From 309189077d0f760248bbdaadab42ecbff4f3ea2d Mon Sep 17 00:00:00 2001 From: Chris R Date: Mon, 19 Oct 2026 19:47:40 +1100 Subject: [PATCH] Derive QQ16 ordered-query residual and restricted Schur obstruction --- research/qq16-query-schur/PROOF.md | 126 + research/qq16-query-schur/README.md | 72 + research/qq16-query-schur/RESULT.json | 9618 +++++++++++++++++++ research/qq16-query-schur/REVIEWS.json | 28 + research/qq16-query-schur/SOURCES.json | 150 + research/qq16-query-schur/TASK.json | 79 + research/qq16-query-schur/VERIFICATION.json | 37 + research/qq16-query-schur/VERIFY.json | 56 + research/qq16-query-schur/test_verify.py | 105 + research/qq16-query-schur/verify.py | 220 + 10 files changed, 10491 insertions(+) create mode 100644 research/qq16-query-schur/PROOF.md create mode 100644 research/qq16-query-schur/README.md create mode 100644 research/qq16-query-schur/RESULT.json create mode 100644 research/qq16-query-schur/REVIEWS.json create mode 100644 research/qq16-query-schur/SOURCES.json create mode 100644 research/qq16-query-schur/TASK.json create mode 100644 research/qq16-query-schur/VERIFICATION.json create mode 100644 research/qq16-query-schur/VERIFY.json create mode 100644 research/qq16-query-schur/test_verify.py create mode 100644 research/qq16-query-schur/verify.py diff --git a/research/qq16-query-schur/PROOF.md b/research/qq16-query-schur/PROOF.md new file mode 100644 index 0000000000..eb5424089e --- /dev/null +++ b/research/qq16-query-schur/PROOF.md @@ -0,0 +1,126 @@ +# The ordered Schur residual at the actual future-query boundary + +Chris R / Clear1nsight, with substantial OpenAI Codex assistance. Apache-2.0. +This is an exact source-bound logical obstruction to one proposed factorization. +It is not a lower bound on native children or a supplier admission. + +## Boundary and source + +The source is the F0/B1 full-recovery word of ywz65's PR2707, using the +retained Arham Tahir PR2681 source reconstruction. All runtime dependencies are +pinned at canonical main `20ecf2891d80b5acf18d980b2164fb44ea7faa90`. +PR3985, head `400df7fca8f60c19bf163c77564fe3fbe9154b04`, motivates the +question; its executable package is not a dependency. Its rectangular future +correction reads the 104 U+T fields and writes only the eight A fields. + +Write r_p for column p of the actual 8-by-112 matrix R. The selected minors obey +R_A R_A^t=R_T R_T^t=4I, R_U R_U^t=48I. Let g_{s,p} be the actual +involutive owner route at stage s. An ordered route [g][h] means first h, +then g. The source routes are orthogonal; under the inherited pushforward +owner convention their action on a character labelled v is labelled ghv. These are +logical array operators; native convolution changes the physical frame and +must still be charged by any implementation. + +At the first stage-2 event, the literal source prefix gives, with a=Q1(Y), + + W_p = Y_p - (1/4) sum_j R[j,p] [g1,p] a_j (p in U), + W_p = Y_p + X_p - (1/4) sum_j R[j,p] [g1,p] a_j (p in T). + +Here X and Y are the current borrowed arrays at entry, not an earlier record. +The verifier reconstructs all 104 rows from the actual prefix and checks these +identities in the rational owner group ring with all 224 current sources free. + +## Missing correction + +Replacing those W_p reads with borrowed Y_p loses exactly + + Q2(W_(U+T)) - Q2(Y_(U+T)) = Q2(X_T) - M21 a, + M21 = (1/4) sum_(p in U+T) r_p r_p^t [g2,p g1,p]. + +The multiplication order is essential. All 104 products g2,p g1,p are distinct, +and reversing the products changes the action already on character v=1. +The formula includes the eight T-port X terms: they are not part of the +rank-eight correction and cannot be omitted. + +All actual g2,p fix q_p. Therefore mapping the borrowed Y_p hole frame with +the actual affine shift really does reach the common F16 frame without the +negative C_q child. This is checked for all 104 terms using the full quadratic +phase polynomial. The proposed bypass passes that frame check but loses the +logical residual above. A legal frame is insufficient to identify the value. + +## Why the scalar Schur shortcut passes constants and fails arrays + +The trivial owner character v=0 sends every owner permutation to 1. On that +subspace M21 becomes (48I+4I)/4=13I. Thus constant-owner tests would accept a +scalar correction 13a. + +On the single nontrivial character v=1, however, the 104 images + + (g2,p g1,p) 1, p in U+T + +are pairwise distinct. For entry (0,0), 52 ports have R[0,p]^2=1. Its action +on a_0=chi_1 is a sum of 52 distinct