From 7bc62998ba3fc9f15f6f455d41d923d1ca3945be Mon Sep 17 00:00:00 2001 From: Nick Petalas Date: Mon, 2 Nov 2026 21:30:38 +0000 Subject: [PATCH] perf(research): cache exact G20 census containment --- research/g20-member-bank-cache/.gitattributes | 2 + research/g20-member-bank-cache/BENCHMARK.json | 118 + research/g20-member-bank-cache/FROZEN.json | 111 + research/g20-member-bank-cache/PROFILE.json | 65 + research/g20-member-bank-cache/PROOF.md | 82 + research/g20-member-bank-cache/README.md | 141 + research/g20-member-bank-cache/SOURCES.json | 18 + research/g20-member-bank-cache/TASK.json | 68 + research/g20-member-bank-cache/VERIFY.json | 46 + research/g20-member-bank-cache/benchmark.py | 72 + .../frozen/FULL-CENSUS.json | 1 + .../g20-member-bank-cache/frozen/ORACLE.json | 1 + .../g20-member-bank-cache/frozen/PROOF.md | 392 + .../g20-member-bank-cache/frozen/RESULT.json | 4249 ++ .../frozen/SOURCE-PINS.json | 81 + .../frozen/oracle_witness.py | 504 + .../frozen/sources/FRAMES.json | 56126 ++++++++++++++++ .../frozen/sources/NOTICE.md | 7 + .../frozen/sources/PATHS.json | 16585 +++++ .../frozen/sources/WORD.json.gz | Bin 0 -> 63053 bytes .../frozen/sources/gap-PROOF.md | 85 + .../frozen/sources/gap-source.py | 443 + .../frozen/sources/prior-PROOF.md | 139 + .../frozen/sources/prior-source.py | 306 + .../frozen/sources/source-README.md | 92 + .../frozen/verify_excess.py | 463 + .../frozen/verify_full_census.py | 500 + research/g20-member-bank-cache/replay.py | 101 + .../g20-member-bank-cache/test_controls.py | 87 + research/g20-member-bank-cache/verify.py | 96 + 30 files changed, 80981 insertions(+) create mode 100644 research/g20-member-bank-cache/.gitattributes create mode 100644 research/g20-member-bank-cache/BENCHMARK.json create mode 100644 research/g20-member-bank-cache/FROZEN.json create mode 100644 research/g20-member-bank-cache/PROFILE.json create mode 100644 research/g20-member-bank-cache/PROOF.md create mode 100644 research/g20-member-bank-cache/README.md create mode 100644 research/g20-member-bank-cache/SOURCES.json create mode 100644 research/g20-member-bank-cache/TASK.json create mode 100644 research/g20-member-bank-cache/VERIFY.json create mode 100644 research/g20-member-bank-cache/benchmark.py create mode 100644 research/g20-member-bank-cache/frozen/FULL-CENSUS.json create mode 100644 research/g20-member-bank-cache/frozen/ORACLE.json create mode 100644 research/g20-member-bank-cache/frozen/PROOF.md create mode 100644 research/g20-member-bank-cache/frozen/RESULT.json create mode 100644 research/g20-member-bank-cache/frozen/SOURCE-PINS.json create mode 100644 research/g20-member-bank-cache/frozen/oracle_witness.py create mode 100644 research/g20-member-bank-cache/frozen/sources/FRAMES.json create mode 100644 research/g20-member-bank-cache/frozen/sources/NOTICE.md create mode 100644 research/g20-member-bank-cache/frozen/sources/PATHS.json create mode 100644 research/g20-member-bank-cache/frozen/sources/WORD.json.gz create mode 100644 research/g20-member-bank-cache/frozen/sources/gap-PROOF.md create mode 100644 research/g20-member-bank-cache/frozen/sources/gap-source.py create mode 100644 research/g20-member-bank-cache/frozen/sources/prior-PROOF.md create mode 100644 research/g20-member-bank-cache/frozen/sources/prior-source.py create mode 100644 research/g20-member-bank-cache/frozen/sources/source-README.md create mode 100644 research/g20-member-bank-cache/frozen/verify_excess.py create mode 100644 research/g20-member-bank-cache/frozen/verify_full_census.py create mode 100644 research/g20-member-bank-cache/replay.py create mode 100644 research/g20-member-bank-cache/test_controls.py create mode 100644 research/g20-member-bank-cache/verify.py diff --git a/research/g20-member-bank-cache/.gitattributes b/research/g20-member-bank-cache/.gitattributes new file mode 100644 index 0000000000..4192266b8b --- /dev/null +++ b/research/g20-member-bank-cache/.gitattributes @@ -0,0 +1,2 @@ +frozen/** -text +frozen/sources/FRAMES.json whitespace=blank-at-eol,blank-at-eof,space-before-tab,cr-at-eol diff --git a/research/g20-member-bank-cache/BENCHMARK.json b/research/g20-member-bank-cache/BENCHMARK.json new file mode 100644 index 0000000000..e7f4e8e687 --- /dev/null +++ b/research/g20-member-bank-cache/BENCHMARK.json @@ -0,0 +1,118 @@ +{ + "bindings_sha256": { + "FROZEN.json": "3e74a49400d174b61049815a4ece5ff1ac3226d28e1eeac6f2b856b013989d47", + "benchmark.py": "28381cfbbc00922dd74883ff07525c31752ef561c17a73adc1558faa19b63d5a", + "replay.py": "be6ba7b9f3c3a20508fc46085c6dcebd5a606404acad747898d4cdbb7086c2d8" + }, + "commands": { + "cached": [ + "/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12", + "-I", + "-W", + "error", + "-B", + "/Users/nick/git/imb-research-11/research/g20-member-bank-cache/replay.py" + ], + "original": [ + "/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12", + "-I", + "-W", + "error", + "-B", + "/Users/nick/git/imb-research-11/research/g20-member-bank-cache/frozen/verify_full_census.py" + ] + }, + "coverage": "Both commands recompute the complete census and compare FULL-CENSUS.json; all successes have exactly the source CLI output. Cached command also authenticates its seventeen frozen inputs.", + "errors": 0, + "limits": "One shared macOS host, warm filesystem cache; no host-wide isolation or cross-host speed guarantee.", + "median_fraction_saved": 0.09775719817118311, + "pairs": 5, + "platform": "macOS-27.0.1-arm64-arm-64bit", + "python": "3.12.15 (main, Oct 14 2026, 00:55:37) [Clang 23.1.3 ]", + "rows": [ + { + "output_matches": true, + "pair": 0, + "returncode": 0, + "seconds": 4.448015083093196, + "side": "original" + }, + { + "output_matches": true, + "pair": 0, + "returncode": 0, + "seconds": 4.115210375050083, + "side": "cached" + }, + { + "output_matches": true, + "pair": 1, + "returncode": 0, + "seconds": 4.285522875143215, + "side": "original" + }, + { + "output_matches": true, + "pair": 1, + "returncode": 0, + "seconds": 3.929358124965802, + "side": "cached" + }, + { + "output_matches": true, + "pair": 2, + "returncode": 0, + "seconds": 4.115515916841105, + "side": "original" + }, + { + "output_matches": true, + "pair": 2, + "returncode": 0, + "seconds": 3.8665821661707014, + "side": "cached" + }, + { + "output_matches": true, + "pair": 3, + "returncode": 0, + "seconds": 4.238487374968827, + "side": "original" + }, + { + "output_matches": true, + "pair": 3, + "returncode": 0, + "seconds": 3.719846999971196, + "side": "cached" + }, + { + "output_matches": true, + "pair": 4, + "returncode": 0, + "seconds": 4.802233333000913, + "side": "original" + }, + { + "output_matches": true, + "pair": 4, + "returncode": 0, + "seconds": 3.6852905419655144, + "side": "cached" + } + ], + "status": "PASS_COMPLETE_CENSUS_BENCHMARK", + "summary": { + "cached": { + "maximum_seconds": 4.115210375050083, + "median_seconds": 3.8665821661707014, + "minimum_seconds": 3.6852905419655144 + }, + "original": { + "maximum_seconds": 4.802233333000913, + "median_seconds": 4.285522875143215, + "minimum_seconds": 4.115515916841105 + } + }, + "timing_boundary": "Before subprocess creation through complete exit and captured output; validation after timer." +} diff --git a/research/g20-member-bank-cache/FROZEN.json b/research/g20-member-bank-cache/FROZEN.json new file mode 100644 index 0000000000..9f76df24eb --- /dev/null +++ b/research/g20-member-bank-cache/FROZEN.json @@ -0,0 +1,111 @@ +{ + "repository": "https://github.com/ToikY/integer-mult-bounds", + "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/6396", + "commit": "2a5bc94df6d741b49afbadd36d96eb2aea0f6f1f", + "tree": "5068e27893c375eb704b7e5af059ddcea40a3d62", + "package": "research/g20-member-bank-excess", + "files": [ + { + "path": "FULL-CENSUS.json", + "sha256": "9d36dbd0889fa72e67ccbb91cd97e5d0fb2548b4f0190358d8148db4d6533718", + "git_blob": "2ebbfe38be32644343de165cc5e315572e133422", + "mode": 33188 + }, + { + "path": "ORACLE.json", + "sha256": "b726e0c8e7350226a701c9eed4c53537e81d355a91e1b7904b37a5845e934248", + "git_blob": "00da73cdc91bfafa86e308cbd6a1613417d1d2e6", + "mode": 33188 + }, + { + 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a/research/g20-member-bank-cache/PROFILE.json b/research/g20-member-bank-cache/PROFILE.json new file mode 100644 index 0000000000..05b2d10d1c --- /dev/null +++ b/research/g20-member-bank-cache/PROFILE.json @@ -0,0 +1,65 @@ +{ + "kind": "Separate untimed-for-benchmark cProfile run of the complete original command", + "total_seconds": 12.013104185000001, + "total_calls": 73612940, + "rows": [ + { + "file": "verify_full_census.py", + "line": 237, + "function": "evaluate", + "calls": 1328544, + "own_seconds": 0.5509447080000001, + "cumulative_seconds": 4.7845580210000005 + }, + { + "file": "oracle_witness.py", + "line": 104, + "function": "contains", + "calls": 14788, + "own_seconds": 0.055117075, + "cumulative_seconds": 3.3628777230000004 + }, + { + "file": "verify_full_census.py", + "line": 312, + "function": "run", + "calls": 1, + "own_seconds": 0.38836302100000003, + "cumulative_seconds": 9.232434542 + }, + { + "file": "verify_full_census.py", + "line": 188, + "function": "extension_profile", + "calls": 1241489, + "own_seconds": 2.4170578810000003, + "cumulative_seconds": 4.093578312 + }, + { + "file": "verify_full_census.py", + "line": 92, + "function": "__init__", + "calls": 1, + "own_seconds": 0.007632416, + "cumulative_seconds": 2.772876209 + }, + { + "file": "verify_full_census.py", + "line": 253, + "function": "replace", + "calls": 1328544, + "own_seconds": 1.501980102, + "cumulative_seconds": 7.192428852000001 + }, + { + "file": "oracle_witness.py", + "line": 80, + "function": "rational_space", + "calls": 15433, + "own_seconds": 0.471399628, + "cumulative_seconds": 3.069970955 + } + ], + "source_manifest_sha256": "3e74a49400d174b61049815a4ece5ff1ac3226d28e1eeac6f2b856b013989d47", + "limits": "Profiler overhead affects these durations; use BENCHMARK.json for the unprofiled gain." +} diff --git a/research/g20-member-bank-cache/PROOF.md b/research/g20-member-bank-cache/PROOF.md new file mode 100644 index 0000000000..d47df3612d --- /dev/null +++ b/research/g20-member-bank-cache/PROOF.md @@ -0,0 +1,82 @@ +# Exact reuse of immutable containment queries + +This contribution was produced by Nick Petalas. Apache-2.0. + +The claim is implementation equivalence for the one complete census command +in ToikY's PR6396 at `2a5bc94df6d741b49afbadd36d96eb2aea0f6f1f`. +Its scientific result and proof are credited premises. This contribution +does not audit, admit or extend that result. + +The frozen oracle represents each rational space as a tuple of eight-entry +tuples of immutable `Fraction` values. Its `contains(outer, inner)` computes +`rational_space(outer + inner) == outer`, with temporary list conversions. +The function and the called rational elimination read their arguments, +allocate local temporaries and return a Boolean. They change neither an +argument nor external state. Containment is directional, so the ordered pair +of complete spaces is the key. No frame identifier, rank, digest or object +identity substitutes for either space. + +The new adapter authenticates seventeen frozen files, loads the unchanged +census and oracle into private namespaces, and replaces exactly the oracle +namespace's `contains` binding. This also reaches `route_edges` through that +function's own globals. The retained function object remains the miss handler. +No source file, compiler statement, census loop or scientific receipt changes. + +Induct on calls of the replaced binding. On a miss, the original function +computes the same result as before. The adapter stores it under the full +ordered input pair if capacity remains. On a hit, the key equals the pair +used for a previous completed call, whose result equals the original pure +function's value on these immutable arguments. Returning that stored Boolean +therefore preserves the result. Python dictionaries resolve hash collisions +by equality of the complete keys; a hash alone is never a containment test. +When the table is full, a miss still evaluates the original function and +returns its answer. Exhaustion changes reuse only. Exceptions from a miss +propagate without creating an entry. + +Consequently each successful query returns the same Boolean, so the census +executes the same branches, context replacements, direct checks and receipt +construction. It retains the original full `FULL-CENSUS.json` comparison, +including both per-cut digests, every category and every first positive +checkpoint. The independent direct kernels and nonzero Schur control still +execute. No prior census answer is substituted for a current context. + +The table is created inside each run and discarded afterwards. It holds at +most 32,768 pairs. Space arguments have at most eight rows of eight rational +coordinates in this fixed source domain. The finite run's observed entry +count is recorded by the new verifier. This is a bound on retained cache +entries, not on all allocations of the original census or Python runtime. + +The proof is conditional on the authenticated source's stated immutable input +contract. It gives no theorem for mutable arguments, a stateful predicate, +changed frame geometry or a different caller. Finite controls corroborate +the adapter and source binding; they do not establish the predecessor's +mathematics or independent scientific acceptance. + +## Engineering decisions + +Build the Lever led to the opt-in replay and alternating benchmark commands. +Prove It Works led to complete receipt equality and actual source corruption +and implementation mutation controls. Explain the Number and the benchmark +checklist led to a separate profile, complete fresh-process measurements, +output/error checks and five alternating pairs. + +Power of Ten inspection covers the four new Python programs and their +fixed source-loading boundary. New functions are below sixty lines. There +is no recursion. The cache has a hard entry limit and safe fallback. Fixture +loops have fixed finite domains; benchmark pairs are restricted to five +through ten and each subprocess has a 120-second timeout. Source iteration +is exactly seventeen declared files, and the receipt inventory is bounded +at sixty-four files. + +Rules 3, 8 and 9 need managed-runtime deviations. Python allocates dictionary +entries and immutable objects, so no allocation-free steady state is claimed. +The cache entry bound and fixed eight-coordinate source domain constrain its +additional retained state. Dynamic compilation is restricted to authenticated +source modules and the two explicit implementation mutants in the verifier. +The original predicate callback and fixed dictionary function lookups are +required to preserve the private source namespace; no caller-selected code +or plugin discovery is provided. Before adopting this in a service or a +different caller, supply its own input, allocation and dispatch limits. +Warning-strict normal and optimized commands are the available Python +diagnostics. The frozen predecessor code retains its own resource behavior +and is not refactored here. diff --git a/research/g20-member-bank-cache/README.md b/research/g20-member-bank-cache/README.md new file mode 100644 index 0000000000..fdeb2d6ee1 --- /dev/null +++ b/research/g20-member-bank-cache/README.md @@ -0,0 +1,141 @@ +# Faster complete member-bank census through exact containment reuse + +This contribution was produced by Nick Petalas. Apache-2.0. + +A bounded cache lowers the local median time of ToikY's complete PR6396 +independent census from **4.2855 seconds to 3.8666 seconds**, a **9.78%** +reduction over five alternating fresh-process pairs. Every pair improves. +All ten processes return the exact original success output without errors. +The complete scientific receipt and its checks remain unchanged. + +Claim type: scoped implementation-equivalence proof, exact finite +conformance and a local performance observation. No new kappa, admission +or selected-frontier change follows. + +## Change and evidence + +The source is [PR6396](https://github.com/CrocSwap/integer-mult-bounds/pull/6396) +at `2a5bc94df6d741b49afbadd36d96eb2aea0f6f1f`. Its mathematical result is a +credited premise. The new result is a cheaper equivalent execution of one +complete census command, not a new audit of that result. + +[PROFILE.json](PROFILE.json) records a separate profile of that command. +Rational containment takes 3.363 of 12.013 profiled seconds, about 28%. +The adapter retains the original containment predicate and caches its Boolean +result by the complete ordered pair of immutable rational spaces. It avoids +11,194 of 14,788 predicate evaluations and retains 3,594 entries. The hard +capacity is 32,768; an uncached miss after capacity exhaustion still evaluates +the original predicate. + +[PROOF.md](PROOF.md) proves equivalence under the source's pure-predicate +and immutable-space contract. The census class, event loop, geometry, +elimination, direct checkpoint checks and receipt construction retain their +original bytes. Every current context still participates. The original +comparison against `FULL-CENSUS.json` remains active, and `--emit` returns +the same canonical scientific object. This does not reuse a previous +context's rank result as a substitute for evaluating a new context. + +The new checker includes 432 ordered positive/negative containment +comparisons at capacities zero, one, two and 32,768. Four invalid capacities +and two actual wrong-result implementation mutants reject. The separate CLI +controls run normal and optimized replay after Git-free relocation with +empty PATH and read-only source files. Changed frozen bytes, a changed +source manifest and a removed cache installation reject. + +## Complete-command measurement + +[BENCHMARK.json](BENCHMARK.json) binds the benchmark and adapter bytes and +contains every process result. Both sides run the same CPython 3.12.15 with +isolated mode, bytecode writes disabled and warnings treated as errors. +The timer includes process startup, all current census work, checks, +receipt comparison, output capture and exit. The new side also authenticates +all seventeen frozen files. Output validation follows the timer. + +| Complete command | Median seconds | Observed range | +| --- | ---: | ---: | +| Original source | 4.2855 | 4.1155 to 4.8022 | +| Cached adapter | 3.8666 | 3.6853 to 4.1152 | + +These are five serial alternating pairs on one shared macOS arm64 host, +with warm filesystem cache. Startup and the remainder of the census still +cost time; containment accounts for only part of the complete command. +Profiler overhead prevents comparing its absolute times with the unprofiled +benchmark. The measurements give no cross-host speed guarantee or claim of +an optimal cache policy. No further optimization followed the first gain. + +## Reproduce + +From the repository root, using the supplied interpreter: + +```sh +/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/g20-member-bank-cache/verify.py +/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -O -W error -B research/g20-member-bank-cache/verify.py +TMPDIR=/absolute/private/run /Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/g20-member-bank-cache/test_controls.py +/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/g20-member-bank-cache +/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/g20-member-bank-cache --check-source-history --check-modes +``` + +Create the private external temporary directory before using it. Substitute +an existing CPython 3.12 path