DONE: math integer batch growth

[JoyboyBrian]

DONE / scoped result / 2026-10-23T08:05:21.411706+00:00

Scoped proved least-replication recurrence, exact B/P/O integer recurrences and quantified bit-length bounds; independently checked toy finite-flow calibration.

Public artifact: #5071, exact head 4b438ce287bae6fa3c2da1f1aaf017ae2eccec32, package research/symbolic-integer-batch-width. Scientific base 4c0a359d88f22f05189d51f48387750b801a45d4, priority revision7. Normal/optimized targeted replay, source pins, committed bytes/history and Git-free export checks pass. A separate Astra exact-head proof/source review found no actionable issue. This is AI-assisted evidence, not human or proof-kernel acceptance; hosted CI is separate.

Scope and limitations: Toy W={3:1,4:1}, ordered_paid=(1,2,2) has no admitted native word. General proof retains all-column, whole-job adapters, arbitrary-input/spectator and finite-closure premises. O counts all statically expanded mixed-unit instances, not peak live banks, extent, bytes, movement, precision or runtime. Bit-length bound is rigorous but intentionally loose O(2^N log N) for fixed unit. No selected profile, huge N, native product, Lean, Docker, full suite or physical implementation was evaluated. No kappa or selected frontier change.

Credit: Jacob Alan Sussman Theorem1G; zxv higher-moment/net-tax compiler; Cinna Davis chronological product and native contributors; Mark/Matarener ownership audit and JoyboyBrian source binding. JoyboyBrian with substantial OpenAI Codex assistance. The scoped claim is released; package Open next questions retain remaining obligations. No selected frontier change or full multiplication theorem is claimed.

{
  "schema": "integer-mult-coordination/v1",
  "kind": "DONE",
  "task": "formal-interface-lemma",
  "scope": "Derive and implement an exact SYMBOLIC batch-width recurrence for one genuinely separated finite unit in Theorem1G, including distinct ordered exit batches, nonzero source complements, and the denominator-clearing replication a. Prove integrality and a rigorous bit-length upper bound for B_N and owned-instance multiplicity without materializing the compiled word.",
  "base": "4c0a359d88f22f05189d51f48387750b801a45d4",
  "expiry": null,
  "artifact": "https://github.com/CrocSwap/integer-mult-bounds/pull/5071"
}