characters, each with coefficient 1/4; +none is chi_1. This cannot equal 13chi_1. RESULT.json records every image, +coefficient and source port so that the witness is directly inspectable. + +These are attainable query inputs, not an enlarged-domain fiction. For any +eight logical arrays a, set X=0, Y_(U+T)=0, and + + Y_p = (1/4) sum_j R[j,p] [g1,p] a_j, p in A. + +Then Q1(Y)=a because g1,p is involutive and R_A R_A^t=4I. The verifier checks +this with eight independent array inputs. On this legitimate current input, +the borrowed-Y bypass query is zero and the actual query is -M21 a. +The A response cannot hide this discrepancy: undoing its eight stage-2 routes +and applying R_A recovers the query. Hence the actual recovery boundary +requires a correction; scalar 13I does not supply it for general arrays. + +## Exact scope of the 104-branch bound + +Consider only expressions of the form + + M21 = sum_(b=1)^B C_b [h_b], + +where C_b is an arbitrary constant 8-by-8 rational matrix and each branch +applies a single common linear owner permutation h_b to all eight channels. +Scalar mixing before or after that route is included in C_b. There are no +character-dependent projections, Fourier transforms, extra native kernels, +sequentially reused intermediate branches, or sums of owner routes hidden +inside a branch. + +Apply the expression to eight independent amplitudes times chi_1. A branch +has one output character h_b 1, so B branches have at most B different +character labels. The source expression has 104 distinct labels, with +nonzero coefficient matrix r_p r_p^t/4 at each. Linear independence of +characters gives B >= 104. The displayed source expression attains 104, +so the restricted branch count is exactly 104. This uses the actual owner +permutation representation, not an assumption that a formal group algebra +acts faithfully. It also excludes the 8- or 16-branch versions of this model. + +This is **not** a claim that every implementation needs 104 H1 children, +104 scalar additions, 104 physical cover sweeps, or 104 storage banks. +A sequential circuit can reuse routes, and a genuine harmonic decomposition +could use different primitives. Their frames, coefficient operations, +restoration, precision and physical tariffs must be supplied separately. + +## Obligation ledger and stopping decision + +| Obligation | Status | Evidence or missing object | +|---|---|---| +| Actual prefix residual, including T-port X reads | Proved within pinned logical model | All 104 source rows and full operator equality | +| Constant-character 13I and nontrivial counterexample | Proved | Exact rational character arithmetic | +| Arbitrary query attainability and nonzero A response | Proved | Source A minor and actual involutive routes | +| Single-owner-route branch optimum 104 | Proved for stated model | Character support bound and explicit 104-term expression | +| Physical legality of borrowed-Y hole maps | Proved within inherited frame model | 104 full phase-polynomial equalities | +| Cheaper complete residual circuit with fewer native children | Unknown | No typed literal construction supplied | +| Retaining eight prefix queries across native calls | Unknown | Source private scratch is cleared; it cannot be kept for free | +| Physical maps, storage, movement, all-depth precision and restoration | Unknown | A changed complete provider/consumer contract is required | +| Supplier coverage, both moment budgets and improved kappa | Unknown | Local branch count supplies none of these | + +Stop the scalar-Schur/8-or-16-one-route-branch repair here. Its intended saving +was removal of 104 negative normalizers from PR3985, but the residual is real +and the proposed compressed repair fails. No native cost saving is claimed. +A viable reopening must exhibit a different typed circuit for the ordered +operator, price its retained inputs and final cleanup, and bind the result to +an actual outer consumer. The conditional incidence budget of PR3976 is only +an optimistic screen, not permission to treat unknown costs as zero. diff --git a/research/qq16-query-schur/README.md b/research/qq16-query-schur/README.md new file mode 100644 index 0000000000..e2ef3e95d0 --- /dev/null +++ b/research/qq16-query-schur/README.md @@ -0,0 +1,72 @@ +# QQ16 ordered-query Schur obstruction + +The missing correction in the borrowed-current-Y shortcut is +`Q2(X_T) - M21 Q1(Y)`, with +`M21 = (1/4) sum_(p in U+T) r_p r_p^t [g2,p g1,p]`. +The actual source has 104 distinct ordered owner routes. One