on another host. `verify.py` emits +`PASS_G20_MEMBER_BANK_CACHE`, actual cache statistics, the scientific digest +and hashes of every package file. `test_controls.py` emits +`PASS_G20_CACHE_CLI_CONTROLS`. The registered runner must print +`PASS_REGISTERED_RESEARCH_PACKAGE`. + +For the optimized complete caller alone, run `replay.py`. Its `--emit` option +prints the complete canonical source result; `--stats` reports cache counts +on stderr. Normal replay writes no files. To repeat the local measurement, +run `benchmark.py --pairs 5` and redirect its JSON outside the checkout. +The benchmark is deliberately outside registered CI checks; timing is noisy +on a shared runner. + +[FROZEN.json](FROZEN.json) binds seventeen necessary source files by SHA256 +and Git blob ID, with the exact repository, commit, path and tree. Their +bytes and modes were compared with the public source tree. They are retained +unchanged in `frozen/`, including the source notices. This self-contained +committed export makes the pending source available without relying on +foreign objects in a local Git cache. [SOURCES.json](SOURCES.json) separately +binds the main-branch catalogue and selected record as historical provenance. +Its source-history check covers those declared pins; the external origin is +recorded in the frozen export manifest. + +## Scope and limitations + +This refines the current `replay-runtime` card. The base is canonical main +`7c49fe32c55de02c2c873655c804b16e4c3fef0a`, priority revision 8. The selected +metadata baseline passed before work. Live open and recent account PRs, +handoffs, active Discussions, local reservations, merged searches and main +README terms were checked before the +[advance claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/1166#discussioncomment-19360872). +The overlap cache covered 355 open PRs and 6,261 Discussion records, with +complete reported remote pagination. Only 101 of 8,917 main note paths were +materialized locally; separate Git searches covered the named object. +Unpublished work, arbitrary diffs and omitted historical notes remain limits. + +This changes one isolated opt-in package. It does not change the source +default, typed word, targets, paid bill, native implementation, physical +restoration, compiler, ordinary supplier or outer bound. All five framework +assumptions retain their status. The other seven PR6396 registered commands, +the selected supplier cold replay, Lean and Docker are outside this cost +result and were not run. No independent human or formal proof-kernel review +is claimed. Engineering bounds and managed-runtime deviations are in the +proof. Hosted CI status belongs in the PR body. + +## Open next questions + +Should a future version of the original census adopt this bounded cache? +Bind one exact new source head and its immutable-space and pure-predicate +contract, then preserve the complete receipt and failure controls. This +isolated adapter does not cover a changed geometry or a stateful predicate. +No adoption or further optimization is reserved. The question is structured +in [TASK.json](TASK.json). + +## Credit + +Credit ToikY for PR6396's census, independent oracle and complete coverage +contract; Ali Romman for PR5679/5708; unpaidmoon for the bank-gap handoff; +Nick Petalas for PR5983/5609; and Dugongue, ai-nanachi, compact436, Cinna +Davis, DreamingOfClouds, eumemic, rohanarun, zxv, Jacob Alan Sussman and the +full lineage in the unchanged frozen notices and source README. Memoization +is classical. The new contribution is this bounded source-specific adapter, +its equivalence and failure controls, and its complete-command measurement. diff --git a/research/g20-member-bank-cache/SOURCES.json b/research/g20-member-bank-cache/SOURCES.json new file mode 100644 index 0000000000..594089b9c7 --- /dev/null +++ b/research/g20-member-bank-cache/SOURCES.json @@ -0,0 +1,18 @@ +{ + "schema_version": 1, + "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "d59b5035e7b4cbaa9d688a1d32dd0d6eb79c466a", + "sha256": "9b8d0eea95b3bf0dfcb7938a732a6439b87a2685dec2a5ab9e525b3b34debbfa" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "3404fbdd5e7529a0674eef26114b5071e4586cec", + "sha256": "ead6cdc9d0af6d58e8a49744d8ec8c7c15e13d2ba93c276c434bcf9b51b93a81" + } + ] +} diff --git a/research/g20-member-bank-cache/TASK.json b/research/g20-member-bank-cache/TASK.json new file mode 100644 index 0000000000..dc12b00561 --- /dev/null +++ b/research/g20-member-bank-cache/TASK.json @@ -0,0 +1,68 @@ +{ + "schema_version": 1, + "task_id": "replay-runtime", + "priority_revision": 8, + "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a", + "original_card": { + "id": "replay-runtime", + "question": "Can one measured replay bottleneck be sped up without dropping coverage?", + "starting_points": [ + "scripts/run_isolated_tests.py", + "scripts/verify_replay_coverage.py", + "certificates/selected-result.json" + ], + "methods": [ + "Profile one isolated replay and optimize the measured bottleneck.", + "Design source-bound reuse with explicit dependency invalidation and negative controls." + ], + "acceptance_gate": "Report before/after wall time on the same fixture, retained checks and invalidation behavior.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_selected_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Resolve the current selected review, separate complex/ordinary BIT/admitted BIT/outer budgets, and compare the card against live handoffs before starting. Historical ceilings require exact source/model equivalence.", + "scope": "Source-binding orientation only; not a scientific replay or all-size proof. Materialize selected inputs if this checkout is sparse." + }, + "first_experiment": "Measure one unchanged fixture, preserve check coverage, and test one optimization with invalidation controls.", + "bottleneck_link": "Faster trustworthy replays increase review throughput and let mechanism candidates be checked sooner.", + "allowed_variations": [ + "Profile one stage or design one source-bound cache boundary." + ], + "scope_change_triggers": [ + "Skipping coverage or comparing different fixtures to claim speedup." + ], + "overlap_terms": [ + "replay runtime", + "cache invalidation", + "isolated tests" + ] + }, + "scope_status": "refined", + "actual_scope": "Bounded exact containment reuse in the complete PR6396 independent member-to-occupied-bank census.", + "scope_change_reason": "Choose one fresh concrete caller for replay-runtime. Predecessor mathematics is a cited premise; the contribution is an opt-in equivalent implementation and its measured complete-command cost.", + "bottleneck_link": "This lowers the cost of exact source-bound BIT research evidence. It does not supply a changed helper word, new productive entitlement or supplier admission.", + "budget_minutes": 60, + "stop_rule": "Stop at the first verified speed improvement and package it without extending the optimization.", + "outcome": "completed", + "evidence": "PROOF.md, replay.py and verify.py establish adapter equivalence; BENCHMARK.json binds five alternating complete-command pairs.", + "author": "Nick Petalas", + "ai_assistance": "Independent human and formal proof-kernel review are unclaimed.", + "open_questions": [ + { + "question": "Should the same bounded containment reuse be adopted in a future version of the original census?", + "why_it_matters": "An isolated adapter does not change the source default or establish equivalence after its geometry or predicate contract changes.", + "first_step": "Bind a specific new source head and its immutable space and pure-predicate contract, then preserve its complete receipt and failure controls.", + "blocked_by": "Source adoption and any changed caller contract remain outside this isolated package." + } + ], + "environment": { + "python": "3.12.15", + "platform": "macOS arm64", + "source_head": "2a5bc94df6d741b49afbadd36d96eb2aea0f6f1f", + "main": "7c49fe32c55de02c2c873655c804b16e4c3fef0a" + }, + "claim": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1166#discussioncomment-19360872" +} diff --git a/research/g20-member-bank-cache/VERIFY.json b/research/g20-member-bank-cache/VERIFY.json new file mode 100644 index 0000000000..8ba1e9b587 --- /dev/null +++ b/research/g20-member-bank-cache/VERIFY.json @@ -0,0 +1,46 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 120, + "checks": "Complete exact source receipt, ordered Boolean cache equivalence, capacity exhaustion, six failure controls and hash-bound receipt" + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-W", + "error", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 120, + "checks": "Same complete scientific and adapter checks under optimized Python" + }, + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/test_controls.py" + ], + "timeout_seconds": 180, + "checks": "Two Git-free read-only CLI runs, frozen-source/manifest rejection and omitted-cache-installation mutant" + } + ] +} diff --git a/research/g20-member-bank-cache/benchmark.py b/research/g20-member-bank-cache/benchmark.py new file mode 100644 index 0000000000..8513f12962 --- /dev/null +++ b/research/g20-member-bank-cache/benchmark.py @@ -0,0 +1,72 @@ +"""Alternate complete fresh-process census commands; emit a hash-bound receipt. + +Produced by Nick Petalas. Apache-2.0. Timing is a local observation. +""" + +import argparse +import hashlib +import json +from pathlib import Path +import platform +import statistics +import subprocess +import sys +import time + +ROOT = Path(__file__).resolve().parent +SUCCESS = b"PASS independent complete normalized G20 census receipt\n" + + +def digest(path): + return hashlib.sha256(path.read_bytes()).hexdigest() + + +def benchmark(pairs): + if type(pairs) is not int or not 5 <= pairs <= 10: + raise ValueError("Use five through ten alternating pairs") + commands = { + "original": [sys.executable, "-I", "-W", "error", "-B", + str(ROOT / "frozen" / "verify_full_census.py")], + "cached": [sys.executable, "-I", "-W", "error", "-B", str(ROOT / "replay.py")], + } + rows, errors = [], [] + for pair in range(pairs): + for side in ("original", "cached"): + start = time.perf_counter() + completed = subprocess.run(commands[side], capture_output=True, timeout=120, check=False) + seconds = time.perf_counter() - start + ok = completed.returncode == 0 and completed.stdout == SUCCESS and not completed.stderr + rows.append({"pair": pair, "side": side, "seconds": seconds, + "returncode": completed.returncode, "output_matches": ok}) + if not ok: + errors.append({"pair": pair, "side": side, + "stderr": completed.stderr.decode(errors="replace")[:4096]}) + if errors: + raise ValueError("Benchmark process/output failures: " + json.dumps(errors)) + summary = {} + for side in commands: + values = [row["seconds"] for row in rows if row["side"] == side] + summary[side] = {"median_seconds": statistics.median(values), + "minimum_seconds": min(values), "maximum_seconds": max(values)} + gain = 1 - summary["cached"]["median_seconds"] / summary["original"]["median_seconds"] + bindings = {"replay.py": digest(ROOT / "replay.py"), + "benchmark.py": digest(ROOT / "benchmark.py"), + "FROZEN.json": digest(ROOT / "FROZEN.json")} + return {"status": "PASS_COMPLETE_CENSUS_BENCHMARK", "pairs": pairs, + "python": sys.version, "platform": platform.platform(), "commands": commands, + "errors": 0, "rows": rows, "summary": summary, "median_fraction_saved": gain, + "bindings_sha256": bindings, + "timing_boundary": "Before subprocess creation through complete exit and captured output; validation after timer.", + "coverage": "Both commands recompute the complete census and compare FULL-CENSUS.json; all successes have exactly the source CLI output. Cached command also authenticates its seventeen frozen inputs.", + "limits": "One shared macOS host, warm filesystem cache; no host-wide isolation or cross-host speed guarantee."} + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--pairs", type=int, default=5) + args = parser.parse_args() + print(json.dumps(benchmark(args.pairs), indent=2, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/g20-member-bank-cache/frozen/FULL-CENSUS.json b/research/g20-member-bank-cache/frozen/FULL-CENSUS.json new file mode 100644 index 0000000000..2ebbfe38be --- /dev/null +++ b/research/g20-member-bank-cache/frozen/FULL-CENSUS.json @@ -0,0 +1 @@ +{"bank_state_evaluations":6702,"coverage_method":"Subtract/add changed context categories in active histograms, then weight every full histogram at each cut; separate geometry multiplicities count each cut's 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follows.","singleton":{"boundary_matrix_rows":[],"boundary_rank":0,"eligible_input_supports":[],"eligible_output_supports":[],"internal_matrix_rows":[],"internal_rank":0,"left_kernel_dimension":0,"left_kernel_role_supports":[],"right_kernel_dimension":0,"right_kernel_role_supports":[],"simultaneous_unit_pair":null,"slots":[323]},"target_dimension":4},{"augmented":{"boundary_matrix_rows":[[0]],"boundary_rank":1,"eligible_input_supports":[[222]],"eligible_output_supports":[[222]],"internal_matrix_rows":[[0]],"internal_rank":1,"left_kernel_dimension":1,"left_kernel_role_supports":[[222]],"right_kernel_dimension":1,"right_kernel_role_supports":[[222]],"simultaneous_unit_pair":{"a_roles":[222],"b_roles":[222],"boundary_pairing":1,"c_input_support":[222],"d_output_support":[222],"internal_pairing":1},"slots":[221,222]},"base":{"boundary_matrix_rows":[],"boundary_rank":0,"eligible_input_supports":[],"eligible_output_supports":[],"internal_matrix_rows":[],"internal_rank":0,"left_kernel_dimension":0,"left_kernel_role_supports":[],"right_kernel_dimension":0,"right_kernel_role_supports":[],"simultaneous_unit_pair":null,"slots":[221]},"boundary_excess_over_both":0,"cut_t":0,"edge":[1,635,1],"field":222,"group_dimensions":[8,0],"group_members":[222,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,320,321,322,323,324,325,326,327,328,329,330,332,333,334,335,336,337,338,339,340,341,342,343,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,372,373,374,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,464,467,478,479,480,481,482,483,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657],"inherited_pivot_quotient":{"available":true,"boundary_matrix_rows":[],"boundary_rank":0,"internal_matrix_rows":[],"internal_rank_on_actual_changed_bases":0,"pivot_role":222,"simultaneous_unit_pair":null},"internal_excess_over_both":0,"paid_edge_rank":1,"qualification":"Necessary normalized pairing evidence only; no extra independent target, typed continuation or profit follows.","singleton":{"boundary_matrix_rows":[[0]],"boundary_rank":1,"eligible_input_supports":[[222]],"eligible_output_supports":[[222]],"internal_matrix_rows":[[0]],"internal_rank":1,"left_kernel_dimension":1,"left_kernel_role_supports":[[222]],"right_kernel_dimension":1,"right_kernel_role_supports":[[222]],"simultaneous_unit_pair":{"a_roles":[222],"b_roles":[222],"boundary_pairing":1,"c_input_support":[222],"d_output_support":[222],"internal_pairing":1},"slots":[222]},"target_dimension":7}],"controls":{"augmentation_ranks":[1,1,2],"foreign_coordinate_rejected":true,"internal_only_rejected":true,"synthetic_not_source_evidence":true},"cut_convention":"cut_t is the number of literal source records already applied; prefix[:t],suffix[t:]","limits":["This is a bounded direct-cut oracle, not an independent complete-census exclusion.","Published edges and frame compatibility are exact rational geometry inQ^8; normalized scalar pairing is overF2.","A positive excess or simultaneous unit pair is only a necessary algebraic gate; no extra productive target or profitable split is certified.","No retargeted chronological continuation, native phase/all columns, physical erasure, complete paid/target invoice, ordinary admission or selected frontier change is supplied."],"normalized_convention":"All685 entrance coordinates, including dirty owned coordinates, start as independent formal variables; ERASE is an owned projection, INIT requires a zero row, and queries are normalized identity maps.","schema_version":1,"source_git_blobs":{"FRAMES.json":"9edf8d95b45a9c9c766a956bfcd3c19cf07bc13c","NOTICE.md":"accbc28384515af7b94b33e5f4eb57a150e0d9a1","PATHS.json":"efbdf632746a971f9a593f57ccbb7d2cc67a6760","WORD.json.gz":"3877a72d8a15adb03f6492f7d2fd8fa902ecb639","gap-PROOF.md":"26f776a79accbb8a6378e5ad5ebefc3693a26501","gap-source.py":"93bf7baf7c01de63a57a8ad1e4653ca48047eaae","prior-PROOF.md":"c6d2f2c7626a7c42da025ef360ce1673f6a116dc","prior-source.py":"13326f590033f6633bc91f919c802b6ddaf576bc","source-README.md":"b1655b59134ae7a5734628ba1efef6611b2dcd31"},"source_sha256":{"FRAMES.json":"0d99fc6b8f45c03dfba5252a03dd9e7fe23be3a7593dfe15368e34da6629a654","NOTICE.md":"a4fdb5e2dfeeb216f3f58417891fc0a084c218d9a75228fb977e3cb82973be72","PATHS.json":"f4dd58b78121040b1f054c0f7a626b25f6ef8d39f3de044d3456ea7dea8a6a5e","WORD.json.gz":"8dd441fdb9c8923df06eb5ebfda37d03e4539f2305763e688d8c7025d196c4b1","gap-PROOF.md":"121649b47271f45e18a1053ca5615c94e1cc81cc42136d8ccf3b2dca7d93f706","gap-source.py":"91e201fd3c96267c878863abba794a16025070c98145ae598ee0ed7383c7f9c6","prior-PROOF.md":"af88b44f1c61fb91d63ace7a2ece8d798bf6378864b2c4e1d44e01070fd485db","prior-source.py":"a9aea8b108ebbeae8041770cefecfdabdfaf91b72ba7b5cfa2ff13408f1d16dd","source-README.md":"e443b2fd7b988316953bfc7d21045690ea0d3ce9069ce1a06880f6ccfc7ec054"},"status":"PASS_BOUNDED_NECESSARY_PAIRING_CHECKPOINTS"} diff --git a/research/g20-member-bank-cache/frozen/PROOF.md b/research/g20-member-bank-cache/frozen/PROOF.md new file mode 100644 index 0000000000..2ccdae3579 --- /dev/null +++ b/research/g20-member-bank-cache/frozen/PROOF.md @@ -0,0 +1,392 @@ +# A paid member exit: boundary excess rather than an inherited channel + +This checkpoint certifies one finite, source-bound example in which a public +helper moved along one published frame edge into an **occupied** compatible +bank exposes more boundary-pairing rank than either that bank or the helper +singleton already exposes. A bare positive rank is not the success criterion. +The normalized linear algebra below supplies necessary conditions; it does +not supply a typed consumer, new productive target, favorable bill or new kappa. + +## 1. Exact source and retained premises + +The word is PR5708's `research/g20-conjugation-admission/WORD.json.gz`, +originating at head `829d01fc031f7323ffcfa423fdfd1f24dcbe3190`, together +with its published PATHS and retained FRAMES data. The exact source WORD blob +is `3877a72d8a15adb03f6492f7d2fd8fa902ecb639`; the route blob is +`efbdf632746a971f9a593f57ccbb7d2cc67a6760`. Source bytes, the nine retained +inputs and their Git/SHA256 pins are in [SOURCE-PINS.json](SOURCE-PINS.json). +Author and predecessor Python files are inert source evidence, not imports +or executable dependencies of a new scientific checker. + +Two coefficient fields must be kept distinct: + +- Physical frame **shapes** are the rational row spaces of the literal + FRAMES `B` matrices in `Q^8`, canonically reduced over the rationals. + Frame aliases with the same row space occupy the same shape bank. +- Normalized scalar dependencies and the pairing forms are over `F_2`. + Their rows/columns are binary formal-coordinate vectors, not rational + physical frame bases. + +The source normalized-coordinate contract, native frame induction, helper +identity endpoints and interpretation of owned fields/erasures are retained +premises. This package does not prove those native/physical facts anew. +Keeping them explicit is essential when comparing a hypothetical new