Reduce complete member-bank census time by 9.78% (no κ)

research/g20-member-bank-cache/.gitattributes

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research/g20-member-bank-cache/BENCHMARK.json

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research/g20-member-bank-cache/FROZEN.json

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research/g20-member-bank-cache/PROFILE.json

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research/g20-member-bank-cache/PROOF.md

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+# 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.