From 6c8c9a0d3f9c219474a2e47ca093965e930ed3e5 Mon Sep 17 00:00:00 2001 From: ToikY <27568617+ToikY@users.noreply.github.com> Date: Tue, 10 Nov 2026 21:26:43 -0800 Subject: [PATCH 1/2] Reuse selected replay navigation for hosted checks Reuse the exact documentation blob carried by #7161 at bb36fc65ee0b161229169505f4840c436c5ca2b9, following #7147 and #7156. --- docs/ci-verification.md | 19 ++++++++++++++++++- 1 file changed, 18 insertions(+), 1 deletion(-) diff --git a/docs/ci-verification.md b/docs/ci-verification.md index 63ba3e9aa8..52b62d0481 100644 --- a/docs/ci-verification.md +++ b/docs/ci-verification.md @@ -1,8 +1,25 @@ # CI verification -## Current selected-family replay: #6030 +## Current selected-family replay: #7000 with #7001 The [selected record](../certificates/selected-result.json) binds conditional +κ = 0.00363005817 to the [application review](research/pr-intake-evidence/pr7000-application/PROOF-REVIEW.md), +[validation receipts](research/pr-intake-evidence/pr7000-application/VALIDATION.json), +and [explicit source closure](../certificates/frontier7000-source.json). +`make frontier7000-verify` follows that exact-source selected replay. The review +reuses eleven authenticated preceding executions and records seven fresh serial +application, scalar and complete native-catalogue executions. The earlier +monolithic timeout is retained separately and is not completed coverage. +Consult the receipts for exact commands, source heads and limits. + +The five inherited framework assumptions remain. No complete uniform word, +literal multiplier execution, independent human proof or formal-kernel proof +is asserted. Routine research submissions do not need to rerun this +selected-family replay. The sections below preserve historical checkpoints. + +## Historical selected-family replay: #6030 + +The [historical checkpoint](../certificates/checkpoints/frontier6030.json) binds conditional κ = 0.003125804 to the [proof review](research/pr-intake-evidence/pr6030-audit/PROOF-REVIEW.md), [validation receipts](research/pr-intake-evidence/pr6030-audit/VALIDATION.json), and [explicit source closure](../certificates/frontier6030-source.json). From 6efb5d028b3212fba68edfb725608413622d6ab6 Mon Sep 17 00:00:00 2001 From: ToikY <27568617+ToikY@users.noreply.github.com> Date: Tue, 10 Nov 2026 23:24:41 -0800 Subject: [PATCH 2/2] Bound rectangular adapters for paid Clifford MOVE pairs --- .../ADAPTER.json | 298 +++ .../INPUTS.json | 34 + .../PROOF.md | 42 + .../README.md | 21 + .../SOURCES.json | 18 + .../TASK.json | 94 + .../VERIFY.json | 35 + .../inputs/PEER-NOTICE.txt | 14 + .../inputs/caller/CALLER.json | 1 + .../inputs/caller/interval_gate.py | 128 ++ .../inputs/gaussian/clifford_exact.py | 149 ++ .../inputs/gaussian/native_verify.py | 277 +++ .../p104-rank8-exit-funded-split/RESULT.json | 1599 +++++++++++++++++ .../p104-rank8-exit-funded-split/WORD.json.gz | Bin 0 -> 381194 bytes .../inputs/prior/owned.py | 622 +++++++ .../verify.py | 201 +++ 16 files changed, 3533 insertions(+) create mode 100644 research/p104-rectangular-clifford-adapter-bound/ADAPTER.json create mode 100644 research/p104-rectangular-clifford-adapter-bound/INPUTS.json create mode 100644 research/p104-rectangular-clifford-adapter-bound/PROOF.md create mode 100644 research/p104-rectangular-clifford-adapter-bound/README.md create mode 100644 research/p104-rectangular-clifford-adapter-bound/SOURCES.json create mode 100644 research/p104-rectangular-clifford-adapter-bound/TASK.json create mode 100644 research/p104-rectangular-clifford-adapter-bound/VERIFY.json create mode 100644 research/p104-rectangular-clifford-adapter-bound/inputs/PEER-NOTICE.txt create mode 100644 research/p104-rectangular-clifford-adapter-bound/inputs/caller/CALLER.json create mode 100644 research/p104-rectangular-clifford-adapter-bound/inputs/caller/interval_gate.py create mode 100644 research/p104-rectangular-clifford-adapter-bound/inputs/gaussian/clifford_exact.py create mode 100644 research/p104-rectangular-clifford-adapter-bound/inputs/gaussian/native_verify.py create mode 100644 research/p104-rectangular-clifford-adapter-bound/inputs/peer/research/p104-rank8-exit-funded-split/RESULT.json create mode 100644 research/p104-rectangular-clifford-adapter-bound/inputs/peer/research/p104-rank8-exit-funded-split/WORD.json.gz create mode 100644 research/p104-rectangular-clifford-adapter-bound/inputs/prior/owned.py create mode 100644 research/p104-rectangular-clifford-adapter-bound/verify.py diff --git a/research/p104-rectangular-clifford-adapter-bound/ADAPTER.json b/research/p104-rectangular-clifford-adapter-bound/ADAPTER.json new file mode 100644 index 0000000000..17a3672a7c --- /dev/null +++ b/research/p104-rectangular-clifford-adapter-bound/ADAPTER.json @@ -0,0 +1,298 @@ +{ + "complete_pair_price": { + "census": { + "events": 76349, + "lifetimes": 66, + "opcodes": { + "ADD": 66213, + "CLEAR": 66, + "COPY": 1, + "INIT": 66, + "MOVE": 6279, + "SCALE": 3724 + }, + "owned_labels": 63, + "peak": 48, + "public": 1499 + }, + "ideal_pairs": 33991, + "ideal_raw_moment": [ + "2403102453237867321005805946700478980683750305098972197952460268616761174833490473/50000000000000000000000000000000000000000000000000000000000000000000000000000000", + "2403102453237867321005805946700478980683750305098972197952460268616761174853004251/50000000000000000000000000000000000000000000000000000000000000000000000000000000" + ], + "invoice": { + "P": { + "1": 68367, + "2": 14501, + "3": 14093, + "4": 3825, + "5": 5848, + "6": 238, + "7": 170, + "8": 741, + "9": 32, + "16": 416, + "24": 416, + "32": 416, + "40": 416, + "48": 416, + "56": 416, + "64": 208 + }, + "S": 1424, + "T": { + "1": 289, + "137": 208, + "17": 416, + "2": 357, + "25": 416, + "3": 799, + "33": 416, + "4": 3791, + "41": 416, + "49": 416, + "5": 1343, + "57": 416, + "6": 731, + "65": 416, + "7": 323, + "73": 208, + "8": 578, + "9": 10888 + }, + "paid_position_sha256": "f562c24ef3c0e657936f45baa50a921964282dbcbc1ed85ebae85422bc567ed1" + }, + "minimum_ideal_pairs_needed": 25328, + "native_call_bindings": [ + { + "caller_event": 43, + "helper_owner": [ + "helper", + 43, + 1479 + ], + "stage": 1 + }, + { + "caller_event": 137, + "helper_owner": [ + "helper", + 137, + 1479 + ], + "stage": 2 + }, + { + "caller_event": 268, + "helper_owner": [ + "helper", + 268, + 1479 + ], + "stage": 3 + }, + { + "caller_event": 432, + "helper_owner": [ + "helper", + 432, + 1479 + ], + "stage": 4 + }, + { + "caller_event": 633, + "helper_owner": [ + "helper", + 633, + 1479 + ], + "stage": 5 + }, + { + "caller_event": 867, + "helper_owner": [ + "helper", + 867, + 1479 + ], + "stage": 6 + }, + { + "caller_event": 1138, + "helper_owner": [ + "helper", + 1138, + 1479 + ], + "stage": 7 + }, + { + "caller_event": 1423, + "helper_owner": [ + "helper", + 1423, + 1479 + ], + "stage": 8 + }, + { + "caller_event": 3058, + "helper_owner": [ + "helper", + 3058, + 1479 + ], + "stage": 9 + }, + { + "caller_event": 3377, + "helper_owner": [ + "helper", + 3377, + 1479 + ], + "stage": 10 + }, + { + "caller_event": 3674, + "helper_owner": [ + "helper", + 3674, + 1479 + ], + "stage": 11 + }, + { + "caller_event": 3934, + "helper_owner": [ + "helper", + 3934, + 1479 + ], + "stage": 12 + }, + { + "caller_event": 4149, + "helper_owner": [ + "helper", + 4149, + 1479 + ], + "stage": 13 + }, + { + "caller_event": 4337, + "helper_owner": [ + "helper", + 4337, + 1479 + ], + "stage": 14 + }, + { + "caller_event": 4485, + "helper_owner": [ + "helper", + 4485, + 1479 + ], + "stage": 15 + }, + { + "caller_event": 4606, + "helper_owner": [ + "helper", + 4606, + 1479 + ], + "stage": 16 + }, + { + "caller_event": 4691, + "helper_owner": [ + "helper", + 4691, + 1479 + ], + "stage": 17 + } + ], + "omitted_paid_occurrence_rejected": true, + "pair_price_saving": [ + "69348986502188680728923643600707147136626390775099307653604924748900855616451/12500000000000000000000000000000000000000000000000000000000000000000000000000000", + "277395946008754722915694574402828588546505563100397230614419698995603422465867/50000000000000000000000000000000000000000000000000000000000000000000000000000000" + ], + "rank1_native_by_owner_class": { + "main": 971, + "owned": 20, + "public_helper": 3008 + }, + "rank1_outer_paid": 384, + "signed_raw_moment": [ + "-7025863147545714465621568331826067572600520290246630067862279719942794758201653291/50000000000000000000000000000000000000000000000000000000000000000000000000000000", + "-3512931573772857232810784165913033786300260145123315033931139859971397379092140473/25000000000000000000000000000000000000000000000000000000000000000000000000000000" + ] + }, + "destructive_projection_controls": [ + { + "omitted_reciprocal_rejected": 4, + "padding_volume_factor": 2, + "rank1_support": 2, + "rank2_support": 4, + "reciprocal_gain_squared": 2, + "signed_columns": 4, + "width": 1 + }, + { + "omitted_reciprocal_rejected": 8, + "padding_volume_factor": 4, + "rank1_support": 4, + "rank2_support": 16, + "reciprocal_gain_squared": 4, + "signed_columns": 8, + "width": 2 + }, + { + "omitted_reciprocal_rejected": 16, + "padding_volume_factor": 8, + "rank1_support": 8, + "rank2_support": 64, + "reciprocal_gain_squared": 8, + "signed_columns": 16, + "width": 3 + }, + { + "omitted_reciprocal_rejected": 32, + "padding_volume_factor": 16, + "rank1_support": 16, + "rank2_support": 256, + "reciprocal_gain_squared": 16, + "signed_columns": 32, + "width": 4 + } + ], + "exact_signed_move": { + "absolute_phase_mutants_rejected": 512, + "event": 535, + "role": 1479, + "shift": 52, + "sign_mask": 20, + "signed_columns": 512, + "source": 3, + "target": 595 + }, + "pins": { + "caller/CALLER.json": "255d89f38cd45e38e5770f559bc43dc217e989032359768cdc7e8cdfd64b47bc", + "caller/interval_gate.py": "60a743d13f668ef86db4b8215b4d5d04430a671ba6f1fe06d9c1c4c3dfe86da5", + "gaussian/clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "gaussian/native_verify.py": "3049471905b47b385c88378a1a3be7a18b8858aadd035b8a6da2f4a03b470f38", + "peer/research/p104-rank8-exit-funded-split/RESULT.json": "59080d75e7281b1a8c1353930917fd15869ad747ff4200948898f78f11c14089", + "peer/research/p104-rank8-exit-funded-split/WORD.json.gz": "c1caec11ca3ee264ef03018dd91037eac10c3e28950c4c525ee1b4bf5ee210e2", + "peer/research/p104-rank8-exit-funded-split/WORD.json.gz#decompressed": "9eff91418d838f1ffa20fe5c5975dc2c43a79b32d501fcbe30b90c50a7b11ce3", + "prior/owned.py": "53da0a7b551b34f3baf633083a4362570ebe694a694e2d0b6226d01c08a6ab3b" + }, + "seed": null, + "status": "SCOPED_RECTANGULAR_ADAPTER_OBSTRUCTION", + "target": "10018846261809/2500000000000000" +} diff --git a/research/p104-rectangular-clifford-adapter-bound/INPUTS.json b/research/p104-rectangular-clifford-adapter-bound/INPUTS.json new file mode 100644 index 0000000000..0953851d4f --- /dev/null +++ b/research/p104-rectangular-clifford-adapter-bound/INPUTS.json @@ -0,0 +1,34 @@ +{ + "PEER-NOTICE.txt": { + "sha256": "fb25cd50d8e99fd749e4aa567a1a453b353d90bf74e2b20bd8395aae62d18100", + "source": "https://raw.githubusercontent.com/ToikY/integer-mult-bounds/16ea35caeeca1a166113ad21c76127f04889f6f5/research/p104-owned-move-transport-bound/inputs/PEER-NOTICE.txt" + }, + "caller/CALLER.json": { + "sha256": "255d89f38cd45e38e5770f559bc43dc217e989032359768cdc7e8cdfd64b47bc", + "source": "https://raw.githubusercontent.com/ToikY/integer-mult-bounds/16ea35caeeca1a166113ad21c76127f04889f6f5/research/p104-owned-move-transport-bound/inputs/caller/CALLER.json" + }, + "caller/interval_gate.py": { + "sha256": "60a743d13f668ef86db4b8215b4d5d04430a671ba6f1fe06d9c1c4c3dfe86da5", + "source": "https://raw.githubusercontent.com/ToikY/integer-mult-bounds/16ea35caeeca1a166113ad21c76127f04889f6f5/research/p104-owned-move-transport-bound/inputs/caller/interval_gate.py" + }, + "gaussian/clifford_exact.py": { + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "source": "https://raw.githubusercontent.com/rohanarun/integer-mult-bounds/07a76c5e2738882c0cb322278e56f6cae3c9885d/research/signed-caller-8x9/replay/supplier7112/short-caller/admission-source/frozen/clifford_exact.py" + }, + "gaussian/native_verify.py": { + "sha256": "3049471905b47b385c88378a1a3be7a18b8858aadd035b8a6da2f4a03b470f38", + "source": "https://raw.githubusercontent.com/rohanarun/integer-mult-bounds/07a76c5e2738882c0cb322278e56f6cae3c9885d/research/signed-caller-8x9/replay/supplier7112/short-caller/admission-source/frozen/native_verify.py" + }, + "peer/research/p104-rank8-exit-funded-split/RESULT.json": { + "sha256": "59080d75e7281b1a8c1353930917fd15869ad747ff4200948898f78f11c14089", + "source": "https://raw.githubusercontent.com/ToikY/integer-mult-bounds/16ea35caeeca1a166113ad21c76127f04889f6f5/research/p104-owned-move-transport-bound/inputs/peer/research/p104-rank8-exit-funded-split/RESULT.json" + }, + "peer/research/p104-rank8-exit-funded-split/WORD.json.gz": { + "sha256": "c1caec11ca3ee264ef03018dd91037eac10c3e28950c4c525ee1b4bf5ee210e2", + "source": "https://raw.githubusercontent.com/ToikY/integer-mult-bounds/16ea35caeeca1a166113ad21c76127f04889f6f5/research/p104-owned-move-transport-bound/inputs/peer/research/p104-rank8-exit-funded-split/WORD.json.gz" + }, + "prior/owned.py": { + "sha256": "53da0a7b551b34f3baf633083a4362570ebe694a694e2d0b6226d01c08a6ab3b", + "source": "https://raw.githubusercontent.com/ToikY/integer-mult-bounds/16ea35caeeca1a166113ad21c76127f04889f6f5/research/p104-owned-move-transport-bound/checks/owned.py" + } +} diff --git a/research/p104-rectangular-clifford-adapter-bound/PROOF.md b/research/p104-rectangular-clifford-adapter-bound/PROOF.md new file mode 100644 index 0000000000..c85683dffd --- /dev/null +++ b/research/p104-rectangular-clifford-adapter-bound/PROOF.md @@ -0,0 +1,42 @@ +# One rank-two child with rectangular ordinary adapters + +**NO VERIFIED GAIN.