frame +placement with the already checked source schedule. + +## 2. Prefix, suffix, cuts and operational typing + +There are 685 formal role labels and 14794 source records. Use **cut `t` = +the number of records already applied**, so cuts run from0 through14794. +The opening cut is0; applying the old source event with zero-based index `i` +leads to cut `i+1`. A predecessor's cut labelled `i` after that event is +therefore this package's cut `i+1`. + +Use column states. Let `A_t` map entrance formal coordinates to the cut +state, and let `B_t` map that cut state to the exit coordinates. Row +`A_t[i,:]` is role `i`'s normalized prefix functional; column `B_t[:,i]` +is its normalized suffix response. In particular, prefix rows and suffix +columns are different objects; replacing either by a transpose of the other +would not compute this contract. + +The pinned normalized model begins with `A_0=I`; the terminal suffix is +`B_14794=I`. Its elementary scalar rules are: + +- `ADD d,s`: the cut state changes by the binary transvection + `E=I+e_d e_s^T`. Advancing the prefix applies `A[d,:] ^= A[s,:]`. + Reading the suffix backwards applies `B[:,s] ^= B[:,d]`. Because + `E^2=I` over `F_2`, removing that ADD from a suffix while advancing + the cut uses the same column update. +- `ERASE d`: its formal scalar map is the projection that kills coordinate + `d`. A prefix row is set to zero; backward suffix construction sets + column `d` to zero. This map is not invertible. To advance past it, + one must use the suffix appropriate to the later cut, for example by + restoring the column saved during backward construction, rather than + pretending that zeroing a column is its own inverse. +- `Q`, `ZERO_Q` and `INIT` update frame/role metadata but have no + additional normalized scalar action in the cited source convention. + This convention is not a new theorem about physical initialization, + inactive coordinates, zero preparation or erasure. Owned formal labels + remain in the dependency bookkeeping, including outside-group tests. + +Physical placement is tracked separately by each role's current literal +frame label. An ADD requires active source and destination at its declared +common frame. A query requires its actual source frame and changes it to +the declared destination. INIT/ERASE follow their source record's frame +update. Inactive labels are not occupied bank fields. Grouping equal row +spaces for the pairing test does not authorize free retargeting of literal +frame labels, nor does a normalized coefficient identity validate a changed +chronological word. + +## 3. Groups, occupied banks and one-edge candidates + +A retained public helper is a role at least222 which is not in the source +owned set. Its endpoint group `G` consists of all such roles with the same +entrance shape `U` and exit shape `V`. All formal coordinates outside `G`, +including main roles, owned labels and other helper groups, belong to the +outside restriction. + +At a fixed cut, an occupied bank `S` contains **every** active role with +one common frame shape `F`. It may contain main, owned and helper roles; +no bank-size or support restriction is implicit. Compatibility with `G` +means strict physical row-space containment + +`V < F < U` in `Q^8`. + +A candidate names a member `h in G`, its current literal frame label `u`, +and a published route `(u,v,q)` with target shape `F`, positive paid rank +`q=dim(u)-dim(v)`, and nonempty target bank `S`. Strict dimension drop +ensures `h` is not already in `S`. The hypothetical move produces bank +`S'=S union {h}`. The old source prefix/suffix coefficients are retained +under the normalized-transport premise; only the proposed bank membership +changes for this necessary test. + +This is a changed hypothesis from PR5983's existing common-frame bank: +the paid move introduces an extra physical coordinate into that bank at +this exact cut. It is not a rerun with another seed inside the old bank. +If the purported new bank is merely an already realized source-bank state +with the same coefficients, its old coverage remains old coverage. + +## 4. Full eligibility and the two pairing forms + +For a bank `T`, let `E_T` be its cut-coordinate space, embedded by zeros +outside `T`. Define the complete eligible spaces + +`L_T={a in E_T^*: (a A_t)|outside(G)=0}`, + +`R_T={b in E_T: (B_t b)|outside(G)=0}`. + +These are full kernels of the corresponding outside-coordinate restrictions, +not a search over sparse candidate vectors. For `a in L_T`, put `c=aA_t`; +for `b in R_T`, put `d=B_t b`. By eligibility, both `c` and `d` are +supported only on the helper boundary group. + +There are two distinct bilinear forms on `L_T x R_T`: + +`eta_T(a,b)=a b` (internal cut pairing), + +`beta_T(a,b)=(a A_t)(B_t b)=c d` (boundary pairing). + +Matrices of these forms must use complete kernel bases, and their ranks +are independent of the chosen bases. In particular, boundary rank is not +the rank of the internal form and is not simply a nonzero kernel dimension. +PR5983's examples with a nonzero internal form but zero boundary form +already demonstrate why that distinction matters. + +An abstract one-coordinate extraction/substitution needs the **same** pair +`a,b` with + +`eta_T(a,b)=1` and `beta_T(a,b)=1`. + +The internal equation permits treating the extraction as one cut coordinate. +For the boundary equation, use the retained identity endpoint on `G`. +Replacing the extracted coordinate by an independent formal successor `z` +would give the combined boundary map + +`(h,z) -> (c h, (I-dc)h+d z)`. + +If `cd=0`, the nonzero input `(h,z)=(d,1)` is killed, including the case +`d=0`. Thus independent boundary outputs require `cd=1` over `F_2`. +If `cd=1`, the displayed abstract boundary map is injective: its kernel +has `h=dz` and `0=ch=(cd)z=z`. This elementary conditional calculation +does not provide a physical implementation or productive target entitlement. + +A finite positive case must publish actual cut-coordinate `a,b`, their +boundary images `c,d`, all outside-zero equations and both unit pairings. +Reporting ranks alone does not exhibit those vectors or their operational +realization. Several claimed split channels would require appropriate +nonsingular pairing matrices and simultaneous realizability; one unit pair +does not establish that larger conclusion. + +## 5. The sharpened excess test and a one-coordinate bound + +Write `rho(T)=rank(beta_T)` for this fixed cut and group. The necessary +success test in this package is + +`rho(S') > max(rho(S),rho({h}))`. + +A positive augmented rank with equality here is an **inherited** channel, +not extra boundary rank attributable to the occupied bank. In particular, +the already known member singleton at an empty bank is not a new result. +This excess test is an algebraic screening criterion, not a count of newly +admitted independent productive fields. + +Embedding `E_S` into `E_S'` by a zero `h` coordinate embeds each old +eligible space into the new one. The map from `L_S'` to `F_2` which takes +the `h` coefficient has kernel exactly `L_S`; hence +`dim(L_S'/L_S)<=1`. The same argument gives +`dim(R_S'/R_S)<=1`. This does not require any invertibility of the +prefix/suffix maps and therefore remains valid in the presence of ERASE. + +If the old bank has zero boundary form, choose bases extending its eligible +spaces by at most one new row and one new column. The augmented boundary +matrix then has the form + +```text + old right | new right +old left 0 | p +new left q | z +``` + +with missing blocks when a kernel does not grow. Its rank is at most2: +the new column has rank at most1 and the new row adds at most1. More +generally adding this one physical coordinate can increase boundary rank +by at most2 over the old bank. Thus a purported larger increase would +signal a wrong domain, incomplete kernels, changed prefix/suffix or an +implementation error; it cannot be explained by this one-coordinate move. + +### Quotient out a known singleton pivot + +If the singleton is eligible on both sides with boundary pairing1, its +coefficient vectors are the literal `e_h^T,e_h`, and its internal pairing +is also1. Extend these to eligible bases of `S'`, placing the singleton +first. Its boundary matrix has a pivot block + +```text +1 p +q C +``` + +and row/column elimination gives + +`rank(beta_S')=1+rank(C-q p)`. + +Over `F_2` subtraction equals addition. If the augmented rank is only1, +the quotient after this inherited pivot is zero. Publishing the same pivot +as a new bank-enabled channel would overcount it. An actual residual +nonzero quotient must be shown explicitly when claiming boundary excess. +Its existence still does not prove physical multi-channel implementation. + +## 6. Two immediate completion cautions + +### The added-query tariff in a deliberately restricted model + +Suppose a proposed one-helper edit changes exactly one productive target +from rank `r+k` to two targets of ranks `r,k`, adds one paid query of rank +`r`, and retains every other paid job/target. Under that **declared special +model**, the productive-minus-paid margin change is + +`H_r+H_k-H_(r+k)-H_r = H_k-H_(r+k) < 0` + +for `r>0,k>0` and a strictly increasing tariff `H`. In particular the +inequality holds for `H_j=j^s`, `00`, in particular for `0= minimum, "Strict integer required") + return value + + +def rational(value): + require(type(value) in (str, int, Fraction), "Exact rational coordinate required") + return Fraction(value) + + +def rational_space(rows): + """Unique reduced rational row space, with greatest-coordinate pivots.""" + require(type(rows) is list, "Frame basis list") + basis = {} + for source in rows: + require(type(source) is list and len(source) == 8, "Frame coordinate width") + row = list(map(rational, source)) + for pivot in sorted(basis, reverse=True): + scale = row[pivot] + if scale: + row = [a-scale*b for a, b in zip(row, basis[pivot])] + pivot = next((i for i in reversed(range(8)) if row[i]), None) + if pivot is None: + continue + scale = row[pivot] + row = [a/scale for a in row] + for previous in basis: + scale = basis[previous][pivot] + if scale: + basis[previous] = [a-scale*b for a, b in zip(basis[previous], row)] + basis[pivot] = row + return tuple(tuple(basis[p]) for p in sorted(basis, reverse=True)) + + +def contains(outer, inner): + return rational_space([list(row) for row in outer+inner]) == outer + + +def frame_geometry(payload): + require(type(payload) is dict and set(payload) == {"frames"}, "Frame table schema") + frames = payload["frames"] + require(type(frames) is dict, "Frame table object") + spaces = {} + for key, entry in frames.items(): + require(type(key) is str and key.isascii() and key.isdigit() and str(int(key)) == key, + "Canonical frame identifier") + require(type(entry) is dict and set(entry) in ({"A", "B", "dim"}, {"A", "B", "dim", "origin"}), "Frame entry schema") + if "origin" in entry: + require(type(entry["origin"]) is str, "Frame origin metadata") + shape = rational_space(entry["B"]) + require(integer(entry["dim"]) == len(shape), "Frame dimension") + spaces[int(key)] = shape + return spaces + + +def word_contract(word, spaces): + require(type(word) is dict and set(word) == {"records", "start", "final", "owned"}, "Word schema") + start, final, owned, records = (word[k] for k in ("start", "final", "owned", "records")) + require(all(type(v) is list for v in (start, final, owned, records)), "Word lists") + require(len(start) == len(final) == 685 and len(records) == 14794, "Frozen word dimensions") + for value in start+final: + require(value is None or (type(value) is int and value in spaces), "Declared frame identifier") + for role in owned: + require(integer(role) < len(start), "Owned role range") + require(owned == sorted(set(owned)) and len(owned) == 48, "Owned inventory") + for event in records: + require(type(event) is list and event and type(event[0]) is str, "Event list/opcode") + op = event[0] + require(op in ("ADD", "ERASE", "INIT", "Q", "ZERO_Q"), "Event opcode") + require(len(event) == {"ADD": 4, "ERASE": 3, "INIT": 3, "Q": 5, "ZERO_Q": 5}[op], "Event arity") + require(integer(event[1]) < len(start), "Destination role") + if op == "ADD": + require(integer(event[2]) < len(start) and event[1] != event[2], "Distinct ADD source") + require(type(event[3]) is int and event[3] in spaces, "ADD frame") + elif op in ("ERASE", "INIT"): + require(event[1] in owned, "Only owned ERASE/INIT") + require(event[2] is None or (type(event[2]) is int and event[2] in spaces), "Owned header") + else: + require(all(type(x) is int and x in spaces for x in event[2:4]), "Query frame identifiers") + integer(event[4], 1) + return start, final, set(owned), records + + +def route_edges(payload, spaces): + require(type(payload) is dict, "Route catalogue object") + edges = set() + for key, path in payload.items(): + require(type(key) is str and type(path) is list and path, "Nonempty route path") + parts = key.split(":") + require(len(parts) == 2 and all(p.isascii() and p.isdigit() for p in parts), "Route key") + current = int(parts[0]) + for edge in path: + require(type(edge) is list and len(edge) == 3, "Route edge schema") + source, target, rank = edge + require(all(type(v) is int for v in edge) and source in spaces and target in spaces, + "Route edge integer identifiers") + require(current == source, "Route continuity") + require(len(spaces[source])-len(spaces[target]) == rank > 0, + "Published strict dimension drop") + require(contains(spaces[source], spaces[target]), "Published rational nesting") + current = target + edges.add(tuple(edge)) + require(current == int(parts[1]), "Route endpoint") + return edges + + +def traces(word, spaces, cuts): + start, final, owned, records = word_contract(word, spaces) + require(all(type(t) is int and 0 <= t <= len(records) for t in cuts), "Cut number of applied records") + wanted = set(cuts) + n = len(start) + rows = [1 << i for i in range(n)] + state = start[:] + before, after, headers = {}, {}, {} + if 0 in wanted: + before[0], headers[0] = rows[:], state[:] + for t, event in enumerate(records, 1): + op, d = event[:2] + if op == "ADD": + s, frame = event[2:] + require(state[d] == state[s] == frame, "Literal ADD exact common frame") + rows[d] ^= rows[s] + elif op == "ERASE": + rows[d] = 0 + state[d] = event[2] + elif op == "INIT": + require(rows[d] == 0, "Owned INIT whole normalized zero") + state[d] = event[2] + else: + a, b, rank = event[2:] + require(state[d] == a, "Literal query source header") + require(len(spaces[a])-len(spaces[b]) == rank and contains(spaces[a], spaces[b]), + "Literal query geometry") + if op == "ZERO_Q": + require(rows[d] == 0, "ZERO_Q whole normalized zero") + state[d] = b + if t in wanted: + before[t], headers[t] = rows[:], state[:] + require(state == final, "Literal final frame contract") + require(all(rows[i] == 0 for i in owned), "Final owned normalized zero rows") + # B's columns are rebuilt directly from the final identity, independently + # of the forward sweep or the predecessor's erased-column restoration. + columns = [1 << i for i in range(n)] + if len(records) in wanted: + after[len(records)] = columns[:] + for index in reversed(range(len(records))): + event = records[index] + op, d = event[:2] + if op == "ADD": + columns[event[2]] ^= columns[d] + elif op == "ERASE": + columns[d] = 0 + if index in wanted: + after[index] = columns[:] + require(set(before) == set(after) == set(headers) == wanted, "Direct checkpoint coverage") + return before, after, headers + + +def xor_combine(rows, coefficients): + require(type(coefficients) is int and coefficients >= 0 and coefficients.bit_length() <= len(rows), "Binary coefficient width") + result = 0 + while coefficients: + bit = coefficients & -coefficients + result ^= rows[bit.bit_length()-1] + coefficients ^= bit + return result + + +def rank(rows): + pivots = {} + for source in rows: + value = source + while value: + pivot = value.bit_length()-1 + if pivot not in pivots: + pivots[pivot] = value + break + value ^= pivots[pivot] + return len(pivots) + + +def kernels(rows): + # Lowest pivots, opposite to the predecessor's highest-pivot dependencies. + pivots, nullspace = {}, [] + for index, source in enumerate(rows): + value, coefficients = source, 1 << index + while value: + pivot = (value & -value).bit_length()-1 + if pivot not in pivots: + pivots[pivot] = (value, coefficients) + break + old, combination = pivots[pivot] + value ^= old + coefficients ^= combination + if value == 0: + nullspace.append(coefficients) + require(len(nullspace) + rank(rows) == len(rows), "Complete eligible kernel dimension") + require(rank(nullspace) == len(nullspace), "Eligible kernel independence") + require(all(xor_combine(rows, c) == 0 for c in nullspace), "Eligible kernel defining equations") + return nullspace + + +def independent_basis(rows): + pivots = {} + for value in rows: + while value: + pivot = (value & -value).bit_length()-1 + if pivot not in pivots: + pivots[pivot] = value + break + value ^= pivots[pivot] + return list(pivots.values()) + + +def support(value): + result = [] + while value: + bit = value & -value + result.append(bit.bit_length()-1) + value ^= bit + return result + + +def dot(a, b): + return (a & b).bit_count() & 1 + + +def matrices(left, right, prefix, suffix): + inputs = [xor_combine(prefix, a) for a in left] + outputs = [xor_combine(suffix, b) for b in right] + boundary = [sum(dot(c, d) << j for j, d in enumerate(outputs)) for c in inputs] + internal = [sum(dot(a, b) << j for j, b in enumerate(right)) for a in left] + return inputs, outputs, boundary, internal + + +def validate_unit_pair(a, b, prefix, suffix, outside): + c, d = xor_combine(prefix, a), xor_combine(suffix, b) + require((c & outside) == (d & outside) == 0, "Full boundary support eligibility") + require(dot(a, b) == dot(c, d) == 1, "Simultaneous internal and boundary unit equations") + return c, d + + +def simultaneous_pair(left, right, prefix, suffix, slots, outside): + inputs, outputs, boundary, internal = matrices(left, right, prefix, suffix) + if not rank(boundary) or not rank(internal): + return None + ci = next(i for i, row in enumerate(boundary) if row) + di = next(i for i, row in enumerate(internal) if row) + if internal[ci]: + lc = 1 << ci + elif boundary[di]: + lc = 1 << di + else: + lc = (1 << ci) ^ (1 << di) + cfunctional = xor_combine(boundary, lc) + dfunctional = xor_combine(internal, lc) + require(cfunctional and dfunctional, "Simultaneous functional construction") + overlap = cfunctional & dfunctional + if overlap: + rc = overlap & -overlap + else: + rc = (cfunctional & -cfunctional) ^ (dfunctional & -dfunctional) + a, b = xor_combine(left, lc), xor_combine(right, rc) + c, d = validate_unit_pair(a, b, prefix, suffix, outside) + return {"a_roles": [slots[i] for i in support(a)], "b_roles": [slots[i] for i in support(b)], + "c_input_support": support(c), "d_output_support": support(d), + "internal_pairing": 1, "boundary_pairing": 1} + + +def bank_view(prefix, suffix, slots, outside): + p, s = [prefix[i] for i in slots], [suffix[i] for i in slots] + left, right = kernels([v & outside for v in p]), kernels([v & outside for v in s]) + inputs, outputs, boundary, internal = matrices(left, right, p, s) + require(all(v & outside == 0 for v in inputs+outputs), "Kernel images full support") + result = {"slots": slots, "left_kernel_dimension": len(left), "right_kernel_dimension": len(right), + "boundary_rank": rank(boundary), "internal_rank": rank(internal), + "left_kernel_role_supports": [[slots[i] for i in support(a)] for a in left], + "right_kernel_role_supports": [[slots[i] for i in support(b)] for b in right], + "eligible_input_supports": [support(v) for v in inputs], + "eligible_output_supports": [support(v) for v in outputs], + "boundary_matrix_rows": [support(v) for v in boundary], + "internal_matrix_rows": [support(v) for v in internal], + "simultaneous_unit_pair": simultaneous_pair(left, right, p, s, slots, outside)} + return result, left, right, p, s + + +def inherited_quotient(left, right, p, s, slots, member, outside): + position = slots.index(member) + pivot = 1 << position + if (p[position] & outside) or (s[position] & outside) or not dot(p[position], s[position]): + return {"available": False, "reason": "The literal singleton is not an eligible boundary-unit pivot."