character, +`v=1`, separates all 104, establishing an exact **104-branch** optimum for +constant channel mixing with one common owner route per parallel branch. +This excludes the proposed 8- or 16-branch factorization in that precise model. + +The constant-character restriction is `13I`; using it on general arrays is +wrong. A diagonal entry sends one character to 52 distinct characters with +coefficient 1/4 each. All eight query inputs are attainable from actual current +Y supported on A, and the A response is injective, so this failure applies to +the real F0/B1 recovery boundary. The bypass's 104 hole-frame maps are legal; +they do not repair its omitted value correction. + +This result does not lower native cost, establish native-child optimality or +improve kappa. It supplies the exact missing operator and a discriminating +counterexample before investing in an invalid compressed repair. +See [PROOF.md](PROOF.md) for the model, proof, complete obligation ledger and +stop decision. [RESULT.json](RESULT.json) retains the full source-bound receipt. + +## Reproduction + +Python 3.12, standard library, from the repository root: + +```sh +python3 -I -B research/qq16-query-schur/verify.py +python3 -I -O -Werror -B research/qq16-query-schur/test_verify.py +python3 -B scripts/research_package.py --package research/qq16-query-schur +``` + +The verifier authenticates every declared transitive runtime source before +executing inherited code. It compares the whole typed receipt, works in a +minimal Git-free read-only export, and rejects source/receipt changes and +semantic controls. It does not rerun the full selected supplier or prior +native-kernel theorem. The inherited frame identities are checked only for +the 104 maps involved in this proposed bypass. + +## Workflow and predecessor credit + +Canonical main is `20ecf2891d80b5acf18d980b2164fb44ea7faa90`, priority revision 6. +This is the assigned representation-theory/harmonic-analysis item within the +[coordinated claim](https://github.com/CrocSwap/integer-mult-bounds/pull/3985#issuecomment-6263114494). +The live overlap check included PR1969: its source-level `M=12I` is for one +chart's Gram identity; the cross-chart ordered `M21` here is a different +operator. The current result retains Ali Romman's joint-query construction, +ywz65's PR2707 line-normalized decoder, Arham Tahir's PR2681 source-bound +recovery checker, and their credited native geometry and supplier lineage. +Their files are unchanged. PR3985 at +`400df7fca8f60c19bf163c77564fe3fbe9154b04` supplied the rectangular-correction +question and failed borrowed-Y bypass; no pending PR executable is imported. + +This focused audit refines the `joint-query-controller` card. The family +expansion decision is bounded: derive the actual residual, test a cheap +factorization, and stop at a precise failure. Unknown complete physical costs +remain unknown. The source archive is not a new supplier admission. + +New work: Chris R / Clear1nsight, with substantial OpenAI Codex assistance in +mathematical derivation, implementation and review. Apache-2.0. No independent +human review is claimed. + +## Open next questions + +Can a genuinely different typed circuit implement the ordered `M21` residual +more cheaply than the 104 removed normalizers? First pin its retained-query +input frames and dirty/owned lifetime contract, then exhibit a literal word +and compare its full invoice with the source operations it replaces. Sequential +route reuse, a paid character decomposition, or a changed producer may evade +the restricted parallel-branch bound. Their costs and outer supplier binding +are unresolved. 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residual and restricted single-owner-route-per-branch lower bound. 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Scientific receipt unchanged." + }, + { + "reviewer": "Coordinating OpenAI Codex agent; no human review claimed", + "scope": "Independent optimized warning-strict replay and bounded proof/code review; inherited exact logical/frame semantics only", + "result": "PASS, exit0 at08:44UTC; no blocker", + "reviewed_sha256": { + "PROOF.md": "51e4c90f8aa068925814f9cbc860a087575b61857cad2a7d0b6faea356f857b0", + "verify.py": "5c8d1d917acbaa6369cf68b1bd4a0f24725850ac1201b91b55a0c85da9b27507", + "RESULT.json": "743a45c9751cc8005ff003a6f3f52f99d3270cd8048bb63f5eee2bce2e7e18cf" + }, + "command": "python3 -I -O -Werror -B research/qq16-query-schur/verify.py", + "limitations": "No general native lower bound, formal