** Keep the signed #7161/#7113 caller and the retained all-width Gaussian Clifford child. The proposed replacement is one rank-two job for two independent equal-width rank-one jobs. The first necessary condition permits destructive scratch erasure and arbitrary output projection. The second permits arbitrary coefficients and requires bounded-support recovery of the whole post-child state. Both grant free coframing and a common clock. + +## The full price opportunity + +The exact #7161 signed bill has 110,519 paid positions and 22,427 targets. Among the 6,279 native MOVEs per invocation are 3,999 rank-one MOVEs, with 971 main, 3,008 public-helper and 20 owned recipients. There are 17 native invocations and 384 additional rank-one caller jobs. Keep the target bill and all nonparticipating positions. At C = 0.0040075385047236, the directed target-minus-paid moment is below −140.51726295091428931243136. + +Grant every native rank-one paid job an equal-volume rank-two partner with free setup, routing, restoration, storage, precision and tape overhead. Each pair saves \(2-2^{1-C}\). The directed sign changes at **25,328** ideal pairs. The maximum **33,991** disjoint pairs give a raw margin above 48.06204906475734. This relaxation can reach the target and leaves the separate BIT premise unchanged. + +## A rectangular amplitude requirement + +For positive slot width \(f\), the normalized rank-\(r\) child \(K\) on each spectator block is the unitary tensor of \(rf\) copies of the symmetric two-by-two matrix \(C_1\) with diagonal \(a=(1+i)/2\) and off-diagonal \(b=(1-i)/2\). Its nonzero entries have modulus \(2^{-rf/2}\), including under permutation and unit rephasing. Each column of the desired direct sum \(T\) of two independent rank-one jobs has \(2^f\) nonzero entries of modulus \(2^{-f/2}\). + +Write the external map as \(T=BKA+H\), where \(A\) encodes into the child, \(B\) reads it out, and \(H\) is a bypass. The maps may be rectangular, vary with \(f\), prepare arbitrary zero workspace and erase scratch output. Coordinates are coefficients of complete arrays in the retained normalization. Write \(c(H)\) for maximum column support, \(\lVert A\rVert_1\) for maximum absolute column sum and \(\lVert B\rVert_\infty\) for maximum absolute row sum. + +For any column \(j\), if \(c(H)<2^f\), some target nonzero \((i,j)\) is absent from \(H\). The triangle inequality gives +\[ +2^{-f/2}=|(BKA)_{ij}| +\le 2^{-rf/2}\lVert B_{i,*}\rVert_1\lVert A_{*,j}\rVert_1. +\] +Thus \(\lVert B\rVert_\infty\lVert A\rVert_1\ge 2^{(r-1)f/2}\). A fixed number of layers with bounded row sums, column sums and column support gives uniform bounds by submultiplicativity. Such a route fails for sufficiently large \(f\) when \(r>1\). This includes fixed finite pointwise ADD, bounded scale and monomial-routing layers with rectangular zero preparation or owned scratch erasure. The argument uses the declared amplitude normalization and needs no inverse. + +## A reversible support requirement + +Suppose the postprocessing has a linear left inverse \(L\) on the relevant pre-output states, including the child and any bypass. Let the full declared result on input column \(j\) be \((Te_j,0)\), with clean additional workspace. Suppose the child input has a nonzero spectator block \(x\) in this column, with \(s\) nonzeros. Its flat unitary block has \(N=2^{rf}\) coordinates. Cauchy–Schwarz gives \(\lVert Kx\rVert_\infty\le N^{-1/2}\sqrt{s}\lVert x\rVert_2\). Unitarity gives \(\lVert Kx\rVert_2=\lVert x\rVert_2\), so \(Kx\) has at least \(N/s\) nonzeros. The full post-child state comes from \(L(Te_j,0)\) and has support at most \(c(L)2^f\). Since \(s\le c(A)\), necessarily +\[ +c(A)c(L)\ge 2^{(r-1)f}. +\] +Only the left inverse on the resulting states is used. The rectangular encoder needs no inverse. If the declared result also returns arbitrary input coordinates, include their support alongside the \(2^f\) entries. A column that never visits the child must be supplied by the bypass. In the bounded-support bypass class, every target column must visit the child for large enough \(f\). + +These are support and amplitude requirements. The cost of an unbounded-width adapter depends on its actual layout, precision and tape. Changed recursion, coefficient normalization or physical child call need separate analyses. + +## Exact controls + +The native check pins MOVE535, helper 1479, chart 3 to 595. It checks all 512 Gaussian signed columns independently of the compiler recipe, including shift 52, sign mask 20 and the absolute phase. Changing the whole-job phase fails on every column. The caller binds 17 distinct helper owners, including stages 1 and 2 at events 43 and 137. Omitting the MOVE from the paid list fails the complete physical binding. + +For a positive control beyond the amplitude hypothesis, use \(C_1^{\otimes f}\otimes C_1^{\otimes f}\). Embed with the second block in a fixed basis coordinate and project it back to that coordinate. The result is \(a^f C_1^{\otimes f}\). Multiplying by \(a^{-f}\) exactly returns the rank-one map with destructive scratch. The Gaussian replay exhausts both independent lanes and all input columns for \(f=1,2,3,4\), totaling 60. Omitting the reciprocal fails on all 60 columns. This construction requires bank expansion \(2^f\) and a row-norm gain of \(2^{f/2}\). Under the favorable comparison where two old children each cost \(A V f^{1-C}\) and the replacement costs \(A c V(2f)^{1-C}\), a saving requires \(c<2^C<2\). The projected construction has \(c\ge 2^f\). This price applies to the exhibited control. + +## Attribution + +Clear1nsight #7161 supplies the native word and exact paid invoice. Rohan Arun #7113 supplies the signed caller and inherited Gaussian compiler/interpreter closure. ToikY #7165 supplies the independent paid-position reconstruction. [#4932](https://github.com/CrocSwap/integer-mult-bounds/pull/4932) uses a Fourier-grade obstruction for rectangular free controls in a fixed columnwise Clifford subgroup algebra. [#4045](https://github.com/CrocSwap/integer-mult-bounds/pull/4045) treats the monomial support obstruction in staged544. [#3989](https://github.com/CrocSwap/integer-mult-bounds/pull/3989) gives a finite nonmonomial fusion and charges its uniform transfer. The inequalities here use row/column norms or supports in place of a fixed Clifford algebra, and the second treats left-invertible rectangular postprocessing. OpenAI Codex and subagents materially assisted the proof, implementation and verification. diff --git a/research/p104-rectangular-clifford-adapter-bound/README.md b/research/p104-rectangular-clifford-adapter-bound/README.md new file mode 100644 index 0000000000..6e69bd3785 --- /dev/null +++ b/research/p104-rectangular-clifford-adapter-bound/README.md @@ -0,0 +1,21 @@ +# A rectangular adapter bound for paid complex MOVE pairs + +**NO VERIFIED GAIN.** At κ = 0.0040075385047236 the exact #7161/#7113 invoice would need 25,328 ideal rank-one pairs. A one-child rank-two replacement with bounded-norm rectangular linear adapters cannot implement the required arbitrary-input map for all widths, even with destructive scratch erasure. A separate reversible bound applies with arbitrary coefficients and bounded-support recovery. [Proof and price](PROOF.md) · [Exact receipt](ADAPTER.json) + +## Reproduction + +Use CPython 3.12 with assertions enabled. From a clean checkout: + +```sh +python3.12 -B scripts/research_package.py --package research/p104-rectangular-clifford-adapter-bound +``` + +The verifier authenticates bundled sources, reconstructs the full paid invoice, and checks 512 signed chart columns and 60 Gaussian projection controls. [Source paths and hashes](INPUTS.json) + +## Open next questions + +Can an adapter with growing norms satisfy the same complete tape, precision and ownership budget? Begin with the two independent stage-1 and stage-2 occurrences of MOVE535. Construct a literal all-width pair with priced bank expansion below $2^C$, then charge its setup, routing, returned state and precision. The projection control in the proof instead uses expansion $2^f$. + +## Credit + +Clear1nsight #7161 supplied the native word. Rohan Arun #7113 supplied the signed caller and the inherited Gaussian compiler/interpreter closure. The #7165 paid-position verifier is reused. [Proof attribution](PROOF.md#attribution) and the [upstream source notice](inputs/PEER-NOTICE.txt) preserve the earlier lineage. OpenAI Codex and subagents materially assisted. New work is Apache-2.0. diff --git a/research/p104-rectangular-clifford-adapter-bound/SOURCES.json b/research/p104-rectangular-clifford-adapter-bound/SOURCES.json new file mode 100644 index 0000000000..5335fa97d9 --- /dev/null +++ b/research/p104-rectangular-clifford-adapter-bound/SOURCES.json @@ -0,0 +1,18 @@ +{ + "schema_version": 1, + "base_commit": "e54523517d0f03e58352e647c403a5af3e525a57", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "75d77b328ea02ded535e7f23aee5b1e55d0bb1a8", + "sha256": "154c3d30455d778fd3343b6b4851f0fa4665f0f7625b0adb3675e2bafbbf6bf1" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "3404fbdd5e7529a0674eef26114b5071e4586cec", + "sha256": "ead6cdc9d0af6d58e8a49744d8ec8c7c15e13d2ba93c276c434bcf9b51b93a81" + } + ] +} diff --git a/research/p104-rectangular-clifford-adapter-bound/TASK.json b/research/p104-rectangular-clifford-adapter-bound/TASK.json new file mode 100644 index 0000000000..f7f85fd06e --- /dev/null +++ b/research/p104-rectangular-clifford-adapter-bound/TASK.json @@ -0,0 +1,94 @@ +{ + "schema_version": 1, + "task_id": "selected-packing", + "priority_revision": 8, + "base_commit": "e54523517d0f03e58352e647c403a5af3e525a57", + "original_card": { + "id": "selected-packing", + "question": "Is there meaningful uncovered packing headroom for an exact current word and boundary contract?", + "starting_points": [ + "docs/research/current-priorities.md", + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md", + "docs/research/recursive-invoice-preflight.md" + ], + "methods": [ + "Construct and independently check one source-bound instance of the stated first experiment.", + "Seek an exact counterexample or target-specific complete-budget obstruction to that same proposed change." + ], + "acceptance_gate": "Check live overlap and exact model/source binding first. Distinguish a chronological construction from a pooled optimum. State the applicable fixed-inventory ceiling and remaining headroom; changed words or interfaces require a new fully charged model. Do not launch a residual search without an explicit scope and time cap.