} + lzero = independent_basis([a ^ (pivot if a & pivot else 0) for a in left]) + rzero = independent_basis([b ^ (pivot if b & pivot else 0) for b in right]) + require(len(lzero)+1 == len(left) and len(rzero)+1 == len(right), "Inherited pivot eligible kernel decomposition") + # Clear the boundary pivot using actual row/column basis changes. Internal + # pairings are recomputed on these changed bases rather than assumed equal. + newleft = [a ^ (pivot if dot(xor_combine(p, a), s[position]) else 0) for a in lzero] + newright = [b ^ (pivot if dot(p[position], xor_combine(s, b)) else 0) for b in rzero] + _, _, oldboundary, _ = matrices(left, right, p, s) + inputs, outputs, boundary, internal = matrices(newleft, newright, p, s) + require(all(dot(c, s[position]) == 0 for c in inputs) and all(dot(p[position], d) == 0 for d in outputs), + "Inherited boundary pivot orthogonalization") + require(rank(boundary)+1 == rank(oldboundary), "Exact inherited boundary rank debit") + require(rank(newleft) == len(newleft) and rank(newright) == len(newright), "Inherited quotient basis independence") + return {"available": True, "pivot_role": member, "boundary_rank": rank(boundary), + "internal_rank_on_actual_changed_bases": rank(internal), + "boundary_matrix_rows": [support(v) for v in boundary], + "internal_matrix_rows": [support(v) for v in internal], + "simultaneous_unit_pair": simultaneous_pair(newleft, newright, p, s, slots, outside)} + + +def checkpoint(spec, word, spaces, edges, prefix, suffix, state): + member, edge = spec["field"], tuple(spec["edge"]) + require(type(member) is int and 222 <= member < len(state) and member not in word["owned"], "Public helper member") + require(len(edge) == 3 and all(type(v) is int for v in edge) and edge in edges, "Published edge membership") + source, target, paid_rank = edge + require(state[member] == source, "Literal member source frame") + entrance, exit_space = spaces[word["start"][member]], spaces[word["final"][member]] + require(len(exit_space) < len(spaces[target]) < len(entrance), "Strict intermediate target dimension") + require(contains(entrance, spaces[target]) and contains(spaces[target], exit_space), "Rational target compatibility") + members = [i for i in range(222, len(state)) if i not in word["owned"] + and spaces[word["start"][i]] == entrance and spaces[word["final"][i]] == exit_space] + slots = [i for i, frame in enumerate(state) if frame is not None and spaces[frame] == spaces[target]] + require(member in members and member not in slots and slots, "Member move into occupied different bank") + if "group_members" in spec: + require(members == spec["group_members"], "Frozen full group identification") + if "bank" in spec: + require(slots == spec["bank"], "Frozen entire occupied bank identification") + outside = ((1 << len(state))-1) ^ sum(1 << h for h in members) + base, _, _, _, _ = bank_view(prefix, suffix, slots, outside) + singleton, _, _, _, _ = bank_view(prefix, suffix, [member], outside) + augmented_slots = sorted(slots+[member]) + augmented, left, right, p, s = bank_view(prefix, suffix, augmented_slots, outside) + boundary_excess = augmented["boundary_rank"]-max(base["boundary_rank"], singleton["boundary_rank"]) + internal_excess = augmented["internal_rank"]-max(base["internal_rank"], singleton["internal_rank"]) + return {"cut_t": spec["cut_t"], "field": member, "edge": list(edge), "group_members": members, + "group_dimensions": [len(entrance), len(exit_space)], "target_dimension": len(spaces[target]), + "paid_edge_rank": paid_rank, "base": base, "singleton": singleton, "augmented": augmented, + "boundary_excess_over_both": boundary_excess, "internal_excess_over_both": internal_excess, + "inherited_pivot_quotient": inherited_quotient(left, right, p, s, augmented_slots, member, outside), + "qualification": "Necessary normalized pairing evidence only; no extra independent target, typed continuation or profit follows."} + + +def synthetic_controls(): + # Two projections each have rank1, while their joint bank has rank2. + # These are explicit synthetic algebra controls, not a G20 source witness. + prefix, suffix = [1, 2], [1, 2] + base = bank_view(prefix, suffix, [0], 0)[0] + single = bank_view(prefix, suffix, [1], 0)[0] + both = bank_view(prefix, suffix, [0, 1], 0)[0] + require(base["boundary_rank"] == single["boundary_rank"] == 1 and both["boundary_rank"] == 2, + "Synthetic genuine augmentation excess") + require(both["simultaneous_unit_pair"] is not None, "Synthetic simultaneous unit pair") + # Boundary and internal tests must both be applied: this has internal1, + # but disjoint images and hence boundary0. + no_boundary = bank_view([1], [2], [0], 0)[0] + require(no_boundary["boundary_rank"] == 0 and no_boundary["internal_rank"] == 1 + and no_boundary["simultaneous_unit_pair"] is None, "Synthetic internal-only rejection") + foreign = bank_view([1], [1], [0], 1)[0] + require(foreign["left_kernel_dimension"] == foreign["right_kernel_dimension"] == 0, + "Foreign-coordinate eligibility rejection") + return {"augmentation_ranks": [1, 1, 2], "internal_only_rejected": True, + "foreign_coordinate_rejected": True, "synthetic_not_source_evidence": True} + + +def compute(): + data = source_inputs() + spaces = frame_geometry(data["FRAMES.json"]) + edges = route_edges(data["PATHS.json"], spaces) + word = data["WORD.json.gz"] + require(CHECKPOINTS, "No frozen bounded checkpoints configured") + cuts = [spec["cut_t"] for spec in CHECKPOINTS] + prefix, suffix, states = traces(word, spaces, cuts) + views = [checkpoint(spec, word, spaces, edges, prefix[spec["cut_t"]], suffix[spec["cut_t"]], states[spec["cut_t"]]) + for spec in CHECKPOINTS] + candidate, control = views + require(candidate["boundary_excess_over_both"] > 0 and candidate["augmented"]["simultaneous_unit_pair"] is not None, + "Source-bound necessary excess and simultaneous unit witness") + require([control[k]["boundary_rank"] for k in ("base", "singleton", "augmented")] == [0, 1, 1] + and control["boundary_excess_over_both"] == 0 + and control["inherited_pivot_quotient"]["boundary_rank"] == 0, + "Opening inherited-only positive is not excess") + # Removing the transported member from the actual right witness must fail + # the same complete-support guard used to certify the unmodified pair. + slots = candidate["augmented"]["slots"] + pair = candidate["augmented"]["simultaneous_unit_pair"] + a = sum(1 << slots.index(i) for i in pair["a_roles"]) + b = sum(1 << slots.index(i) for i in pair["b_roles"]) + require(candidate["field"] in pair["b_roles"], "Actual witness uses transported member") + outside = ((1 << len(word["start"]))-1) ^ sum(1 << h for h in candidate["group_members"]) + bad_b = b ^ (1 << slots.index(candidate["field"])) + p = [prefix[candidate["cut_t"]][i] for i in slots] + s = [suffix[candidate["cut_t"]][i] for i in slots] + foreign_outputs = support(xor_combine(s, bad_b) & outside) + require(foreign_outputs, "Omitted member has concrete foreign output support") + rejection = None + try: + validate_unit_pair(a, bad_b, p, s, outside) + except ValueError as exc: + rejection = str(exc) + require(rejection == "Full boundary support eligibility", "Omitted-member witness control must reject") + return {"schema_version": 1, "status": "PASS_BOUNDED_NECESSARY_PAIRING_CHECKPOINTS", + "source_sha256": {name: pins[0] for name, pins in PINS.items()}, + "source_git_blobs": {name: pins[1] for name, pins in PINS.items()}, + "cut_convention": "cut_t is the number of literal source records already applied; prefix[:t],suffix[t:]", + "normalized_convention": "All685 entrance coordinates, including dirty owned coordinates, start as independent formal variables; ERASE is an owned projection, INIT requires a zero row, and queries are normalized identity maps.", + "checkpoints": views, "controls": synthetic_controls(), + "actual_witness_control": {"mutation": "Remove transported member323 from b's role support", + "observed_error": rejection, "foreign_output_support": foreign_outputs}, + "limits": ["This is a bounded direct-cut oracle, not an independent complete-census exclusion.", + "Published edges and frame compatibility are exact rational geometry inQ^8; normalized scalar pairing is overF2.", + "A positive excess or simultaneous unit pair is only a necessary algebraic gate; no extra productive target or profitable split is certified.", + "No retargeted chronological continuation, native phase/all columns, physical erasure, complete paid/target invoice, ordinary admission or selected frontier change is supplied."]} + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--emit", action="store_true") + args = parser.parse_args() + result = compute() + if args.emit: + print(canonical(result)) + else: + path = ROOT / "ORACLE.json" + require(path.is_file(), "Retained receipt ORACLE.json required") + require(canonical(decode(path.read_bytes())) == canonical(result), "Retained receipt mismatch") + print("PASS independent bounded G20 pairing receipt") + + +if __name__ == "__main__": + try: + main() + except (ValueError, KeyError, TypeError, OSError) as exc: + print("FAIL: " + str(exc), file=sys.stderr) + sys.exit(1) diff --git a/research/g20-member-bank-cache/frozen/sources/FRAMES.json b/research/g20-member-bank-cache/frozen/sources/FRAMES.json new file mode 100644 index 0000000000..9edf8d95b4 --- /dev/null +++ b/research/g20-member-bank-cache/frozen/sources/FRAMES.json @@ -0,0 +1,56126 @@ +{ + "frames": { + "0": { + "A": [ + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + 0, + 1, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + 0, + 0, + 1, + 0, + 0, + 0, + 0 + ], + [ + 0, + 0, + 0, + 0, + 1, + 0, + 0, + 0 + ], + [ + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 0 + ], + [ + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0 + ], + [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1 + ] + ], + "B": [], + "dim": 0 + }, + "1": { + "A": [], + "B": [ + [ + 2, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + 2, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + 0, + 2, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + 0, + 0, + 2, + 0, + 0, + 0, + 0 + ], + [ + 0, + 0, + 0, + 0, + 2, + 0, + 0, + 0 + ], + [ + 0, + 0, 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b/research/g20-member-bank-cache/frozen/sources/NOTICE.md new file mode 100644 index 0000000000..accbc28384 --- /dev/null +++ b/research/g20-member-bank-cache/frozen/sources/NOTICE.md @@ -0,0 +1,7 @@ +# Attribution + +Dugongue PR5665 supplies the causal deferred-input theorem, nine G20 cut rows and informal ordinary proposal. The exact proposal files are retained under proposal/. Ali Romman PR5667 supplies the completed predecessor, strict-margin theorem and adapted native, global, ordinary and separate checking code under prior/. PR5662 audits Dugongue PR5657 source refinements and supplies the frame-506 matcher. PR5653 and Dugongue PR5629/5639 supply the prior retirements and snapshots. + +Retain ai-nanachi PR5512; Ali Romman PR5421; DreamingOfClouds PR589 and eumemic PR555; Cinna Davis's native, ROW, controller, cover and ordinary interfaces; rohanarun PR185/199/204; zxv, Jacob Alan Sussman and all cumulative compiler, precision and fixed-tape contributors. Every frozen source notice stays unchanged. INPUTS.json and SOURCES.json bind consumed bytes to exact upstream objects. + +New emitted integration, complete first-read census, separate census check, full replay and documentation: Ali Romman with substantial OpenAI Codex assistance. No independent human review or literature priority claim is made. 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literal 0 HcmV?d00001 diff --git a/research/g20-member-bank-cache/frozen/sources/gap-PROOF.md b/research/g20-member-bank-cache/frozen/sources/gap-PROOF.md new file mode 100644 index 0000000000..26f776a79a --- /dev/null +++ b/research/g20-member-bank-cache/frozen/sources/gap-PROOF.md @@ -0,0 +1,85 @@ +# A frame conversion and its inverse do not both emit + +## Contract + +The word is Ali Romman's PR #5708 scalar program, +`research/g20-conjugation-admission/WORD.json.gz`, together with that +package's `PATHS.json` and frame table. A published route is one triple +`(u, v, r)` in the route table. The cut algebra is the one in Nick Petalas's +free-carrier certificate: prefix rows and suffix columns over `F_2`, a +carrier bank of fields that share a frame shape, and the boundary pairing +of the eligible kernels outside one helper group. Queries change the frame +and do not change those normalized rows. This note does not rerun the +common-frame census. It asks whether one published conversion and the +inverse conversion can create a nonzero boundary pairing. + +## No inverse route + +The route table has 2369 edges. On every edge the destination dimension is +strictly smaller than the source dimension, and the recorded rank equals +that difference. Frame 1 is the only dimension-8 frame, and no edge enters +it. An inverse edge would raise dimension or repeat an endpoint pair. None +exists. A conversion followed by the inverse conversion therefore does not +emit. + +## The opening schedule still needs frame 1 + +Helper 222 is one of the 413 public members of the large endpoint group. +It starts at frame 1 and is not an owned field. Its first six scalar +records, at event indices 5638 through 5643, are `ADD`s whose declared +frame is 1. The cut traversal accepts an `ADD` only when both endpoints +already occupy that frame. Because no route returns to frame 1, any +earlier published exit leaves those `ADD`s ill-typed. + +## One published exit does open a singleton channel + +At the opening cut the prefix is the identity. For every one of the 413 +public helpers, the suffix column is supported inside the group and meets +that helper's own coordinate. The one-field carrier therefore has left +rank 1, right rank 1, boundary rank 1 and internal rank 1. Both necessary +scalar equations `a b = 1` and `c d = 1` hold for that singleton. + +Frame 1 has 189 published edges into frame shapes that are empty at the +opening cut and lie strictly between the group's entrance and exit +dimensions: 9 of rank 1 and 180 of rank 2. `(1, 517, 1)` is one rank-1 +edge. Moving helper 222 along that edge creates the singleton channel +above. The same pairing occurs for every other +public helper and every other empty compatible exit. The move is not a +typed continuation: the helper never returns to frame 1, so the six +opening `ADD`s fail. + +## Non-member exits do not open a channel + +A field outside a helper group never has an odd singleton boundary +pairing at any of the 14795 cuts. An exit into an empty shape is that +singleton case, so it stays rank 0. An exit into an occupied compatible +shape was passed to the same pairing routine whenever the new row could +enlarge either kernel. That span filter admitted 2650155 pairings. Every +boundary rank stayed 0. No published one-edge move of a non-member +exposes a boundary channel. + +## The detector is not blind + +After event 7407, field 208 occupies frame 622. The bank of frame 509 +has 11 other fields, boundary rank 0 and right kernel 0. Adding field 208 +raises the boundary rank to 1 and the internal rank to 1. The route table +has no edge `622 → 509`, so the census does not count this bank. The same +pairing routine records the hit. A route-legal channel would have been +counted. + +## Invoice + +There is no route-legal pair of queries, so there is no two-query +paid/target delta. The route moment used for these edges is +`Σ_r n_r r^t`. One rank-1 query contributes `1^t = 1` and does not change +a normalized target row. That increment is not an invoice of this word: +the following frame-1 `ADD`s are ill-typed. Selected κ stays +`781451/250000000`. The five framework assumptions remain. This is not a +supplier admission or a multiplication theorem. + +## Credit + +The word, the route table and the different-physical-role question are +Ali Romman's PR #5679 and PR #5708. The common-frame obstruction and the +cut algebra are Nick Petalas's. Gaussian elimination and rank-nullity are +classical. The route census and the opening-schedule obstruction are new. diff --git a/research/g20-member-bank-cache/frozen/sources/gap-source.py b/research/g20-member-bank-cache/frozen/sources/gap-source.py new file mode 100644 index 0000000000..93bf7baf7c --- /dev/null +++ b/research/g20-member-bank-cache/frozen/sources/gap-source.py @@ -0,0 +1,443 @@ +#!