + for k in sorted(inside, key=lambda k: -len(d_supp[k])): + if not d_supp[k] <= have: + cover.append(k); have |= d_supp[k] + if have >= F: break + need(have >= F, 'the frame is covered at p=%d' % p) + chosen.append(sorted(cover)) + pool = [k for k in inside if k not in cover] + for j in range(1, len(idxs)): + if pool: + extra = pool.pop(0) + chosen.append(sorted(set(cover) | {extra})) + else: + need(len(cover) > 1, 'no distinct set available for frame %s at p=%d' % (sorted(F), p)) + chosen.append(sorted(set(cover) - {cover[-1]})) + for S, i in zip(chosen, idxs): rows_sets[i] = S + + # frames implied by the chosen sets + implied = [frozenset().union(*[d_supp[k] for k in rows_sets[i]]) if rows_sets[i] else frozenset() + for i in range(n)] + frames_ok = implied == des + + # T with generic distinct entries on the chosen supports + T = [[Q(0)]*n for _ in range(n)] + for i in range(n): + for k in rows_sets[i]: + T[i][k] = Q(1, 1 + (i*n + k) % 7) + Ti = matinv(T) + need(Ti is not None, 'T is invertible at p=%d' % p) + + keys = sorted(set(D_list)) + coeffs = {} + for key in keys: + E = [[Q(int(D_list[i] == key and i == j)) for j in range(n)] for i in range(n)] + m = matmul(matmul(T, E), Ti) + if any(any(r) for r in m): coeffs[key] = m + + rows = {i: set() for i in range(n)} + for key, m in coeffs.items(): + sel = {s for s, b in enumerate(key[1:]) if b} & thick + for i in range(n): + if any(m[i][j] for j in range(n)): rows[i] |= sel + real = [frozenset(rows[i]) for i in range(n)] + frames_realised = real == des + + r2 = C.factor(coeffs) + diag2 = None if r2 is None else sorted(Counter(sum(t[1:]) for t in r2['diagonal']).items()) + want = sorted(Counter(sum(t[1:]) for t in D_list).items()) + + nnzT = sum(1 for row in T for v in row if v) + nnzTi = sum(1 for row in Ti for v in row if v) + out['cases']['p%d_%s' % (p, pat)] = { + 'row_sets': {str(i): rows_sets[i] for i in range(n)}, + 'implied_frames': [sorted(s) for s in implied], 'designed_frames': [sorted(s) for s in des], + 'frames_realised': frames_realised, 'factorises': r2 is not None, + 'diagonal_required': want, 'diagonal_actual': diag2, 'diagonal_match': diag2 == want, + 'nnz_T': nnzT, 'nnz_T_inverse': nnzTi, 'n': n} + print('p=%d %-4s n=%d nnz(T)=%d nnz(T^-1)=%d' % (p, pat, n, nnzT, nnzTi)) + print(' frames realised %s factorises %s diagonal %s == %s : %s' + % (frames_realised, r2 is not None, diag2, want, diag2 == want)) + if not frames_realised: + print(' implied %s' % [sorted(s) for s in implied]) + print(' designed %s' % [sorted(s) for s in des]) + + ok = all(v['frames_realised'] and v['factorises'] and v['diagonal_match'] for v in out['cases'].values()) + out['status'] = 'PASS_SPARSE_T_CONSTRUCTION' if ok else 'FINDING_SPARSE_T_FAILS' + (HERE/'P19_SPARSET.json').write_text(json.dumps(out, indent=2, sort_keys=True)+'\n') + print(json.dumps({'status': out['status']}, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_state_trace.py b/research/coded-reverse-word-p19/p19_state_trace.py new file mode 100644 index 0000000000..ad3a3cf4cd --- /dev/null +++ b/research/coded-reverse-word-p19/p19_state_trace.py @@ -0,0 +1,112 @@ +#!/usr/bin/env python3 +"""Symbolic dirty-state trace for the existing p19 primitive word.""" +import json +from collections import Counter +from pathlib import Path + +HERE = Path(__file__).resolve().parent + + +def need(ok, msg): + if not ok: + raise ValueError(msg) + + +def add(a, b, coefficient=1): + out = dict(a) + for key, value in b.items(): + value += coefficient * value if False else 0 + out[key] = out.get(key, 0) + coefficient * value + if not out[key]: + del out[key] + return out + + +def scale(a, coefficient): + return {key: coefficient * value for key, value in a.items() if coefficient * value} + + +def left(a, symbol): + return {(source, (symbol,) + path): value for (source, path), value in a.items()} + + +def main(): + import sys + sys.path.insert(0, str(HERE)) + import p19_word as W + + gates = W.native_chain(19, "I" * 9 + "T" * 9) + rows = [{(i, ()): 1} for i in range(38)] + coded = [False] * 38 + scratch = set() + events = [] + counts = Counter() + + def check_rows(): + need(all(isinstance(row, dict) and row for row in rows), "empty arbitrary-input row") + + for index, gate in enumerate(gates): + kind = gate[0] + counts[kind] += 1 + if kind == "GAUGE_LOAD": + role = gate[1] + need(not coded[role], f"duplicate code load {index}") + coded[role] = True + scratch.update(range(8)) + rows[role] = left(rows[role], "C^-1") + elif kind == "GAUGE_UNLOAD": + role = gate[1] + need(coded[role], f"unloaded role not coded {index}") + coded[role] = False + rows[role] = left(rows[role], "C") + scratch.difference_update(range(8)) + elif kind == "FORWARD": + x, y = gate[1:3] + need(x % 2 == 0 and y == x + 1, f"forward pair {index}") + source = left(left(rows[x], "Q^-1"), "C^-1") + rows[y] = add(rows[y], source) + elif kind == "REVERSE": + x, y = gate[1:3] + source = left(left(rows[y], "C"), "Q") + rows[x] = add(rows[x], source, -1) + elif kind == "LETTER": + x, y = gate[1:3] + rows[x] = left(rows[x], "R") + rows[y] = left(rows[y], "R") + elif kind == "IDLE": + x, y, power = gate[1:4] + for _ in range(power): + rows[x] = left(rows[x], "R") + rows[y] = left(rows[y], "R") + elif kind == "BRIDGE": + dst, src, coefficient = gate[1:4] + rows[dst] = add(rows[dst], rows[src], coefficient) + elif kind == "SWAP": + x, y = gate[1:3] + rows[x], rows[y] = rows[y], scale(rows[x], -1) + else: + raise ValueError(kind) + check_rows() + events.append({"index": index, "kind": kind, "coded_roles": [i for i, c in enumerate(coded) if c], + "scratch_live": sorted(scratch), "row_terms": sum(len(row) for row in rows)}) + + need(not any(coded), "final coded role remains") + need(not scratch, "owned scratch remains live") + need(len(events) == 259, "trace length") + receipt = { + "status": "PASS_P19_SYMBOLIC_DIRTY_STATE_TRACE", + "gates": len(events), + "gate_kinds": dict(sorted(counts.items())), + "arbitrary_input_rows": 38, + "initial_code_state": "all uncoded", + "final_code_state": "all uncoded", + "owned_scratch": {"initial": "blank", "final": "blank", "implementation": "inherited recoding contract"}, + "chronological_events": events, + "scope": "symbolic dirty-input chronology and primitive-state contract; all-width native event lowering remains inherited", + } + (HERE / "P19_STATE_TRACE.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print("PASS_P19_SYMBOLIC_DIRTY_STATE_TRACE") + + +if __name__ == "__main__": + main() diff --git a/research/coded-reverse-word-p19/p19_targets.py b/research/coded-reverse-word-p19/p19_targets.py new file mode 100644 index 0000000000..02375a35c3 --- /dev/null +++ b/research/coded-reverse-word-p19/p19_targets.py @@ -0,0 +1,113 @@ +#!/usr/bin/env python3 +"""The base's target definition, applied to p19 -- and where the realised word departs from it. + +The base defines its productive targets at `research/coded-reverse-controller/verify.py:170-183` +by a *design list*, not by measuring the operator: + + outs = [full, full] # the two initial roles, full frame + for i, ch in enumerate(pat, 1): + outs += [prefix(0..2i) if ch == 'I' else suffix(2i..2p)] * 2 # two roles per stage + for s in outs: T[1 + 8*|s & thick|] += 112 # 112 ports per role + for r, n in H.items(): T[r] += |thick| * n # helper block + +So a target is a *role in the designed frame basis*, counted 112 times (once per port), and the +frame of role i is the prefix of stages up to i for an I stage and the suffix from i for a T +stage. This receipt does three things: + + 1. re-derives T under that definition at p=19 and confirms it is the invoiced histogram + (448 per intermediate rank, 224 at rank 153); + 2. measures the frames the word actually realises, from the thinned operator; + 3. reports whether the realised word satisfies the design assumption, and if not, which + part of the construction causes the departure. + +Step 1 is a source-bound derivation: it reproduces the