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_selected_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read revision 8, the selected review and live exact-source handoffs. Then follow this card's bounded first_experiment.", + "scope": "Source-bound orientation only, not a supplier replay or theorem proof." + }, + "first_experiment": "Derive or authenticate a ceiling for the exact current paid/target inventory before searching. Old #1240/#4091 caps do not constrain #5599 automatically. Require an unclaimed domain, time cap and useful complete margin. Stop at the applicable ceiling; change the word or boundary instead of adding seeds.", + "bottleneck_link": "Judge the actual current supplier contract and complete signed target/paid bill; frozen-profile ceilings require an applicability proof.", + "allowed_variations": [ + "One exact source head, helper/cut region or quantified proposition and changed hypothesis; check live handoffs first. Different seeds are not different scopes." + ], + "scope_change_triggers": [ + "Changing source head, helper/cut domain, operation alphabet or caller boundary without recording the new scope.", + "Treating an archived proposal or local numerical pass as complete supplier admission." + ], + "overlap_terms": [ + "T16", + "owner exchange", + "packing", + "4091", + "4088", + "staged-fourth-mixture-ceiling", + "staged544-mixed-fourth-entry" + ], + "existing_checks": [ + { + "scope": "PR #4091: pooled optimum at one-third staging for pinned fixed words; not a chronological fill.", + "evidence": "research/staged-fourth-mixture-ceiling/README.md", + "remaining": "Independent scope/source check; any residual optimization is explicitly bounded and optional.", + "status": "author-checked", + "source_commit": "a29bdd8f56cd18b805917775cdec09ff935eddc4", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4088: later 1090-call literal fill improves the earlier 1080-call witness.", + "evidence": "research/staged544-mixed-fourth-entry/README.md", + "remaining": "Complete admission remains separate; old residual-bin instructions must not be copied blindly.", + "status": "author-checked", + "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "Selected PR5599: complete helper-subspace construction and independent caller replay; five framework assumptions remain.", + "evidence": "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md", + "remaining": "The next experiment must identify uncovered source-specific work. Successor archive intake does not transfer this admission.", + "status": "reviewed", + "source_commit": "09dd0965711ca7eeb169057a420abab1c9052137", + "selected_record_sha256": "2a0220e866417774606e0f991e41b9c1d26b1f43b97857238cf478dbc7d330b5" + } + ] + }, + "scope_status": "changed", + "actual_scope": "Exact #7161/#7113 equal-width rank-one pair substitution with one rank-two child and rectangular linear adapters.", + "scope_change_reason": "The same-square and monomial obstructions leave arbitrary rectangular preparation/readout and owned scratch erasure open.", + "bottleneck_link": "A rank-one pairing family can close the current complex raw moment gap at the price level if 25,328 pairs attain the ideal cost.", + "budget_minutes": 60, + "stop_rule": "Prove or disprove the all-width bounded-adapter identity after exact price and source checks. Cap the finite control at 512 native columns and widths 1\u20134.", + "outcome": "negative-result", + "evidence": "Source-bound complete paid invoice and directed price. All 512 literal signed columns and 60 projection controls, with omitted-phase, omitted-call and missing-reciprocal negatives. Two all-width necessary inequalities.", + "author": "ToikY", + "ai_assistance": "OpenAI Codex and subagents materially assisted the proof, implementation, independent price calculation and verification.", + "open_questions": [ + { + "question": "Can an adapter with growing norms and a priced width-dependent layout implement one exact pair within the allowed bank volume?", + "why_it_matters": "The ideal invoice has enough room if the unchanged all-width contracts and full price hold.", + "first_step": "At the literal MOVE535 pair, derive a two-lane adapter with width-independent priced bank expansion. Compute row and column growth and all signed phases before pricing.", + "blocked_by": "An all-width identity with charged setup, routing, precision, ownership and returned state." + } + ] +} diff --git a/research/p104-rectangular-clifford-adapter-bound/VERIFY.json b/research/p104-rectangular-clifford-adapter-bound/VERIFY.json new file mode 100644 index 0000000000..f5633a8b4c --- /dev/null +++ b/research/p104-rectangular-clifford-adapter-bound/VERIFY.json @@ -0,0 +1,35 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/p104-rectangular-clifford-adapter-bound/ADAPTER.json", + "research/p104-rectangular-clifford-adapter-bound/INPUTS.json", + "research/p104-rectangular-clifford-adapter-bound/inputs/PEER-NOTICE.txt", + "research/p104-rectangular-clifford-adapter-bound/inputs/caller/CALLER.json", + "research/p104-rectangular-clifford-adapter-bound/inputs/caller/interval_gate.py", + "research/p104-rectangular-clifford-adapter-bound/inputs/gaussian/clifford_exact.py", + "research/p104-rectangular-clifford-adapter-bound/inputs/gaussian/native_verify.py", + "research/p104-rectangular-clifford-adapter-bound/inputs/peer/research/p104-rank8-exit-funded-split/RESULT.json", + "research/p104-rectangular-clifford-adapter-bound/inputs/peer/research/p104-rank8-exit-funded-split/WORD.json.gz", + "research/p104-rectangular-clifford-adapter-bound/inputs/prior/owned.py" + ], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/verify.py", + "{package}/inputs", + "--expected", + "{package}/ADAPTER.json", + "--source-map", + "{package}/INPUTS.json" + ], + "timeout_seconds": 120, + "checks": "Authenticate the exact inputs, reconstruct the signed invoice, and replay the Gaussian controls and frozen receipt." + } + ] +} diff --git a/research/p104-rectangular-clifford-adapter-bound/inputs/PEER-NOTICE.txt b/research/p104-rectangular-clifford-adapter-bound/inputs/PEER-NOTICE.txt new file mode 100644 index 0000000000..ad393f2b6e --- /dev/null +++ b/research/p104-rectangular-clifford-adapter-bound/inputs/PEER-NOTICE.txt @@ -0,0 +1,14 @@ +Prepared for Clear1nsight with substantial OpenAI Codex and ChatGPT Pro +assistance. New work is Apache-2.0. + +Rohan Arun supplied the exact #7156 word, its directed supplier/caller +application, and the signed #7113 caller. His #7142 charged an input +boundary for a different split. Ali Romman supplied the causal-history +owned-buffer identity. Jerry Chen / CubeJerry supplied contact-free +retiming and temporal verification. Matarener supplied the helper +kernels. dillona supplied the temporal constructor, chart-595 source and +scalar-width work. ToikY supplied the pricing engines and earlier chart +leads. The #7155 composition and guarded suffix retain their authors. +Douglas Colkitt and the #7000/#7001 reviewers supplied the retained +all-width application and fixed-tape proof. All original source credits, +licenses and notices remain in the authenticated #7156 archive. diff --git a/research/p104-rectangular-clifford-adapter-bound/inputs/caller/CALLER.json b/research/p104-rectangular-clifford-adapter-bound/inputs/caller/CALLER.json new file mode 100644 index 0000000000..9451ceaf6e --- /dev/null +++ b/research/p104-rectangular-clifford-adapter-bound/inputs/caller/CALLER.json @@ -0,0 +1 @@ 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k): R[x] *= q^k, one paid rank-1 job on one register (new op; not in the retained alphabet).; source interval457..575 replaced by a three-QUERY even-basis factorization; no QSELF"} \ No newline at end of file diff --git a/research/p104-rectangular-clifford-adapter-bound/inputs/caller/interval_gate.py b/research/p104-rectangular-clifford-adapter-bound/inputs/caller/interval_gate.py new file mode 100644 index 0000000000..e24dc46079 --- /dev/null +++ b/research/p104-rectangular-clifford-adapter-bound/inputs/caller/interval_gate.py @@ -0,0 +1,128 @@ +#!/usr/bin/env python3 +"""Independent certified fixed-grid intervals (80 decimal places). +ln via 2 atanh after binary range reduction; exp(-x) via alternating +Taylor brackets. Uses only integer floor/ceiling, not Decimal transcendents. +""" +from fractions import Fraction as F +from functools import lru_cache +from pathlib import Path +import json,argparse +if not __debug__: raise RuntimeError('Run without -O; assertions are proof checks.') +B=10**80 + +def ceildiv(a,b):return -((-a)//b) +def exact(q): + q=F(q);return q.numerator*B//q.denominator,ceildiv(q.numerator*B,q.denominator) +def add(a,b):return a[0]+b[0],a[1]+b[1] +def sub(a,b):return a[0]-b[1],a[1]-b[0] +def mul(a,b): + p=[a[i]*b[j] for i in (0,1) for j in (0,1)];return min(p)//B,ceildiv(max(p),B) +def div(a,b): + assert b[0]>0 + p=[F(a[i]*B,b[j]) for i in (0,1) for j in (0,1)] + return min(p).__floor__(),max(p).__ceil__() +def smul(a,q):return mul(a,exact(q)) +def atanh_log(y): + yi=exact(y);yy=mul(yi,yi);p=yi;s=(0,0) + for j in range(100):s=add(s,smul(p,F(2,2*j+1)));p=mul(p,yy) + # 0 <= tail <= 2 y^201/[201(1-y^2)] < 3*(1/3)^201. + return s[0],s[1]+ceildiv(3*B,3**201) +@lru_cache(None) +def log(r): + assert r>=1 + k=r.bit_length()-1;y=F(r-2**k,r+2**k) + a=atanh_log(y);b=atanh_log(F(1,3));return add(a,smul(b,k)) +def expminus(x): + assert 0<=x[0]<=x[1]0 and margins[str(hi)][1]<0 and margins[str(tested)][0]>0 + target=moment(T,tested);paid=moment(P,tested) + alpha=div(paid,target) + # Tail exponent = 1-tested+1/7; argument exp may not be negative. + # r^(1-tested+1/7)=r^(1-tested)* exp(log(r)/7). + def exppos(x): + assert 0<=x[0]<=x[1]0 and gap.numerator==1;step=gap.denominator + wins=lambda j:(step*j+1)**written<2**j + l,h=1,2 + while not wins(h):l,h=h,2*h + while h-l>1: + m=(l+h)//2 + if wins(m):h=m + else:l=m + assert wins(h) and not wins(h-1) + # Monotonicity: upper derivative bound on [0, cap]. + derivative=(0,0) + for rr in T.keys()|P.keys(): + c=T.get(rr,0)-P.get(rr,0);r=int(rr) + term=mul(power(r,cap if c>=0 else 0),log(r));derivative=add(derivative,smul(term,-c)) + assert derivative[1]<0 + result=dict(claim=str(claim),tested=str(tested),raw_bracket=[str(lo),str(hi)],moment_margins={k:show(v) for k,v in margins.items()},moment_margin_float={k:value(v) for k,v in margins.items()},derivative_upper=float(F(derivative[1],B)),alpha=value(alpha),gamma=value(gamma),delta=value(delta),minimum_log_power=lp,written_log_power=written,compiler_gap=str(gap),H=str(step*h),BIT_pin=str(cap),BIT_margin=str(cap-tested)) + # Outer formulas evaluated independently after algebraically substituting + # b=k+5g,a=k+4g,q=k+3g,epsilon=1-g,beta=1-3g. + k=claim;g=gap;b=k+5*g;a=k+4*g;q=k+3*g;ep=1-g;be=1-3*g;r0=g/10;stop=layout=g + sig=1-b;tau=1-a;internal=tau+(1-stop)*max(sig-tau,0);leaf=sig+stop*(1-sig);lam=1-(q+a)/2;xi=ep*(1+q)-F(3,32)+layout;key=be+1-ep + M=[ep*q,a,1-ep+q*be,1-ep+a*be,1-ep+be,F(3,32)+xi-ep,xi+F(1,2)-ep,ep,1-(ep+be+48-128+2)] + checks=[cap-a,b-a,q,b-q,a-q,stop,1-stop,(1-stop)*b-a,1-internal-q,1-leaf-q,lam-tau,lam-sig,lam-internal,1-q-lam,1-q-leaf,ep,1-ep,xi-F(1,2),ep-xi,be,ep-be,1-be,1-(2*xi-2)-r0-be,1-(2*xi-2)-be,1-ep-r0,1-ep,r0,1-key,1-be-2*(1-ep),128-48-be,layout,ep-a,F(1,32)-b,F(2**45-7**16),F(2),2-xi,F(5),1-be,1-be,1-ep,M[2]-M[0],g,k-F('.001730970419199163702738'),1-ep,F(11,2)]+[x-k for x in M] + functional=[1-be,be*(1-F(3,1000)),128-48-ep-be-1,be*(1-F(1,250))] + assert len(checks)==54 and len(functional)==4 and min(checks+functional)>0 + result['outer']=dict(strict_count=54,functional_count=4,minimum_margin=str(min(checks+functional)),BIT_just_below_effective_rejected=(a-F(1,10**12))-a<0) + # Input-lift is only needed on [1-tested_complex,1]. A stronger BIT + # pin is irrelevant to this interval; the source's crude BIT-wide bound + # is not imported beyond its valid