/usr/bin/env python3 +"""Published G20 frame routes have no inverse, and non-member moves stay unpaired. + +The cut algebra is Nick Petalas's free-carrier checker for Ali Romman's +PR5708 word. This file does not import that package. Apache-2.0. +""" +from collections import Counter, defaultdict +import gzip +import hashlib +import itertools +import json +from pathlib import Path + +PACKAGE = Path(__file__).resolve().parent +ROOT = PACKAGE.parents[1] +WORD = "research/g20-conjugation-admission/WORD.json.gz" +PATHS = "research/g20-conjugation-admission/PATHS.json" +FRAMES = ("research/g20-conjugation-admission/prior/prior/prior/source/" + "vendor/g20/inputs/FRAMES.json") +HELPER_BEGIN = 222 +WITNESS_HELPER = 222 +WITNESS_EDGE = (1, 517, 1) +OFFROUTE_CUT = 7407 +OFFROUTE_FIELD = 208 +OFFROUTE_FRAME = 509 + + +def require(ok, message): + if not ok: + raise ValueError(message) + + +def dependencies(rows): + basis, result = {}, [] + width = max((row.bit_length() for row in rows), default=0) + for i, source in enumerate(rows): + row, coefficients = source, 1 << i + for _ in range(width + 1): + if not row: + result.append(coefficients) + break + pivot = row.bit_length() - 1 + if pivot not in basis: + basis[pivot] = row, coefficients + break + old, combination = basis[pivot] + row ^= old + coefficients ^= combination + else: + raise ValueError("dependency elimination bound") + return result + + +def rank_low(rows): + basis = {} + width = max((row.bit_length() for row in rows), default=0) + for source in rows: + row = source + for _ in range(width + 1): + if not row: + break + pivot = (row & -row).bit_length() - 1 + if pivot not in basis: + basis[pivot] = row + break + row ^= basis[pivot] + else: + raise ValueError("rank elimination bound") + return len(basis) + + +def combine(rows, coefficients): + value = 0 + require(coefficients.bit_length() <= len(rows), "coefficient width") + for i, row in enumerate(rows): + if coefficients >> i & 1: + value ^= row + return value + + +def eligible(rows, outside): + masked = [row & outside for row in rows] + kernel = dependencies(masked) + require(len(kernel) == len(rows) - rank_low(masked), "kernel dimension") + require(rank_low(kernel) == len(kernel), "kernel independence") + require(all(combine(masked, item) == 0 for item in kernel), "kernel equations") + return kernel, [combine(rows, item) for item in kernel] + + +def pairings(prefix, suffix, outside): + left, inputs = eligible(prefix, outside) + right, outputs = eligible(suffix, outside) + boundary = [sum(((one & two).bit_count() & 1) << j + for j, two in enumerate(outputs)) for one in inputs] + internal = [sum(((one & two).bit_count() & 1) << j + for j, two in enumerate(right)) for one in left] + return len(left), len(right), rank_low(boundary), rank_low(internal) + + +def frame_shapes(frames): + from fractions import Fraction + + def rows_of(entry): + basis = {} + for source in entry["B"]: + row = list(map(Fraction, source)) + for pivot in sorted(basis): + factor = row[pivot] + row = [x - factor * y for x, y in zip(row, basis[pivot])] + pivot = next((i for i, x in enumerate(row) if x), None) + if pivot is None: + continue + factor = row[pivot] + row = [x / factor for x in row] + for old in tuple(basis): + factor = basis[old][pivot] + basis[old] = [x - factor * y for x, y in zip(basis[old], row)] + basis[pivot] = row + return tuple(tuple(row) for _, row in sorted(basis.items())) + + spaces = {int(i): rows_of(entry) for i, entry in frames.items()} + shapes = sorted(set(spaces.values())) + labels = {i: shapes.index(space) for i, space in spaces.items()} + labels[None] = None + return labels, shapes + + +def group_contract(word, labels, shapes): + groups = defaultdict(set) + owned = set(word["owned"]) + for helper in range(HELPER_BEGIN, len(word["start"])): + if helper not in owned: + key = labels[word["start"][helper]], labels[word["final"][helper]] + groups[key].add(helper) + compatible, masks = defaultdict(list), {} + full = (1 << len(word["start"])) - 1 + for group, members in groups.items(): + entrance, exit_frame = group + masks[group] = full ^ sum(1 << helper for helper in members) + for index, shape in enumerate(shapes): + if not len(shapes[exit_frame]) < len(shape) < len(shapes[entrance]): + continue + if frame_contains(shapes[entrance], shape) and frame_contains(shape, shapes[exit_frame]): + compatible[index].append(group) + return groups, compatible, masks + + +def frame_contains(outer, inner): + from fractions import Fraction + basis = {} + for source in list(outer) + list(inner): + row = list(map(Fraction, source)) + for pivot in sorted(basis): + factor = row[pivot] + row = [x - factor * y for x, y in zip(row, basis[pivot])] + pivot = next((i for i, value in enumerate(row) if value), None) + if pivot is None: + continue + factor = row[pivot] + row = [value / factor for value in row] + for old in tuple(basis): + factor = basis[old][pivot] + basis[old] = [x - factor * y for x, y in zip(basis[old], row)] + basis[pivot] = row + return tuple(tuple(row) for _, row in sorted(basis.items())) == outer + + +def basis_of(rows): + basis = {} + for source in rows: + row, guard = source, 0 + while row: + pivot = row.bit_length() - 1 + if pivot not in basis: + basis[pivot] = row + break + row ^= basis[pivot] + guard += 1 + require(guard <= 800, "elimination bound") + return basis + + +def in_span(basis, vec): + for pivot, row in basis.items(): + if (vec >> pivot) & 1: + vec ^= row + return vec == 0 + + +def load(): + manifest = json.loads((PACKAGE / "SOURCES.json").read_text()) + expected = {row["path"]: row["sha256"] for row in manifest["files"] if row["usage"] == "input"} + require(set(expected) == {WORD, PATHS, FRAMES}, "three live inputs") + payloads = {} + for path in (WORD, PATHS, FRAMES): + raw = (ROOT / path).read_bytes() + require(hashlib.sha256(raw).hexdigest() == expected[path], "hash " + path) + decoded = gzip.decompress(raw) if path.endswith(".gz") else raw + payloads[path] = json.loads(decoded) + frames = payloads[FRAMES]["frames"] + edges = [tuple(edge) for bundle in payloads[PATHS].values() for edge in bundle] + return payloads[WORD], frames, edges + + +def suffix_start(events, count): + columns, erased = [1 << i for i in range(count)], {} + for index in reversed(range(len(events))): + event = events[index] + op, dest = event[:2] + if op == "ADD": + columns[event[2]] ^= columns[dest] + elif op == "ERASE": + erased[index] = columns[dest] + columns[dest] = 0 + return columns, erased + + +def apply_event(event, index, prefix, suffix, erased, state, labels, banks): + op, dest = event[:2] + before = labels[state[dest]] + if op == "ADD": + source = event[2] + require(state[dest] == state[source] == event[3], "ADD common frame") + prefix[dest] ^= prefix[source] + suffix[source] ^= suffix[dest] + return {labels[state[dest]]} + if op == "ERASE": + prefix[dest] = 0 + suffix[dest] = erased[index] + state[dest] = event[2] + elif op in ("Q", "ZERO_Q"): + require(state[dest] == event[2], "query entrance") + state[dest] = event[3] + elif op == "INIT": + state[dest] = event[2] + else: + raise ValueError("unknown event") + after = labels[state[dest]] + banks[before].remove(dest) + banks[after].add(dest) + return {before, after} + + +def kernel_controls(): + checked = 0 + for rows in itertools.product(range(8), repeat=3): + kernel = dependencies(rows) + exhaustive = {x for x in range(8) if combine(rows, x) == 0} + generated = {combine(kernel, x) for x in range(1 << len(kernel))} + require(generated == exhaustive, "exhaustive dependency control") + checked += 1 + require(pairings([1], [1], 0)[2] == 1, "unit boundary channel") + require(pairings([1], [2], 0)[2] == 0, "orthogonal images") + return checked + 2 + + +def route_facts(frames, edges): + dims = {int(i): entry["dim"] for i, entry in frames.items()} + require(len(edges) == 2369, "route count") + reverses = {(b, a) for a, b, _ in edges} + for src, dst, rank in edges: + require(dims[dst] < dims[src], "dimension drop") + require(rank == dims[src] - dims[dst], "rank equals dimension drop") + require((src, dst) not in reverses, "reverse edge") + require(sum(entry["dim"] == 8 for entry in frames.values()) == 1, "one dim-8 frame") + require(dims[1] == 8, "frame 1 is dim 8") + require(not any(dst == 1 for _, dst, _ in edges), "frame 1 has an entrance") + require(WITNESS_EDGE in edges, "witness edge published") + return dims + + +def opening_witness(word, labels, shapes, groups, compatible, masks, edges): + group = next(key for key, members in groups.items() if len(members) == 413) + mask, members = masks[group], groups[group] + require(WITNESS_HELPER in members, "witness helper is public") + require(word["start"][WITNESS_HELPER] == 1, "helper starts at frame 1") + prefix = [1 << i for i in range(len(word["start"]))] + suffix, _ = suffix_start(word["records"], len(word["start"])) + odd = [] + for helper in sorted(members): + row, column = prefix[helper], suffix[helper] + require((row & mask) == 0 and (column & mask) == 0, "helper support") + if (row & column).bit_count() & 1: + odd.append(helper) + require(odd == sorted(members), "every public helper has odd self-pairing") + require(pairings([prefix[WITNESS_HELPER]], [suffix[WITNESS_HELPER]], mask) == (1, 1, 1, 1), + "witness singleton channel") + occupied = Counter(labels[frame] for frame in word["start"] if frame is not None) + exits = [] + for src, dst, rank in edges: + if src != 1: + continue + shape = labels[dst] + if occupied[shape] == 0 and group in compatible[shape]: + exits.append((src, dst, rank)) + require(WITNESS_EDGE in exits, "witness exit is an empty compatible route") + require(min(rank for _src, _dst, rank in exits) == 1, "cheapest empty exit") + first = next(i for i, event in enumerate(word["records"]) + if event[1] == WITNESS_HELPER or (event[0] == "ADD" and event[2] == WITNESS_HELPER)) + require(first == 5638 and word["records"][first][:4] == ["ADD", 222, 98, 1], "frame-1 ADD") + require(all(event[0] == "ADD" and event[3] == 1 for event in word["records"][5638:5644]), + "six opening ADDs stay on frame 1") + ranks = Counter(rank for _src, _dst, rank in exits) + return {"public_helpers": len(members), "empty_compatible_exits": len(exits), + "empty_exit_ranks": dict(sorted(ranks.items())), + "witness_edge": list(WITNESS_EDGE), "first_add": first} + + +def scan(word, labels, shapes, groups, compatible, masks, edges): + count = len(word["start"]) + events = word["records"] + prefix = [1 << i for i in range(count)] + suffix, erased = suffix_start(events, count) + state = word["start"][:] + banks = defaultdict(set) + for index, frame in enumerate(state): + banks[labels[frame]].add(index) + adjacency = defaultdict(list) + for src, dst, rank in edges: + adjacency[src].append((dst, rank, labels[dst])) + members = {group: set(helpers) for group, helpers in groups.items()} + cache = {} + + def rebuild(shape): + if shape is None: + return + slots = banks.get(shape) + if not slots or shape not in compatible: + cache.pop(shape, None) + return + built = [] + for group in compatible[shape]: + mask = masks[group] + built.append((group, mask, + basis_of([prefix[i] & mask for i in slots]), + basis_of([suffix[i] & mask for i in slots]), + tuple(slots))) + cache[shape] = built + + for shape in list(banks): + rebuild(shape) + singleton_hits = 0 + published_hits = 0 + tested = 0 + offroute = None + + def parity(cut): + nonlocal singleton_hits + for field in range(count): + for group, mask in masks.items(): + if field in members[group]: + continue + row, column = prefix[field] & mask, suffix[field] & mask + if row == 0 and column == 0 and ((prefix[field] & suffix[field]).bit_count() & 1): + singleton_hits += 1 + + def published(field, cut): + nonlocal tested, published_hits + frame = state[field] + if frame is None: + return + row, column = prefix[field], suffix[field] + for _dst, _rank, shape in adjacency[frame]: + built = cache.get(shape) + if not built or field in banks[shape]: + continue + for group, mask, left, right, slots in built: + if field in members[group]: + continue + if not (in_span(left, row & mask) or in_span(right, column & mask)): + continue + tested += 1 + outcome = pairings([prefix[i] for i in slots] + [row], + [suffix[i] for i in slots] + [column], mask) + published_hits += int(outcome[2] > 0) + + def consider(cut): + parity(cut) + for field in range(count): + published(field, cut) + + consider(-1) + for index, event in enumerate(events): + dirty = apply_event(event, index, prefix, suffix, erased, state, labels, banks) + for shape in dirty: + rebuild(shape) + if index == OFFROUTE_CUT: + offroute = offroute_view(state, banks, prefix, suffix, labels, masks, groups) + retest = {event[1]} + if event[0] == "ADD": + retest.add(event[2]) + for field in range(count): + frame = state[field] + if frame is None: + continue + if any(shape in dirty for _dst, _rank, shape in adjacency[frame]): + retest.add(field) + parity(index) + for field in retest: + published(field, index) + require(state == word["final"], "final frames") + require(suffix == [1 << i for i in range(count)], "suffix closure") + require(singleton_hits == 0, "non-member singleton channel") + require(published_hits == 0, "published non-member channel") + require(offroute is not None, "off-route control ran") + return {"singleton_hits": singleton_hits, "published_hits": published_hits, + "span_admitted_pairings": tested, "offroute": offroute} + + +def offroute_view(state, banks, prefix, suffix, labels, masks, groups): + require(state[OFFROUTE_FIELD] == 622, "off-route field frame") + shape = labels[OFFROUTE_FRAME] + slots = tuple(sorted(banks[shape])) + require(OFFROUTE_FIELD not in slots and len(slots) == 11, "off-route bank") + group = next(key for key, members in groups.items() if len(members) == 413) + mask = masks[group] + base = pairings([prefix[i] for i in slots], [suffix[i] for i in slots], mask) + augmented = pairings([prefix[i] for i in slots] + [prefix[OFFROUTE_FIELD]], + [suffix[i] for i in slots] + [suffix[OFFROUTE_FIELD]], mask) + require(base[2] == 0 and augmented[2] == 1 and augmented[3] == 1, "off-route detector") + return {"field": OFFROUTE_FIELD, "src": 622, "dst": OFFROUTE_FRAME, + "base": list(base), "augmented": list(augmented)} + + +def main(): + word, frames, edges = load() + controls = kernel_controls() + dims = route_facts(frames, edges) + labels, shapes = frame_shapes(frames) + groups, compatible, masks = group_contract(word, labels, shapes) + opening = opening_witness(word, labels, shapes, groups, compatible, masks, edges) + census = scan(word, labels, shapes, groups, compatible, masks, edges) + require((622, 509) not in {(a, b) for a, b, _ in edges}, "off-route edge absent") + report = {"claim_type": "finite route obstruction with one off-route pairing witness", + "edges": len(edges), "frame_1_dimension": dims[1], + "opening": opening, "census": census, "controls": controls, + "round_trip_emits": False, "new_kappa": False} + print(json.dumps(report, sort_keys=True, indent=2)) + print("PASS_G20_FRAME_ROUND_TRIP_GAP") + + +if __name__ == "__main__": + main() diff --git a/research/g20-member-bank-cache/frozen/sources/prior-PROOF.md b/research/g20-member-bank-cache/frozen/sources/prior-PROOF.md new file mode 100644 index 0000000000..c6d2f2c762 --- /dev/null +++ b/research/g20-member-bank-cache/frozen/sources/prior-PROOF.md @@ -0,0 +1,139 @@ +# A free choice of carrier does not expose another G20 split + +## Contract and new claim + +Fix Ali Romman's PR5708 word, `WORD.json.gz`, at +`829d01fc031f7323ffcfa423fdfd1f24dcbe3190`. Its scalar normalized +coordinates, native frame induction and existing helper endpoints are cited +premises. This proof does not establish those source results again. + +A helper group G consists of all retained public helper roles with the same +entrance subspace U and exit subspace V. Fix an event cut and one entire bank +S of fields having the same physical frame F, where V is strictly contained +in F and F is strictly contained in U. Include every field in S, including +main fields and existing owned fields. No member of G need occur in S. +Binary changes of basis at the input, cut and output may use every eligible +coordinate. A split must preserve independence and restore every output +outside G. Adding paid frame changes, changing the scalar word, mixing +boundary groups with different endpoint frames and using address-dependent +coefficients are outside this contract. + +The new finite claim is that all 1,981 distinct eligible contexts with +`S intersect G` empty have zero boundary pairing. There are 46 such contexts +with two nonzero kernel spaces; 45 even have nonzero internal pairing. +Thus the failure is not merely the absence of a scalar pivot or the absence +of available kernel vectors. No free choice of an existing physical carrier +repairs the boundary pairing on this word. + +The executable also obtains zero boundary pairing in all 7,870 contexts, +including the helper-pivot domain reported in PR5708. Those old cases are +context for the expansion, not a separate contribution or supplier audit. + +## The necessary boundary pairing + +Use column states. Let A be the complete normalized prefix map from all +entrance fields to the cut, and let B be the suffix map from that cut to all +exit fields. The maps include the scalar effects of owned erasures. Queries +change physical frames and leave normalized coefficients unchanged under +the cited native contract. + +For a row a supported on S, eligibility means c = a A has no coordinates +outside G. For a column b supported on S, eligibility means d = B b has no +coordinates outside G. The full spaces of such a and b are kernels of the +restrictions of A and B to the complementary boundary coordinates. + +An independent one-coordinate split requires + + a b = 1 and c d = 1. + +The internal equation permits extraction and substitution in a cut basis. +The boundary equation is necessary even if the cut carrier and the boundary +helper pivot are different physical roles. To see this, write h for the +original helper inputs and z for the new independent successor input. +Extracting c h and substituting z along b changes the final helper vector to + + h + d (z - c h). + +This uses the cited identity normalized endpoint on the helper group. The +new combined output is + + (c h, (I - d c) h + d z). + +If c d = 0, the nonzero input pair (h,z) = (d,1) maps to zero. If d = 0, +then the successor input is itself lost. Either case contradicts independent +output jobs. Invertible boundary bases cannot repair this rank loss. +The equation c d = 1 follows for an independent split over F2. +For several simultaneously split coordinates the same argument requires an +invertible boundary pairing matrix; a zero matrix excludes every positive +number of channels. + +The zero-pairing conclusion is unchanged by extending scalars to any field +of characteristic two. The kernel spaces extend by scalar extension, and +the zero bilinear matrix remains zero. Over an extension field the required +one-channel pairing is nonzero and can be normalized to one; it is still +excluded here. + +## What the executable enumerates + +There are 685 fields, 14,794 events and 14,795 event cuts, including both +boundaries. Exact rational reduced row spaces identify 645 physical frame +classes. The retained helper endpoint groups have sizes 413, 1 and 1. +For each group, the checker lists every source frame strictly between its +two endpoints. It does not impose a bank-size or kernel-support cutoff. + +The backward sweep computes the suffix columns. For `ADD d,s`, it applies +`B[:,s] ^= B[:,d]`. For an erasure of d it stores B's old d column, then +sets that column to zero. In the forward sweep it removes one event from the +suffix: ADD is its own inverse, and an erasure restores the stored column. +Prefix rows advance by `A[d,:] ^= A[s,:]` or by setting an erased row to +zero. Frame transitions update the bank partition. At the final boundary +the suffix must be the identity and every frame must equal its declared exit. + +An ADD changes only its one common-frame bank. An erasure, initialization or +query changes only the old and new banks of its destination. Every initial +bank and every changed bank is checked. Other banks retain their exact prefix +rows, suffix columns and membership. Exact keys consisting of group, frame, +slots, prefix rows and suffix columns remove repeated contexts. They do not +merge distinct linear-algebra problems. + +For each context the checker computes bases L and R of the two eligible +kernel spaces. It verifies their defining equations and independence. +Opposite-pivot rank elimination separately checks completeness through +`dim kernel = |S| - rank(restriction)`. It then forms every entry + + C_ij = (L_i A) (B R_j). + +Every C is zero. This certifies the entire eligible spaces by bilinearity, +rather than a bounded-support search for a and b. The result excludes a +necessary equation; there is no delivery cost to optimistically set to zero. + +The output records every count and a deterministic digest of the context +summaries. The source hashes are checked before parsing. The generated +execution receipt separately binds the exact package bytes. + +## Controls and scope + +The checker compares the complete dependency space against literal exhaustive +enumeration for all 512 triples of three-bit rows. A two-role borrowed-carrier +example has a real channel in a bank containing no helper role and must be +accepted. Orthogonal-image, unit-channel and foreign-coordinate controls +separate the boundary and eligibility conditions. All checks use explicit +exceptions and remain enabled under optimized Python. + +This is a finite exact certificate plus a scoped algebraic obstruction. +It supplies neither a global BIT lower bound nor a complete multiplication +theorem. It adds no native word, target, paid saving or kappa. Source native, +compiler, precision, ownership, tape, outer-assembly and the five framework +assumptions remain outside