verification, physical implementation or complete supplier review." + } + ] +} diff --git a/research/qq16-query-schur/SOURCES.json b/research/qq16-query-schur/SOURCES.json new file mode 100644 index 0000000000..aeb15fec96 --- /dev/null +++ b/research/qq16-query-schur/SOURCES.json @@ -0,0 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-0,0 +1,79 @@ +{ + "schema_version": 1, + "task_id": "joint-query-controller", + "priority_revision": 6, + "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90", + "original_card": { + "id": "joint-query-controller", + "question": "Can a literal QQ16 producer meet the proposed completed-output error budgets with dirty helpers and an affordable physical consumer?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/joint-query/README.md", + "research/joint-query/evidence/QQ16-SELECTED-WITNESS.md", + "research/joint-query/evidence/JOINT-QUERY-TRANSFER.md", + "docs/research/community-efficient1000-review.md", + "research/qq16-producer-defect-transfer/README.md" + ], + "methods": [ + "Derive one literal producer's completed-output defects and intermediate dirty-helper bounds, with its physical bill.", + "Design or audit one consumer, retention or hosting boundary and its complete cost for the pinned producer/decoder." + ], + "acceptance_gate": "Name the changed premise of the fixed F0/B1 observation obstruction. Show exactly which query is recovered, legal native reads and restoration, and a full favorable budget including cover maps, helpers and endpoints. Local inverse identities alone do not close the global controller. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read the revision-6 family record and #2965 producer-defect transfer after the local QQ16 decoder contract. Its author-checked output-error estimate does not implement producer interiors, bound dirty helpers, or pay for the consumer; independently check the implication used.", + "scope": "Source-bound orientation only. Read the named package and review before relying on its local evidence; this command is not its replay or supplier admission." + }, + "first_experiment": "Pin one literal F0/B1 producer and its native-child contracts; derive the actual intermediate magnitude ledger and completed-output defects, including dirty helpers and correlations. Compare with #2965 budgets and price storage, movement, cleanup and F17 consumption. Stop with a precise missing bound if no producer contract supplies it; do not optimize another decoder precision constant in isolation.", + "bottleneck_link": "The native local words exist; retained query information and its physical access are the missing link to a composed recursive interface.", + "allowed_variations": [ + "One paid query, one changed first pair, or one precisely specified affine helper state.", + "A counterexample or lower bound for that exact proposed repair.", + "One unresolved obligation of a newer local decoder, with exact source heads and a distinct claim/domain." + ], + "scope_change_triggers": [ + "Retaining the fixed first pair and ordinary schedule while allowing only homogeneous selected-only control, already excluded by the witness.", + "Treating cover-map counts as zero-cost physical address operations.", + "Recreating the pending complete local decoder or early-record/output-bank coalescing already under investigation without a distinct audit or changed premise.", + "Treating a completed-output defect inequality as a producer-interior, dirty-range or physical-cost certificate." + ], + "overlap_terms": [ + "QQ16", + "joint-query", + "changing-chart controller", + "selected observation", + "1969", + "2540", + "early record", + "output-bank retention", + "complete native decoder", + "2965", + "producer defect", + "dirty-helper range", + "F17 consumer" + ] + }, + "scope_status": "refined", + "actual_scope": "Derive the actual F0/B1 future-query residual and test a scalar/one-owner-route Schur factorization using an exact separating character.", + "scope_change_reason": "Assigned contrasting representation-theory audit of the failed PR3985 borrowed-current-Y bypass; keep its complete physical obligations explicit.", + "bottleneck_link": "Removing104 negative native children requires computing the actual ordered correction; scalar Gram rank does not provide that module.", + "budget_minutes": 60, + "stop_rule": "Stop after exact residual and decisive restricted-factorization obstruction; no unpriced decoder expansion.", + "outcome": "completed", + "evidence": "PROOF.md, RESULT.json, verify.py and