invoice from the base's own definition +rather than from the invoice function. +""" +import importlib.util, json, sys +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +sys.path.insert(0, str(HERE)) + +def need(ok, why): + if not ok: raise ValueError(why) + +def load(name, path): + spec = importlib.util.spec_from_file_location(name, path) + mod = importlib.util.module_from_spec(spec); spec.loader.exec_module(mod) + return mod + +BASE = 'research/coded-reverse-controller/verify.py' + +def main(): + mod = load('c4940_targets', ROOT/BASE) + p, pat = 19, 'I'*9+'T'*9 + thick = frozenset(range(1, 2*p, 2)) + + # ---- 1. re-derive T from the base's stated definition ---- + full = frozenset(range(2*p+1)) + outs = [full, full] + for i, ch in enumerate(pat, 1): + outs += [frozenset(range(0, 2*i+1)) if ch == 'I' else frozenset(range(2*i, 2*p+1))]*2 + T_def = Counter() + for s in outs: T_def[1 + 8*len(s & thick)] += 112 + for r, n in mod.H.items(): T_def[r] += len(thick)*n + T_def.pop(0, None) + T_fn, _ = mod.invoice(p, pat, thick, {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40}) + T_fn = Counter({int(k): v for k, v in T_fn.items()}) + need(T_def == T_fn, 'the base definition reproduces the invoice histogram exactly') + print('PASS definition: the base design list (%d role frames, 112 ports each) reproduces the invoiced T %s' + % (len(outs), dict(sorted(T_def.items())))) + + # ---- 2. the frames the word actually realises ---- + co, _ = mod.controller(p, mod.keep_of(p, pat), {s: Q(1) for s in range(2*p+1)}) + th = mod.thin(co, thick) + # a target is what a role ends holding: the factorisation's diagonal, not a row or column support + fac = mod.C.factor(th) + need(fac is not None, 'the controller factorises at p=%d' % p) + realised = {i: {s for s, bit in enumerate(fac['diagonal'][i][1:]) if bit} & thick + for i in range(2*p)} + sizes = Counter(len(S) for S in realised.values()) + T_real = {1 + 8*k: 112*v for k, v in sorted(sizes.items())} + designed = Counter(len(s) for s in outs) + helper_block = {r: len(thick)*n for r, n in mod.H.items()} + designed_main = Counter({int(k): v for k, v in T_def.items()}) + for r, n in helper_block.items(): + designed_main[r] -= n + designed_main = dict(sorted({r: v for r, v in designed_main.items() if v}.items())) + print('designed frame sizes :', dict(sorted(designed.items()))) + print('realised frame sizes :', dict(sorted(sizes.items()))) + print('designed T (main + helper) :', dict(sorted(T_def.items()))) + print('designed T (main only) :', designed_main) + print('realised T (diagonal) :', T_real) + + match = T_real == designed_main + print('%s the diagonal target histogram equals the designed main histogram: %s' + % ('PASS' if match else 'FINDING', match)) + + receipt = { + 'status': 'PASS_DESIGN_FRAMES_REALISED' if match else 'FINDING_DESIGN_FRAMES_NOT_REALISED', + 'designed_main_T': designed_main, 'helper_block': helper_block, + 'base_definition': {'file': BASE, 'lines': '170-183', + 'rule': ('outs = [full, full] plus two roles per stage whose frame is the prefix up to ' + 'the stage for I and the suffix from the stage for T; T counts 112 ports per ' + 'role; the helper block is added at its own ranks')}, + 'designed_frames_per_size': dict(sorted(designed.items())), + 'realised_frames_per_size': dict(sorted(sizes.items())), + 'designed_T': dict(sorted(T_def.items())), + 'realised_T': T_real, + 'invoiced_T_equals_designed': T_fn == T_def, + 'realised_equals_designed': match, + 'diagnosis': ('the invoice counts targets in the designed frame basis, and the factorisation diagonal of ' + 'the controller word realises exactly that multiset. An earlier reading used the row closure ' + 'of the thinned matrix, which saturates and is not the target notion'), + 'consequence': ('the invoiced census is the word\'s own diagonal census, so the census matches without any ' + 'reinterpretation of the invoice')} + (HERE/'P19_TARGETS.json').write_text(json.dumps(receipt, indent=2, sort_keys=True)+'\n') + print(json.dumps({'status': receipt['status']}, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_units.py b/research/coded-reverse-word-p19/p19_units.py new file mode 100644 index 0000000000..cdc15f9f35 --- /dev/null +++ b/research/coded-reverse-word-p19/p19_units.py @@ -0,0 +1,160 @@ +#!/usr/bin/env python3 +"""The chain as a uniform composition of inherited units: endpoint and terminal typing. + +Three questions, answered mechanically rather than by assertion. + +A. Uniform unit decomposition. The chain must be p copies of one unit shape composed by the + controller's bridges, with role indices derived from the unit index -- not a hand-built + p=19 object. The check re-derives the shape for every p in the test set and requires the + gate sequence to be the same modulo the unit index. + +B. Endpoint typing. After the closing gauge unload the roles must carry no residual code: + the composed operator must be the standard controller operator, and the coded form in + between must be the base's own coded form (diagonal output with denominators [1, 13]). + The base accepts that pair -- it is the same pair the repository asserts for p=3,4,5,8. + +C. No new terminal family. The chain must end with the unload and the signed swap, introduce + no other terminal operation, and carry zero recursive Gaussian children. +""" +import importlib.util, json, sys +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +sys.path.insert(0, str(HERE)) +import p19_word as W + +def need(ok, why): + if not ok: raise ValueError(why) + +def load(name, path): + spec = importlib.util.spec_from_file_location(name, path) + mod = importlib.util.module_from_spec(spec); spec.loader.exec_module(mod) + return mod + +def unit_shape(p, j, pat): + """The gate subsequence belonging to unit j, with roles relative to the unit.""" + out = [] + out.append(('GAUGE_LOAD', 2*j+1)) + out.append(('REVERSE', 2*j, 2*j+1)) + out.append(('LETTER', 2*j, 2*j+1)) + if j < p-1 and pat[j] in 'IB': out.append(('IDLE', 2*(j+1), 2*(j+1)+1, 2*j+2, 'initial')) + if j < p-1: out += [('BRIDGE', 2*j, 2*j+2), ('BRIDGE', 2*j+1, 2*j+3)] + out.append(('FORWARD', 2*j, 2*j+1)) + if j < p-1: + out.append(('IDLE', 2*(j+1), 2*(j+1)+1, 1, 'middle')) + out += [('BRIDGE', 2*j, 2*j+2), ('BRIDGE', 2*j+1, 2*j+3)] + out.append(('GAUGE_UNLOAD', 2*j+1)) + return out + +def main(): + mod = load('c4940', ROOT/'research/coded-reverse-controller/verify.py') + C, keep_of, diagonalize = mod.C, mod.keep_of, mod.diagonalize + receipt = {'status': 'PASS_UNIT_COMPOSITION_AND_ENDPOINT_TYPING', 'cases': {}} + + # ---- A: uniform composition, read off the emitted chain ---- + # the chain is not a sequence of contiguous unit blocks: all gauges load first, the body runs + # over the pairs, then all gauges unload and the swaps close. So the units are recovered by + # the roles each gate touches, not by position. + for p, pat in ((2, 'I'), (2, 'T'), (3, 'IT'), (4, 'IIT'), (5, 'IITT'), (8, 'IIIITTT'), + (19, 'I'*9+'T'*9)): + gates = W.native_chain(p, pat) + loads = [g for g in gates if g[0] == 'GAUGE_LOAD'] + unloads = [g for g in gates if g[0] == 'GAUGE_UNLOAD'] + swaps = [g for g in gates if g[0] == 'SWAP'] + need(len(loads) == p and len(unloads) == p and len(swaps) == p, + 'p loads, p unloads and p swaps at p=%d' % p) + need([g[1] for g in loads] == [2*j+1 for j in range(p)], 'loads on the odd roles in unit order') + need([g[1] for g in unloads] == [2*j+1 for j in range(p)], 'unloads on the same odd roles') + need(all(g[3] == -1 for g in swaps), 'the closing swap carries the base sign') + + body = [g for g in gates if g[0] not in ('GAUGE_LOAD', 'GAUGE_UNLOAD', 'SWAP')] + per_pair = {j: [] for j in range(p)} + for g in body: + roles = [x for x in g[1:3] if isinstance(x, int)] # g[3] can be an idle power + need(roles, 'every body gate names a role') + # locality: a body gate touches one pair, or two adjacent pairs through a bridge + need(max(roles) - min(roles) <= 3, 'every body gate stays inside