[JoyboyBrian]

The prior nonzero-high R437 certificate returns a whole child packet before the actual SOURCE87 XOR consumer. This contribution gives an opt-in prefix-major interface: finish one complete local leaf, consume its return immediately, erase local copies, then advance. A source-level direct-product proof preserves every primitive and callback in its original per-prefix order, for every finite complete producer directory, including the full high cube when supplied.

The new boundary is functional composition and returned-packet lifetime. The directory, borrowed payload, final output, setup, primitive workspace and visited backing remain paid; no physical-space/runtime gain, complete caller, supplier admission or κ change is claimed. Successful callback/primitive restoration and a read-only observer are hypotheses; arbitrary inherited exception cleanup is not repaired. Equivalence concerns payload and borrowed logical state, excluding meters, allocation order and global callback logs; deterministic cache bookkeeping may differ.

The actual differential executes the original leaf, coefficients and consumer at q3,w2 on #4793's two distinct complete nonzero-high prefixes. Both schedules execute 24 callbacks and 13,122 dirty bits, agree with every bit of the independent permutation oracle, and have identical per-prefix callback chronology. The fused consumer observes two 6,561-bit returns. Source/target/Program bytes and heads, numeric live sets and erased owned backing are checked, with omitted-prefix, role-alias, truncation, high-digit, rank, wrong-return and wrong-weight controls. This finite evidence is outside the selected numerical root domain; it does not execute all 3^4096 highs or establish admitted ancestry.

Credit #4793 8ef4afcfba50c7f118d4787e34dda437192458ea, Chris R / Clear1nsight #4176, and the unchanged packet/callback/consumer/compiler/arithmetic lineage. #4759 is metadata-only dispatch; Nick Petalas #4854 is local quotient traversal; Discussion #4927 is directory/reserve auditing. Those distinct obligations are not repeated or silently assumed. New work: JoyboyBrian, substantial OpenAI Codex assistance, Apache-2.0.

Validation: exact normal local differential; package metadata; committed-byte/source-history preflight at canonical base b91956876e5b4122fd89179f1b57557ff8378f15 (410 files, no foreign source ancestor); official export and integrity check. Git-free cold normal/optimized replays pass (91.051s/88.901s), with empty bytecode caches. Live source and retained historical source mutations reject at authentication; bool→int RESULT mutation rejects at typed comparison after replay. All 411 export files are unchanged. The final documentation-only source-review clarification was re-exported and integrity/preflight checked; bytewise old/new export comparison proves only PROOF.md and export metadata changed, with every execution/scientific input and receipt byte identical. The planner selects only this package. Hosted CI is unverified.

Canonical investigation: #4682 (comment) . README and PROOF retain the complete hypotheses, cost boundary and Open next questions for producer/allocator and admitted-root composition. Only research/r437-prefix-consumer-fusion/ changes; four meaningful commits separate interface/proof, checks, evidence, and review-driven observational-equivalence clarification.

Independent same-session source review found no blocking discrepancy. Its precision suggestions about observer effects, memoization and observational equivalence are incorporated in a documentation-only final commit; execution/scientific input bytes remain identical.

Final submission checkpoint: official main refreshed at 05:13 UTC remains b91956876e5b4122fd89179f1b57557ff8378f15, with unchanged guidance and affected inputs. Complete fresh overlap coverage is 323 open PRs (05:14:01 UTC), 4,077 discussion records (05:14:50 UTC), and 6,636 current-base local notes; scoped exact queries identify this round's canonical claims and credited distinct predecessors. A coordinating Codex review independently checked the final proof and executable boundary, retaining the stated conditional interface and open obligations. This is not a novelty certificate or human/proof-kernel acceptance.

[jwr404]

Post-merge independent replay of head 0acc7bac on Linux (CPython 3.12.14, PYTHONPATH unset). Both registered commands, -I -B and -I -O -B, print PASS_R437_PREFIX_CONSUMER_FUSION, followed by PASS_REGISTERED_RESEARCH_PACKAGE research/r437-prefix-consumer-fusion outcome=partial. The total time was 3 m 39 s, about 110 s per command against timeout_seconds: 240. The hosted replay took 4 m 47 s for the job, so the margin is adequate but not large.

The stated counts are consistent: each q = 3, w = 2 return is 3^8 = 6,561 bits, and two returns give the 13,122 dirty bits. I did not re-derive the direct-product chronology proof. This is a replay check, not acceptance, and κ is unchanged.

Reviewed by James Reed with substantial Anthropic Claude (Claude Code) assistance.