[JoyboyBrian]

The existing R437 sharp entry validates host parameters, while the local batched quotient has not been joined to an admitted root's actual binary Count and caller consumers. This package completes that join at q=2^127−1, e=n=64,w=2,h=0 and exact L255/I8/Q520213: the original authenticated entry encodes the real 1,040,413-bit root stock, executes the opt-in quotient, literal NODE ingress and 9475 guard, saves leading, and executes the initial fibre=Count.product(leading,gap). All three observed outputs are 9475.

The full pre-payload diagnostic reached original multiply_atom_power but exceeded its external 90-second budget. Its exact harness remains in commit 5fc3091bf853b9f19a155e03ce0750a2104dc135; DIAGNOSTIC.json preserves the 90.505-second interruption and phases. The successful current projection keeps all 17 original NODE statements through the first fibre product and appends an explicit ownership return. It stops before exponent expansion. The original next segment still requires 256 Word divisions and 256 Count multiplications, eventually a 32,526-bit fibre. No final fibre, complete NODE, full Context, payload or supplier execution is claimed.

The returned local Count is explicitly disposed before testing source temporary cleanup. Actual borrowed Program/count bytes and heads, dirty Count173/Word37, numerical live sets and erased record backing pass; wrong precision/index/Q/rows/history/source identity reject before the continuation. Runtime Word decoding is forbidden. The 56.311-second successful q127 run uses no tiny replacement witness.

The invoice includes full source construction/execution/disposal and distinct NODE lane counters, plus 3,122,293 visited record cells. The batch divisor has 520,192 bits; its 13 host construction products have 90,200,420,437 schoolbook bit-products. Those diagnostics do not price the full compiler, large-divisor host arithmetic, finite control, allocator or physical binary-TM tariff. No uniform performance improvement follows.

Credit David Arias #2753, Chris R / Clear1nsight #4176, #4794 4cc9b9719fdab59f0f33243b9c323fe4d69346f5, Nick Petalas #4854 2877e4920338d9a2e56aa960bdb5663f8f96b2d8, codyw912 #4734, ToikY #4025 and the pinned stock/compiler lineage. Discussion #4927 independently audits complete-directory reserve; this package neither repeats it nor treats its payload/lifetime assumptions as discharged. New composition and checks: JoyboyBrian, substantial OpenAI Codex assistance, Apache-2.0.

Validation: actual q127 exact replay; package metadata; committed-byte/source-history preflight at canonical base b91956876e5b4122fd89179f1b57557ff8378f15 (413 files, no foreign source ancestor); official export and integrity check. Git-free cold normal/optimized replays pass (55.993s/55.552s), with empty bytecode caches. Generic live and retained-source corruptions reject, as do explicit mutations of the newly composed #4794 quotient and #4757 ordinal inputs. A bool→int RESULT mutation rejects at typed comparison after replay. All 414 cold export files restore unchanged. The affected-package planner selects only this package. Hosted CI is unverified.

Canonical investigation and documented scope change: #4682 (comment) . Only research/r437-admitted-count-consumer/ changes, with four substantive commits preserving the initial interface, measured full-path diagnostic, narrowed checked boundary and final evidence. Open next questions retain the original expansion, complete physical cost, Context and payload obligations.

Final submission checkpoint: official main refreshed at 05:13 UTC remains b91956876e5b4122fd89179f1b57557ff8378f15; guidance and affected source inputs are unchanged. Fresh overlap covers 323 open PRs (05:14:01 UTC), 4,077 discussion records (05:14:50 UTC), and all 6,636 current-base notes. The scoped final query identifies the credited distinct predecessor obligations and this round's claims, not an exhaustive novelty certificate. Root independently read the authenticated AST projection, original checked_entry continuation, actual runtime methods, disposal checks and exact excluded expansion/cost obligations, with no blocker.

[jwr404]

Independent replay at head da6860a3 on Linux (CPython 3.12.14, PYTHONPATH unset). Both registered commands pass: -I -B and -I -O -B each print PASS_R437_ADMITTED_INITIAL_COUNT_CONSUMER, followed by PASS_REGISTERED_RESEARCH_PACKAGE … outcome=partial. The total harness time was 97.5 s, about 48 s per command.

Timeout margin. Each command has timeout_seconds: 120. The hosted replay job passed but took 3 m 54 s for the two commands, so each ran at roughly 105–110 s once setup is excluded. That is within about 10–15 s of the cap. Slower or busier runners could turn this into a spurious timeout; a package of mine on the same hosted CI ran about 2.5× slower than locally before I fixed it. Consider raising the per-command timeout (the harness allows up to 600 s) or splitting the two phases.

I did not re-derive the R437 quotient or the stock arithmetic. This is an independent replay, not acceptance, and κ is unchanged.

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