range. + pos={7:1,3:1,5:1};neg={9:1,4:1,1:2};d1=(0,0);curvature=(0,0) + for hist,sign in ((pos,1),(neg,-1)): + for r,c in hist.items(): + d1=add(d1,smul(log(r),sign*c*r)) + curvature=add(curvature,smul(mul(log(r),log(r)),c*r)) + lift_cap=cap if cap<=F('.00376669') else tested + assert tested<=lift_cap and F(d1[1],B)+lift_cap*F(curvature[1],B)<0 + lifts={} + for price in (claim,tested): + lift=sub(moment(pos,price),moment(neg,price));assert lift[0]>0 + assert price*(-F(d1[1],B))-price*price*F(curvature[1],B)/2>0 + lifts[str(price)]=show(lift) + result['input_lift']=dict(margins=lifts,interval_kappa_cap=str(lift_cap),derivative_upper_on_required_interval=str(F(d1[1],B)+lift_cap*F(curvature[1],B)),source_BIT_wide_crude_bound_would_be=str(F(d1[1],B)+cap*F(curvature[1],B))) + return result +if __name__=='__main__': + p=argparse.ArgumentParser();p.add_argument('audit');p.add_argument('--claim',default='.00362852408');p.add_argument('--tested',default='.00362852408007');p.add_argument('--lower',default='.00362852408398727978896072723289');p.add_argument('--upper',default='.00362852408398727978896072723290');p.add_argument('--out',required=True);p.add_argument('--bit-pin',default='.00376669');a=p.parse_args() + r=gate(json.loads(Path(a.audit).read_text())['invoice'],a.claim,a.tested,a.lower,a.upper,a.bit_pin);Path(a.out).write_text(json.dumps(r,indent=2)+'\n');print(json.dumps(r,indent=2)) diff --git a/research/p104-rectangular-clifford-adapter-bound/inputs/gaussian/clifford_exact.py b/research/p104-rectangular-clifford-adapter-bound/inputs/gaussian/clifford_exact.py new file mode 100644 index 0000000000..166841a037 --- /dev/null +++ b/research/p104-rectangular-clifford-adapter-bound/inputs/gaussian/clifford_exact.py @@ -0,0 +1,149 @@ +"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals. +Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d. +The tableau is supplemented by a literal circuit, so global phases are kept. +""" +from dataclasses import dataclass + +def parity(x):return x.bit_count()&1 +def rank(rows): + p={} + for x in rows: + while x: + b=x.bit_length()-1 + if b not in p:p[b]=x;break + x^=p[b] + return len(p) +def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<>j&1);a[j],a[k]=a[k],a[j] + for i in range(n): + if i!=j and a[i]>>j&1:a[i]^=a[j] + assert [r&((1<>n for r in a) +def basis_extend(cols,n): + out=[] + for x in list(cols)+[1<len(out):out.append(x) + assert len(out)==n + return tuple(out) +def nullspace(rows,n): + a=list(rows);p=[];k=0 + for j in range(n): + t=next((i for i in range(k,len(a)) if a[i]>>j&1),None) + if t is None:continue + a[t],a[k]=a[k],a[t] + for i in range(len(a)): + if i!=k and a[i]>>j&1:a[i]^=a[k] + p.append(j);k+=1 + return tuple((1<>j)&1)<>i&1:out=pmul(out,T[i]) + for i in range(n): + if z>>i&1:out=pmul(out,T[n+i]) + return out +def compose(A,B):return tuple(apply(A,p) for p in B) +def inverse(T): + n=len(T)//2;cols=[x|(z<>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4)) + return tuple(out) +def qvalue(Q,alpha,x,n): + return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4 +def mul_i(a,p): + x,y=a;p%=4 + return [(x,y),(-y,x),(-x,-y),(y,-x)][p] +@dataclass +class Op: + n:int + tab:tuple + circuit:list + def then(self,b): + assert self.n==b.n + return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit) + def adjoint(self): + circ=[] + for e in reversed(self.circuit): + if e[0]=='P':circ.append(('P',inv(e[1],self.n))) + elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2]))) + elif e[0]=='C':circ.append(('C',e[1],-e[2])) + elif e[0]=='phase':circ.append(('phase',(-e[1])%4)) + else:circ.append(e) + return Op(self.n,inverse(self.tab),circ) + def zero_state(self,basis=0): + N=1<>i)&1 for i in range(n)) + assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n)) + return Op(n,tuple([(1<>i&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>i)&1)) for i in range(n)]),[('X',b)]) +def fourier(n,axes=None): + out=ident(n) + for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<len(selected):picks.append(j);selected.append(x) + assert len(picks)==r and all(x>>r==0 for x in Bcols) + Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<> j) & 1) << i for i, row in enumerate(matrix)) for j in range(len(matrix))) + + +def inverse(matrix): + n = len(matrix) + rows = [row | (1 << (n+i)) for i, row in enumerate(matrix)] + for j in range(n): + pivot = next((i for i in range(j, n) if rows[i] >> j & 1), None) + require(pivot is not None, 'singular binary chart') + rows[j], rows[pivot] = rows[pivot], rows[j] + for i in range(n): + if i != j and rows[i] >> j & 1: + rows[i] ^= rows[j] + require([row & ((1 << n)-1) for row in rows] == [1 << i for i in range(n)], 'binary inverse') + return tuple(row >> n for row in rows) + + +def extend(vectors, n): + columns, pivots = [], {} + for value in tuple(vectors) + tuple(1 << i for i in range(n)): + reduced = value + while reduced: + j = reduced.bit_length()-1 + if j not in pivots: + pivots[j] = reduced + columns.append(value) + break + reduced ^= pivots[j] + require(len(columns) == n, 'frame basis extension') + return tuple(columns) + + +def adjoint(circuit): + out = [] + for gate in reversed(circuit): + if gate[0] == 'P': + out.append(('P', inverse(gate[1]))) + elif gate[0] == 'D': + out.append(('D', gate[1], tuple(-a % 4 for a in gate[2]))) + elif gate[0] == 'C': + out.append(('C', gate[1], -gate[2])) + elif gate[0] == 'phase': + out.append(('phase', -gate[1] % 4)) + else: + require(gate[0] == 'X', 'adjoint gate type') + out.append(gate) + return tuple(out) + + +def fourier(rank): + return tuple(('C', 1 << i, 1) for i in range(rank)) + + +def frame(vectors, n): + rank = len(vectors) + if rank == 0: + return () + if rank == n: + return fourier(n) + matrix = transpose(extend(vectors, n)) + columns = transpose(inverse(matrix)) + quadratic = tuple((1 << i) ^ sum(parity(a & b) << j for j, b in enumerate(columns)) for i, a in enumerate(columns)) + diagonal = tuple((row >> i) & 1 for i, row in enumerate(quadratic)) + chart = (('P', matrix), ('D', quadratic, diagonal)) + return adjoint(chart) + fourier(rank) + chart + + +def monomial(record): + matrix = tuple(record['matrix_rows']) + quadratic = tuple(record['quadratic_rows']) + linear = tuple(record['linear_Z4']) + require(transpose(quadratic) == quadratic, 'quadratic symmetry') + require(len(matrix) == len(quadratic) == len(linear) == 9, 'monomial dimension') + require(all(a % 2 == (quadratic[i] >> i) & 1 for i, a in enumerate(linear)), 'diagonal parity') + inverse(matrix) + return (('D', quadratic, linear), ('P', matrix), ('X', record['offset']), ('phase', record['phase'])) + + +def recipe(record): + rank = record['rank'] + require(isinstance(rank, int) and 0 <= rank <= 9, 'child rank') + if rank == 0: + require(record['right'] is None, 'rank zero right factor') + return monomial(record['left']) + return monomial(record['right']) + fourier(rank) + monomial(record['left']) + + +def tableau(circuit, n=9): + rows = [(1 << i, 0, 0) for i in range(n)] + [(0, 1 << i, 0) for i in range(n)] + for gate in circuit: + tag = gate[0] + out = [] + inverse_transpose = transpose(inverse(gate[1])) if tag == 'P' else None + for x, z, phase in rows: + if tag == 'P': + x, z = mul(gate[1], x), mul(inverse_transpose, z) + elif tag == 'X': + phase += 2 * parity(z & gate[1]) + elif tag == 'C': + if parity(z & gate[1]): + x ^= gate[1] + phase += 3 * gate[2] + elif tag == 'D': + quadratic, linear = gate[1:] + phase += sum(linear[i] for i in range(n) if x >> i & 1) + phase += 2 * sum(parity((quadratic[i] >> (i+1)) & (x >> (i+1))) for i in range(n) if x >> i & 1) + z ^= mul(quadratic, x) + else: + require(tag == 'phase', 'tableau gate type') + out.append((x, z, phase % 4)) + rows = out + return tuple(rows) + + +@lru_cache(maxsize=512) +def action(gate): + if gate[0] == 'P': + return tuple(mul(gate[1], x) for x in range(512)) + require(gate[0] == 'D', 'state action type') + quadratic, linear = gate[1:] + return tuple((sum(linear[i] for i in range(9) if x >> i & 1) + + 2 * sum(parity((quadratic[i] >> (i+1)) & (x >> (i+1))) for i in range(9) if x >> i & 1)) % 4 for x in range(512)) + + +def rotate(pair, power): + a, b = pair + return ((a, b), (-b, a), (-a, -b), (b, -a))[power % 4] + + +def state(circuit, basis=0): + value, denominator = {basis: (1, 0)}, 0 + for gate in circuit: + tag = gate[0] + result = {} + if tag == "C": + direction, sign = gate[1:] + for address, (a, b) in value.items(): + for target, pair in ((address, (a - sign*b, b + sign*a)), + (address ^ direction, (a + sign*b, b - sign*a))): + old = result.get(target, (0, 0)) + result[target] = (old[0] + pair[0], old[1] + pair[1]) + denominator += 1 + else: + for address, pair in value.items(): + if tag == "P": + target = mul(gate[1], address) + elif tag == "X": + target = address ^ gate[1] + else: + target = address + if tag == "D": + pair = rotate(pair, action(gate)[address]) + else: + require(tag == "phase", "Unknown Gaussian state gate") + pair = rotate(pair, gate[1]) + require(target not in result, "A monomial address map is not injective") + result[target] = pair + value = {address: pair for address, pair in result.items() if pair != (0, 0)} + while denominator and all((a | b) % 2 == 0 for a, b in value.values()): + denominator -= 1 + value = {address: (a//2, b//2) for address, (a, b) in value.items()} + return value, denominator + + +def equal(actual, expected, label): + require(tableau(actual) == tableau(expected), label + ": signed Pauli action") + require(state(actual) == state(expected), label + ": exact global phase") + + +def verify(data, certificate): + word = data["word"] + original, clean = data["programs"], data["clean_programs"] + source_recipes = data["recipes"] + residuals = data["residuals"]["recipes"] + native_tags = {"climb", "adapter", "residual_adapter"} + for orientation in ("forward", "backward"): + native = [event for event in clean[orientation] if event[0] in native_tags] + require(native == [event for event in original[orientation] if event[0] in native_tags], + "A retained native event changed") + require(len(native) == 5056, "The retained native event count changed") + frames = [frame(tuple(vectors), 9) for vectors in word["frames"]] + used = {(event[3], event[4]) for program in clean.values() + for event in program if event[0] == "climb"} + children = {(record["old"], record["new"]): record for record in source_recipes["children"]} + require(len(children) == len(source_recipes["children"]) and used <= set(children), + "The retained child recipe coverage is incomplete") + for old, new in sorted(used): + record = children[old, new] + require(record["rank"] == len(word["frames"][new]) - len(word["frames"][old]), + "A retained child has the wrong rank") + equal(recipe(record), adjoint(frames[old]) + frames[new], "Retained child") + endpoints = {(record["role"], record["port"]): record + for record in source_recipes["endpoint_adapters"]} + require(len(endpoints) == len(source_recipes["endpoint_adapters"]) + and set(endpoints) == {(role, p) for role in ("source", "target") for p in range(112)}, + "The endpoint adapter coverage is incomplete") + for (role, port), record in endpoints.items(): + direction = word["ports"][port] + conventional = (("C", direction, 1),) if role == "source" else ( + ("C", direction, -1),) + fourier(9) + index = word["start"][port] if role == "source" else word["final"][112 + port] + require(record["frame"] == index and record["rank"] == 0, "An endpoint frame changed") + equal(recipe(record), adjoint(conventional) + frames[index], "Endpoint adapter") + used_residuals = set() + for program in clean.values(): + for event in program: + if event[0] != "residual_adapter": + continue + _, position, register, entry, *tail = event + terminal = tail[0] if tail else 1 + key = str(entry) if terminal == 1 else str(entry) + ":" + str(terminal) + require(key in residuals and position in ("pre", "post"), "A residual binding changed") + require(entry == word["start"][register] and terminal == word["final"][register], + "A residual endpoint changed") + used_residuals.add(key) + for key in sorted(used_residuals): + record = residuals[key] + equal(recipe(record), adjoint(frames[record["frame"]]) + frames[record.get("terminal", 1)], + "Residual adapter") + records = certificate["input_recipes"] + ports = certificate["compensation_ports"] + require([record["port"] for record in records] == ports and len(records) == 8, + "The eight input recipes changed") + columns = 0 + for item in records: + port, label = item["port"], item["label"] + require(label == word["ports"][port] and item["canonical_start_frame_id"] == word["start"][port], + "An input recipe has the wrong supplier label") + record = item["recipe"] + require(record["rank"] == 1, "An input copy has the wrong child rank") + for side in ("left", "right"): + factor = record[side] + require(factor["quadratic_rows"] == [0] * 9 and factor["linear_Z4"] == [0] * 9 + and factor["offset"] == factor["phase"] == 0, + "An input factor is not an address permutation") + actual, expected = recipe(record), (("C", label, 1),) + equal(actual, expected, "Positive inherited input line") + for basis in range(512): + require(state(actual, basis) == state(expected, basis), "A complete input Gaussian column differs") + columns += 1 + negative = monomial(record["right"]) + (("C", 1, -1),) + monomial(record["left"]) + require(tableau(negative) != tableau(expected) or state(negative) != state(expected), + "An inverse input child was not detected") + phased = actual + (("phase", 1),) + require(tableau(phased) == tableau(actual) and state(phased) != state(expected), + "An input phase-only error was not detected") + return {"status": "PASS_EXACT_INPUT_NATIVE_FRAMES", "retained_native_events_per_orientation": 5056, + "retained_child_recipes": len(used), "endpoint_adapter_recipes": len(endpoints), + "residual_adapter_recipes": len(used_residuals), "new_input_recipes": len(records), + "new_exact_gaussian_columns": columns, "inverse_input_child_controls": len(records), + "phase_only_controls": len(records), "address_permutation_factors": 2 * len(records), + "method": "Independent signed Pauli and exact Gaussian interpretation; no compiler import", + "scope": "Positive inherited input frames before every retained adapter. No recursive hosting claim."} diff --git a/research/p104-rectangular-clifford-adapter-bound/inputs/peer/research/p104-rank8-exit-funded-split/RESULT.json b/research/p104-rectangular-clifford-adapter-bound/inputs/peer/research/p104-rank8-exit-funded-split/RESULT.json new file mode 100644 index 0000000000..60edfac362 --- /dev/null +++ b/research/p104-rectangular-clifford-adapter-bound/inputs/peer/research/p104-rank8-exit-funded-split/RESULT.json @@ -0,0 +1,1599 @@ +{ + "adapter": { + "adapted_sha256": { + "check_odd_partial_admission.py": "de75cd93b9bfffb2a13781209435d31a84edd97f0fe313d3ecb9542ce8383dac", + "check_odd_precision.py": "59d811dd0eddca0a761e935341e7bee51cf66b9d9481ce8eb500c9ae5723bbcb", + "emit_odd_type_ab.py": "6fd9f61f9ba6c726524d1a585d0201b0eac61829ccae6be598f0f0fc1cb64f1a" + }, + "edits": [ + { + "file": "emit_odd_type_ab.py", + "new": "invoice=json.loads((root/\"COHORT-PRICE.json\").read_text())", + "old": "invoice=next(x for x in json.loads((root/\"SHORT-CALLER-RAW-PRICE.json\").read_text())[\"rows\"] if tuple(x[\"shape\"])==shape)" + }, + { + "file": "check_odd_partial_admission.py", + "new": "actual_native=ind.native(w)\nassert actual_native==N and not N[\"bad_inputs\"], \"Fresh complete native inventory and arbitrary-input adjoint\"", + "old": "previous=json.loads((root/\"SHORT-ADMISSION-PARTIAL.json\").read_text())\nassert previous[\"native_sha256\"]==digest and not N[\"bad_inputs\"]" + }, + { + "file": "check_odd_partial_admission.py", + "new": "claim=Q('0.00364489006794')", + "old": "claim=Q(\".00363797977\")" + }, + { + "file": "check_odd_partial_admission.py", + "new": "tested=claim+Q(7,10**17)\nwhile tested>=Q(reference[\"raw_bracket\"][0]):\n tested=claim+(tested-claim)/10", + "old": "tested=claim+Q(7,10**17)" + }, + { + "file": "check_odd_partial_admission.py", + "new": "g=gate(invoice,claim,tested,*bracket,r[\"gate\"][\"BIT_pin\"])\ntry:\n gate(invoice,claim,Q(bracket[0]),*bracket,r[\"gate\"][\"BIT_pin\"])\nexcept AssertionError:\n crossing_probe_rejected=True\nelse:\n raise AssertionError(\"Probe at lower crossing unexpectedly accepted\")", + "old": "g=gate(invoice,claim,tested,*bracket,r[\"gate\"][\"BIT_pin\"])" + }, + { + "file": "check_odd_partial_admission.py", + "new": "\"crossing_probe_rejected\":crossing_probe_rejected,\"scope\":\"Fresh exact current native arbitrary-input adjoint;", + "old": "\"scope\":\"Reuse exact same native word all-column adjoint;" + }, + { + "file": "check_odd_precision.py", + "new": "patch('(life, peak, owned_count) == (54, 43, 51)','(life, peak, owned_count) == (66, 48, 63)')\nenv=ModuleType(\"short_envelope\")", + "old": "env=ModuleType(\"short_envelope\")" + }, + { + "file": "check_odd_precision.py", + "new": "", + "old": "previous=json.loads((root/\"SHORT-PRECISION.json\").read_text())" + }, + { + "file": "check_odd_precision.py", + "new": "assert grid_receipt[\"caller_sha256\"]==sha256(cpath.read_bytes()).hexdigest()", + "old": "assert previous[\"native_sha256\"]==sha and grid_receipt[\"caller_sha256\"]==sha256(cpath.read_bytes()).hexdigest()" + }, + { + "file": "check_odd_precision.py", + "new": "wg=grid.word_run(w, frac=25)\nwp,wr=env.native_envelope(w)\nwg=json.loads(json.dumps(wg,default=str));wr=json.loads(json.dumps(wr,default=str))\nassert wg==r[\"precision\"][\"word\"] and wr==r[\"precision\"][\"rounded_native\"], \"Fresh changed-native grid and envelope\"", + "old": "wg=previous[\"native_grid\"]\nwr=previous[\"rounded_native\"]\nwp={key:(Q(v[\"exact\"]),v[\"witness\"]) for key,v in wr[\"bounds\"].items()}" + } + ] + }, + "caller_sha256": "255d89f38cd45e38e5770f559bc43dc217e989032359768cdc7e8cdfd64b47bc", + "catalogue": [ + { + "catalogue_digest": "789580be599f2c712cda0ef0622d3fff6c86bf1ffdcd49c73b2f7f839aae5f23", + "catalogue_size": 3036, + "checked_maps": 1000, + "distinct_helper_maps": 187, + "distinct_paid_maps": 2950, + "exact_recipe_digest": "430c467e9c73ef00ddc325b7cf95aba8a34187f362eae67791aafd26b117e4b9", + "main_boundary_digest": "4f53cda18c2baa0c0354bb5f9a3ecbe5ed12ab4d8e11ba873c2f11161202b945", + "main_boundary_pairs": 0, + "phase_control_rejected": true, + "scope": "Complete signed Pauli action plus exact Gaussian global phase; for Clifford maps these determine every matrix column. Generic tensor-product and physical grammar application is written in the review. No random-field substitution.", + "slice_start": 0, + "slice_stop": 1000, + "status": "PASS_CURRENT_NATIVE_CATALOGUE_SLICE", + "word_sha256": "c1caec11ca3ee264ef03018dd91037eac10c3e28950c4c525ee1b4bf5ee210e2" + }, + { + "catalogue_digest": "789580be599f2c712cda0ef0622d3fff6c86bf1ffdcd49c73b2f7f839aae5f23", + "catalogue_size": 3036, + "checked_maps": 1000, + "distinct_helper_maps": 187, + "distinct_paid_maps": 2950, + "exact_recipe_digest": "2cae048f253c10a701476eaa4486931f22766daf994d44d80688b0f8f2fc530f", + "main_boundary_digest": "4f53cda18c2baa0c0354bb5f9a3ecbe5ed12ab4d8e11ba873c2f11161202b945", + "main_boundary_pairs": 0, + "phase_control_rejected": true, + "scope": "Complete signed Pauli action plus exact Gaussian global phase; for Clifford maps these determine every matrix column. Generic tensor-product and physical grammar application is written in the review. No random-field substitution.", + "slice_start": 1000, + "slice_stop": 2000, + "status": "PASS_CURRENT_NATIVE_CATALOGUE_SLICE", + "word_sha256": "c1caec11ca3ee264ef03018dd91037eac10c3e28950c4c525ee1b4bf5ee210e2" + }, + { + "catalogue_digest": "789580be599f2c712cda0ef0622d3fff6c86bf1ffdcd49c73b2f7f839aae5f23", + "catalogue_size": 3036, + "checked_maps": 1000, + "distinct_helper_maps": 187, + "distinct_paid_maps": 2950, + "exact_recipe_digest": "c8524029578adf6749ecc9b72b848a9933ea23b54951d7349c0614c18603fea9", + "main_boundary_digest": "4f53cda18c2baa0c0354bb5f9a3ecbe5ed12ab4d8e11ba873c2f11161202b945", + "main_boundary_pairs": 0, + "phase_control_rejected": true, + "scope": "Complete signed Pauli action plus exact Gaussian global phase; for Clifford maps these determine every matrix column. Generic tensor-product and physical grammar application is written in the review. No random-field substitution.", + "slice_start": 2000, + "slice_stop": 3000, + "status": "PASS_CURRENT_NATIVE_CATALOGUE_SLICE", + "word_sha256": "c1caec11ca3ee264ef03018dd91037eac10c3e28950c4c525ee1b4bf5ee210e2" + }, + { + "catalogue_digest": "789580be599f2c712cda0ef0622d3fff6c86bf1ffdcd49c73b2f7f839aae5f23", + "catalogue_size": 3036, + "checked_maps": 36, + "distinct_helper_maps": 187, + "distinct_paid_maps": 2950, + "exact_recipe_digest": "01651736571052e77f70be25553d3f726b5325a89c93cb9459a54c3634ee1f38", + "main_boundary_digest": "ad959887c990b8862a0e60db3f53d5195a1c9d667c1593f0101adc8db18f27fa", + "main_boundary_pairs": 104, + "phase_control_rejected": true, + "scope": "Complete signed Pauli action plus exact Gaussian global phase; for Clifford maps these determine every matrix column. Generic tensor-product and physical grammar application is written in the review. 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Generic tensor-product and physical grammar application is written in the review. No random-field substitution.", + "slice_start": 3000, + "slice_stop": 3036, + "status": "PASS_CURRENT_NATIVE_CATALOGUE_SLICE", + "word_sha256": "c1caec11ca3ee264ef03018dd91037eac10c3e28950c4c525ee1b4bf5ee210e2" + } + ], + "fixed_tape_counts": { + "H": 16510400000000000000000, + "Kstar_bits": 14093, + "actual_ambient": 145, + "caller_odd_scale": 675, + "caller_sha256": "255d89f38cd45e38e5770f559bc43dc217e989032359768cdc7e8cdfd64b47bc", + "common_grid": { + "fractional": "p+D", + "signed_width": "p+h+2D+3", + "temp_padding": 26 + }, + "compiler_ambient_cap": 153, + "context_bound_bits": 14104, + "context_c": 2430, + "elementary_records_per_map_upper": 85264, + "elementary_records_upper": 25471767360, + "log_power": 2237, + "max_scalar_numerator_bits": 24, + "monomial_map_slots": 298740, + "native_invocations": 17, + "native_sha256": "9eff91418d838f1ffa20fe5c5975dc2c43a79b32d501fcbe30b90c50a7b11ce3", + "owned_banks_per_raw_occurrence": 1071, + "scalar_macro_inputs": { + "caller": 117856, + "conversions": 58454, + "native": 1191190 + }, + "scalar_services_upper": 43760000, + "scalar_steps_coefficient": 45885685760000, + "scope": "Exact finite-cost and common-format substitutions in the selected #7000 conditional application proof, using the conservative primitive movement and scalar constants there. The premise is the complete signed native/physical binding and retained compiler, BIT, stock, and outer contracts. This script counts the raw occurrence, not an enumerated top-level compiled multiplier.", + "tested_claim": "182244503397/50000000000000" + }, + "native_archive_sha256": "c1caec11ca3ee264ef03018dd91037eac10c3e28950c4c525ee1b4bf5ee210e2", + "native_canonical_sha256": "9eff91418d838f1ffa20fe5c5975dc2c43a79b32d501fcbe30b90c50a7b11ce3", + "numeric_gate": { + "BIT_margin": "12179993205993/100000000000000000", + "BIT_pin": "376669/100000000", + "H": "16510400000000000000000", + "alpha": [ + 1.0, + 1.0 + ], + "claim": "182244503397/50000000000000", + "compiler_gap": "1/100000000000000000", + "delta": [ + 0.9066684778947387, + 0.9066684778947387 + ], + "derivative_upper": -381691.382745105, + "gamma": [ + 0.9407507620286742, + 0.9407507620286742 + ], + "input_lift": { + "derivative_upper_on_required_interval": "-2299831290525933154178526076272396899996972093654613095735772838275432653960006518819/2500000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + 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Checks every normalized endpoint, every paid/helper nested chart map up to exact signed Pauli and absolute phase, caller occurrence/phase, precision, finite scalar and route bounds, and numeric gates. Does not run a compiled Turing machine, select an upstream frontier, or claim human/formal review.", + "source_unit_ordinary": { + "all_caller_scalar_surcharge": 