{
  "_doc": "One result, read from the codebase’s own files at the commit named here. Every value is that file’s own, copied verbatim; nothing here is written by hand. A value replaced by {withheld: true, sha256_of_value, bytes} is committed by its sha256 instead of published, for the reason it states, and is never edited. Each whole source file is committed by sha256 below, and its bytes are published only where its visibility says so. The codebase is named by the public subject its files are published under.",
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    "id": "essentiality-bits-floor",
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    "title": "The >=T*n bits essentiality floor, composed and in bits",
    "claim": "A zero-leak AND full-reuse pooled-KV policy over T tenants and n cache blocks needs at least 2^(T*n) states, i.e. at least T*n bits, as one machine-checked theorem general in T and n.",
    "scope": "22 theorems in serving_limits/formal/lean/EssentialBits.lean, axioms subset of {propext, Quot.sound}, mathlib-free, Lean 4.31.0. A NECESSARY condition on STATE only — it says nothing about timing channels, content channels, or probabilistic isolators. Both spec hypotheses are required: zero-leak alone is provably 0 bits.",
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    "witness_command": "cd serving_limits/formal/lean && lake build EssentialBits && cd - >/dev/null && python3 statefabric/experiments/gen_essential_bits_report.py",
    "witness_result": "exit=0 | ⚠ [5/7] Replayed InjectivityFloor",
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    "claim": "A zero-leak AND full-reuse pooled-KV policy over T tenants and n cache blocks needs at least 2^(T*n) states, i.e. at least T*n bits, as one machine-checked theorem general in T and n.",
    "class": "ASSERTING",
    "why": "The proof kernel re-checks the claim in this run; the report is regenerated from the build rather than read from a stored witness. Planted defect: the arithmetic witness `64 * 1024 = 65536` becomes `= 65535`, so `by decide` cannot close it — the witness exits 1.",
    "witness_command": "cd serving_limits/formal/lean && lake build EssentialBits && cd - >/dev/null && python3 statefabric/experiments/gen_essential_bits_report.py",
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      "target": "serving_limits/formal/lean/EssentialBits.lean",
      "defect": "the arithmetic witness `64 * 1024 = 65536` in theorem kv_cache_witness_64x1024 becomes `= 65535`, so `by decide` cannot close it — a mutation of a claimed number that the Lean kernel has to reject",
      "witness_command": "cd serving_limits/formal/lean && lake build EssentialBits && cd - >/dev/null && python3 statefabric/experiments/gen_essential_bits_report.py",
      "recorded_exit": 0,
      "recorded_assertion": "\"certified\": true",
      "mutation": "replaced 2 of 2 occurrences of '65536' with '65535'",
      "mutated_exit": 1,
      "mutated_first_line": "✔ [2/7] Built IsolationBound (5.8s)",
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    "attested": true
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