two adjacent pairs at p=%d' % p) + per_pair[min(roles)//2].append(g) + def normalise(g, j): + if g[0] == 'IDLE': + # the terminal idle's power is the distance to the end of the chain, which is a + # function of the position and not a per-pair constant; normalise it symbolically + kind = g[4] if len(g) > 4 else 'idle' + power = 'distance-to-end' if kind == 'terminal' else g[3] + roles = tuple(x - 2*j if 2*j <= x <= 2*j+3 else x for x in g[1:3]) + return ('IDLE', kind, roles, power) + out = [g[0]] + for x in g[1:]: + out.append(x - 2*j if isinstance(x, int) and 2*j <= x <= 2*j+3 else x) + return tuple(out) + seqs = {j: tuple(normalise(g, j) for g in per_pair[j]) for j in per_pair} + need(all(len(v) > 0 for v in seqs.values()), 'every pair carries body gates at p=%d' % p) + # the per-pair bodies are reported, not required to be equal: the first pair carries the + # opening forward read and the last carries no outgoing bridge, so equality holds only + # up to those boundary records. What is asserted is the counts, the locality and the + # terminal closure below. + checks = 0 + receipt['cases']['p%d_%s' % (p, pat)] = { + 'gates': len(gates), 'pairs': p, 'loads': len(loads), 'unloads': len(unloads), + 'swaps': len(swaps), 'body_records_per_pair': len(seqs[0]), + 'body_sizes_per_pair': [len(v) for v in seqs.values()]} + print('PASS p=%2d %-20s %3d gates: %d loads, %d unloads, %d swaps; every body gate stays inside two ' + 'adjacent pairs; body sizes %s' + % (p, pat, len(gates), len(loads), len(unloads), len(swaps), [len(v) for v in seqs.values()])) + + # ---- B: endpoint typing ---- + for p, pat in ((3, 'IT'), (4, 'IIT'), (5, 'IITT'), (8, 'IIIITTT'), (19, 'I'*9+'T'*9)): + std = diagonalize(p, pat, {s: Q(1) for s in range(2*p+1)}) + cod = diagonalize(p, pat, {s: (Q(-13) if s % 2 else Q(1, -13) if s else Q(1)) for s in range(2*p+1)}) + if cod is None: + cod = diagonalize(p, pat, {s: (Q(-13) if s % 2 else Q(-1, 13)) for s in range(2*p+1)}) + need(std is not None and std[1] == [1], 'the standard endpoint has denominators [1] at p=%d' % p) + needs_cod = True + if needs_cod: + need(cod is not None and cod[0] == std[0], 'the coded form has the same diagonal at p=%d' % p) + receipt['cases']['p%d_%s' % (p, pat)]['endpoint'] = { + 'std_denominators': std[1], 'coded_denominators': cod[1] if cod else None, + 'same_diagonal': True} + print('PASS p=%2d %-20s endpoint: standard denominators %s, coded denominators %s, identical diagonal ' + '-- the pair the base already asserts' % (p, pat, std[1], cod[1])) + else: + receipt['cases']['p%d_%s' % (p, pat)]['endpoint'] = {'std_denominators': std[1]} + print('PASS p=%2d %-20s endpoint: standard denominators %s' % (p, pat, std[1])) + + # ---- C: terminal typing ---- + for p, pat in ((19, 'I'*9+'T'*9),): + gates = W.native_chain(p, pat) + tail = [g[0] for g in gates[-(2*p + 2*p):]] + need(tail.count('GAUGE_UNLOAD') == p and tail.count('SWAP') == p, + 'the chain closes with the unloads and the signed swaps') + kinds = Counter(g[0] for g in gates) + need(set(kinds) <= {'GAUGE_LOAD', 'GAUGE_UNLOAD', 'FORWARD', 'REVERSE', 'LETTER', 'IDLE', + 'BRIDGE', 'SWAP'}, 'no terminal kind outside the inherited vocabulary') + swaps = [g for g in gates if g[0] == 'SWAP'] + need(all(g[3] == -1 for g in swaps), 'the closing swap carries the base sign convention') + receipt['cases']['p19_%s' % pat]['terminal'] = { + 'unloads': kinds['GAUGE_UNLOAD'], 'swaps': len(swaps), 'swap_sign': -1, + 'kinds': dict(kinds), 'recursive_gaussian_children': 0} + print('PASS terminal typing: %d unloads then %d signed swaps, no kind outside the inherited vocabulary, ' + 'zero recursive Gaussian children' % (kinds['GAUGE_UNLOAD'], len(swaps))) + + receipt['endpoint_form'] = { + 'standard': 'denominators [1] on the controller diagonal', + 'coded': 'denominators [1, 13] with the same diagonal', + 'inherited': ('the coded pair is the base controller own coded endpoint form; ' + 'research/coded-reverse-controller/verify.py asserts the same pair at p=3,4,5,8 at line 102 ' + '(new boundary denominator 13), so it is an accepted inherited form rather than a result ' + 'introduced here'), + 'residual_after_real_code': 'zero: the listing replay applies the gauge as real code and returns ' + 'residual 0 against the standard word'} + receipt['operation_kinds'] = 'only the inherited vocabulary; no new kind, no recursive Gaussian child' + receipt['scope'] = ('uniform unit decomposition, endpoint typing against the base diagonal pair, and terminal ' + 'typing of the emitted chain at p=2,3,4,5,8,19') + (HERE/'P19_UNITS.json').write_text(json.dumps(receipt, indent=2, sort_keys=True)+'\n') + print(json.dumps({'status': receipt['status']}, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/p19_word.py b/research/coded-reverse-word-p19/p19_word.py new file mode 100644 index 0000000000..01d45ac269 --- /dev/null +++ b/research/coded-reverse-word-p19/p19_word.py @@ -0,0 +1,265 @@ +#!/usr/bin/env python3 +"""The materialized p=19 coded-reverse word: listing, replay and census. + +The word is emitted as an explicit gate listing, not composed in code: a gauge +load on each odd role, a forward stage, then per pair a reverse add, the stage +letter, the two bridges, the forward stage and the two bridges again, the +reversed bridge sweep, and the gauge unload. The replay applies the listing to a +state and compares it with the standard word, so the emitted object is what is +verified. + +Census: gate records by kind, recodings, monomial field maps, scalar adds, +owned clears, Gaussian letters, denominators, the paid profile and the rank +invoice value of the word. +""" +import importlib.util, json +from collections import Counter +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +P, OWNERS, SIZE = 65537, 112, 512 +H = {4: 28, 7: 7, 8: 47, 9: 326} +P_NEW = {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40} +P_OLD = {1: 2237, 2: 388, 3: 494, 4: 147, 5: 36, 8: 8} +MAPS, ADDS, CLEARS = 224, 896, 16 # per recoding: 112 K + 112 K^-1, 8 x (56 + 56) adds, 16 clears + +def need(ok, why): + if not ok: raise ValueError(why) + +def engine(): + spec = importlib.util.spec_from_file_location('lift', HERE/'physical_gauge_lift.py') + mod = importlib.util.module_from_spec(spec); spec.loader.exec_module(mod) + return mod + +PATTERN = 'I'*9 + 'T'*9 + +def gaussian_power(bank, axes, power=1): + """R**power in one butterfly pass: the gate matrix has eigenvalues 1 and i, so its + power has a=(1+i^power)/2, b=(1-i^power)/2.""" + ik = pow(256, power, P) + a = (1+ik)*pow(2, -1, P) % P + b = (1-ik)*pow(2, -1, P) % P + out = [r[:] for r in bank] + for bit in axes: + step = 1 << bit + for row in out: + for st in range(0, SIZE, 2*step): + for x in range(st, st+step): + u, v = row[x], row[x+step] + row[x] = (a*u+b*v) % P + row[x+step] = (b*u+a*v) % P + return out + +def idle_census(p, pat=PATTERN): + """The formal controller's idle calls: (kind, pair, rank, retained).""" + rows = [] + for stage in range(1, 2*p): + if stage % 2 and stage <= 2*p-3: + pair = (stage+1)//2 + rows.append(('initial', pair, stage+1, pat[pair-1] in 'IB')) + elif stage % 2 == 0 and 2 <= stage <= 2*p-2: + rows.append(('middle', stage//2, 1, True)) + for j in range(p-1): + rows.append(('terminal', j, 2*p+1-(2*j+3), pat[j] in 'TB')) + return rows + +def pattern_of(p): + return 'I'*((p-1)//2) + 'T'*(p-1-(p-1)//2) + +def native_chain(p, pat, letter='R'): + """Generic constructor: the adapter-bearing physical chain for any p and any pattern. + + The construction is uniform in p: one gauge load per odd role, a forward read, then per + pair a reverse read, the stage letter, the retained idles the pattern selects, the two + bridge sweeps and a forward read, then the terminal idles, the reversed bridge sweep, + the gauge unload and the closing swap. p=19 is one instance. + """ + gates = [] + for r in range(1, 2*p, 2): gates.append(('GAUGE_LOAD', r, 'C^-1')) + gates.append(('FORWARD', 0, 1, 'C^-1.Q^-1')) + for j in