2248928, + "caller_items": { + "A": { + "envelope": 102076416, + "field_boundary": 89856, + "fused_routes": 0, + "idle_routes": 170112000, + "output_routes": 213120000, + "query_routes": 1152000, + "thin": 6144 + }, + "B": { + "envelope": 35730432, + "field_boundary": 7488, + "fused_routes": 1168000, + "idle_routes": 18016000, + "output_routes": 17760000, + "query_routes": 0, + "thin": 0 + } + }, + "caller_total": 559238336, + "charged_caller_odd_conversions": 479232, + "conservative_total": 782129100, + "init_clear_allowance": 264, + "lambda_paid_rank1_would_reduce_S_by": 11280, + "lambda_second_charge": 11280000, + "margin_to_billion": 217870900, + "odd_divisions": { + "ADD": 5829, + "SCALE": 71 + }, + "per_input_conversion": 2650232, + "raw_upper": 765470708, + "route_items": { + "first_main_adapter": 416, + 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Each LAMBDA, QUERY and signed/unsigned idle is one unitary with one child defect. The caller allocation assumes independent stage helpers. Full physical application remains separate." + }, + "ODD-TYPE-AB-REPLAY.json": { + "caller_sha256": "255d89f38cd45e38e5770f559bc43dc217e989032359768cdc7e8cdfd64b47bc", + "paid": { + "1": 68367, + "16": 416, + "2": 14501, + "24": 416, + "3": 14093, + "32": 416, + "4": 3825, + "40": 416, + "48": 416, + "5": 5848, + "56": 416, + "6": 238, + "64": 208, + "7": 170, + "8": 741, + "9": 32 + }, + "raw_bracket": [ + "36448900679400754544078619670439/10000000000000000000000000000000000", + "911222516985018863601965491761/250000000000000000000000000000000" + ], + "replay": { + "bad_outputs": [], + "caller_denominator_height_bound": 578, + "caller_mass_bound": "854474036861847560509026474008040300059938928517783661039773198072080884690114508581583887358835968277340425788985297793555303569703690223623950838857161290503004459697662544865276977234864184443860251086668962688762176068520364648820282528496698239206689277049335412289161443623602012468587331439851515703/168151253906250000000000000000000", + "caller_mass_ceiling_bits": 910, + "max_terms": 3752 + }, + "scope": "Exact emitted signed Laurent caller endpoint and recomputed native/caller paid and target profiles. 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b/research/p104-rectangular-clifford-adapter-bound/inputs/prior/owned.py @@ -0,0 +1,622 @@ +"""Exact #7161 charged owned-MOVE sharing ceilings on retained contact clocks.""" +import argparse +from collections import Counter, defaultdict +from fractions import Fraction +from functools import lru_cache +import gzip +from hashlib import sha256 +from importlib.util import module_from_spec, spec_from_file_location +from itertools import combinations, product +import json +from pathlib import Path +from time import monotonic + +PACKAGE = 'research/p104-rank8-exit-funded-split' +HEAD = 'e3f8d39c43b07063dfc5b800f71c5d21015259e6' +PINS = { + f'peer/{PACKAGE}/WORD.json.gz': 'c1caec11ca3ee264ef03018dd91037eac10c3e28950c4c525ee1b4bf5ee210e2', + f'peer/{PACKAGE}/WORD.json.gz#decompressed': '9eff91418d838f1ffa20fe5c5975dc2c43a79b32d501fcbe30b90c50a7b11ce3', + f'peer/{PACKAGE}/RESULT.json': '59080d75e7281b1a8c1353930917fd15869ad747ff4200948898f78f11c14089', + 'caller-inputs/CALLER.json': '255d89f38cd45e38e5770f559bc43dc217e989032359768cdc7e8cdfd64b47bc', + 'caller-inputs/interval_gate.py': '60a743d13f668ef86db4b8215b4d5d04430a671ba6f1fe06d9c1c4c3dfe86da5', +} +TARGET = Fraction('0.0040075385047236') +PRIME = 2147483647 +STAGES = 17 +PUBLIC_SEEDS = (0, 1, 4, 6, 7, 8) +HOSTED_SEEDS = (2, 3, 5, 9, 10, 11) + + +def pinned(path, label): + raw = path.read_bytes() + assert sha256(raw).hexdigest() == PINS[label], path + return raw + + +def canonical_digest(value): + return sha256(json.dumps(value, sort_keys=True, separators=(',', ':')).encode()).hexdigest() + + +def span(vectors): + result = {0} + for vector in vectors: + assert vector not in result + result.update(value ^ vector for value in tuple(result)) + return frozenset(result) + + +def dimension(space): + assert len(space) > 0 and len(space) & (len(space) - 1) == 0 + return len(space).bit_length() - 1 + + +def distance(a, b): + return dimension(a) + dimension(b) - 2 * dimension(a & b) + + +def overlap_interval(a, b, c, d): + low1, high1 = (a, b) if a < b else (b, a) + low2, high2 = (c, d) if c < d else (d, c) + joint_lower = {u ^ v for u in low1 for v in low2} + joint_upper = high1 & high2 + ranks = (dimension(joint_lower), dimension(joint_upper)) + return ranks, ranks[1] - ranks[0] if joint_lower <= joint_upper else None + + +def scan_word(word, check_time, event_cap): + public = word['public'] + fields = word['owned_fields'] + spaces = list(map(span, word['frames'])) + charts = word['initial'] + [None] * fields + active = set() + contacts = defaultdict(list) + native_moves, owned_moves = [], [] + opcodes = Counter() + lifetimes = peak = 0 + program = word['program'] + assert len(program) <= event_cap, {'first_pending_native_event': event_cap} + for i, event in enumerate(program): + if i % 1024 == 0: + check_time() + op, r, *args = event + assert 0 <= r < len(charts) + opcodes[op] += 1 + if op != 'SCALE': + contacts[r].append((i, op if op not in ('ADD', 'COPY') else op + '_DEST')) + if op == 'MOVE': + a, b, owned = args + assert charts[r] == a and owned == (r >= public) + assert spaces[a] < spaces[b] or owned and spaces[b] < spaces[a] + rank = distance(spaces[a], spaces[b]) + move = dict(event=i, role=r, source=a, target=b, rank=rank) + native_moves.append(move) + if owned: + assert r in active + owned_moves.append(move) + charts[r] = b + elif op == 'INIT': + assert r >= public and charts[r] is None and r not in active + charts[r] = args[0] + active.add(r) + lifetimes += 1 + peak = max(peak, len(active)) + elif op == 'CLEAR': + assert r >= public and charts[r] == args[0] and r in active + charts[r] = None + active.remove(r) + elif op in ('ADD', 'COPY'): + s, coeff, frame = args + assert 0 <= s < len(charts) and s != r + assert charts[r] == charts[s] == frame and Fraction(coeff) + contacts[s].append((i, op + '_SOURCE')) + else: + assert op == 'SCALE' and charts[r] == args[1] and Fraction(args[0]) + assert charts == word['final'] + [None] * fields and not active + for move in owned_moves: + history = contacts[move['role']] + j = history.index((move['event'], 'MOVE')) + assert 0 < j < len(history) - 1 + before, after = history[j-1], history[j+1] + move.update(window=[before[0]+1, after[0]], previous=before, following=after) + assert (public, fields, lifetimes, peak, len(program), len(owned_moves)) == (1499, 63, 66, 48, 76349, 47) + return spaces, native_moves, owned_moves, dict( + public=public, owned_labels=fields, lifetimes=lifetimes, peak=peak, events=len(program), opcodes=opcodes, + ) + + +def full_invoice(word, caller, result, native_moves): + dports = word['hosted']['Dports'] + second = dict(zip(dports, zip(word['hosted']['X2'], word['hosted']['Y2']))) + assert caller['types']['A']['ports'] == dports + assert sorted(dports + caller['types']['B']['ports']) == list(range(104)) + assert caller['ambient_rank'] == 145 and caller['stages'] == STAGES + main = set(word['live']) | {r+112 for r in word['live']} | set(word['hosted']['X2']) | set(word['hosted']['Y2']) + helpers = set(range(word['public'])) - main + positions, staged = [], [] + paid = Counter() + for ce, event in enumerate(caller['events']): + if event[0] == 'J': + stage, pa, pb = event[1:] + staged.append(stage) + mapping = {} + for pi, r in enumerate(word['live']): + a, b = pa[:2] if pi in second else pb[:2] + mapping[r] = ('main', pi, a) + mapping[r+112] = ('main', pi, b) + if pi in second: + x, y = second[pi] + mapping[x] = ('main', pi, pa[2]) + mapping[y] = ('main', pi, pa[3]) + assert set(mapping) == main and len(set(mapping.values())) == len(main) + mapping.update((r, ('helper', ce, r)) for r in helpers) + for r in range(word['public'], word['public'] + word['owned_fields']): + mapping[r] = ('owned', ce, r-word['public']) + assert len(mapping) == len(set(mapping.values())) == word['public'] + word['owned_fields'] + for move in native_moves: + rank = move['rank'] + paid[rank] += 1 + positions.append([ce, move['event'], mapping[move['role']], rank, move['source'], move['target']]) + else: + kind, op, role, *args = event + if op not in ('IDLE_ONE', 'IDLE_ODD', 'QUERY'): + assert op in ('ADD', 'SWAP', 'SCALE', 'LAMBDA') + continue + rank = 1 if op == 'QUERY' else 8 * len(args[0]) + (op == 'IDLE_ODD') + for pi in caller['types'][kind]['ports']: + owner = ('query_scratch', ce, pi) if op == 'QUERY' else ('main', pi, role) + paid[rank] += 1 + positions.append([ce, op, owner, rank]) + assert staged == list(range(1, STAGES+1)) + binding = result['checks']['ODD-PHYSICAL-BINDING.json'] + assert binding['native_sha256'] == PINS[f'peer/{PACKAGE}/WORD.json.gz#decompressed'] + assert binding['caller_sha256'] == PINS['caller-inputs/CALLER.json'] + assert result['caller_sha256'] == binding['caller_sha256'] + geom = binding['occurrence_and_geometry'] + positions_sha = canonical_digest(positions) + assert positions_sha == geom['complete_paid_position_digest'] + invoice = result['price']['after'] + assert paid == {int(r): n for r, n in invoice['P'].items()} + assert invoice['T'] == geom['targets'] + assert sum(paid.values()) == geom['paid_positions'] == 110519 + assert sum(invoice['T'].values()) == geom['productive_fields'] == 22427 + signed = Counter({int(r): n for r, n in invoice['T'].items()}) + signed.subtract(paid) + assert sum(r*n for r, n in signed.items()) == invoice['S'] == 1424 + return signed, dict(P=paid, T=invoice['T'], S=1424, paid_position_sha256=positions_sha) + + +def overlap(left, right): + lo = max(left[0], right[0]) + hi = min(left[1], right[1]) + return [lo, hi] if lo <= hi else None + + +def match_max(edges): + graph = defaultdict(dict) + for i, j, weight in edges: + if weight > 0: + graph[i][j] = graph[j][i] = weight + + @lru_cache(None) + def best(vertices): + if not vertices: + return 0, () + i = min(vertices, key=lambda v: (len(graph[v].keys() & vertices), v)) + rest = vertices - {i} + winner = best(rest) + for j in sorted(graph[i].keys() & rest): + total, matching = best(rest - {j}) + pair = tuple(sorted((i, j))) + winner = max(winner, (total + graph[i][j], tuple(sorted((pair,) + matching)))) + return winner + + value, chosen = best(frozenset(graph)) + return value, chosen, best.cache_info().currsize + + +def scan_pairs(owned, spaces, gate, check_time, pair_cap): + counts = Counter({k: 0 for k in ('pairs', 'same_owner', 'distinct_owner', 'disjoint_windows', + 'overlap_windows', 'common_positive_interval', 'same_source', + 'same_target', 'cross_supply')}) + compatible, pending = [], None + for left, right in combinations(owned, 2): + i, j = left['event'], right['event'] + if counts['pairs'] == pair_cap: + pending = [i, j] + break + check_time() + counts['pairs'] += 1 + if left['role'] == right['role']: + counts['same_owner'] += 1 + continue + counts['distinct_owner'] += 1 + clock = overlap(left['window'], right['window']) + if clock is None: + counts['disjoint_windows'] += 1 + continue + counts['overlap_windows'] += 1 + a, b, c, d = (spaces[move[key]] for move in (left, right) for key in ('source', 'target')) + ranks, width = overlap_interval(a, b, c, d) + relations = dict(common_positive_interval=width is not None and width > 0, + same_source=a == c, same_target=b == d, cross_supply=a == d or c == b) + counts.update(key for key, present in relations.items() if present) + credit = gate.moment(Counter((left['rank'], right['rank'])), TARGET) + compatible.append(dict(events=[i, j], owners=[left['role'], right['role']], clock=clock, + paid_ranks=[left['rank'], right['rank']], overlap_ranks=ranks, + width=width, relations=relations, both_debits=gate.show(credit), + distances=[distance(a, b), distance(c, d), distance(a, d), + distance(c, b), distance(b, d)])) + return counts, compatible, pending + + +def pair_weights(pairs, gate, check_time): + @lru_cache(None) + def weight(rank): + return gate.power(rank, TARGET) if rank else (0, 0) + + @lru_cache(None) + def star(ab, ac, bc): + # If a length exceeds this