test_verify.py", + "author": "Chris R / Clear1nsight with substantial OpenAI Codex assistance", + "ai_assistance": "Substantial OpenAI Codex assistance in source analysis, derivation, implementation, semantic controls, independent AI cross-review and publication.", + "open_questions": [ + { + "question": "Can a different typed circuit compute the ordered M21 correction with a complete native and physical saving?", + "why_it_matters": "The borrowed-Y bypass omits a real104-term correction; the simple13I and8/16 one-route-branch repairs fail.", + "first_step": "Pin retained query frames and ownership, then provide a literal sequential or harmonic circuit and its complete replacement invoice.", + "blocked_by": "No paid retained-query/provider/consumer or physical circuit contract; branch count is not native-child optimality." + } + ] +} diff --git a/research/qq16-query-schur/VERIFICATION.json b/research/qq16-query-schur/VERIFICATION.json new file mode 100644 index 0000000000..03868ddb60 --- /dev/null +++ b/research/qq16-query-schur/VERIFICATION.json @@ -0,0 +1,37 @@ +{ + "status": "author_checked_and_independent_AI_cross_checked", + "utc": "2026-10-19T08:46:55Z", + "python": "3.12.3", + "canonical_main_checkpoint": "20ecf2891d80b5acf18d980b2164fb44ea7faa90", + "priority_revision": 6, + "checks": [ + { + "command": "python3 -B scripts/research_package.py --package research/qq16-query-schur", + "result": "PASS_REGISTERED_RESEARCH_PACKAGE; primary optimized exact checker and5boundary groups passed; boundary suite128.843seconds." + }, + { + "command": "python3 -I -O -Werror -B research/qq16-query-schur/verify.py", + "result": "PASS independently run by coordinator and centre_budget reviewer; hashes inREVIEWS.json." + }, + { + "command": "python3 -B scripts/research_package.py --package research/qq16-query-schur --check-only", + "result": "PASS_PACKAGE_METADATA_AND_PINS" + } + ], + "coverage": [ + "104source-prefix residual rows and complete ordered operator", + "104distinct character images and52-image diagonal witness", + "Actual8-query surjection andA-response injectivity", + "104hole-frame phase identities", + "Four semantic controls", + "Normal/optimized minimal Git-free read-only replay", + "Whole typed receipt andsource/manifest/generation rejection controls" + ], + "unrun": [ + "No new native implementation or native-child lower bound", + "No full selected supplier cold replay", + "No physical routing, storage or all-depth precision proof", + "No productive-family coverage, bothsupplier budgets or kappa improvement" + ], + "publication": "Exactcommit-byte/source-history preflight and hosted CI are reported externally afterGitHub publication." +} diff --git a/research/qq16-query-schur/VERIFY.json b/research/qq16-query-schur/VERIFY.json new file mode 100644 index 0000000000..e4f3f78cf0 --- /dev/null +++ b/research/qq16-query-schur/VERIFY.json @@ -0,0 +1,56 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/qq16-line-normalized-decoder/WORD.json", + "research/community-frontier1042-audit/selected-replay.tar.gz", + "research/joint-query/certificate.json.gz", + "research/joint-query/evidence/JOINT-QUERY-TRANSFER.md", + "research/joint-query/verify_native.py", + "research/joint-query/verify_scalar.py", + "research/qq16-line-normalized-decoder/PREDECESSORS.json", + "research/qq16-line-normalized-decoder/PROOF.md", + "research/qq16-line-normalized-decoder/README.md", + "research/qq16-line-normalized-decoder/RESULT.json", + "research/qq16-line-normalized-decoder/SOURCES.json", + "research/qq16-line-normalized-decoder/TASK.json", + "research/qq16-line-normalized-decoder/VERIFY.json", + "research/qq16-line-normalized-decoder/vendor/pr2681/PROOF.md", + "research/qq16-line-normalized-decoder/vendor/pr2681/README.md", + "research/qq16-line-normalized-decoder/vendor/pr2681/RESULT.json", + "research/qq16-line-normalized-decoder/vendor/pr2681/SOURCES.json", + "research/qq16-line-normalized-decoder/vendor/pr2681/WORD.json", + "research/qq16-line-normalized-decoder/vendor/pr2681/references/PR2540-PROOF.md", + "research/qq16-line-normalized-decoder/vendor/pr2681/references/PR2540-README.md", + "research/qq16-line-normalized-decoder/vendor/pr2681/verify.py", + "research/qq16-line-normalized-decoder/verify.py" + ], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-O", + "-Werror", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 120, + "checks": "Source-derived ordered residual, actual current-query surjection, character obstruction and complete typed receipt." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-Werror", + "-B", + "{package}/test_verify.py" + ], + "timeout_seconds": 300, + "checks": "Normal/optimized Git-free read-only replay and semantic/source/receipt rejection controls." + } + ] +} diff --git a/research/qq16-query-schur/test_verify.py b/research/qq16-query-schur/test_verify.py new file mode 100644 index 0000000000..ecb6942555 --- /dev/null +++ b/research/qq16-query-schur/test_verify.py @@ -0,0 +1,105 @@ +"""Boundary tests: minimal offline export, immutable sources and typed receipt.""" +import hashlib +import importlib.util +import json +from pathlib import Path +import shutil +import subprocess +import sys +import tempfile +import unittest +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] + +class Boundary(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.tmp = tempfile.TemporaryDirectory(prefix='qq16-query-schur-') + cls.root = Path(cls.tmp.name) + cls.package = cls.root / 'research/qq16-query-schur' + shutil.copytree(HERE, cls.package, ignore=shutil.ignore_patterns('__pycache__')) + inputs = json.loads((HERE / 'VERIFY.json').read_text())['inputs'] + for name in inputs: + dst = cls.root / name + dst.parent.mkdir(parents=True, exist_ok=True) + shutil.copyfile(ROOT / name, dst) + + @classmethod + def tearDownClass(cls): + for p in cls.root.rglob('*'): + p.chmod(0o755 if p.is_dir() else 0o644) + cls.root.chmod(0o755) + cls.tmp.cleanup() + + def run_check(self, options=(), tail=()): + return subprocess.run([sys.executable, '-I', '-Werror', '-B', *options, + str(self.package / 'verify.py'), *tail], + cwd=self.root, text=True, stdout=subprocess.PIPE, + stderr=subprocess.STDOUT, timeout=180) + + def test_normal_optimized_readonly_export(self): + files = [p for p in self.root.rglob('*') if p.is_file()] + before = {str(p): hashlib.sha256(p.read_bytes()).hexdigest() for p in files} + for p in files: + p.chmod(0o444) + for p in sorted((p for p in self.root.rglob('*') if p.is_dir()), reverse=True): + p.chmod(0o555) + self.root.chmod(0o555) + try: + for opt in ((), ('-O',)): + run = self.run_check(opt) + self.assertEqual(run.returncode, 0, run.stdout) + self.assertIn('PASS_QQ16_ORDERED_SCHUR_OBSTRUCTION', run.stdout) + self.assertEqual(before, {str(p): hashlib.sha256(p.read_bytes()).hexdigest() for p in files}) + finally: + self.root.chmod(0o755) + for p in self.root.rglob('*'): + p.chmod(0o755 if p.is_dir() else 0o644) + + def test_source_before_execution(self): + p = self.root / 'research/qq16-line-normalized-decoder/verify.py' + raw = p.read_bytes() + try: + p.write_bytes(b"raise RuntimeError('MUTATED_EXECUTED')\n" + raw) + run = self.run_check(('-O',)) + self.assertNotEqual(run.returncode, 0) + self.assertIn('source SHA256:', run.stdout) + self.assertNotIn('RuntimeError: MUTATED_EXECUTED', run.stdout) + finally: + p.write_bytes(raw) + + def test_complete_typed_receipt(self): + path = self.package / 'RESULT.json' + raw = path.read_bytes() + try: + value = json.loads(raw) + value['response_injective'] = 1 + path.write_text(json.dumps(value)) + run = self.run_check(('-O',)) + self.assertNotEqual(run.returncode, 0) + self.assertIn('complete typed result mismatch', run.stdout) + finally: + path.write_bytes(raw) + + def test_manifest_reclassification(self): + path = self.package / 'SOURCES.json' + raw = path.read_bytes() + try: + value = json.loads(raw) + next(x for x in value['files'] if x['usage'] == 'input')['usage'] = 'provenance' + path.write_text(json.dumps(value)) + run = self.run_check(('-O',)) + self.assertNotEqual(run.returncode, 0) + self.assertIn('source manifest integrity', run.stdout) + finally: + path.write_bytes(raw) + + def test_generation_refuses_overwrite(self): + raw = (self.package / 'RESULT.json').read_bytes() + run = self.run_check(tail=('--write',)) + self.assertNotEqual(run.returncode, 0) + self.assertIn('refuse overwrite', run.stdout) + self.assertEqual(raw, (self.package / 'RESULT.json').read_bytes()) + +if __name__ == '__main__': + unittest.main(verbosity=2) diff --git a/research/qq16-query-schur/verify.py b/research/qq16-query-schur/verify.py new file mode 100644 index 0000000000..454b28fa58 --- /dev/null +++ b/research/qq16-query-schur/verify.py @@ -0,0 +1,220 @@ +#!