this proof. Independent human and formal +proof-kernel review are unclaimed. + +## Credit + +This contribution was produced by Nick Petalas. Credit Ali Romman for the +PR5679 independent-split construction and its different-physical-role open +question, PR5708's exact final word and helper-pivot census, and PR5609's +prefix/suffix cut method on the older word. The source construction retains +Dugongue, ai-nanachi and the compact436, native, controller, helper, ordinary +and stock lineage cited in those packages. Gaussian elimination, rank-nullity +and bilinear base change are classical. No predecessor executable is imported +and no predecessor credit line is changed. New material is Apache-2.0. diff --git a/research/g20-member-bank-cache/frozen/sources/prior-source.py b/research/g20-member-bank-cache/frozen/sources/prior-source.py new file mode 100644 index 0000000000..13326f5900 --- /dev/null +++ b/research/g20-member-bank-cache/frozen/sources/prior-source.py @@ -0,0 +1,306 @@ +"""Exact expanded-domain G20 cut obstruction, produced by Nick Petalas. + +The cut contract is due to Ali Romman, PR5679/5708 and PR5609. +This standalone implementation imports no predecessor executable. Apache-2.0. +""" +from collections import Counter, defaultdict +from fractions import Fraction +import gzip +import hashlib +import itertools +import json +from pathlib import Path + +PACKAGE = Path(__file__).resolve().parent +ROOT = PACKAGE.parents[1] +WORD = "research/g20-conjugation-admission/WORD.json.gz" +FRAMES = "research/g20-conjugation-admission/prior/prior/prior/source/vendor/g20/inputs/FRAMES.json" +MAX_FIELDS = 700 +MAX_EVENTS = 20000 +MAX_CONTEXTS = 30000 + + +def require(ok, message): + if not ok: + raise ValueError(message) + + +def canonical(rows): + """Unique rational row space, at most sixteen rows and eight columns.""" + basis = {} + for source in rows: + row = list(map(Fraction, source)) + for pivot in sorted(basis): + factor = row[pivot] + row = [x - factor*y for x, y in zip(row, basis[pivot])] + pivot = next((i for i, x in enumerate(row) if x), None) + if pivot is None: + continue + factor = row[pivot] + row = [x / factor for x in row] + for old in tuple(basis): + factor = basis[old][pivot] + basis[old] = [x - factor*y for x, y in zip(basis[old], row)] + basis[pivot] = row + return tuple(tuple(row) for _, row in sorted(basis.items())) + + +def dependencies(rows): + """A basis of all binary row dependencies, retaining coefficients.""" + basis, result = {}, [] + width = max((row.bit_length() for row in rows), default=0) + for i, source in enumerate(rows): + row, coefficients = source, 1 << i + for _ in range(width + 1): + if not row: + result.append(coefficients) + break + pivot = row.bit_length() - 1 + if pivot not in basis: + basis[pivot] = row, coefficients + break + old, combination = basis[pivot] + row ^= old + coefficients ^= combination + else: + raise ValueError("dependency elimination bound") + return result + + +def rank_low(rows): + """Rank with the opposite pivot order and no dependency bookkeeping.""" + basis = {} + width = max((row.bit_length() for row in rows), default=0) + for source in rows: + row = source + for _ in range(width + 1): + if not row: + break + pivot = (row & -row).bit_length() - 1 + if pivot not in basis: + basis[pivot] = row + break + row ^= basis[pivot] + else: + raise ValueError("rank elimination bound") + return len(basis) + + +def combine(rows, coefficients): + value = 0 + require(coefficients.bit_length() <= len(rows), "coefficient width") + for i, row in enumerate(rows): + if coefficients >> i & 1: + value ^= row + return value + + +def eligible(rows, outside): + masked = [row & outside for row in rows] + kernel = dependencies(masked) + require(len(kernel) == len(rows) - rank_low(masked), "kernel dimension") + require(rank_low(kernel) == len(kernel), "kernel independence") + require(all(combine(masked, x) == 0 for x in kernel), "kernel equations") + return kernel, [combine(rows, x) for x in kernel] + + +def pairings(prefix, suffix, outside): + left, inputs = eligible(prefix, outside) + right, outputs = eligible(suffix, outside) + boundary = [sum(((c & d).bit_count() & 1) << j + for j, d in enumerate(outputs)) for c in inputs] + internal = [sum(((a & b).bit_count() & 1) << j + for j, b in enumerate(right)) for a in left] + return len(left), len(right), rank_low(boundary), rank_low(internal) + + +def geometry(frames): + require(1 <= len(frames) <= 2000, "frame inventory bound") + for entry in frames.values(): + require(0 <= entry["dim"] <= 8, "frame dimension bound") + require(len(entry["B"]) == entry["dim"], "frame row count") + require(all(len(row) == 8 for row in entry["B"]), "frame width") + spaces = {int(i): canonical(entry["B"]) for i, entry in frames.items()} + shapes = sorted(set(spaces.values())) + labels = {i: shapes.index(space) for i, space in spaces.items()} + labels[None] = None + return labels, shapes + + +def group_contract(word, labels, shapes, helper_begin): + groups = defaultdict(set) + owned = set(word["owned"]) + for h in range(helper_begin, len(word["start"])): + if h not in owned: + groups[labels[word["start"][h]], labels[word["final"][h]]].add(h) + compatible = defaultdict(list) + masks = {} + full = (1 << len(word["start"])) - 1 + for group, members in groups.items(): + entrance, exit_frame = group + masks[group] = full ^ sum(1 << h for h in members) + for f, shape in enumerate(shapes): + if not len(shapes[exit_frame]) < len(shape) < len(shapes[entrance]): + continue + if canonical(shapes[entrance] + shape) != shapes[entrance]: + continue + if canonical(shape + shapes[exit_frame]) == shape: + compatible[f].append(group) + return groups, compatible, masks + + +def suffix_start(events, n): + columns = [1 << i for i in range(n)] + erased = {} + for k in reversed(range(len(events))): + event = events[k] + op, d = event[:2] + if op == "ADD": + columns[event[2]] ^= columns[d] + elif op == "ERASE": + erased[k] = columns[d] + columns[d] = 0 + return columns, erased + + +def inspect_bank(f, cut, state, banks, prefix, suffix, contract, seen, counts, digest): + groups, compatible, masks = contract + if f not in compatible or not banks[f]: + return + slots = tuple(sorted(banks[f])) + aa, bb = tuple(prefix[i] for i in slots), tuple(suffix[i] for i in slots) + for group in compatible[f]: + key = group, f, slots, aa, bb + if key in seen: + continue + require(len(seen) < MAX_CONTEXTS, "context resource bound") + seen.add(key) + ldim, rdim, boundary_rank, internal_rank = pairings(aa, bb, masks[group]) + free_carrier = not (set(slots) & groups[group]) + counts["contexts"] += 1 + counts["without_helper_slot"] += int(free_carrier) + counts["both_kernels_nonzero"] += int(ldim > 0 and rdim > 0) + counts["boundary_nonzero"] += int(boundary_rank > 0) + counts["internal_nonzero"] += int(internal_rank > 0) + if free_carrier: + counts["new_both_kernels_nonzero"] += int(ldim > 0 and rdim > 0) + counts["new_boundary_nonzero"] += int(boundary_rank > 0) + counts["new_internal_nonzero"] += int(internal_rank > 0) + record = [cut, list(group), state[slots[0]], list(slots), + ldim, rdim, boundary_rank, internal_rank, free_carrier] + digest.update((json.dumps(record, separators=(",", ":")) + "\n").encode()) + + +def move(event, k, prefix, suffix, erased, state, labels, banks): + op, d = event[:2] + before = labels[state[d]] + touched = {before} + if op == "ADD": + source, frame = event[2:] + require(state[d] == state[source] == frame, "literal ADD common frame") + prefix[d] ^= prefix[source] + suffix[source] ^= suffix[d] + elif op in ("ERASE", "INIT", "Q", "ZERO_Q"): + if op == "ERASE": + prefix[d] = 0 + suffix[d] = erased[k] + if op in ("Q", "ZERO_Q"): + require(state[d] == event[2], "query entrance") + state[d] = event[3] + else: + state[d] = event[2] + banks[before].remove(d) + banks[labels[state[d]]].add(d) + touched.add(labels[state[d]]) + else: + raise ValueError("unknown event") + return touched + + +def scan(word, labels, shapes, helper_begin=222): + n, events = len(word["start"]), word["records"] + require(1 <= n <= MAX_FIELDS and len(events) <= MAX_EVENTS, "word bounds") + require(len(word["final"]) == n, "boundary lengths") + for event in events: + require(2 <= len(event) <= 5 and 0 <= event[1] < n, "event destination") + if event[0] == "ADD": + require(len(event) == 4 and 0 <= event[2] < n, "ADD source") + contract = group_contract(word, labels, shapes, helper_begin) + prefix = [1 << i for i in range(n)] + suffix, erased = suffix_start(events, n) + state = word["start"][:] + banks = defaultdict(set) + for i, frame in enumerate(state): + banks[labels[frame]].add(i) + counts, seen, digest = Counter(), set(), hashlib.sha256() + for f in sorted(f for f in banks if f is not None): + inspect_bank(f, -1, state, banks, prefix, suffix, contract, seen, counts, digest) + for k, event in enumerate(events): + touched = move(event, k, prefix, suffix, erased, state, labels, banks) + for f in sorted(f for f in touched if f is not None): + inspect_bank(f, k, state, banks, prefix, suffix, contract, seen, counts, digest) + require(state == word["final"], "cut traversal reaches declared frames") + require(suffix == [1 << i for i in range(n)], "suffix traversal closure") + return dict(counts), digest.hexdigest(), contract[0] + + +def controls(): + checked = 0 + for rows in itertools.product(range(8), repeat=3): + kernel = dependencies(rows) + exhaustive = [x for x in range(8) if combine(rows, x) == 0] + generated = {combine(kernel, x) for x in range(1 << len(kernel))} + require(generated == set(exhaustive), "exhaustive dependency control") + checked += 1 + # A genuine nonhelper carrier: swap an arbitrary helper into the borrowed + # role, cross the intermediate frame there, return and undo the swap. + shapes = [(), ((Fraction(1),) + (Fraction(0),)*7,), + tuple(tuple(Fraction(i == j) for j in range(8)) for i in range(8))] + labels = {0: 0, 1: 1, 2: 2, None: None} + swap = [["ADD", 0, 1, 2], ["ADD", 1, 0, 2], ["ADD", 0, 1, 2]] + word = {"start": [2, 2], "final": [0, 2], "owned": [1], + "records": swap + [["Q", 1, 2, 1, 7], ["Q", 1, 1, 2, 7]] + + swap + [["Q", 0, 2, 0, 8]]} + result, _, _ = scan(word, labels, shapes, 0) + require(result["new_boundary_nonzero"] == 1, "true outside-carrier accepted") + require(pairings([1], [2], 0)[2] == 0, "orthogonal nonzero images") + require(pairings([1], [1], 0)[2] == 1, "unit boundary channel") + require(pairings([1], [1], 1)[2] == 0, "foreign-coordinate exclusion") + return checked + 4 + + +def load_sources(): + manifest = json.loads((PACKAGE / "SOURCES.json").read_text()) + expected = {row["path"]: row["sha256"] for row in manifest["files"] + if row["usage"] == "input"} + require(set(expected) == {WORD, FRAMES}, "exact two-input boundary") + payloads = {} + for path in (WORD, FRAMES): + raw = (ROOT / path).read_bytes() + require(len(raw) <= 16 * 1024 * 1024, "input size bound") + require(hashlib.sha256(raw).hexdigest() == expected[path], "source hash " + path) + decoded = gzip.decompress(raw) if path.endswith(".gz") else raw + require(len(decoded) <= 16 * 1024 * 1024, "decoded input bound") + payloads[path] = json.loads(decoded) + return payloads[WORD], payloads[FRAMES]["frames"] + + +def main(): + word, frames = load_sources() + labels, shapes = geometry(frames) + count_controls = controls() + counts, digest, groups = scan(word, labels, shapes) + require(counts["boundary_nonzero"] == 0, "zero boundary pairing at every context") + report = {"claim_type": "finite exact certificate and scoped algebraic obstruction", + "fields": len(word["start"]), "events": len(word["records"]), + "all_cuts": len(word["records"]) + 1, + "frame_classes": len(shapes), + "helper_group_sizes": sorted(map(len, groups.values())), + "counts": counts, "controls": count_controls, + "context_digest": digest} + print(json.dumps(report, sort_keys=True, indent=2)) + print("PASS_G20_FREE_CARRIER_SPLIT_OBSTRUCTION") + + +if __name__ == "__main__": + main() diff --git a/research/g20-member-bank-cache/frozen/sources/source-README.md b/research/g20-member-bank-cache/frozen/sources/source-README.md new file mode 100644 index 0000000000..b1655b5913 --- /dev/null +++ b/research/g20-member-bank-cache/frozen/sources/source-README.md @@ -0,0 +1,92 @@ +# G20 scalar conjugation admission + +The complete changed caller admits conditional ordinary BIT saving +**0.003507719059749**, an increase of **0.000000308321340** over +[PR5679](https://github.com/CrocSwap/integer-mult-bounds/pull/5679). +This is a component bound. A whole multiplication kappa is not claimed. + +Two scalar conjugations change the paid profile by +`Pnew-Pold=36H1-72H2+36H3`, with `Tnew=Told`. Strict concavity gives a +positive saving for every exponent `0 0, "route rank/direction") + return n, shapes, label, groups, outside, compatible, sorted(edges) + + +def synthetic_controls(): + inherited = details([1, 2], [0, 2], 0) + inherited_single = details([2], [2], 0) + genuine = details([1, 0], [0, 1], 0) + foreign = details([4], [4], 4) + internal_only = details([1], [2], 0) + need(inherited["ranks"][2] == inherited_single["ranks"][2] == 1, "inherited singleton control") + need(genuine["ranks"][2] == 1 and details([0], [1], 0)["ranks"][2] == 0, "bank essential control") + witness = unit_pair(genuine["left"], genuine["right"], genuine["inputs"], genuine["outputs"]) + need(witness is not None and foreign["ranks"][:3] == [0, 0, 0], "eligibility control") + need(internal_only["ranks"][2:] == [0, 1], "internal is not boundary control") + return {"inherited_singleton": inherited["ranks"], "inherited_singleton_alone": inherited_single["ranks"], + "genuine_bank_excess": genuine["ranks"], "genuine_unit_pair": witness, + "foreign_support": foreign["ranks"], "internal_only": internal_only["ranks"], + "qualification": "Synthetic algebra fixtures are not source edits, typed continuations, native checks or invoices."} + + +def scan(word, prepared, diagnostic=None): + n, shapes, label, groups, outside, compatible, edges = prepared + events = word["records"] + prefix = [1 << i for i in range(n)] + suffix = [1 << i for i in range(n)] + erased = {} + for index in range(len(events)-1, -1, -1): + e = events[index] + need(type(e) is list and e and e[0] in ("ADD", "Q", "ZERO_Q", "ERASE", "INIT"), "event opcode") + op, d = e[:2] + need(type(d) is int and 0 <= d < n, "event destination") + if op == "ADD": + need(len(e) == 4 and type(e[2]) is int and 0 <= e[2] < n and type(e[3]) is int and e[3] in label, "ADD schema") + suffix[e[2]] ^= suffix[d] + elif op == "ERASE": + need(len(e) == 3 and (type(e[2]) is int or e[2] is None) and e[2] in label, "ERASE schema") + erased[index], suffix[d] = suffix[d], 0 + else: + need(len(e) == (5 if op in ("Q", "ZERO_Q") else 3), "query/INIT schema") + need(all(type(x) is int and x in label for x in e[2:4]), "event frame types") + if op in ("Q", "ZERO_Q"): + need(type(e[4]) is int and len(shapes[label[e[2]]])-len(shapes[label[e[3]]]) == e[4] > 0, "literal query rank") + state = word["start"][:] + banks = defaultdict(set) + for role, frame in enumerate(state): + banks[label[frame]].add(role) + member_group = {h: g for g, (_, members) in enumerate(groups) for h in members} + member_sources = defaultdict(set) + for h in member_group: + member_sources[state[h]].add(h) + outgoing, incoming = defaultdict(list), defaultdict(list) + for edge in edges: + outgoing[edge[0]].append(edge) + incoming[label[edge[1]]].append(edge) + active = {} + active_by_shape = defaultdict(set) + active_by_member = defaultdict(set) + bank_cache = {} + census, transitions = Counter(), Counter() + digest = hashlib.sha256() + hits = [] + evaluations = 0 + maximum_active = 0 + maximum_cache_bytes = 0 + + def bank_data(g, shape): + key = g, shape + if key not in bank_cache: + slots = tuple(sorted(banks[shape])) + rows, columns = [prefix[i] for i in slots], [suffix[i] for i in slots] + ld, rd = decomposition(rows, outside[g]), decomposition(columns, outside[g]) + boundary, internal = form(ld[2], rd[2]), form(ld[1], rd[1]) + rank = binary_rank(boundary) + need(rank == 0, "prior zero-bank boundary premise independently recounted") + input_sha = hashlib.sha256(canonical([slots, rows, columns]).encode()).hexdigest() + bank_cache[key] = (slots, rows, columns, ld, rd, rank, binary_rank(internal), input_sha) + return bank_cache[key] + + def flush(key, at): + old = active.pop(key, None) + if old is None: + return + first, summary = old + active_by_shape[summary[5]].remove(key) + active_by_member[key[0]].remove(key) + length = at-first + need(length > 0, "nonempty context interval") + g, h, src, dst, rank, shape, base4, singleton4, augmented4, bankhash, carrierhash = summary + category = (g, base4, singleton4, augmented4) + census[category] += length + digest.update((canonical([first, at-1, summary])+"\n").encode()) + transitions["context_intervals"] += 1 + + def inspect(h, edge, cut): + nonlocal evaluations, maximum_active + src, dst, paid_rank = edge + g, shape = member_group[h], label[dst] + key = h, src, dst + flush(key, cut) + if state[h] != src or shape not in compatible[g] or not banks[shape] or h in banks[shape]: + return + slots, rows, columns, ld, rd, base, baseinternal, bankhash = bank_data(g, shape) + left, ins = extend(ld, rows, prefix[h], outside[g]) + right, outs = extend(rd, columns, suffix[h], outside[g]) + boundary, internal = form(ins, outs), form(left, right) + augmented, irank = binary_rank(boundary), binary_rank(internal) + sl = int((prefix[h] & outside[g]) == 0) + sr = int((suffix[h] & outside[g]) == 0) + singleton = sl * sr * ((prefix[h] & suffix[h]).bit_count() & 1) + need(augmented <= base+2, "one-coordinate rank bound") + carrierhash = hashlib.sha256(canonical([prefix[h], suffix[h]]).encode()).hexdigest() + base4 = (len(ld[1]), len(rd[1]), base, baseinternal) + singleton4 = (sl, sr, singleton, sl*sr) + augmented4 = (len(left), len(right), augmented, irank) + summary = (g, h, src, dst, paid_rank, shape, base4, singleton4, augmented4, bankhash, carrierhash) + active[key] = cut, summary + active_by_shape[shape].add(key) + active_by_member[h].add(key) + evaluations += 1 + maximum_active = max(maximum_active, len(active)) + need(len(active) <= 160000, "bounded active context cache") + if augmented > max(base, singleton): + transitions["excess_evaluations"] += 1 + if not hits or not any(item["group"] == g for item in hits): + need(len(hits) < 3, "one retained complete witness per endpoint group") + item = {"cut_t": cut, "record_index_after": cut-1, "group": g, "member": h, "edge": list(edge), "bank": list(slots), + "base_ranks": [len(ld[1]), len(rd[1]), base, baseinternal], + "singleton_ranks": list(singleton4), + "augmented": {"left": list(map(str, left)), "right": list(map(str, right)), + "inputs": list(map(str, ins)), "outputs": list(map(str, outs)), + "boundary": list(map(str, boundary)), "internal": list(map(str, internal)), + "ranks": [len(left), len(right), augmented, irank]}, + "simultaneous_unit_pair": unit_pair(left, right, ins, outs), + "coordinate_order": list(slots)+[h]} + if singleton: + hc, hd, eh = prefix[h], suffix[h], 1 << len(slots) + qleft = [a ^ (eh if (c & hd).bit_count() & 1 else 0) for a, c in zip(left, ins)] + qright = [b ^ (eh if (hc & d).bit_count() & 1 else 0) for b, d in zip(right, outs)] + qins = [xor_sum(rows+[prefix[h]], a) for a in qleft] + qouts = [xor_sum(columns+[suffix[h]], b) for b in qright] + qboundary, qinternal = form(qins, qouts), form(qleft, qright) + need(binary_rank(qboundary) == augmented-1, "inherited unit-pivot quotient