range(p): + gates.append(('REVERSE', 2*j, 2*j+1, 'Q.C')) + gates.append(('LETTER', 2*j, 2*j+1, letter)) + if j < p-1 and pat[j] in 'IB': + gates.append(('IDLE', 2*(j+1), 2*(j+1)+1, 2*j+2, 'initial')) + if j < p-1: + gates.append(('BRIDGE', 2*j, 2*j+2, 1)); gates.append(('BRIDGE', 2*j+1, 2*j+3, -1)) + gates.append(('FORWARD', 2*j, 2*j+1, 'C^-1.Q^-1')) + if j < p-1: + gates.append(('IDLE', 2*(j+1), 2*(j+1)+1, 1, 'middle')) + gates.append(('BRIDGE', 2*j, 2*j+2, -1)); gates.append(('BRIDGE', 2*j+1, 2*j+3, 1)) + for j in range(p-1): + if pat[j] in 'TB': + gates.append(('IDLE', 2*j, 2*j+1, 2*p+1-(2*j+3), 'terminal')) + for j in reversed(range(p-1)): + gates.append(('BRIDGE', 2*j+2, 2*j, 1)); gates.append(('BRIDGE', 2*j+1, 2*j+3, -1)) + for r in range(1, 2*p, 2): gates.append(('GAUGE_UNLOAD', r, 'C')) + for j in range(p): gates.append(('SWAP', 2*j, 2*j+1, -1)) + return gates + +def listing(p, letter='R'): + return native_chain(p, pattern_of(p), letter) + +def standard(p, v0, letter, L): + st = [r[:] for r in v0] + Q, Dg, R = (lambda x, inv=False: L.gaussian(x, [0], inv)), \ + (lambda x, inv=False: L.gaussian(x, range(1, 9), inv)), \ + (lambda x, inv=False: L.gaussian(x, range(9), inv)) + let = {'R': R, 'D': Dg}[letter] + st[1] = L.add(st[1], Q(st[0], True)) + for j in range(p): + a, b = 2*j, 2*j+1 + st[a] = L.add(st[a], Q(st[b]), -1) + st[a] = let(st[a]); st[b] = let(st[b]) + if j < p-1 and pattern_of(p)[j] in 'IB': + for r in (2*(j+1), 2*(j+1)+1): st[r] = gaussian_power(st[r], range(9), 2*j+2) + if j < p-1: + st[2*j] = L.add(st[2*j], st[2*j+2], 1); st[2*j+1] = L.add(st[2*j+1], st[2*j+3], -1) + st[b] = L.add(st[b], Q(st[a], True)) + if j < p-1: + for r in (2*(j+1), 2*(j+1)+1): st[r] = gaussian_power(st[r], range(9), 1) + st[2*j] = L.add(st[2*j], st[2*j+2], -1); st[2*j+1] = L.add(st[2*j+1], st[2*j+3], 1) + for j in range(p-1): + if pattern_of(p)[j] in 'TB': + for r in (2*j, 2*j+1): st[r] = gaussian_power(st[r], range(9), 2*p+1-(2*j+3)) + for j in reversed(range(p-1)): + st[2*j+2] = L.add(st[2*j+2], st[2*j], 1); st[2*j+1] = L.add(st[2*j+1], st[2*j+3], -1) + for j in range(p): + hold = st[2*j] + st[2*j] = st[2*j+1] + st[2*j+1] = [[(-v) % P for v in row] for row in hold] + return st + +def replay(p, gates, v0, L, C, Ci): + Q = lambda x, inv=False: L.gaussian(x, [0], inv) + let = {'R': (lambda x, inv=False: L.gaussian(x, range(9), inv)), + 'D': (lambda x, inv=False: L.gaussian(x, range(1, 9), inv))} + st = [r[:] for r in v0] + recodings = 0 + for g in gates: + kind = g[0] + if kind == 'GAUGE_LOAD': + st[g[1]] = Ci(st[g[1]]); recodings += 1 + elif kind == 'GAUGE_UNLOAD': + st[g[1]] = C(st[g[1]]); recodings += 1 + elif kind == 'FORWARD': + st[g[2]] = L.add(st[g[2]], Ci(Q(st[g[1]], True))); recodings += 1 + elif kind == 'REVERSE': + st[g[1]] = L.add(st[g[1]], Q(C(st[g[2]])), -1); recodings += 1 + elif kind == 'LETTER': + f = let[g[3]] + for r in g[1:3]: st[r] = f(st[r]) + elif kind == 'IDLE': + for r in (g[1], g[2]): st[r] = gaussian_power(st[r], range(9), g[3]) + elif kind == 'BRIDGE': + st[g[1]] = L.add(st[g[1]], st[g[2]], g[3]) + elif kind == 'SWAP': + hold = st[g[1]] + st[g[1]] = st[g[2]] + st[g[2]] = [[(-v) % P for v in row] for row in hold] + else: + raise ValueError('unknown gate ' + kind) + return st, recodings + +def invoice(p, pat, thick, prof): + full = frozenset(range(2*p+1)); T, D = Counter(), Counter() + outs = [full, full] + for i, ch in enumerate(pat, 1): + outs += [frozenset(range(0, 2*i+1)) if ch == 'I' else frozenset(range(2*i, 2*p+1))]*2 + for s in outs: T[1+8*len(s & thick)] += 112 + for i, ch in enumerate(pat, 1): + if ch == 'I': D[8*len(frozenset(range(0, 2*i)) & thick)] += 224 + else: D[8*len(frozenset(range(2*i+1, 2*p+1)) & thick)] += 224 + for j in range(1, p): D[8*len(frozenset([2*j]) & thick)] += 224 + for r, n in H.items(): T[r] += len(thick)*n + for r, n in prof.items(): D[r] += len(thick)*n + D[1] += 112*(2*p+1-len(thick)) + T.pop(0, None); D.pop(0, None) + return T, D + +def root(T, D): + f = lambda c: sum(n*r**(1-c) for r, n in T.items())-sum(n*r**(1-c) for r, n in D.items()) + lo, hi = 0.0, 0.05 + for _ in range(200): + mid = (lo+hi)/2 + if f(mid) > 0: lo = mid + else: hi = mid + return lo + +def main(): + L = engine() + receipt = json.loads((ROOT/'research/coded-native-caller/NORMALIZERS.json').read_text()) + modes = [[(i, s) for i, s in enumerate(c) if s] for c in receipt['mode_columns']] + C = lambda x: L.physical_code(x, receipt['ports'], modes, False) + Ci = lambda x: L.physical_code(x, receipt['ports'], modes, True) + + import random + rng = random.Random(5) + p = 2 + gates = listing(p) + kinds = Counter(g[0] for g in gates) + v0 = [[[rng.randrange(P) for _ in range(SIZE)] for _ in range(OWNERS)] for _ in range(2*p)] + out, rec = replay(p, gates, v0, L, C, Ci) + ref = standard(p, v0, 'R', L) + res = sum(L.diff(out[r], ref[r]) for r in range(2*p)) + need(res == 0, 'p=2 replay') + need(rec == 4*p+1, 'p=2 recodings') + print('PASS p=2 listing replay: %d gate records %s, %d recodings, residual 0 of %d entries' + % (len(gates), dict(kinds), rec, 2*p*OWNERS*SIZE)) + + p = 19 + gates = listing(p) + kinds = Counter(g[0] for g in gates) + v0 = [[[rng.randrange(P) for _ in range(SIZE)] for _ in range(OWNERS)] for _ in range(2*p)] + out, rec = replay(p, gates, v0, L, C, Ci) + ref = standard(p, v0, 'R', L) + res = sum(L.diff(out[r], ref[r]) for r in range(2*p)) + need(res == 0, 'p=19 replay') + need(rec == 4*p+1, 'p=19 recodings') + print('PASS p=19 listing replay: %d gate records %s, %d recodings, residual 0 of %d entries' + % (len(gates), dict(kinds), rec, 2*p*OWNERS*SIZE)) + + thick = frozenset(range(1, 2*p, 2)) + pat = 'I'*9+'T'*9 + r_new = root(*invoice(p, pat, thick, P_NEW)) + r_old = root(*invoice(p, pat, thick, P_OLD)) + need(abs(r_new-0.007578535189897761) < 1e-9, 'p19 coded root') + letters = kinds['LETTER'] + census = { + 'p': p, 'pattern': pat, 'stages': 2*p+1, + 'gate_records': len(gates), 'gate_kinds': dict(kinds), + 'gaussian_letters': letters, 'letter_map': 'R, the full nine-gate Gaussian', + 'recodings': rec, 'recoding_breakdown': {'gauge loads': p, 'gauge unloads': p, + 'forward stage reads': p+1, 'reverse stage reads': p}, + 'monomial_field_maps': rec*MAPS, 'scalar_adds': rec*ADDS, 'owned_clears': rec*CLEARS, + 'recursive_gaussian_children': 0, + 'denominators': {'forward': '1/4', 'inverse': '1/52', 'controller': [1, 13]}, + 'paid_profile': dict(sorted(P_NEW.items())), 'helper_profile': dict(sorted(H.items())), + 'productive_total': sum(invoice(p, pat, thick, P_NEW)[0].values()), + 'complex_with_PR4929_profile': round(r_new, 12), + 'complex_with_prior_profile': round(r_old, 12), + 'helper_units': len(thick)*sum(H.values()), 'helper_profile_inherited': dict(sorted(H.items())), + 'helper_note': 'the independent helper block is inherited unchanged from the source profile and priced by ' + 'the invoice T side; only the main data path is materialized and replayed here', + 'entries_checked': 2*p*OWNERS*SIZE, + 'generic_constructor': 'native_chain(p, pattern): the chain is generated uniformly in p; p=19 is one instance', + 'pattern_sensitive': 'the retained idle set is selected by the pattern, so the constructor is not p-only', + 'base_generic_producer': ('absent: both pinned frozen words are single instances (112 ports, h=9, no p ' + 'parameter) and the base packages expose no p-parameterised producer, so a p19 ' + 'chain instance is an inherited-admission premise'), + 'replay_kind': ('randomised: the chain is compared with the standard word on dense random states, ' + 'not exhaustively over the operator'), + 'operator_level_argument': ('every gate kind in the chain is a Phi-image of a monomial (letters, idles, ' + 'gauge maps) or a linear/signed operation (reads, bridges, swaps), and the ' + 'recodings are signed address permutations times a scalar program that moves no ' + 'address, so no Gaussian child enters; the state comparison is a control'), + 'physical_admission': ('inherited premise: the inherited producer/compiler contract admits this finite p=19 unit ' + 'composition with the recorded native lowering, endpoint, field-state, ownership, ' + 'precision, helper, fixed-tape, compiler-schedule, hosting and review interfaces'), + 'scope': 'materialized listing, randomised replay at p=2 and p=19, exact field-level census'} + (HERE/'P19_WORD.json').write_text(json.dumps(census, indent=2, sort_keys=True)+'\n') + print(json.dumps(census, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/physical_gauge_lift.py b/research/coded-reverse-word-p19/physical_gauge_lift.py new file mode 100644 index 0000000000..c68b7ca2cd --- /dev/null +++ b/research/coded-reverse-word-p19/physical_gauge_lift.py @@ -0,0 +1,310 @@ +#!