/usr/bin/env python3 +"""Exact routed Schur residual, character witness and restricted branch bound. +Chris R / Clear1nsight with substantial OpenAI Codex assistance. Apache-2.0. +Source reconstruction: ywz65 PR2707 and Arham Tahir PR2681, retained unchanged. +""" +import argparse +from collections import Counter +from fractions import Fraction as Q +from functools import lru_cache +import hashlib +import json +from pathlib import Path +import types +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] + +def need(ok, message): + if not ok: + raise ValueError(message) + +def canonical(value): + return json.dumps(value, sort_keys=True, separators=(',', ':'), allow_nan=False).encode() + +def typed(value): + if isinstance(value, dict): + return ('dict', tuple((k, typed(v)) for k, v in sorted(value.items()))) + if isinstance(value, list): + return ('list', tuple(map(typed, value))) + return (type(value).__name__, value) + +def authenticate(): + raw_manifest = (HERE / 'SOURCES.json').read_bytes() + need(hashlib.sha256(raw_manifest).hexdigest() == '7ff0d58d63d7e0053655b22d8d6252254da52fa54375ae37cdba403050fc1dc2', 'source manifest integrity') + rows = json.loads(raw_manifest)['files'] + pins = {} + for item in rows: + if item['usage'] != 'input': + continue + raw = (ROOT / item['path']).read_bytes() + need(hashlib.sha256(raw).hexdigest() == item['sha256'], 'source SHA256: ' + item['path']) + need(hashlib.sha1(b'blob ' + str(len(raw)).encode() + b'\0' + raw).hexdigest() == item['git_blob'], 'source blob') + pins[item['path']] = item['sha256'] + return pins + +def load(): + path = ROOT / 'research/qq16-line-normalized-decoder/verify.py' + m = types.ModuleType('authenticated_line_decoder') + m.__file__ = str(path) + exec(compile(path.read_bytes(), str(path), 'exec'), m.__dict__) + return m, m.load_source() + +# Independent exact binary-column and sparse group-ring implementation. +def action(columns, value): + result = 0 + for j, column in enumerate(columns): + if value & (1 << j): + result ^= column + return result + +@lru_cache(None) +def product(left, right): + return tuple(action(left, v) for v in right) + +def add(left, right, coefficient=Q(1)): + out = dict(left) + for key, value in right.items(): + out[key] = out.get(key, Q(0)) + coefficient * value + if not out[key]: + del out[key] + return out + +def route(columns, row): + return {(source, product(columns, owner)): coefficient for (source, owner), coefficient in row.items()} + +def query(R, routes, stage, bank, ports): + result = [{} for _ in range(8)] + for k in range(8): + for p in ports: + if R[k][p]: + result[k] = add(result[k], route(routes[stage][p], bank[p]), R[k][p]) + return result + +def serialize(rows): + return [[[s, list(g), str(c)] for (s, g), c in sorted(row.items())] for row in rows] + +def prefix_rows(word, stop, P, routes): + rows = {s + str(p): {(s + str(p), P.AXES): Q(1)} for s in ('X', 'Y', 'Z', 'W') for p in range(112)} + for event in word[:stop]: + op = event[0] + if op == 'clear': + rows[event[1]] = {} + elif op == 'add': + rows[event[1]] = add(rows[event[1]], rows[event[2]], Q(event[3])) + elif op == 'map': + rows[event[1]] = route(routes[event[2]][event[3]], rows[event[1]]) + elif op in ('line', 'begin', 'end'): + pass # Native changes are frames, not logical array values. + else: + raise ValueError('unexpected prefix opcode: ' + op) + return rows + +def schur(R, routes, ports, bank, reverse=False): + result = [{} for _ in range(8)] + for p in ports: + g = product(routes[1][p], routes[2][p]) if reverse else product(routes[2][p], routes[1][p]) + for k in range(8): + for j in range(8): + c = R[k][p] * R[j][p] / 4 + if c: + result[k] = add(result[k], route(g, bank[j]), c) + return result + +def characters(rows, character): + result = [] + for row in rows: + out = {} + for (source, owner), c in row.items(): + key = (source, action(owner, character)) + out[key] = out.get(key, Q(0)) + c + if not out[key]: + del out[key] + result.append(out) + return result + +def compute(): + pins = authenticate() # Before any inherited executable source. + L, (P, R, routes, labels, _) = load() + word = json.loads((ROOT / 'research/qq16-line-normalized-decoder/WORD.json').read_text()) + need(canonical(word) == canonical(L.lower(P, R)), 'literal source word') + stop = next(i for i, e in enumerate(word) if e[0] == 'map' and e[2] == 2) + rows = prefix_rows(word, stop, P, routes) + x = [rows['X' + str(p)] for p in range(112)] + y = [rows['Y' + str(p)] for p in range(112)] + a = query(R, routes, 1, y, range(112)) + delta = [{} for _ in range(112)] + for p in P.U + P.T: + if p in P.T: + delta[p] = dict(x[p]) + for j in range(8): + delta[p] = add(delta[p], route(routes[1][p], a[j]), -R[j][p] / 4) + need(rows['W' + str(p)] == add(y[p], delta[p]), 'actual prefix residual at port ' + str(p)) + direct = query(R, routes, 