rank") + item["inherited_pivot_quotient"] = {"left": list(map(str, qleft)), "right": list(map(str, qright)), + "boundary": list(map(str, qboundary)), "internal": list(map(str, qinternal)), + "ranks": [binary_rank(qboundary), binary_rank(qinternal)], + "simultaneous_unit_pair": unit_pair(qleft, qright, qins, qouts)} + hits.append(item) + + def refresh(dirty_shapes, changed_members, cut): + nonlocal maximum_cache_bytes + for key in list(bank_cache): + if key[1] in dirty_shapes: + del bank_cache[key] + targets = set() + for shape in dirty_shapes: + if shape is None: + continue + for edge in incoming[shape]: + for h in member_sources[edge[0]]: + targets.add((h, edge)) + # Old active contexts must close even when the bank just emptied. + for key in active_by_shape[shape]: + targets.add((key[0], (key[1], key[2], len(shapes[label[key[1]]])-len(shapes[shape])))) + for h in changed_members: + for edge in outgoing[state[h]]: + targets.add((h, edge)) + for key in active_by_member[h]: + targets.add((h, (key[1], key[2], len(shapes[label[key[1]]])-len(shapes[label[key[2]]])))) + for h, edge in sorted(targets): + inspect(h, edge, cut) + # Current-bank decompositions only; no all-cut map or context snapshots. + cache_bytes = sum(sys.getsizeof(key)+sys.getsizeof(value)+ + sum(sys.getsizeof(x) for x in value[:3]) for key, value in bank_cache.items()) + maximum_cache_bytes = max(maximum_cache_bytes, cache_bytes) + need(cache_bytes <= 128*1024*1024, "bounded current-bank cache") + + refresh(set(banks), set(member_group), 0) + end = len(events) if diagnostic is None else min(diagnostic, len(events)) + for index, e in enumerate(events[:end]): + op, d = e[:2] + before_frame = state[d] + before = label[before_frame] + changed = {d} & member_group.keys() + if op == "ADD": + s = e[2] + need(state[d] == state[s] == e[3], "ADD literal common frame") + prefix[d] ^= prefix[s] + suffix[s] ^= suffix[d] + changed |= {s} & member_group.keys() + dirty = {before} + else: + if op == "ERASE": + prefix[d] = 0 + suffix[d] = erased[index] + state[d] = e[2] + elif op in ("Q", "ZERO_Q"): + need(state[d] == e[2], "query actual entrance frame") + state[d] = e[3] + elif op == "INIT": + state[d] = e[2] + after = label[state[d]] + banks[before].remove(d) + banks[after].add(d) + if d in member_group: + member_sources[before_frame].remove(d) + member_sources[state[d]].add(d) + dirty = {before, after} + refresh(dirty, changed, index+1) + for key in sorted(list(active)): + flush(key, end+1) + if diagnostic is None: + need(state == word["final"], "complete final frame array") + need(suffix == [1 << i for i in range(n)], "complete suffix identity closure") + return {"scope": "complete" if diagnostic is None else "bounded diagnostic only", + "cuts": end+1, "recomputed_contexts": evaluations, + "weighted_cut_edge_contexts": sum(census.values()), + "categories": [{"group": k[0], "base_ranks": k[1], "singleton_ranks": k[2], "augmented_ranks": k[3], + "cut_edge_contexts": v} for k, v in sorted(census.items())], + "interval_digest": digest.hexdigest(), "intervals": transitions["context_intervals"], + "excess_recomputed_contexts": transitions["excess_evaluations"], + "excess_cut_edge_contexts": sum(v for k, v in census.items() if k[3][2] > max(k[1][2], k[2][2])), + "peak_active_contexts": maximum_active, + "witnesses": hits} + + +def run(diagnostic=None): + word, frames, paths = read_inputs() + prepared = setup(word, frames, paths) + result = scan(word, prepared, diagnostic) + return {"schema_version": 1, "source_pins": PINS, + "group_members": [{"group": g, "entrance_shape": key[0], "exit_shape": key[1], + "members": list(members)} for g, (key, members) in enumerate(prepared[3])], + "census": result, "controls": synthetic_controls(), + "limits": ["Necessary scalar kernel/pairing gate only, including all inherited singleton comparisons.", + "No new typed continuation, native phase, independent target, restoration, price or kappa is certified.", + "The unchanged-bank zero boundary checks are predecessor coverage, not counted as a new result.", + "The published edge supplies only the normalized relocation premise; future scalar contacts remain unretargeted."]} + + +if __name__ == "__main__": + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--emit", action="store_true") + parser.add_argument("--diagnostic-events", type=int) + options = parser.parse_args() + need(options.diagnostic_events is None or 0 <= options.diagnostic_events <= 14794, "diagnostic event bound") + result = run(options.diagnostic_events) + payload = (json.dumps(result, sort_keys=True, indent=2, allow_nan=False)+"\n").encode() + if options.emit or options.diagnostic_events is not None: + sys.stdout.buffer.write(payload) + else: + retained = HERE/"RESULT.json" + need(retained.is_file(), "retained RESULT.json receipt required") + parsed = strict(retained.read_bytes()) + need(type(parsed) is dict and type(parsed.get("schema_version")) is int and parsed["schema_version"] == 1, + "typed RESULT receipt schema") + need(canonical(parsed) == canonical(result), "exact typed RESULT receipt") + print("PASS source-bound member-bank excess census and retained receipt") diff --git a/research/g20-member-bank-cache/frozen/verify_full_census.py b/research/g20-member-bank-cache/frozen/verify_full_census.py new file mode 100644 index 0000000000..0b22a661ad --- /dev/null +++ b/research/g20-member-bank-cache/frozen/verify_full_census.py @@ -0,0 +1,500 @@ +#!/usr/bin/env python3 +"""Independent complete G20 census using per-cut active histograms. + +Reuses only the authenticated, independently written frozen oracle kernel. +The primary census and predecessor executables are authenticated as data only. +No full-cut matrix archive is built. No price or typed-continuation claim is +inferred from the necessary normalized pairing conditions. +""" +import argparse +from collections import Counter, defaultdict +import hashlib +import json +from pathlib import Path +import sys + +ROOT = Path(__file__).resolve().parent +FROZEN = { + "SOURCE-PINS.json": "bb0272a4bc86649177ee229e6e6b9fc6ba37edc8cb240fda6cef4ade272f0b61", + "verify_excess.py": "519029e6783bff1845e97f81c7cc92377b64a179f46021274ba6104a6163055f", + "oracle_witness.py": "0a6c57687e5ef9e27db672793549f2253b0899b01ff179553bf52f8382071dee", + "RESULT.json": "c28cd4c7d375ea551a294d364f5b4fcf784b9bbf504dc836e46e53a0fee4f8e1", + "ORACLE.json": "b726e0c8e7350226a701c9eed4c53537e81d355a91e1b7904b37a5845e934248", + "PROOF.md": "381a9736e234b8726b7f8fb389cab72a6b97f7d6838bc2f99597c20cf9b17be3", + "sources/FRAMES.json": "0d99fc6b8f45c03dfba5252a03dd9e7fe23be3a7593dfe15368e34da6629a654", + "sources/NOTICE.md": "a4fdb5e2dfeeb216f3f58417891fc0a084c218d9a75228fb977e3cb82973be72", + "sources/PATHS.json": "f4dd58b78121040b1f054c0f7a626b25f6ef8d39f3de044d3456ea7dea8a6a5e", + "sources/WORD.json.gz": "8dd441fdb9c8923df06eb5ebfda37d03e4539f2305763e688d8c7025d196c4b1", + "sources/gap-PROOF.md": "121649b47271f45e18a1053ca5615c94e1cc81cc42136d8ccf3b2dca7d93f706", + "sources/gap-source.py": "91e201fd3c96267c878863abba794a16025070c98145ae598ee0ed7383c7f9c6", + "sources/prior-PROOF.md": "af88b44f1c61fb91d63ace7a2ece8d798bf6378864b2c4e1d44e01070fd485db", + "sources/prior-source.py": "a9aea8b108ebbeae8041770cefecfdabdfaf91b72ba7b5cfa2ff13408f1d16dd", + "sources/source-README.md": "e443b2fd7b988316953bfc7d21045690ea0d3ce9069ce1a06880f6ccfc7ec054", +} + + +def require(ok, message): + if not ok: + raise ValueError(message) + + +def canonical(value): + return json.dumps(value, sort_keys=True, separators=(",", ":"), allow_nan=False) + + +def load_kernel(): + payloads = {} + for name, sha in FROZEN.items(): + raw = (ROOT / name).read_bytes() + require(hashlib.sha256(raw).hexdigest() == sha, "Frozen scientific sha256 mismatch: " + name) + if name == "oracle_witness.py": + payloads[name] = raw + namespace = {"__name__": "authenticated_independent_witness_kernel", "__file__": str(ROOT / "oracle_witness.py")} + exec(compile(payloads["oracle_witness.py"], namespace["__file__"], "exec"), namespace) + return namespace + + +def span_solver(rows): + """Lowest-pivot row span with explicit source coefficients.""" + pivots = {} + for index, source in enumerate(rows): + value, coefficients = source, 1 << index + while value: + pivot = (value & -value).bit_length()-1 + if pivot not in pivots: + pivots[pivot] = (value, coefficients) + break + old, combination = pivots[pivot] + value ^= old + coefficients ^= combination + return pivots + + +def solve(pivots, value): + coefficients = 0 + while value: + pivot = (value & -value).bit_length()-1 + if pivot not in pivots: + return None + old, combination = pivots[pivot] + value ^= old + coefficients ^= combination + return coefficients + + +def format_profile(profile): + return {"base": list(profile[:4]), "singleton": list(profile[4:8]), + "augmented": list(profile[8:12]), + "inherited_pivot_quotient": None if profile[12] < 0 else list(profile[12:14])} + + +class Census: + def __init__(self, kernel): + self.k = kernel + data = kernel["source_inputs"]() + self.word = data["WORD.json.gz"] + self.spaces = kernel["frame_geometry"](data["FRAMES.json"]) + self.edges = kernel["route_edges"](data["PATHS.json"], self.spaces) + self.start, self.final, self.owned, self.events = kernel["word_contract"](self.word, self.spaces) + self.n = len(self.start) + self.full = (1 << self.n)-1 + representatives = {} + for frame, space in sorted(self.spaces.items()): + representatives.setdefault(space, frame) + self.shape = {frame: representatives[space] for frame, space in self.spaces.items()} + self.shape[None] = None + grouped = defaultdict(list) + for role in range(222, self.n): + if role not in self.owned: + grouped[(self.spaces[self.start[role]], self.spaces[self.final[role]])].append(role) + self.groups = sorted(grouped.values(), key=lambda members: tuple(members)) + self.gid = {role: g for g, members in enumerate(self.groups) for role in members} + require(sum(map(len, self.groups)) == 415, "Complete public helper domain") + self.outside = {g: self.full ^ sum(1 << h for h in members) for g, members in enumerate(self.groups)} + self.legal = defaultdict(lambda: defaultdict(dict)) + self.incoming = defaultdict(list) + for g, members in enumerate(self.groups): + entrance, exit_space = self.spaces[self.start[members[0]]], self.spaces[self.final[members[0]]] + for source, target, rank in sorted(self.edges): + middle = self.spaces[target] + if len(exit_space) < len(middle) < len(entrance) and kernel["contains"](entrance, middle) and kernel["contains"](middle, exit_space): + require(target not in self.legal[g][source], "Unique literal source/target edge") + self.legal[g][source][target] = rank + self.incoming[self.shape[target]].append((g, source, target, rank)) + self.rows = [1 << i for i in range(self.n)] + self.columns = [1 << i for i in range(self.n)] + self.erased = {} + for index in reversed(range(len(self.events))): + event = self.events[index] + op, dest = event[:2] + if op == "ADD": + self.columns[event[2]] ^= self.columns[dest] + elif op == "ERASE": + self.erased[index] = self.columns[dest] + self.columns[dest] = 0 + self.state = self.start[:] + self.banks = defaultdict(set) + for role, frame in enumerate(self.state): + if frame is not None: + self.banks[self.shape[frame]].add(role) + self.members_at = defaultdict(lambda: defaultdict(set)) + for h, g in self.gid.items(): + self.members_at[g][self.state[h]].add(h) + # Geometry-only source-frame multiplicities and occupied outgoing degree + # provide an independent count of the domain at every cut. + self.degree = defaultdict(int) + for shape, incoming in self.incoming.items(): + if self.banks[shape]: + for g, source, _target, _rank in incoming: + self.degree[g, source] += 1 + self.base_cache = {} + self.active = {} + self.keys_by_shape = defaultdict(set) + self.keys_by_member = defaultdict(set) + self.histogram = Counter() + self.positive = Counter() + self.weighted = Counter() + self.weighted_positive = Counter() + self.first_positive = {} + self.coverage = hashlib.sha256() + self.histogram_digest = hashlib.sha256() + self.total_domain = 0 + self.peak_contexts = 0 + self.context_evaluations = 0 + self.base_evaluations = 0 + self.cut_count = 0 + self.direct_cuts = sorted({0, len(self.events), 7670} | {t for i, e in enumerate(self.events) if e[0] == "ERASE" for t in (i, i+1)}) + self.reference_prefix, self.reference_suffix, self.reference_headers = kernel["traces"](self.word, self.spaces, self.direct_cuts) + + def base(self, g, shape): + key = (g, shape) + if key in self.base_cache: + return self.base_cache[key] + self.base_evaluations += 1 + slots = sorted(self.banks[shape]) + p, s = [self.rows[h] for h in slots], [self.columns[h] for h in slots] + mask = self.outside[g] + pm, sm = [v & mask for v in p], [v & mask for v in s] + left, right = self.k["kernels"](pm), self.k["kernels"](sm) + inputs, outputs, boundary, internal = self.k["matrices"](left, right, p, s) + base = {"slots": slots, "p": p, "s": s, "left": left, "right": right, + "inputs": inputs, "outputs": outputs, "C": boundary, "D": internal, + "C_rank": self.k["rank"](boundary), "D_rank": self.k["rank"](internal), + "p_solver": span_solver(pm), "s_solver": span_solver(sm), "memo": {}} + require(len(base["p_solver"])+len(left) == len(slots) and len(base["s_solver"])+len(right) == len(slots), "Independent bank span rank") + self.base_cache[key] = base + return base + + def extension_profile(self, g, shape, h): + base = self.base(g, shape) + p, s, mask = self.rows[h], self.columns[h], self.outside[g] + memo_key = (p, s) + if memo_key in base["memo"]: + return base["memo"][memo_key] + self.context_evaluations += 1 + pm, sm = p & mask, s & mask + lp, rp = solve(base["p_solver"], pm), solve(base["s_solver"], sm) + has_left, has_right = lp is not None, rp is not None + combine, dot, rank = self.k["xor_combine"], self.k["dot"], self.k["rank"] + c = p ^ combine(base["p"], lp) if has_left else 0 + d = s ^ combine(base["s"], rp) if has_right else 0 + require(not (c & mask) and not (d & mask), "Complete augmented image support") + lcount, rcount = len(base["left"]), len(base["right"]) + boundary = list(base["C"]) + internal = list(base["D"]) + if has_right: + for i in range(lcount): + boundary[i] |= dot(base["inputs"][i], d) << rcount + internal[i] |= dot(base["left"][i], rp) << rcount + if has_left: + crow = sum(dot(c, v) << j for j, v in enumerate(base["outputs"])) + irow = sum(dot(lp, v) << j for j, v in enumerate(base["right"])) + if has_right: + crow |= dot(c, d) << rcount + irow |= (dot(lp, rp) ^ 1) << rcount + boundary.append(crow) + internal.append(irow) + cl, cr = int(pm == 0), int(sm == 0) + singleton_C = dot(p, s) if cl and cr else 0 + singleton_D = int(bool(cl and cr)) + quotient_C = quotient_D = -1 + if singleton_C: + # The selected extension vectors are e_h because solve(0)=0. + # Thus clearing the singleton boundary pivot is exactly a rank-one + # Schur update of BOTH actual forms; no internal identity is assumed. + cross_left = [dot(v, s) for v in base["inputs"]] + cross_right = sum(dot(p, v) << j for j, v in enumerate(base["outputs"])) + qc = [v ^ (cross_right if cross_left[i] else 0) for i, v in enumerate(base["C"])] + qd = [v ^ (cross_right if cross_left[i] else 0) for i, v in enumerate(base["D"])] + quotient_C, quotient_D = rank(qc), rank(qd) + require(quotient_C+1 == rank(boundary), "Inherited singleton boundary debit") + profile = (lcount, rcount, base["C_rank"], base["D_rank"], + cl, cr, singleton_C, singleton_D, + lcount+int(has_left), rcount+int(has_right), rank(boundary), rank(internal), quotient_C, quotient_D) + base["memo"][memo_key] = profile + return profile + + def evaluate(self, key): + g, h, target = key + source = self.state[h] + rank = self.legal[g].get(source, {}).get(target) + shape = self.shape[target] + if rank is None or not self.banks[shape] or h in self.banks[shape]: + return None + return self.extension_profile(g, shape, h), (source, target, rank) + + @staticmethod + def excess(profile): + return profile[10] > max(profile[2], profile[6]) + + def positive_key(self, g, edge, profile): + return (g,) + edge + profile + + def replace(self, key, t): + g, h, target = key + shape = self.shape[target] + old = self.active.pop(key, None) + if old is not None: + profile, edge = old + self.histogram[g, profile] -= 1 + if not self.histogram[g, profile]: + del self.histogram[g, profile] + if self.excess(profile): + category = self.positive_key(g, edge, profile) + self.positive[category] -= 1 + if not self.positive[category]: + del self.positive[category] + self.keys_by_shape[shape].discard(key) + self.keys_by_member[h].discard(key) + current = self.evaluate(key) + if current is None: + return + profile, edge = current + self.active[key] = current + self.histogram[g, profile] += 1 + self.keys_by_shape[shape].add(key) + self.keys_by_member[h].add(key) + if self.excess(profile): + category = self.positive_key(g, edge, profile) + self.positive[category] += 1 + if category not in self.first_positive: + self.first_positive[category] = {"cut_t": t, "field": h, "bank": sorted(self.banks[shape])} + + def keys_for_shape(self, shape): + for g, source, target, _rank in self.incoming[shape]: + for h in self.members_at[g].get(source, ()): + yield g, h, target + + def keys_for_member(self, h): + g = self.gid[h] + for target in self.legal[g].get(self.state[h], {}): + if self.banks[self.shape[target]]: + yield g, h, target + + def weight_cut(self, t): + if t in self.reference_prefix: + require(self.rows == self.reference_prefix[t] and self.columns == self.reference_suffix[t] + and self.state == self.reference_headers[t], "Direct full-map/header checkpoint mismatch at cut" + str(t)) + geometric_count = sum(len(members)*self.degree[g, source] + for g, by_source in self.members_at.items() + for source, members in by_source.items() if members) + active_count = sum(self.histogram.values()) + require(active_count == len(self.active) == geometric_count, "Per-cut independent geometry/domain coverage") + require(all(count > 0 for count in self.histogram.values()) and all(count > 0 for count in self.positive.values()), "Positive active histogram counts") + self.total_domain += geometric_count + self.peak_contexts = max(self.peak_contexts, active_count) + self.weighted.update(self.histogram) + self.weighted_positive.update(self.positive) + self.coverage.update((str(t)+":"+str(geometric_count)+"\n").encode()) + self.histogram_digest.update((canonical([t, [[g, list(p), n] for (g, p), n in sorted(self.histogram.items())]])+"\n").encode()) + self.cut_count += 1 + + def run(self): + initial_keys = set() + for shape, bank in self.banks.items(): + if bank: + initial_keys.update(self.keys_for_shape(shape)) + for key in sorted(initial_keys): + self.replace(key, 0) + self.weight_cut(0) + for index, event in enumerate(self.events): + op, dest = event[:2] + touched = {dest} + if op == "ADD": + touched.add(event[2]) + dirty_shapes = {self.shape[self.state[h]] for h in touched} - {None} + affected = set() + for shape in dirty_shapes: + affected.update(self.keys_by_shape[shape]) + changed_members = touched & self.gid.keys() + for h in changed_members: + affected.update(self.keys_by_member[h]) + old_occupied = {shape: bool(self.banks[shape]) for shape in dirty_shapes} + oldframe = self.state[dest] + if op == "ADD": + source, frame = event[2:] + require(self.state[dest] == self.state[source] == frame, "Streamed ADD exact common frame") + self.rows[dest] ^= self.rows[source] + self.columns[source] ^= self.columns[dest] + elif op == "ERASE": + require(dest in self.owned, "Streamed owned erasure") + self.rows[dest] = 0 + require(self.columns[dest] == 0, "Erasure suffix before projection") + self.columns[dest] = self.erased[index] + self.state[dest] = event[2] + elif op == "INIT": + require(dest in self.owned and self.rows[dest] == 0, "Streamed whole-zero owned INIT") + self.state[dest] = event[2] + else: + source, target, rank = event[2:] + require(self.state[dest] == source and (source, target, rank) in self.edges, "Streamed query route/source") + if op == "ZERO_Q": + require(self.rows[dest] == 0, "Streamed whole-zero ZERO_Q") + self.state[dest] = target + newframe = self.state[dest] + if oldframe != newframe: + oldshape, newshape = self.shape[oldframe], self.shape[newframe] + for shape in (oldshape, newshape): + if shape is not None: + old_occupied.setdefault(shape, bool(self.banks[shape])) + affected.update(self.keys_by_shape[shape]) + dirty_shapes.add(shape) + if oldshape is not None: + self.banks[oldshape].remove(dest) + if newshape is not None: + self.banks[newshape].add(dest) + if dest in self.gid: + g = self.gid[dest] + self.members_at[g][oldframe].remove(dest) + self.members_at[g][newframe].add(dest) + for shape in dirty_shapes: + change = int(bool(self.banks[shape]))-int(old_occupied[shape]) + if change: + for g, source, _target, _rank in self.incoming[shape]: + self.degree[g, source] += change + for g in range(len(self.groups)): + self.base_cache.pop((g, shape), None) + affected.update(self.keys_for_shape(shape)) + for h in changed_members: + affected.update(self.keys_for_member(h)) + for key in sorted(affected): + self.replace(key, index+1) + self.weight_cut(index+1) + require(self.state == self.final and self.columns == [1 << i for i in range(self.n)], "Streamed final headers/suffix identity") + require(all(self.rows[h] == 0 for h in self.owned), "Streamed final owned normalized zero") + require(self.cut_count == 14795 and self.total_domain == 386278548, + "Complete frozen386278548-case domain") + require(sum(self.weighted.values()) == self.total_domain, "Full weighted distribution closure") + self.validate_positive_first_contexts() + self.synthetic_algebra_control = self.validate_nonzero_schur_control() + return self.receipt() + + def validate_nonzero_schur_control(self): + # A synthetic two-coordinate example forces a NONZERO outer-product + # correction in both forms. It is not a source census context. + probe = Census.