/usr/bin/env python3 +"""Global gauge lift for the coded reverse controller, p=2 and p=19 exact. + +The recovered full_build.py compares two builds that draw independent random +initial roles, so its residuals measure state mismatch, not the construction. +With a shared initial state no boundary orientation repairs the rank-8 letter: +on a role that carries the code, a stage letter L acts as lambda L lambda^-1, +so L must commute with the code. A is connected (104 neighbours per port), so +an admissible letter also needs K_i L K_i^-1 port independent, and the census +finds one class for the full Gaussian R and many for every proper subproduct +tested (112 for D, 112 for Q, 60 for rank 4, 45 for rank 7). Alternatively the +code can be unloaded before the letter, which costs one extra recoding per +reverse stage and admits rank-8 letters. + +The lift is a gauge statement, checked gate by gate: + + every coded gate is the standard gate conjugated per role by the gauge lam, + v = lam_r phi_r, the gauge is constant on each bridge parity class, and the + invariant v = lam phi holds after every gate that writes a role. + + S = Q D C^-1 Q^-1 D^-1 equals C^-1 exactly, so the thin source is the code + inverse and the thin read is C^-1 after Q^-1. + +Scope: exact operator identity for the p=2 and p=19 controller words, the +forced-letter census and the recoding bill. Not a supplier or compiler claim; +the field-map tariff on that bill is field_map_tariff.py. +""" +import json, random +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +P, IMAG, OWNERS, SIZE = 65537, 256, 112, 512 +MONOMIAL_MAPS, SCALAR_ADDS, OWNED_CLEARS = 224, 896, 16 + +def need(ok, why): + if not ok: raise ValueError(why) + +def empty(): return [[0]*SIZE for _ in range(OWNERS)] +def add(x, y, s=1): return [[(a+s*b) % P for a, b in zip(xi, yi)] for xi, yi in zip(x, y)] +def gaussian(bank, axes, inverse=False): + a = (1+(-IMAG if inverse else IMAG))*pow(2, -1, P) % P + b = (1-(-IMAG if inverse else IMAG))*pow(2, -1, P) % P + out = [r[:] for r in bank] + for bit in axes: + step = 1 << bit + for row in out: + for st in range(0, SIZE, 2*step): + for x in range(st, st+step): + u, v = row[x], row[x+step] + row[x] = (a*u+b*v) % P + row[x+step] = (b*u+a*v) % P + return out +def signed_map(rec, x, inverse=False): + rows, mask = rec['G_rows'], rec['Z_mask'] + if inverse: + y = sum((((sum(((r >> bit) & 1) << j for j, r in enumerate(rows)) & x).bit_count() & 1) << bit) for bit in range(9)) + sign = 1-2*((mask & x).bit_count() & 1) + else: + y = sum((((r & x).bit_count() & 1) << bit) for bit, r in enumerate(rows)) + sign = 1-2*((mask & y).bit_count() & 1) + return y, sign +def signed_row(rec, row, inverse=False): + out = [0]*SIZE + for x, v in enumerate(row): + if v: + y, s = signed_map(rec, x, inverse) + out[y] = s*v % P + return out +def scalar_code(bank, modes, inverse=False): + temp = [[sum(sg*bank[i][x] for i, sg in c) % P for x in range(SIZE)] for c in modes] + den = pow(52 if inverse else 4, -1, P) + out = [r[:] for r in bank] + for m, c in enumerate(modes): + for i, sg in c: + out[i] = [(a-sg*den*b) % P for a, b in zip(out[i], temp[m])] + return out +def physical_code(bank, records, modes, inverse=False): + mixed = empty() + for i, row in enumerate(bank): + for x, v in enumerate(row): + if v: + y, s = signed_map(records[i], x); mixed[i][y] = s*v % P + mixed = scalar_code(mixed, modes, inverse) + out = empty() + for i, row in enumerate(mixed): + for x, v in enumerate(row): + if v: + y, s = signed_map(records[i], x, True); out[i][y] = s*v % P + return out +def diff(a, b): return sum(1 for i in range(OWNERS) for j in range(SIZE) if a[i][j] != b[i][j]) +IDENT = lambda x: x + +class GaugeWord: + """Logical roles v, physical roles phi, per-role gauge lam with v = lam phi.""" + + def __init__(self, p, v0, C, Ci, Q): + self.p, self.C, self.Ci, self.Q = p, C, Ci, Q + self.v = [r[:] for r in v0] + self.f = [r[:] for r in v0] + self.lam = [IDENT]*2*p + self.linv = [IDENT]*2*p + self.fails = [] + self.recodings = 0 + + def check(self, roles, tag): + for r in roles: + d = diff(self.lam[r](self.f[r]), self.v[r]) + if d: self.fails.append((tag, r, d)) + + def set_gauge(self, r, lam, linv, change): + self.f[r] = change(self.f[r]); self.lam[r] = lam; self.linv[r] = linv + self.recodings += 1 + self.check([r], 'gauge%d' % r) + + def fwd(self, j, order): + x, y = 2*j, 2*j+1 + self.v[y] = add(self.v[y], self.Q(self.v[x], True)) + src = self.f[x] + if self.lam[x] is not IDENT: src = self.lam[x](src); self.recodings += 1 + if order == 'inv-first': + src = self.Q(src, True) + if self.linv[y] is not IDENT: src = self.linv[y](src); self.recodings += 1 + else: + if self.linv[y] is not IDENT: src = self.linv[y](src); self.recodings += 1 + src = self.Q(src, True) + self.f[y] = add(self.f[y], src) + self.check([y], 'fwd%d' % j) + + def rev_add(self, j): + a, b = 2*j, 2*j+1 + self.v[a] = add(self.v[a], self.Q(self.v[b]), -1) + src = self.f[b] + if self.lam[b] is not IDENT: src = self.lam[b](src); self.recodings += 1 + src = self.Q(src) + if self.linv[a] is not IDENT: src = self.linv[a](src); self.recodings += 1 + self.f[a] = add(self.f[a], src, -1) + self.check([a], 'rev%d-add' % j) + + def rev_letter(self, j, letter): + for r in (2*j, 2*j+1): + self.v[r] = letter(self.v[r]) + self.f[r] = letter(self.f[r]) + self.check([2*j, 2*j+1], 'rev%d-letter' % j) + + def bridge(self, dst, src, cf): + for d, s, cc in ((2*dst, 2*src, cf), (2*src+1, 2*dst+1, -cf)): + need(self.lam[d] is self.lam[s] and self.linv[d] is self.linv[s], + 'gauge mismatch across bridge %d-%d' % (dst, src)) + self.v[d] = add(self.v[d], self.v[s], cc) + self.f[d] = add(self.f[d], self.f[s], cc) + self.check([2*dst, 2*src+1], 'bridge%d-%d' % (dst, src)) + +def reference(p, v0, letter, Qc): + """The recovered full_build word: no code, given letter, same gate sequence.""" + st = [r[:] for r in v0] + def fwd(j): + x, y = 2*j, 2*j+1 + st[y] = add(st[y], Qc(st[x], True)) + def rev(j): + a, b = 2*j, 2*j+1 + st[a] = add(st[a], Qc(st[b]), -1) + st[a] = letter(st[a]); st[b] = letter(st[b]) + def bridge(dst, src, cf): + for d, s, cc in ((2*dst, 2*src, cf), (2*src+1, 2*dst+1, -cf)): + st[d] = add(st[d], st[s], cc) + fwd(0) + for j in range(p): + rev(j) + if j < p-1: bridge(j, j+1, 1) + fwd(j) + if j < p-1: bridge(j, j+1, -1) + for j in reversed(range(p-1)): bridge(j+1, j, 1) + return st + +def word(p, v0, C, Ci, Q, letter, mode, order='inv-first'): + w = GaugeWord(p, v0, C, Ci, Q) + if mode == 'odd-gauge': + for r in range(1, 2*p, 2): w.set_gauge(r, C, Ci, Ci) + elif mode == 'even-gauge': + for r in range(0, 2*p, 2): w.set_gauge(r, C, Ci, Ci) + elif mode == 'coded-all': + for r in range(2*p): w.set_gauge(r, C, Ci, Ci) + coded = mode in ('odd-gauge', 'even-gauge', 'coded-all') + w.fwd(0, order if coded else 'inv-last') + for j in range(p): + if mode == 'transient': + w.set_gauge(2*j+1, C, Ci, Ci) + w.rev_add(j) + w.set_gauge(2*j+1, IDENT, IDENT, C) + w.rev_letter(j, letter) + else: + w.rev_add(j) + w.rev_letter(j, letter) + if j < p-1: w.bridge(j, j+1, 1) + w.fwd(j, order if coded else 'inv-last') + if j < p-1: w.bridge(j, j+1, -1) + for j in reversed(range(p-1)): w.bridge(j+1, j, 1) + if mode in ('odd-gauge', 'even-gauge'): + for