2, delta, P.U + P.T) + mx = schur(R, routes, P.U + P.T, a) + tx = query(R, routes, 2, x, P.T) + derived = [add(tx[k], mx[k], -1) for k in range(8)] + need(direct == derived, 'ordered residual identity') + basis = [{('a' + str(j), P.AXES): Q(1)} for j in range(8)] + operator = schur(R, routes, P.U + P.T, basis) + term_records = [] + for p in P.U + P.T: + g = product(routes[2][p], routes[1][p]) + r = [int(R[k][p]) for k in range(8)] + term_records.append({'port': p, 'q': labels[p], 'r': r, 'owner_columns': list(g), 'character_one_image': action(g, 1)}) + need(len({tuple(t['owner_columns']) for t in term_records}) == 104, 'distinct ordered products') + need(len({t['character_one_image'] for t in term_records}) == 104, 'character separates all routes') + need(all(sum(c * c for c in t['r']) == 4 for t in term_records), 'nonzero rank-one coefficient matrices') + trivial = characters(operator, 0) + scalar13 = [{('a' + str(k), 0): Q(13)} for k in range(8)] + need(trivial == scalar13, 'trivial character Gram collapse') + one = characters(operator, 1) + need(one != [{('a' + str(k), 1): Q(13)} for k in range(8)], '13I must fail') + diagonal = {v: c for (s, v), c in one[0].items() if s == 'a0'} + need(len(diagonal) == 52 and set(diagonal.values()) == {Q(1, 4)} and 1 not in diagonal, '52-image diagonal witness') + # Arbitrary query a is realized by actual current Y supported only on A. + realizable_y = [{} for _ in range(112)] + for p in P.A: + for j in range(8): + realizable_y[p] = add(realizable_y[p], route(routes[1][p], basis[j]), R[j][p] / 4) + need(query(R, routes, 1, realizable_y, range(112)) == basis, 'actual current query surjection') + # For X=0 and this Y, bypass query is zero; actual query is -M a. + need(all(not realizable_y[p] for p in P.U + P.T), 'zero borrowed bypass input') + # A-response is injective: undo each involutive g2 and apply R_A to recover query. + response = [{} for _ in range(112)] + for p in P.A: + for j in range(8): + response[p] = add(response[p], route(routes[2][p], operator[j]), R[j][p] / 4) + need(query(R, routes, 2, response, P.A) == operator, 'response cannot erase residual') + # Exactly the same full phased-owner type is available to all query terms. + frame_checks = 0 + for p in P.U + P.T: + g = routes[2][p] + need(action(g, labels[p]) == labels[p], 'normal label fixed') + shifted_hole = P.move(P.F17 + ((labels[p], -1),), g, L.bridge(P, g, labels[p])) + need(P.phase(shifted_hole) == P.phase(L.F16), 'bypass hole frame') + frame_checks += 1 + wrong_order = schur(R, routes, P.U + P.T, basis, reverse=True) + need(characters(wrong_order, 1) != one, 'ordered-product control') + need(query(R, routes, 2, delta, P.U) != direct, 'omitted T residual control') + need(any(direct), 'zero correction control') + result = { + 'status': 'PASS_QQ16_ORDERED_SCHUR_OBSTRUCTION', 'source_pins': pins, + 'source_future_start_event': stop, 'prefix_ports_verified': 104, + 'residual_formula': 'Q2(X_T) - (1/4) sum_p r_p r_p^T [g2,p g1,p] Q1(Y)', + 'ordered_terms': term_records, + 'operator_sha256': hashlib.sha256(canonical(serialize(operator))).hexdigest(), + 'residual_sha256': hashlib.sha256(canonical(serialize(direct))).hexdigest(), + 'trivial_character': '13I', 'separating_character': 1, + 'distinct_character_images': 104, 'one_route_branch_lower_bound': 104, + 'diagonal_00_character_witness': [[v, str(c)] for v, c in sorted(diagonal.items())], + 'query_surjection': 'Y_A=K1,A a; Y_(U+T)=0; X=0 gives Q1(Y)=a', + 'response_injective': True, 'bypass_frame_checks': frame_checks, + 'semantic_controls': ['replace M with13I', 'reverse ordered products', 'omit T residual', 'omit entire correction'], + 'scope': 'Exact logical source residual and restricted single-owner-route-per-branch lower bound. Not a native-child lower bound, circuit optimality, scalar tensor-rank bound, physical supplier or kappa improvement.'} + return result + +if __name__ == '__main__': + ap = argparse.ArgumentParser() + ap.add_argument('--write', action='store_true') + args = ap.parse_args() + target = HERE / 'RESULT.json' + if args.write: + need(not target.exists(), 'refuse overwrite') + result = compute() + if args.write: + need(not target.exists(), 'refuse overwrite') + target.write_text(json.dumps(result, indent=2, sort_keys=True) + '\n') + else: + need(typed(json.loads(target.read_text())) == typed(result), 'complete typed result mismatch') + print(result['status']) + print('104 distinct images; 52-image diagonal witness; 104-branch restricted bound; no native-child or kappa claim')