__new__(Census) + probe.k, probe.rows, probe.columns = self.k, [1, 2], [2, 3] + probe.outside, probe.banks = {0: 0}, {0: {0}} + probe.base_cache = {} + probe.base_evaluations = probe.context_evaluations = 0 + observed = probe.extension_profile(0, 0, 1) + full = [] + for slots in ([0], [1], [0, 1]): + view, left, right, p, s = self.k["bank_view"](probe.rows, probe.columns, slots, 0) + full.extend(view[name] for name in ("left_kernel_dimension", "right_kernel_dimension", "boundary_rank", "internal_rank")) + quotient = self.k["inherited_quotient"](left, right, p, s, [0, 1], 1, 0) + require(quotient["available"], "Synthetic inherited pivot availability") + full.extend((quotient["boundary_rank"], quotient["internal_rank_on_actual_changed_bases"])) + expected = (1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 0) + require(observed == tuple(full) == expected, "Nonzero inherited Schur update versus full frozen kernel") + return {"synthetic_not_source_case": True, "prefix_rows": [1, 2], "suffix_columns": [2, 3], + "base_slots": [0], "added_role": 1, "outside_mask": 0, + "checked_profile": format_profile(observed), "full_frozen_kernel_comparison": "PASS"} + + def validate_positive_first_contexts(self): + cuts = sorted({spec["cut_t"] for spec in self.first_positive.values()}) + require(len(cuts) <= 1024, "Direct positive-class check snapshot resource bound") + prefix, suffix, headers = self.k["traces"](self.word, self.spaces, cuts) + digest = hashlib.sha256() + for key, first in sorted(self.first_positive.items()): + g, source, target, paid_rank, *items = key + spec = dict(first, edge=[source, target, paid_rank]) + t = spec["cut_t"] + view = self.k["checkpoint"](spec, self.word, self.spaces, self.edges, prefix[t], suffix[t], headers[t]) + require(view["group_members"] == self.groups[g], "Direct class actual-member group mapping") + profile = [] + for name in ("base", "singleton", "augmented"): + part = view[name] + profile.extend(part[field] for field in ("left_kernel_dimension", "right_kernel_dimension", "boundary_rank", "internal_rank")) + quotient = view["inherited_pivot_quotient"] + profile.extend((quotient["boundary_rank"], quotient["internal_rank_on_actual_changed_bases"]) if quotient["available"] else (-1, -1)) + require(profile == items, "Direct complete augmented-kernel/form class check") + require(view["boundary_excess_over_both"] > 0 and view["augmented"]["simultaneous_unit_pair"] is not None, + "Every positive class first context has direct simultaneous unit witness") + digest.update((canonical([g, spec, profile])+"\n").encode()) + self.positive_direct_validation = {"class_context_count": len(self.first_positive), + "direct_reconstruction_cut_t": cuts, "class_context_sha256": digest.hexdigest(), + "method": "Independent frozen traces reconstruct full original prefix/suffix maps, then full bank_view kernels/forms and simultaneous unit witness via checkpoint(), for every positive edge/profile class first context."} + + def receipt(self): + ranks = [{"group_index": g, "profile": format_profile(p), "weighted_cases": count} + for (g, p), count in sorted(self.weighted.items())] + classes = [] + dimension_counts = Counter() + for key, count in sorted(self.weighted_positive.items()): + g, source, target, paid_rank, *items = key + profile = tuple(items) + source_dim, target_dim = len(self.spaces[source]), len(self.spaces[target]) + dimension_counts[g, source_dim, target_dim, paid_rank] += count + classes.append({"group_index": g, "edge": [source, target, paid_rank], + "source_dimension": source_dim, "target_dimension": target_dim, + "profile": format_profile(profile), "weighted_cases": count, + "first_checkpoint": self.first_positive[key]}) + groups = [{"index": g, "members": members, + "entrance_dimension": len(self.spaces[self.start[members[0]]]), + "exit_dimension": len(self.spaces[self.final[members[0]]])} + for g, members in enumerate(self.groups)] + return {"schema_version": 1, "status": "PASS_INDEPENDENT_COMPLETE_NORMALIZED_PAIRING_CENSUS", + "frozen_scientific_sha256": FROZEN, "kernel_reuse": "Authenticated frozen independent oracle_witness.py; not a third unrelated engine", + "coverage_method": "Subtract/add changed context categories in active histograms, then weight every full histogram at each cut; separate geometry multiplicities count each cut's domain.", + "elimination_method": "Authenticated own-kernel lowest-pivot eligible kernels for current banks, with explicit coefficient-span bordering for augmented kernels; full direct kernels/forms cross-check every positive class first context.", + "groups": groups, "cut_count": self.cut_count, "weighted_domain": self.total_domain, + "per_cut_domain_sha256": self.coverage.hexdigest(), "per_cut_active_histogram_sha256": self.histogram_digest.hexdigest(), + "peak_active_contexts": self.peak_contexts, "bank_state_evaluations": self.base_evaluations, + "distinct_extension_evaluations": self.context_evaluations, + "direct_checkpoint_validation": {"cut_t": self.direct_cuts, "count": len(self.direct_cuts), + "maps_and_headers_compared": "Every685 prefix row,685 suffix column and685 current header at opening,end,witness7670 and both sides of every96 ownedERASE records"}, + "positive_class_direct_validation": self.positive_direct_validation, + "nonzero_inherited_schur_control": self.synthetic_algebra_control, + "rank_profile_distribution": ranks, + "positive_excess_weighted_cases": sum(self.weighted_positive.values()), + "positive_edge_profile_classes": classes, + "positive_dimension_classes": [{"group_index": key[0], "source_dimension": key[1], "target_dimension": key[2], + "paid_rank": key[3], "weighted_cases": count} for key, count in sorted(dimension_counts.items())], + "limits": ["Complete only for the frozen published-one-edge member-to-entire-occupied-bank normalized domain; arbitrary new routes/word rewrites are not enumerated.", + "Boundary excess is rank(S+h)>max(rankS,rank{h}); internal pairing and inherited quotient ranks are reported separately.", + "A positive pairing gate supplies no additional productive target, typed continuation, native/physical erasure permission or profitable invoice.", + "No price theorem, ordinary/compiler/outer admission, newkappa or selected frontier change is supplied."]} + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--emit", action="store_true") + args = parser.parse_args() + kernel = load_kernel() + result = Census(kernel).run() + if args.emit: + print(canonical(result)) + else: + receipt = ROOT / "FULL-CENSUS.json" + require(receipt.is_file(), "Retained receipt FULL-CENSUS.json required") + require(canonical(kernel["decode"](receipt.read_bytes())) == canonical(result), "Retained full-census receipt mismatch") + print("PASS independent complete normalized G20 census receipt") + + +if __name__ == "__main__": + try: + main() + except (ValueError, KeyError, TypeError, OSError) as exc: + print("FAIL: " + str(exc), file=sys.stderr) + sys.exit(1) diff --git a/research/g20-member-bank-cache/replay.py b/research/g20-member-bank-cache/replay.py new file mode 100644 index 0000000000..6ab320d917 --- /dev/null +++ b/research/g20-member-bank-cache/replay.py @@ -0,0 +1,101 @@ +"""Bounded exact containment reuse for the frozen PR6396 census. + +New implementation produced by Nick Petalas. Apache-2.0. +The frozen census, oracle, mathematical claims and notices retain their authors. +""" + +import argparse +import hashlib +import json +from pathlib import Path +import sys + +ROOT = Path(__file__).resolve().parent +MANIFEST_SHA256 = "3e74a49400d174b61049815a4ece5ff1ac3226d28e1eeac6f2b856b013989d47" +CAPACITY = 32768 + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +class ContainmentMemo: + """Cache a pure Boolean function on ordered immutable space pairs.""" + + def __init__(self, original, capacity=CAPACITY): + require(type(capacity) is int and 0 <= capacity <= CAPACITY, "Cache capacity") + require(callable(original), "Containment function required") + self.original = original + self.capacity = capacity + self.memo = {} + self.calls = self.hits = self.misses = 0 + + def __call__(self, outer, inner): + self.calls += 1 + key = (outer, inner) + if key in self.memo: + self.hits += 1 + return self.memo[key] + self.misses += 1 + result = self.original(outer, inner) + require(type(result) is bool, "Boolean containment result required") + if len(self.memo) < self.capacity: + self.memo[key] = result + return result + + def statistics(self): + require(self.calls == self.hits + self.misses, "Cache accounting") + require(len(self.memo) <= self.capacity, "Cache bound") + return {"calls": self.calls, "hits": self.hits, "misses": self.misses, + "entries": len(self.memo), "capacity": self.capacity} + + +def authenticated_source(): + raw = (ROOT / "FROZEN.json").read_bytes() + require(hashlib.sha256(raw).hexdigest() == MANIFEST_SHA256, "Frozen manifest digest") + manifest = json.loads(raw) + require(len(manifest["files"]) == 17, "Frozen file inventory") + for row in manifest["files"]: + payload = (ROOT / "frozen" / row["path"]).read_bytes() + require(hashlib.sha256(payload).hexdigest() == row["sha256"], + "Frozen sha256: " + row["path"]) + blob = hashlib.sha1(b"blob " + str(len(payload)).encode() + b"\0" + payload).hexdigest() + require(blob == row["git_blob"], "Frozen Git blob: " + row["path"]) + path = ROOT / "frozen" / "verify_full_census.py" + namespace = {"__name__": "authenticated_frozen_census", "__file__": str(path)} + exec(compile(path.read_bytes(), str(path), "exec"), namespace) + return namespace + + +def run(emit=False, statistics=False): + source = authenticated_source() + kernel = source["load_kernel"]() + memo = ContainmentMemo(kernel["contains"]) + kernel["contains"] = memo + result = source["Census"](kernel).run() + canonical = source["canonical"] + expected = kernel["decode"]((ROOT / "frozen" / "FULL-CENSUS.json").read_bytes()) + require(canonical(result) == canonical(expected), "Complete frozen census receipt mismatch") + stats = memo.statistics() + require(stats["hits"] > 0 and stats["misses"] > 0, "Containment reuse must execute") + if statistics: + print(json.dumps(stats, sort_keys=True), file=sys.stderr) + print(canonical(result) if emit else "PASS independent complete normalized G20 census receipt") + return result, stats + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--emit", action="store_true") + parser.add_argument("--stats", action="store_true") + args = parser.parse_args() + run(args.emit, args.stats) + + +if __name__ == "__main__": + try: + main() + except (ValueError, KeyError, TypeError, OSError) as exc: + print("FAIL: " + str(exc), file=sys.stderr) + sys.exit(1) diff --git a/research/g20-member-bank-cache/test_controls.py b/research/g20-member-bank-cache/test_controls.py new file mode 100644 index 0000000000..def78e487e --- /dev/null +++ b/research/g20-member-bank-cache/test_controls.py @@ -0,0 +1,87 @@ +"""Real relocated CLI, source corruption and missing-installation controls. + +Produced by Nick Petalas. Apache-2.0. Temporary copies only. +""" + +import hashlib +import json +import os +from pathlib import Path +import shutil +import subprocess +import sys +import tempfile + +ROOT = Path(__file__).resolve().parent +SUCCESS = b"PASS independent complete normalized G20 census receipt\n" + + +def inventory(root): + files = sorted(p for p in root.rglob("*") if p.is_file()) + if len(files) > 64: + raise ValueError("Control export file bound") + return {str(p.relative_to(root)): [hashlib.sha256(p.read_bytes()).hexdigest(), + p.stat().st_mode & 0o777] for p in files} + + +def execute(root, optimized=False): + command = [sys.executable, "-I", "-W", "error", "-B"] + if optimized: + command.append("-O") + command.append(str(root / "replay.py")) + env = dict(os.environ, PATH="", PYTHONOPTIMIZE="") + return subprocess.run(command, cwd=root, env=env, capture_output=True, timeout=120, check=False) + + +def require_failure(root, message): + result = execute(root, optimized=True) + if result.returncode == 0 or message.encode() not in result.stderr or result.stdout: + raise ValueError("Actual CLI failure control did not reject: " + message) + + +def main(): + with tempfile.TemporaryDirectory(prefix="g20-cache-controls-") as folder: + destination = Path(folder) / "export" + shutil.copytree(ROOT, destination) + before = inventory(destination) + for path in destination.rglob("*"): + if path.is_file(): + path.chmod(0o444) + readonly = inventory(destination) + for optimized in (False, True): + result = execute(destination, optimized) + if result.returncode != 0 or result.stdout != SUCCESS or result.stderr: + raise ValueError("Relocated read-only replay failed: " + result.stderr.decode()) + if inventory(destination) != readonly: + raise ValueError("Read-only replay changed bytes or modes") + path = destination / "frozen" / "sources" / "FRAMES.json" + original = path.read_bytes() + path.chmod(0o644) + path.write_bytes(original + b"\n") + require_failure(destination, "Frozen sha256") + path.write_bytes(original) + manifest = destination / "FROZEN.json" + original = manifest.read_bytes() + manifest.chmod(0o644) + manifest.write_bytes(original + b"\n") + require_failure(destination, "Frozen manifest digest") + manifest.write_bytes(original) + adapter = destination / "replay.py" + original = adapter.read_text() + anchor = ' kernel["contains"] = memo\n' + if original.count(anchor) != 1: + raise ValueError("Installation mutation anchor") + adapter.chmod(0o644) + adapter.write_text(original.replace(anchor, "")) + require_failure(destination, "Containment reuse must execute") + for path in destination.rglob("*"): + if path.is_file(): + path.chmod(0o644) + if set(inventory(destination)) != set(before): + raise ValueError("Control export file inventory changed") + print(json.dumps({"status": "PASS_G20_CACHE_CLI_CONTROLS", "readonly_runs": 2, + "rejected": 3, "git_required": False, "path_empty": True}, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/g20-member-bank-cache/verify.py b/research/g20-member-bank-cache/verify.py new file mode 100644 index 0000000000..6e3b06c452 --- /dev/null +++ b/research/g20-member-bank-cache/verify.py @@ -0,0 +1,96 @@ +"""Equivalence, capacity and failure controls for exact containment reuse. + +Produced by Nick Petalas. Apache-2.0. +""" + +import contextlib +from fractions import Fraction +import hashlib +import io +import json +from pathlib import Path + +ROOT = Path(__file__).resolve().parent + + +def load_replay(payload=None): + path = ROOT / "replay.py" + namespace = {"__name__": "cache_control", "__file__": str(path)} + exec(compile(path.read_bytes() if payload is None else payload, str(path), "exec"), namespace) + return namespace + + +def fixtures(source, memo_type): + kernel = source["load_kernel"]() + q = Fraction + zero = (q(0),) * 6 + e0, e1 = (q(1), q(0)) + zero, (q(0), q(1)) + zero + spaces = ((), (e0,), (e1,), ((q(1), q(1)) + zero,), + ((q(2), q(1)) + zero,), (e1, e0)) + comparisons = 0 + for capacity in (0, 1, 2, 32768): + memo = memo_type(kernel["contains"], capacity) + for _ in range(3): + for outer in spaces: + for inner in spaces: + expected = kernel["contains"](outer, inner) + if memo(outer, inner) is not expected: + raise ValueError("Ordered positive/negative containment mismatch") + comparisons += 1 + stats = memo.statistics() + if stats["calls"] != 108 or stats["entries"] > capacity: + raise ValueError("Capacity exhaustion or accounting changed") + return comparisons + + +def failure_controls(source, replay): + rejected = 0 + for capacity in (-1, 32769, True, 1.0): + try: + replay["ContainmentMemo"](lambda _a, _b: True, capacity) + except ValueError: + rejected += 1 + else: + raise ValueError("Invalid capacity accepted") + raw = (ROOT / "replay.py").read_text() + changes = ( + ("return self.memo[key]", "return True"), + ("key = (outer, inner)", "key = tuple(sorted((outer, inner)))"), + ) + for old, new in changes: + if raw.count(old) != 1: + raise ValueError("Mutation anchor changed") + mutant = load_replay(raw.replace(old, new).encode()) + try: + fixtures(source, mutant["ContainmentMemo"]) + except ValueError: + rejected += 1 + else: + raise ValueError("Wrong-result implementation mutant accepted") + return rejected + + +def main(): + replay = load_replay() + source = replay["authenticated_source"]() + comparisons = fixtures(source, replay["ContainmentMemo"]) + rejected = failure_controls(source, replay) + capture = io.StringIO() + with contextlib.redirect_stdout(capture): + result, stats = replay["run"]() + if capture.getvalue() != "PASS independent complete normalized G20 census receipt\n": + raise ValueError("CLI success output changed") + receipt = {"status": "PASS_G20_MEMBER_BANK_CACHE", "comparisons": comparisons, + "rejections": rejected, "cache": stats, + "scientific_sha256": hashlib.sha256(source["canonical"](result).encode()).hexdigest(), + "source_manifest_sha256": replay["MANIFEST_SHA256"]} + files = sorted(p for p in ROOT.rglob("*") if p.is_file() and "__pycache__" not in p.parts) + if len(files) > 64: + raise ValueError("Package file bound") + receipt["package_files_sha256"] = { + str(p.relative_to(ROOT)): hashlib.sha256(p.read_bytes()).hexdigest() for p in files} + print(json.dumps(receipt, sort_keys=True)) + + +if __name__ == "__main__": + main()