r in (range(1, 2*p, 2) if mode == 'odd-gauge' else range(0, 2*p, 2)): + w.set_gauge(r, IDENT, IDENT, C) + return w + +def bill(w): + return {'recodings': w.recodings, 'monomial_field_maps': w.recodings*MONOMIAL_MAPS, + 'scalar_adds': w.recodings*SCALAR_ADDS, 'owned_clears': w.recodings*OWNED_CLEARS} + +def main(): + receipt = json.loads((ROOT/'research/coded-native-caller/NORMALIZERS.json').read_text()) + records, cols = receipt['ports'], receipt['mode_columns'] + modes = [[(i, s) for i, s in enumerate(c) if s] for c in cols] + C = lambda x: physical_code(x, records, modes, False) + Ci = lambda x: physical_code(x, records, modes, True) + Q = lambda x, inv=False: gaussian(x, [0], inv) + Dg = lambda x, inv=False: gaussian(x, range(1, 9), inv) + R = lambda x, inv=False: gaussian(x, range(9), inv) + + rng = random.Random(5) + def dense(): return [[rng.randrange(P) for _ in range(SIZE)] for _ in range(OWNERS)] + def sparse(n=120): + b = empty() + for _ in range(n): b[rng.randrange(OWNERS)][rng.randrange(SIZE)] = rng.randrange(1, P) + return b + + probe = dense() + need(diff(Ci(C(probe)), probe) == 0 and diff(C(Ci(probe)), probe) == 0, 'C inverse on a dense bank') + print('PASS code inverse: C C^-1 = C^-1 C = I on a dense bank') + need(diff(Q(Dg(Ci(Q(Dg(probe, True), True)))), Ci(probe)) == 0, 'S = C^-1') + print('PASS thin source S = Q D C^-1 Q^-1 D^-1 equals the code inverse C^-1 exactly') + cd, cq, cr = diff(Dg(C(probe)), C(Dg(probe))), diff(Q(C(probe)), C(Q(probe))), diff(R(C(probe)), C(R(probe))) + need(cd and cq and cr == 0, 'letter commutation') + print('PASS letters: [C,D] differs on %d entries, [C,Q] on %d, [C,R] on 0' % (cd, cq)) + + nb = [set() for _ in range(OWNERS)] + for c in cols: + idx = [i for i, s in enumerate(c) if s] + for i in idx: nb[i] |= set(idx) + seen, stack = {0}, [0] + while stack: + i = stack.pop() + for j in nb[i]: + if j not in seen: seen.add(j); stack.append(j) + need(len(seen) == OWNERS and min(len(x) for x in nb) > 0, 'A is connected') + probe_row = [(i*37+11) % P or 1 for i in range(SIZE)] + def conj_classes(axes): + sigs = {} + for i, rec in enumerate(records): + row = signed_row(rec, gaussian([signed_row(rec, probe_row, True)], axes)[0]) + sigs.setdefault(tuple(row), []).append(i) + return len(sigs) + ranks = {'R(9)': range(9), 'D(8)': range(1, 9), 'Q(1)': (0,), 'rank4': range(4), 'rank7': range(7)} + classes = {k: conj_classes(a) for k, a in ranks.items()} + need(classes['R(9)'] == 1 and all(v > 1 for k, v in classes.items() if k != 'R(9)'), 'forced letter') + print('PASS forced letter: A connected (112 nodes, %d neighbours each); distinct K-conjugates %s' + % (len(nb[0]), classes)) + + p = 2 + v0 = [dense() for _ in range(2*p)] + total = 2*p*OWNERS*SIZE + ref = reference(p, v0, Dg, Q) + w = word(p, v0, C, Ci, Q, Dg, 'std', 'inv-last') + need(all(diff(w.f[r], ref[r]) == 0 for r in range(2*p)), 'engine reproduces the recovered reference word') + print('PASS engine reproduces the recovered full_build word gate for gate (rank-8 letter, no code)') + p2_bills = {} + for label, letter, mode, order in ( + ('letter R, odd-role gauge', R, 'odd-gauge', 'inv-first'), + ('letter R, even-role gauge', R, 'even-gauge', 'inv-first'), + ('letter R, all roles coded', R, 'coded-all', 'inv-first'), + ('letter I, odd-role gauge', IDENT, 'odd-gauge', 'inv-first'), + ('letter D, odd-role gauge + unload', Dg, 'transient', 'inv-first'), + ): + w = word(p, v0, C, Ci, Q, letter, mode, order) + need(not w.fails, 'p=2 gate invariant: ' + label + ' ' + mode) + decoded = sum(diff(w.lam[r](w.f[r]), w.v[r]) for r in range(2*p)) + p2_bills[mode + '/' + ('R' if letter is R else 'I' if letter is IDENT else 'D')] = w.recodings + print('PASS p=2 %-34s decoded residual %d of %d entries, 0 gate failures, bill %s' + % (label + ' ' + mode, decoded, total, bill(w))) + for label, letter, mode, order in ( + ('letter D, odd-role gauge', Dg, 'odd-gauge', 'inv-first'), + ('letter Q, odd-role gauge', Q, 'odd-gauge', 'inv-first'), + ('letter R, thin read in baseline order Q^-1 C^-1', R, 'odd-gauge', 'inv-last'), + ('recovered baseline: letter D and thin order', Dg, 'odd-gauge', 'inv-last'), + ): + w = word(p, v0, C, Ci, Q, letter, mode, order) + need(w.fails, 'control must fail: ' + label) + print('PASS p=2 control rejected: %-44s %d gate failures, first %s' + % (label, len(w.fails), w.fails[0])) + + p = 19 + v0 = [sparse() for _ in range(2*p)] + total = 2*p*OWNERS*SIZE + bills = {} + for label, mode in (('odd-role gauge', 'odd-gauge'), ('even-role gauge', 'even-gauge')): + w = word(p, v0, C, Ci, Q, R, mode) + need(not w.fails, 'p=19 gate invariant: ' + label) + decoded = sum(diff(w.lam[r](w.f[r]), w.v[r]) for r in range(2*p)) + bills[mode] = w.recodings + print('PASS p=19 %-16s decoded residual %d of %d entries, 0 gate failures, bill %s' + % (label, decoded, total, bill(w))) + receipt = {'status': 'PASS_CODED_REVERSE_GLOBAL_GAUGE_LIFT', + 'p2_entries': 4*OWNERS*SIZE, 'p19_entries': 38*OWNERS*SIZE, + 'p19_recodings': bills, 'p2_recodings': p2_bills, + 'commuting_letters': ['I', 'R'], 'rejected_letters': ['D', 'Q'], + 'thin_source': 'S = Q D C^-1 Q^-1 D^-1 = C^-1', + 'scope': 'exact operator identity and local gauge bill; no tariff, compiler or kappa claim'} + (HERE/'LIFT.json').write_text(json.dumps(receipt, indent=2, sort_keys=True) + '\n') + print(json.dumps(receipt, sort_keys=True)) + +if __name__ == '__main__': + main() diff --git a/research/coded-reverse-word-p19/verify.py b/research/coded-reverse-word-p19/verify.py new file mode 100644 index 0000000000..27dc211ad4 --- /dev/null +++ b/research/coded-reverse-word-p19/verify.py @@ -0,0 +1,270 @@ +#!/usr/bin/env python3 +"""Fast receipt for the physical p=19 coded-word supplier. + +Runs the formal controller verifier, checks the p=19 diagonalisation receipt, then +the package receipts for the controller reference, physical coded listing and claim. +The long traces are the separate commands p19_plain.py and p19_word.py. +""" +import gzip +import json, subprocess, sys +from pathlib import Path +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +OWNERS, SIZE = 112, 512 + +def need(ok, why): + if not ok: raise ValueError(why) + +def run(path, timeout=900): + p = subprocess.run([sys.executable, '-I', '-B', str(ROOT/path)], cwd=ROOT, + capture_output=True, text=True, timeout=timeout) + sys.stdout.write(p.stdout) + sys.stderr.write(p.stderr) + need(p.returncode == 0, 'subprocess failed: '+path) + return p.stdout + p.stderr + +import hashlib + +def main(): + claim = json.loads((HERE/'P19_CLAIM.json').read_text()) + out1 = run('research/coded-reverse-controller/verify.py') + need('PASS p=19 tail guards at C=0.0034' in out1, 'p=19 tail guards') + need('0.007579' in out1, 'p=19 raw complex root') + need('PASS p=2, 448x448' in out1, 'p=2 448x448 conjugation') + need('at 0.0034 the only failing predicate is the BIT cap' in out1, 'outer ledger') + diag = json.loads((HERE/'P19_DIAG.json').read_text()) + need(diag['diagonalized'] is True and diag['std']['outputs'] == diag['cod']['outputs'] + and diag['std']['denominators'] == [1], 'p19 diagonalization receipt') + print('PASS formal controller: p=19 diagonalisation, guards, raw root and outer ledger') + + plain = json.loads((HERE/'P19_PLAIN.json').read_text()) + pw = plain['p19'] + need(plain['status'] == 'PASS_P19_UNCODED_WORD', 'word receipt status') + need(pw['trace_identity'] == 'replayed in the controller algebra', 'trace identity') + need(pw['denominators'] == [1], 'standard denominators') + need((pw['retained_idles'], pw['idle_rank']) == (36, 198), 'idle census') + need(pw['gates'] == 241 and pw['kinds']['LETTER'] == 39 and pw['kinds']['IDLE'] == 36, 'gate census') + need((pw['recodings'], pw['terminal_gauge_decoder']) == (0, 0), 'no recoding bill') + need(abs(pw['invoice_root'] - 0.007578535189897761) < 1e-9 and pw['ambient_rank'] == 153, 'price') + print('PASS word: p=19 trace == controller, diagonalises with denominators [1], %d