limit, clamping it preserves all inequalities. + limit = max(ab, ac, bc) + answer = None + for a in range(limit+1): + for b in range(max(0, ab-a), limit+1): + c = max(0, ac-a, bc-b) + candidate = (weight(a)[0] + weight(b)[0] + weight(c)[0], (a, b, c)) + answer = candidate if answer is None else min(answer, candidate) + return answer + + result = [] + for pair in pairs: + check_time() + ab, cd, ad, cb, bd = pair['distances'] + assert pair['paid_ranks'] == [ab, cd] + old = gate.add(weight(ab), weight(cd)) + star_a, lengths_a = star(ab, ad, bd) + star_c, lengths_c = star(cb, cd, bd) + costs = (old[0], weight(ad)[0]+weight(cb)[0], star_a, star_c) + # Keeping the original charges has exactly zero saving, without roundoff. + upper = max(0, old[1]-min(costs[1:])) + i, j = pair['events'] + result.append((i, j, upper)) + pair.update(reroute_cost_lower=gate.show((min(costs), min(costs)))[0], + reroute_upper=gate.show((upper, upper))[0], star_lengths=[lengths_a, lengths_c]) + return result + + +def probe(word, sites, check_time): + public = word['public'] + main = set(word['live']) | {r+112 for r in word['live']} | set(word['hosted']['X2']) | set(word['hosted']['Y2']) + # Separate seed sets preserve the pair and triple witnesses. + public_seeds = set(PUBLIC_SEEDS) + rows = [] + for r in range(public + word['owned_fields']): + x = tuple(int.from_bytes(sha256(f'owned-7161:{j}:{r}'.encode()).digest(), 'big') % PRIME + if (j in public_seeds and r < public or j not in public_seeds and r in main) + else 0 for j in range(len(PUBLIC_SEEDS) + len(HOSTED_SEEDS))) + rows.append(x) + zero = (0,) * (len(PUBLIC_SEEDS) + len(HOSTED_SEEDS)) + snapshots = {} + seen_coeffs = {} + + def residue(s): + if s not in seen_coeffs: + q = Fraction(s) + assert q.denominator % PRIME + seen_coeffs[s] = q.numerator * pow(q.denominator, -1, PRIME) % PRIME + return seen_coeffs[s] + + for i, (op, role, *args) in enumerate(word['program']): + if i % 1024 == 0: + check_time() + if i in sites: + assert op == 'MOVE' and args[-1] + snapshots[i] = rows[role] + if op == 'INIT': + assert rows[role] == zero + elif op == 'CLEAR': + rows[role] = zero + elif op == 'SCALE': + c = residue(args[0]) + assert c + rows[role] = tuple(c*x % PRIME for x in rows[role]) + elif op in ('ADD', 'COPY'): + s, coeff, _ = args + c = residue(coeff) + if op == 'COPY': + assert rows[role] == zero + rows[role] = tuple((x+c*y) % PRIME for x, y in zip(rows[role], rows[s])) + else: + assert op == 'MOVE' + assert snapshots.keys() == sites + return snapshots, len(seen_coeffs) + + +def determinant(a, b, i, j): + return (a[i]*b[j]-a[j]*b[i]) % PRIME + + +def determinant3(a, b, c, i, j, k): + return (a[i]*determinant(b, c, j, k) - a[j]*determinant(b, c, i, k) + + a[k]*determinant(b, c, i, j)) % PRIME + + +def async_chains(owned, snapshots, spaces, check_time): + graph = defaultdict(set) + pairs = [] + for a, b in combinations(owned, 2): + check_time() + i, j = a['event'], b['event'] + if determinant(snapshots[i], snapshots[j], 0, 1): + continue + graph[i].add(j) + graph[j].add(i) + pairs.append([i, j]) + + move = {m['event']: m for m in owned} + seen = set() + chains = [] + for start in sorted(graph): + if start in seen: + continue + component, stack = set(), [start] + while stack: + node = stack.pop() + if node in component: + continue + component.add(node) + stack.extend(graph[node] - component) + seen.update(component) + itinerary = [move[i] for i in sorted(component)] + first, last = itinerary[0], itinerary[-1] + # The four source/target cases follow one common calculation: later + # original root frames are already required as earlier output frames. + assert all(x['window'][1] < y['window'][0] and x['target'] == y['source'] + for x, y in zip(itinerary, itinerary[1:])) + labels = [first['source']] + [x['target'] for x in itinerary] + assert len(set(spaces[x] for x in labels)) == len(labels) + endpoint_distance = distance(spaces[first['source']], spaces[last['target']]) + assert all(m['rank'] == 1 for m in itinerary[:-1]) + assert endpoint_distance == sum(m['rank'] for m in itinerary) + chains.append(dict(events=sorted(component), labels=labels, ranks=[m['rank'] for m in itinerary], + clocks=[m['window'] for m in itinerary], endpoint_distance=endpoint_distance, + necessary_positive_legs=len(itinerary))) + return dict(zero_minor_pairs=pairs, chains=chains, compatible_pair_count=len(pairs), + screened_pairs=len(owned)*(len(owned)-1)//2, saving_upper=0) + + +def scan_triples(owned, snapshots, gate, check_time, triple_cap): + counts = Counter({k: 0 for k in ('unordered_triples', 'same_owner', 'disjoint_windows', + 'clock_compatible_tested', 'all_public_zero_minor', 'hosted_zero_minor')}) + checked, pending = [], None + ranks = {m['event']: m['rank'] for m in owned} + for group in combinations(owned, 3): + check_time() + counts['unordered_triples'] += 1 + if len({m['role'] for m in group}) != 3: + counts['same_owner'] += 1 + continue + left, center, right = [m['window'] for m in group] + shared = overlap(left, center) + shared = overlap(shared, right) if shared else None + if not shared: + counts['disjoint_windows'] += 1 + continue + events = [m['event'] for m in group] + if counts['clock_compatible_tested'] == triple_cap: + pending = events + break + counts['clock_compatible_tested'] += 1 + a, b, c = map(snapshots.__getitem__, events) + public_minor = determinant3(a, b, c, 0, 1, 4) + hosted_minor = determinant3(a, b, c, 2, 3, 5) + counts['all_public_zero_minor'] += not public_minor + counts['hosted_zero_minor'] += not hosted_minor + checked.append(dict(events=events, clock=shared, all_public_minor=public_minor, + hosted_only_minor=hosted_minor)) + + vertices = {i for triple in checked for i in triple['events']} + survivors = [t for t in checked if not t['all_public_minor']] + survivor_vertices = {i for triple in survivors for i in triple['events']} + + def all_debits_upper(sites): + return gate.smul(gate.moment(Counter(ranks[i] for i in sites), TARGET), STAGES) + + return dict(cap=triple_cap, first_pending=pending, counts=counts, tested=checked, + vertices=sorted(vertices), price_before=gate.show(all_debits_upper(vertices)), + survivors=survivors, survivor_price=gate.show(all_debits_upper(survivor_vertices))) + + +def rank_and_determinant(rows): + matrix = [list(row) for row in rows] + size = len(matrix) + assert all(len(row) == size for row in matrix) + rank = 0 + value = 1 + for col in range(size): + pivot = next((i for i in range(rank, size) if matrix[i][col]), None) + if pivot is None: + continue + if pivot != rank: + matrix[rank], matrix[pivot] = matrix[pivot], matrix[rank] + value = -value + coefficient = matrix[rank][col] + value = value*coefficient % PRIME + inverse = pow(coefficient, -1, PRIME) + for i in range(rank+1, size): + multiple = matrix[i][col]*inverse % PRIME + if multiple: + matrix[i] = [(x-multiple*y) % PRIME for x,y in zip(matrix[i], matrix[rank])] + rank += 1 + return rank, value % PRIME if rank == size else 0 + + +def maximal_clock_sets(owned, snapshots, check_time, cap): + # Every compatible subset has a witness at its latest left endpoint. + starts = sorted({m['window'][0] for m in owned}) + choices = {} + count = 0 + multi_owner_cuts = 0 + for cut in starts: + check_time() + active = defaultdict(list) + for move in owned: + if move['window'][0] <= cut <= move['window'][1]: + active[move['role']].append(move['event']) + multi_owner_cuts += any(len(moves) > 1 for moves in active.values()) + for candidate in product(*active.values()): + if count == cap: + return dict(first_pending=[cut, sorted(candidate)], candidate_count=count, cap=cap) + choices.setdefault(frozenset(candidate), cut) + count += 1 + maximal = [s for s in choices if not any(s < t for t in choices)] + hist = Counter() + tests = [] + for compatible in sorted(maximal, key=lambda x: tuple(sorted(x))): + check_time() + events = sorted(compatible) + width = len(events) + hist[width] += 1 + assert width <= min(len(PUBLIC_SEEDS), len(HOSTED_SEEDS)), 'insufficient deterministic probes' + + def evaluate(seeds): + matrix = [[snapshots[i][s] for s in seeds[:width]] for i in events] + rank, value = rank_and_determinant(matrix) + return dict(rank=rank, determinant=value) + + tests.append(dict(events=events, witness_cut=choices[compatible], + all_public=evaluate(PUBLIC_SEEDS), hosted_only=evaluate(HOSTED_SEEDS))) + pending = [r for r in tests if r['all_public']['rank'] < len(r['events'])] + return dict(first_pending=None, cap=cap, candidate_count=count, tested=tests, maximal_widths=hist, + distinct_count=len(choices), max_width=max(hist), start_count=len(starts), + same_owner_choices_at_cuts=multi_owner_cuts, modular_rank_unresolved=pending) + + +def run(peer_root, caller_path, gate_path, event_cap, pair_cap, triple_cap, seconds): + started = monotonic() + + def check_time(): + assert monotonic()-started <= seconds, 'time cap reached before exhaustion' + + package = peer_root / PACKAGE + compressed = pinned(package/'WORD.json.gz', f'peer/{PACKAGE}/WORD.json.gz') + raw = gzip.decompress(compressed) + assert sha256(raw).hexdigest() == PINS[f'peer/{PACKAGE}/WORD.json.gz#decompressed'] + word = json.loads(raw) + result = json.loads(pinned(package/'RESULT.json', f'peer/{PACKAGE}/RESULT.json')) + caller = json.loads(pinned(caller_path, 'caller-inputs/CALLER.json')) + pinned(gate_path, 'caller-inputs/interval_gate.py') + spec = spec_from_file_location('pinned_owned_interval', gate_path) + gate = module_from_spec(spec) + spec.loader.exec_module(gate) + + # Lucas–Lehmer for the prime exponent 31 verifies the reduction field. + mersenne = 4 + for _ in range(29): + mersenne = (mersenne*mersenne - 2) % PRIME + assert PRIME == 2**31-1 and mersenne == 0 + h0, h1, h2 = (span(xs) for xs in ([], [1], [1, 2])) + h3 = span([2]) + assert overlap_interval(h0, h2, h1, h2) == ((1, 2), 1) + assert overlap_interval(h0, h1, h1, h2) == ((1, 1), 0) + assert overlap_interval(h0, h1, h3, h2) == ((1, 1), None) + assert overlap([1, 2], [2, 3]) == [2, 2] and overlap([1, 2], [3, 4]) is None + assert match_max([(1, 2, 8), (1, 3, 7), (3, 4, 2)])[:2] == (10, ((1, 2), (3, 4))) + assert determinant((1, 2), (2, 4), 0, 1) == 0 + assert determinant((1, 2), (2, 5), 0, 1) == 1 + assert determinant3((1, 0, 0), (0, 1, 0), (1, 1, 0), 0, 1, 2) == 0 + assert determinant3((1, 0, 0), (0, 1, 0), (1, 1, 1), 0, 1, 2) == 1 + assert rank_and_determinant(((0, 1), (1, 0))) == (2, PRIME-1) + assert rank_and_determinant(((0, 1), (0, 2))) == (1, 0) + + spaces, native, owned, census = scan_word(word, check_time, event_cap) + signed, invoice = full_invoice(word, caller, result, native) + lo, hi = map(Fraction, result['price']['gate']['raw_bracket']) + lo_sign, hi_sign = gate.moment(signed, lo), gate.moment(signed, hi) + assert lo_sign[0] > 0 > hi_sign[1] + baseline = gate.moment(signed, TARGET) + hist = Counter(move['rank'] for move in owned) + debit = gate.smul(gate.moment(hist, TARGET), STAGES) + assert gate.add(baseline, debit)[0] > 0 + counts, pairs, pending = scan_pairs(owned, spaces, gate, check_time, pair_cap) + if pending is not None: + return dict(status='PAIR_CAP_PENDING', pins=PINS, census=census, counts=counts, first_pending=pending) + assert counts['pairs'] == len(owned)*(len(owned)-1)//2 + assert counts['overlap_windows'] == len(pairs) + ranks = {m['event']: m['rank'] for m in owned} + candidates = [pair for pair in pairs if any(pair['relations'].values())] + loose_edges = [(i, j, gate.moment(Counter((ranks[i], ranks[j])), TARGET)[1]) + for i, j in (pair['events'] for pair in pairs)] + direct_edges = [(i, j, gate.moment(Counter((ranks[i], ranks[j])), TARGET)[1]) + for i, j in (pair['events'] for pair in candidates)] + time_only = match_max(loose_edges) + direct = match_max(direct_edges) + direct_union = gate.moment(Counter(ranks[i] for i in {k for a,b,_ in direct_edges for k in (a,b)}), TARGET)[1] + assert gate.add(baseline, (0, STAGES*direct_union))[1] < 0 + + detour = pair_weights(pairs, gate, check_time) + detour_before = match_max(detour) + assert gate.add(baseline, (0, STAGES*detour_before[0]))[1] > 0 + snapshots, coeffs = probe(word, set(ranks), check_time) + by_pair = {(i, j): upper for i, j, upper in detour} + left_edges = [] + main_left_edges = [] + for pair in pairs: + i, j = pair['events'] + minor = determinant(snapshots[i], snapshots[j], 0, 1) + main_minor = determinant(snapshots[i], snapshots[j], 2, 3) + pair.update(all_public_minor=minor, hosted_only_minor=main_minor) + if not minor: + left_edges.append((i, j, by_pair[i, j])) + if not main_minor: + main_left_edges.append((i, j, by_pair[i, j])) + after_probe = match_max(left_edges) + after_main_probe = match_max(main_left_edges) + nonzero = sum(any(values[:2]) for values in snapshots.values()) + assert nonzero == 47 + async_result = async_chains(owned, snapshots, spaces, check_time) + triple_result = scan_triples(owned, snapshots, gate, check_time, triple_cap) + maximal_result = maximal_clock_sets(owned, snapshots, check_time, triple_cap) + + def price_report(upper, chosen=(), states=None): + saving = STAGES * upper + return dict(saving_upper=gate.show((saving, saving))[0], matching=chosen, states=states, + moment_upper=gate.show(gate.add(baseline, (0, saving)))[1]) + + return dict(status='EXHAUSTED_OWNED_SHARE_NECESSARY_GATES', head=HEAD, pins=PINS, + target=str(TARGET), census=census, invoice=invoice, raw_bracket=[str(lo), str(hi)], + bracket_moments=[gate.show(lo_sign), gate.show(hi_sign)], baseline=gate.show(baseline), + caps=dict(events=event_cap, pairs=pair_cap, triple_candidates=triple_cap, seconds=seconds), + first_pending=triple_result['first_pending'] or maximal_result['first_pending'], + counts=counts, owned_rank_hist=hist, owned=owned, pairs=pairs, + all_old_debits=gate.show(debit), time_only=price_report(*time_only), + direct_pair=price_report(*direct), direct_vertex_union=price_report(direct_union), + arbitrary_nested_before_probe=price_report(*detour_before), + arbitrary_nested_after_probe=price_report(*after_probe), + arbitrary_nested_hosted_only_after_probe=price_report(*after_main_probe), + asynchronous_cache=async_result, triple_corecovery=triple_result, + maximal_common_clock=maximal_result, + probe=dict(prime=PRIME, distinct_coefficient_tokens=coeffs, snapshots=snapshots, + nonzero_public_rows=nonzero, public_zero_minor_pairs=len(left_edges), + hosted_zero_minor_pairs=len(main_left_edges), + public_positive_credit_survivors=[(i,j) for i,j,u in left_edges if u>0], + hosted_positive_credit_survivors=[(i,j) for i,j,u in main_left_edges if u>0]), + controls=['positive and zero-width intervals', 'incomparable interval', 'inclusive clock', + 'matching cannot reuse one vertex', 'proportional and nonproportional minors', + 'dependent and independent three-lane controls', 'singular and pivot-swap elimination']) + + +if __name__ == '__main__': + if not __debug__: + raise RuntimeError('Run with assertions enabled') + parser = argparse.ArgumentParser(description=__doc__) + for label in ('peer_root', 'caller_path', 'gate_path'): + parser.add_argument(label, type=Path) + parser.add_argument('--event-cap', type=int, default=80000) + parser.add_argument('--pair-cap', type=int, default=4096) + parser.add_argument('--triple-cap', type=int, default=4096) + parser.add_argument('--seconds', type=int, default=600) + args = parser.parse_args() + assert 0 < args.event_cap <= 80000 and 0 < args.pair_cap <= 4096 and 0 < args.seconds <= 600 + assert 0 < args.triple_cap <= 4096 + print(json.dumps(run(**vars(args)), indent=2, sort_keys=True)) diff --git a/research/p104-rectangular-clifford-adapter-bound/verify.py b/research/p104-rectangular-clifford-adapter-bound/verify.py new file mode 100644 index 0000000000..3abc646ede --- /dev/null +++ b/research/p104-rectangular-clifford-adapter-bound/verify.py @@ -0,0 +1,201 @@ +"""Replay the exact #7161 rank-one tariff and rectangular adapter controls.""" + +import argparse +from collections import Counter +from copy import deepcopy +from fractions import Fraction +import gzip +from hashlib import sha256 +from importlib.util import module_from_spec, spec_from_file_location +import json +from pathlib import Path +import sys + + +WORD = 'peer/research/p104-rank8-exit-funded-split/WORD.json.gz' +RESULT = 'peer/research/p104-rank8-exit-funded-split/RESULT.json' +PINS = { + WORD: 'c1caec11ca3ee264ef03018dd91037eac10c3e28950c4c525ee1b4bf5ee210e2', + WORD + '#decompressed': '9eff91418d838f1ffa20fe5c5975dc2c43a79b32d501fcbe30b90c50a7b11ce3', + RESULT: '59080d75e7281b1a8c1353930917fd15869ad747ff4200948898f78f11c14089', + 'caller/CALLER.json': '255d89f38cd45e38e5770f559bc43dc217e989032359768cdc7e8cdfd64b47bc', + 'caller/interval_gate.py': '60a743d13f668ef86db4b8215b4d5d04430a671ba6f1fe06d9c1c4c3dfe86da5', + 'gaussian/clifford_exact.py': '2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962', + 'gaussian/native_verify.py': '3049471905b47b385c88378a1a3be7a18b8858aadd035b8a6da2f4a03b470f38', + 'prior/owned.py': '53da0a7b551b34f3baf633083a4362570ebe694a694e2d0b6226d01c08a6ab3b', +} + + +def checked(root, key): + data = (root / key).read_bytes() + if sha256(data).hexdigest() != PINS[key]: + raise ValueError(f'changed exact input: {key}') + return data + + +def unique_object(items): + result = {} + for key, value in items: + if key in result: + raise ValueError(f'duplicate JSON key: {key}') + result[key] = value + return result + + +def verify_source_map(root, source_map): + declared = json.loads(source_map.read_text(), object_pairs_hook=unique_object) + scientific = {key: digest for key, digest in PINS.items() if '#' not in key} + notice = 'PEER-NOTICE.txt' + assert declared.keys() == scientific.keys() | {notice} + for key, digest in scientific.items(): + assert declared[key]['sha256'] == digest, key + assert sha256((root/notice).read_bytes()).hexdigest() == declared[notice]['sha256'] + + +def load(root, key): + spec = spec_from_file_location('adapter_' + Path(key).stem, root / key) + module = module_from_spec(spec) + sys.modules[spec.name] = module + spec.loader.exec_module(module) + return module + + +def verify_signed_map(word, compiler, gaussian): + event = 535 + assert word['program'][event] == ['MOVE', 1479, 3, 595, False] + assert word['frames'][3] == [] and word['frames'][595] == [52] + reference = gaussian.adjoint(gaussian.frame([], 9)) + gaussian.frame([52], 9) + a = compiler.canonical_frame(9, ()) + b = compiler.canonical_frame(9, (52,)) + recipe, _ = compiler.lower_child(a.adjoint().then(b)) + assert recipe['rank'] == 1 + actual = gaussian.recipe(recipe) + changed = deepcopy(recipe) + changed['left']['phase'] = (changed['left']['phase'] + 1) % 4 + mutant = gaussian.recipe(changed) + signs = Counter() + for column in range(512): + sign = 1 - 2 * ((column & 20).bit_count() % 2) + expected = ({column: (1, 1), column ^ 52: (sign, -sign)}, 1) + assert gaussian.state(actual, column) == gaussian.state(reference, column) == expected + assert gaussian.state(mutant, column) != expected + signs[sign] += 1 + assert signs == {-1: 256, 1: 256} + return dict(event=event, role=1479, source=3, target=595, shift=52, sign_mask=20, + signed_columns=512, absolute_phase_mutants_rejected=512) + + +def multiply(left, right): + a, b = left + c, d = right + return a*c - b*d, a*d + b*c + + +def numerators(gaussian, rank, column): + values, denominator = gaussian.state(gaussian.fourier(rank), column) + shift = rank - denominator + assert shift >= 0 + return {i: (a << shift, b << shift) for i, (a, b) in values.items()} + + +def projection_controls(gaussian): + results = [] + for width in range(1, 5): + bank = 1 << width + low = bank - 1 + diagonal = numerators(gaussian, width, 0) + spectator_factor = diagonal[0] + rejected = 0 + for lane in range(2): + for column in range(bank): + small = numerators(gaussian, width, lane*bank + column) + large = numerators(gaussian, 2*width, lane*bank**2 + column) + assert len(small) == bank and len(large) == bank**2 + assert all(a*a+b*b == bank for a,b in small.values()) + assert all(a*a+b*b == bank**2 for a,b in large.values()) + assert set(large) == set(range(lane*bank**2, (lane+1)*bank**2)) + projected = {lane*bank + (i & low): v + for i, v in large.items() if (i // bank) % bank == 0} + assert projected == {i: multiply(v, spectator_factor) for i,v in small.items()} + assert projected.keys() == small.keys() + rejected += any(projected[i] != (a << width, b << width) + for i, (a, b) in small.items()) + assert rejected == 2*bank + results.append(dict(width=width, signed_columns=2*bank, rank1_support=bank, + rank2_support=bank**2, omitted_reciprocal_rejected=rejected, + reciprocal_gain_squared=bank, padding_volume_factor=bank)) + return results + + +def pair_ceiling(word, caller, result, owned, gate): + _, moves, _, census = owned.scan_word(word, lambda: None, 80000) + signed, invoice = owned.full_invoice(word, caller, result, moves) + target = owned.TARGET + assert target == Fraction('0.0040075385047236') + main = (set(word['live']) | {r+112 for r in word['live']} + | set(word['hosted']['X2']) | set(word['hosted']['Y2'])) + assert 1479 not in main and 1479 < word['public'] + calls = [(i, e[1]) for i,e in enumerate(caller['events']) if e[0] == 'J'] + assert calls[:2] == [(43,1),(137,2)] and len(calls) == 17 + classes = Counter('main' if m['role'] in main else + 'owned' if m['role'] >= word['public'] else 'public_helper' + for m in moves if m['rank'] == 1) + repetitions = len(calls) + ideal_pairs = sum(classes.values()) * repetitions // 2 + delta = gate.sub(gate.exact(2), gate.power(2, target)) + raw = gate.moment(signed, target) + ideal = gate.add(raw, gate.smul(delta, ideal_pairs)) + assert delta[0] > 0 and raw[1] < 0 and ideal[0] > 0 + pairs_needed = (-raw[1] + delta[1] - 1) // delta[1] + previous = gate.add(raw, gate.smul(delta, pairs_needed-1)) + first = gate.add(raw, gate.smul(delta, pairs_needed)) + assert previous[1] < 0 < first[0] + # Deleting the rank-one debit from the literal paid list must fail invoice binding. + try: + owned.full_invoice(word, caller, result, [m for m in moves if m['event'] != 535]) + except AssertionError: + pass + else: + raise AssertionError('omitted paid occurrence accepted') + return dict(census=census, invoice=invoice, rank1_native_by_owner_class=classes, + rank1_outer_paid=invoice['P'][1] - sum(classes.values()) * repetitions, + native_call_bindings=[{'caller_event': i, 'stage': j, + 'helper_owner': ['helper', i, 1479]} for i,j in calls], + pair_price_saving=gate.show(delta), signed_raw_moment=gate.show(raw), + ideal_pairs=ideal_pairs, ideal_raw_moment=gate.show(ideal), + minimum_ideal_pairs_needed=pairs_needed, omitted_paid_occurrence_rejected=True) + + +def run(root): + payload = {key: checked(root, key) for key in PINS if '#' not in key} + raw = gzip.decompress(payload[WORD]) + assert sha256(raw).hexdigest() == PINS[WORD+'#decompressed'] + word, result, caller = (json.loads(p) for p in (raw, payload[RESULT], payload['caller/CALLER.json'])) + compiler = load(root, 'gaussian/clifford_exact.py') + gaussian = load(root, 'gaussian/native_verify.py') + owned = load(root, 'prior/owned.py') + gate = load(root, 'caller/interval_gate.py') + return dict(status='SCOPED_RECTANGULAR_ADAPTER_OBSTRUCTION', + pins=PINS, target=str(owned.TARGET), seed=None, + exact_signed_move=verify_signed_map(word,compiler,gaussian), + destructive_projection_controls=projection_controls(gaussian), + complete_pair_price=pair_ceiling(word,caller,result,owned,gate)) + + +if __name__ == '__main__': + if not __debug__ or sys.implementation.name != 'cpython' or sys.version_info[:2] != (3,12): + raise SystemExit('Use CPython 3.12 with assertions enabled') + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('inputs', type=Path) + parser.add_argument('--expected', type=Path) + parser.add_argument('--source-map', type=Path) + args = parser.parse_args() + if args.source_map is not None: + verify_source_map(args.inputs, args.source_map) + receipt = json.dumps(run(args.inputs), indent=2, sort_keys=True) + '\n' + if args.expected is not None: + if args.expected.read_bytes() != receipt.encode(): + raise ValueError('changed frozen adapter receipt') + print('PASS_P104_RECTANGULAR_CLIFFORD_ADAPTER_BOUND') + else: + print(receipt, end='')