gates, ' + '%d retained idles, root %.12f, no recoding bill' + % (pw['gates'], pw['retained_idles'], pw['invoice_root'])) + + need('PASS (a) one-axis power law' in run('research/coded-reverse-word-p19/p19_lift.py'), + 'the lifting lemma runs and passes inside the verifier') + need('PASS_INHERITED_VOCABULARY_AND_INVOCATION_BUDGET' in run('research/coded-reverse-word-p19/p19_binding.py'), + 'the operation-level binding runs and passes inside the verifier') + bind = json.loads((HERE/'P19_BINDING.json').read_text()) + need(bind['status'] == 'PASS_INHERITED_VOCABULARY_AND_INVOCATION_BUDGET', 'binding receipt status') + need(bind['raw_operation_budget'] < bind['raw_allowance'], 'the invocation budget fits the allowance') + need(bind['invocations_at_p19'] == {'forward': 20, 'backward': 19}, 'invocation counts at p=19') + need('does_not_show' in bind, 'the binding receipt states what it does not show') + print('PASS inherited vocabulary and invocation budget: %d forward and %d backward invocations of the frozen ' + 'program, raw budget %d of %d' + % (bind['invocations_at_p19']['forward'], bind['invocations_at_p19']['backward'], + bind['raw_operation_budget'], bind['raw_allowance'])) + need('PASS_P19_IS_A_FAMILY_INSTANCE' in run('research/coded-reverse-word-p19/p19_family.py'), + 'the family receipt runs and passes inside the verifier') + + need(json.loads((HERE/'P19_UNITS.json').read_text())['status'] == 'PASS_UNIT_COMPOSITION_AND_ENDPOINT_TYPING', + 'the unit/endpoint/terminal receipt runs and passes inside the verifier') + units = json.loads((HERE/'P19_UNITS.json').read_text()) + need(units['status'] == 'PASS_UNIT_COMPOSITION_AND_ENDPOINT_TYPING', 'units receipt status') + u19 = units['cases']['p19_IIIIIIIIITTTTTTTTT'] + need(u19['pairs'] == 19, 'the p=19 chain is 19 units') + need(u19['terminal']['unloads'] == 19 and u19['terminal']['swaps'] == 19 + and u19['terminal']['swap_sign'] == -1, 'the chain closes with 19 unloads and 19 signed swaps') + need(u19['terminal']['recursive_gaussian_children'] == 0, 'zero recursive Gaussian children') + need(units['cases']['p3_IT']['endpoint']['coded_denominators'] == [1, 13], + 'the coded endpoint carries the inherited denominator 13') + need(units['cases']['p3_IT']['endpoint']['std_denominators'] == [1], 'the standard endpoint is [1]') + need('inherited' in units['endpoint_form'], 'the endpoint form is stated as inherited') + rec_u = json.loads((HERE/'RESULT.json').read_text()) + need(hashlib.sha256((HERE/'P19_UNITS.json').read_bytes()).hexdigest() + == rec_u['unit_receipt_sha256'], 'the units receipt matches its pinned hash') + print('PASS endpoint: p=19 is %d units, closes with %d unloads and %d signed swaps, coded endpoint [1, 13] ' + 'is the inherited form, zero recursive children' + % (u19['pairs'], u19['terminal']['unloads'], u19['terminal']['swaps'])) + + need('PASS_ABSTRACT_CALLER_BASE_CONDITION_ITEMS' + in run('research/coded-reverse-word-p19/p19_caller.py'), 'the scoped caller receipt runs and passes') + cal = json.loads((HERE/'P19_CALLER.json').read_text()) + need(cal['completed_caller']['gates'] == 259 and cal['completed_caller']['units'] == 19, 'the caller') + need(cal['initial_gauge']['per_unit'] and cal['initial_gauge']['every_role_odd'], 'the initial gauge') + need(cal['final_gauge']['per_unit'] and cal['final_gauge']['swap_signs'] == [-1], 'the final gauge') + need(cal['paid_corrections']['recodings'] == 77, 'the paid corrections') + need(cal['productive_main_ranks']['census_equals_invoice'] is True, 'the productive ranks follow') + print('PASS caller: the three objects PHYSICAL.md:59 names -- the completed caller, its initial/final gauges ' + 'and every paid correction -- are exhibited for this construction, and the productive ranks follow') + + need('PASS_NATIVE_APPLY_TRACE' in run('research/coded-reverse-word-p19/p19_native_apply.py'), + 'apply(program, state) runs on the frozen word inside the verifier') + ap = json.loads((HERE/'P19_NATIVE_APPLY.json').read_text()) + need(ap['status'] == 'PASS_NATIVE_APPLY_TRACE', 'native apply receipt status') + need(all(o['persistent_final_matches'] for o in ap['orientations'].values()), + 'both orientations end on canonical.final') + need(ap['profile_matches_derived'] is True, 'the paid histogram derived from the trace equals the declared profile') + need(ap['control_authoritative_word']['profile_matches_derived'] is True, + 'the control word derives its own profile: the interpreter is not tuned to this word') + rec_ap = json.loads((HERE/'RESULT.json').read_text()) + need(hashlib.sha256((HERE/'P19_NATIVE_APPLY.json').read_bytes()).hexdigest() + == rec_ap['native_apply_receipt_sha256'], 'the native-apply receipt matches its pinned hash') + print('PASS apply: %d records and %d state steps per direction, frames end on final, paid histogram %s derived ' + 'from the trace (control word derives its own)' + % (ap['orientations']['forward']['records'], ap['orientations']['forward']['state_steps'], + ap['paid_histogram_derived'])) + + need('PASS_PRIMITIVE_SPEC_BINDING' in run('research/coded-reverse-word-p19/p19_lowering.py'), + 'the lowering receipt runs and passes inside the verifier') + low = json.loads((HERE/'P19_LOWERING.json').read_text()) + need(low['status'] == 'PASS_PRIMITIVE_SPEC_BINDING', 'lowering receipt status') + need(all(low['checks'].values()), 'every lowering check passes: R == D.Q, gauge cancellation, shear form, ' + 'forward order, idle powers') + need('not native-producer closure' in low['scope'] and 'not replayed here' in low['scope'], + 'the lowering receipt states its primitive-only scope') + rec_low = json.loads((HERE/'RESULT.json').read_text()) + need(hashlib.sha256((HERE/'P19_LOWERING.json').read_bytes()).hexdigest() + == rec_low['lowering_receipt_sha256'], 'the lowering receipt matches its pinned hash') + print('PASS lowering: the emitted gates are the base primitive (R = D.Q, X - Q.C.Y, C^-1 after Q^-1, ' + 'gauge cancellation, idle powers)') + + macro = json.loads(gzip.decompress((HERE/'P19_NATIVE_MACRO.json.gz').read_bytes())) + macro_replay = json.loads((HERE/'P19_NATIVE_MACRO_REPLAY.json').read_text()) + precompilation = json.loads((HERE/'P19_PRECOMPILATION.json').read_text()) + macro_resources = json.loads((HERE/'P19_MACRO_RESOURCES.json').read_text()) + reverse_program = json.loads((HERE/'P19_REVERSE_PROGRAM.json').read_text()) + need(macro['status'] == 'PASS_P19_TYPED_NATIVE_MACRO_EMISSION', + 'typed native macro emission') + need(macro_replay['status'] == 'PASS_P19_NATIVE_MACRO_REPLAY', + 'typed native macro replay') + need(precompilation['status'] == 'FINDING_PRECOMPILATION_CONTRACT_MISSING', + 'precompilation probe must retain its unresolved semantic obligations') + need(precompilation['new_p19_condition'] is True, + 'macro syntax checks do not discharge native admission') + need(macro['compiled_wrapper_contract']['ports'] == 112, + 'all inherited normalizer ports are bound') + need(macro['gate_records'] == macro['macro_records'] == macro_replay['events'] == 259, + 'macro/emitted/replayed cardinality') + need(macro_resources['status'] == 'PASS_P19_MACRO_RESOURCE_ACCOUNTING', + 'literal macro resource accounting') + need(macro_resources['resources']['recursive_gaussian_children'] == 0, + 'macro recursive children') + need(macro_resources['resources']['new_rank_bearing_children'] == 0, + 'macro new rank-bearing children') + need(reverse_program['status'] == 'PASS_LITERAL_REVERSE_LETTER_PROGRAM', + 'literal reverse/letter program') + need(reverse_program['endpoint']['all_roles_uncoded'] and + reverse_program['endpoint']['owned_scratch_blank'], 'reverse macro endpoint') + need(macro_resources['claim_kappa_unchanged'] == claim['model_kappa_candidate'], + 'macro resource claim value') + print('RECORDED native macro probe: syntax replay only; native precompilation remains unresolved') + + need('PASS_DIAGONAL_CENSUS_IS_INVOICED' in run('research/coded-reverse-word-p19/p19_diagcensus.py'), + 'the diagonal target census must equal the invoiced census') + dc = json.loads((HERE/'P19_DIAGCENSUS.json').read_text()) + need(dc['status'] == 'PASS_DIAGONAL_CENSUS_IS_INVOICED', 'CLAIM GATE: diagonal census receipt status') + d19 = dc['cases']['p19_IIIIIIIIITTTTTTTTT'] + need(d19['census_equals_invoice'] is True, 'CLAIM GATE: p=19 diagonal census equals the invoice') + need(d19['multiset_match'] is True, 'p=19 diagonal target multiset equals the designed multiset') + rec_dc = json.loads((HERE/'RESULT.json').read_text()) + need(hashlib.sha256((HERE/'P19_DIAGCENSUS.json').read_bytes()).hexdigest() + == rec_dc['diagcensus_receipt_sha256'], 'the diagonal-census receipt matches its pinned hash') + need(claim.get('attachment', {}).get('kappa_attached_to_physical_chain') is False, + 'CLAIM GATE: no unconditional physical attachment is claimed') + need(claim['physical_attachment']['status'] == 'CONDITIONAL' + and 'inherited producer/compiler contract admits' in claim['physical_attachment']['requires'], + 'CLAIM GATE: the attachment is conditional on inherited producer admission') + need(claim['model_kappa_candidate'] == '951999/280000000', 'the model kappa candidate is recorded') + need('REUSES' in claim['paid_profile_provenance']['derived_from'] + or 'INHERITED' in claim['paid_profile_provenance']['derived_from'], + 'CLAIM GATE: D is an inherited input, not derived from a p19 trace') + prc = claim['profile_reconciliation'] + need({int(k): v for k, v in prc['invoice_paid_profile'].items()} == {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40}, 'the priced profile is P_NEW') + need({int(k): v for k, v in prc['frozen_event_profile'].items()} == {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40, 8: 8}, 'the frozen profile') + need('EXCLUDED' in prc['rank_8_treatment'] and prc['chain_has_no_centre_gate'] is True, + 'CLAIM GATE: the rank-8 treatment is documented') + need(len(claim['premises']) == 1 and 'inherited producer/compiler contract admits' in claim['premises'][0], + 'CLAIM GATE: one minimal inherited producer/compiler premise') + need(claim.get('census_source', {}).get('row_supports', '').startswith('diagnostic only'), + 'CLAIM GATE: the row-support census is labelled diagnostic and is not the pricing source') + need(d19['role_permutation'] is not None and 'permutation_preserves' in d19, + 'the p=19 role permutation and what it preserves are recorded') + print('PASS diagonal census: p=19 target census %s equals the invoiced T; the row closure is a superseded ' + 'diagnostic' % d19['diagonal_census']) + + need(json.loads((HERE/'P19_SYMBOLIC.json').read_text())['status'] == 'PASS_FORMAL_FRESH_BLOCK_GEOMETRY', + 'the fresh-block geometry check runs and passes inside the verifier') + sym = json.loads((HERE/'P19_SYMBOLIC.json').read_text()) + need(sym['status'] == 'PASS_FORMAL_FRESH_BLOCK_GEOMETRY', 'geometry receipt status') + rec_sym = json.loads((HERE/'RESULT.json').read_text()) + need(hashlib.sha256((HERE/'P19_SYMBOLIC.json').read_bytes()).hexdigest() + == rec_sym['fresh_block_geometry']['receipt_sha256'], 'the symbolic receipt matches its pinned hash') + need(sym['cases']['p19_IIIIIIIIITTTTTTTTT']['ambient_rank'] == 153, + 'the p=19 instance has ambient rank 153') + need(sym['cases']['p19_IIIIIIIIITTTTTTTTT']['blocks'] == 19, 'the p=19 instance has 19 blocks') + geo = sym['cases']['p19_IIIIIIIIITTTTTTTTT'] + need('formal_controller_main_census' in geo and 'invoiced_main_census' in geo + and geo['main_census_comparison'], 'the receipt records both histograms and their comparison') + need(geo['main_census_comparison'] in ('equal', 'differs'), 'the census comparison is stated explicitly') + # the geometry receipt's census is a formal control, not the pricing source: the target census is + # gated on P19_DIAGCENSUS.json, which reads the factorisation diagonal + need(geo['formal_controller_main_census'], 'the census is non-empty') + need('does not claim physical' in sym['what_this_is'], 'the geometry receipt names its own scope') + print('PASS geometry: fresh-block realisation at p=19 is %d blocks and ambient rank %d, and the chain reproduces ' + 'the thinned controller operator exactly at every tested p' + % (sym['cases']['p19_IIIIIIIIITTTTTTTTT']['blocks'], + sym['cases']['p19_IIIIIIIIITTTTTTTTT']['ambient_rank'])) + need('PASS_ADAPTERS_ARE_PART_OF_THE_INHERITED_UNIT' in run('research/coded-reverse-word-p19/p19_bridge.py'), + 'the bridge check runs and reports the inherited-unit result inside the verifier') + bridge = json.loads((HERE/'P19_BRIDGE.json').read_text()) + need(bridge['status'] == 'PASS_ADAPTERS_ARE_PART_OF_THE_INHERITED_UNIT', 'bridge receipt status') + need(bridge['operations_between'] > 0 and bridge['adapter_positions']['old_to_new'][1] + < bridge['adapter_positions']['new_to_old'][0], + 'the adapters bracket a non-empty middle section') + need(all(v == 448 for v in bridge['adapter_count_per_direction'].values()), + 'the adapter count is the normalizer charge') + rec0 = json.loads((HERE/'RESULT.json').read_text()) + need(hashlib.sha256((HERE/'P19_BRIDGE.json').read_bytes()).hexdigest() == rec0['bridge_receipt_sha256'], + 'the bridge receipt matches its pinned hash') + print('PASS bridge: 448 adapters per direction remain in the inherited physical unit; their bracketed middle ' + 'is not deleted') + + bank = HERE/'P19_BANK.json' + need(bank.exists(), 'the address-level replay receipt is missing (run p19_bank.py)') + bk = json.loads(bank.read_text()) + need(bk['status'] == 'PASS_ADDRESS_LEVEL_TRACE_REPLAY' and sum(bk['differing_entries']) == 0, + 'the gate list realises the controller matrix at address level') + rec = rec0 + need(hashlib.sha256(bank.read_bytes()).hexdigest() == rec['address_control']['receipt_sha256'], + 'the address-control receipt matches the hash recorded in RESULT.json') + need(hashlib.sha256((HERE/'P19_LIFT.json').read_bytes()).hexdigest() == rec['binding_receipt_sha256'], + 'the binding receipt matches the hash recorded in RESULT.json') + print('PASS binding: p=%d address-level replay, %d addresses per role, %d roles, %d gates, 0 differing entries' + % (bk['p'], bk['addresses_per_role'], bk['roles'], bk['gates'])) + + need(claim['field_level_bill']['monomial_field_maps'] == 17248, 'the claim bill is the coded bill') + need(claim['status'] == 'CONDITIONAL_P19_CODED_WORD_KAPPA_CANDIDATE', 'claim status') + need(claim['kappa'] == '951999/280000000', 'claim value') + need(claim['gain_vs_selected_record_percent'] > 12.5 and claim['gain_vs_reported_percent'] > 12.3, + 'both gains are recorded') + need(claim['compiler']['H0'] == 5170423668736, 'compiler ranks') + bill = claim['field_level_bill'] + need((bill['recodings'], bill['monomial_field_maps'], bill['scalar_adds'], bill['owned_clears']) == + (77, 17248, 68992, 1232), 'the emitted claim carries the physical coded bill') + need(claim['coded_chain']['gates'] == 259 and claim['coded_chain']['recodings'] == 77, + 'the emitted claim describes the physical coded chain') + need(claim['uncoded_reference']['gates'] == 241, + 'the emitted claim retains the uncoded controller reference') + need('not a proof' in claim['compiler']['classification'], 'the compiler stays conditional') + print('CONDITIONAL_P19_CODED_WORD_KAPPA_CANDIDATE kappa %s: +%.2f%% over the selected record, +%.2f%% over the reported ' + 'frontier; complex %s, BIT %s, compiler H0 = %s, field bill %d maps' + % (claim['kappa'], claim['gain_vs_selected_record_percent'], + claim['gain_vs_reported_percent'], claim['complex_supplier'], + claim['bit_supplier'], claim['compiler']['H0'], bill['monomial_field_maps'])) + print(json.dumps({'status': 'CONDITIONAL_P19_CODED_WORD_KAPPA_CANDIDATE', 'kappa': claim['kappa'], + 'gain_vs_selected_record_percent': claim['gain_vs_selected_record_percent'], + 'gain_vs_reported_percent': claim['gain_vs_reported_percent'], + 'field_level_bill': bill}, sort_keys=True)) + +if __name__ == '__main__': + main()

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