research(qq16): audit first F0 six-tape admission contract

[Clear1nsight]

Result and exact scope

Continues fork PR10 and upstream CrocSwap#3884 by binding the first literal F0 rank-positive child: zero-based event 9894, L546, frame 0→4, rank 1.

The source permits a reachable nonconstant dirty-helper input whose unchanged-grid axis numerators are odd. The actual child returns (1+i)/2 at address 0 and (-1-i)/2 at 459; the exact predecessor tape program rejects with nonexact half. The proof identifies the complete divisibility domain on the 512-coordinate native slice: an index-2^256 sublattice of Z^1024. One extra fractional bit repairs this rank-one child's arithmetic at lambda=1; W=bit_length(M)+4 is sufficient for an explicit component bound M.

This is not a counterexample to PR3303's already finer format. Its 71 reserved fractional bits and width P+215 meet this first child's arithmetic conditions under its original bounded h-grid input premise. The audit checks that implication and a real tape execution separately. The 512-coordinate slice has identity spectators; it is not the full N=2^(73*lambda) payload.

Source last-write CLEARs also identify a legal abstract scratch candidate in four component half-slices of owned C0/C1, requiring no new logical field. Separate physical tapes, origins, input encoding/head positions and paid access remain unbound. The right/left monomials, adjacent L546 -= L561, address/control, movement, eventual borrowed-helper return and consumer are unpriced. No fully costed connection, physical caller admission, complete supplier or new kappa is claimed. This closes the bounded same-grid admission audit and stops at its explicit physical obligations.

Evidence

• Source-authenticated replay of all 9,894 prefix events for the nonconstant witness; actual recipe checks on all 1,024 Gaussian basis columns and all 16 pair parity classes.
• Twenty dense 512-coordinate tape/native cases at widths 5–68, plus the PR3303-format witness at width 216. Successful executions check values, scratch cleanup, head returns, exterior preservation and exact counts.
• Fifteen behavioral groups, including 81 separately calculated signed pair cases, source/prefix/recipe/private-scope/receipt corruption, parity versus width, overflow and borrowed-scratch rejection.
• Normal and optimized warning-strict Python 3.12 direct checks and registered replay; exact commands, environment, timings and source preservation in VERIFICATION.json. Hosted execution is reported separately in the PR checks.

python3 -I -Werror -B research/qq16-f0-first-caller/verify.py
python3 -I -O -Werror -B research/qq16-f0-first-caller/test_verify.py
python3 -B scripts/research_package.py --package research/qq16-f0-first-caller

Full producer/native/selected cold replay, full payload execution, Lean and independent human review are unrun. Elementary parity/grid facts and the predecessor tape kernel are not claimed as new; this result binds their exact conditions to the actual first caller.

Source, overlap and credit

Scientific and refreshed canonical base: 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority revision 6. Current AGENTS.md, autoresearch.md, CONTRIBUTING.md, priorities, selected record and family gate were read. This task was explicitly assigned. Live targeted PR bodies, the QQ16 Discussion index and original handoff were checked; the repository helper could not refresh its remote corpus because gh is absent, so coverage remains partial. Relevant canonical package notes were also searched. No exhaustive novelty claim.

Only research/qq16-f0-first-caller/ is changed in this upstream scientific submission. Frozen inputs, shared verifiers and the selected frontier are unchanged. The exact PR3884 tape source is retained byte-for-byte with its notice and pre-execution hash check, avoiding a cold dependency on an unmerged commit. Fork PR10's independently added P112 workflow fix is preserved there and excluded from this focused upstream copy.

Credit Ali Romman and the QQ16/native lineage; Douglas Colkitt's joint-query certificate; Nick Petalas CrocSwap#3270/CrocSwap#3303; Tekalign/PR3017 and Sricharan Vagvala's native semantics; ToikY CrocSwap#3652 and CrocSwap#3671; Sagar Thakrar CrocSwap#3241/CrocSwap#3377; Dugongue CrocSwap#3394; retained predecessor attribution. CrocSwap#3181 and CrocSwap#3908 remain adjacent, separately scoped results. New audit by Chris R / Clear1nsight with substantial OpenAI ChatGPT assistance. Apache-2.0; no independent human or formal-kernel acceptance.

Open next questions

Bind a real physical entry protocol to the proposed bounded grid and C0/C1 scratch candidate, then price one actual child/adjacent-ADD pair including monomials, movement, addressing and return. Before broader construction, check whether CrocSwap#3908's fixed-profile consumer-budget obstruction applies; a changed premise needs its own complete favorable bill.

Fork continuation head: 002fa176697d75046b001300c4006226d9a39e99, preserving the separately added P112 workflow fix. The package-only scientific copy is published upstream as CrocSwap PR3932, head 12c324c576821f78070627c5eeb684d03704e20e.

[Clear1nsight]

Publication verification completed. Upstream PR3932 at 12c324c576821f78070627c5eeb684d03704e20e passed the registered research replay: Python 3.12.15, the exact first-caller audit, all 15 test groups, and committed-input preservation. The fork replay also passed at this PR's head 002fa176697d75046b001300c4006226d9a39e99.

Committed-byte and source-history preflights pass for both heads, including all ten package files and five live inputs. The local checkout is aligned to the published fork head with a recovery snapshot retained. The precise unchanged-grid obstruction and conditional finer-grid arithmetic result are complete; the physical connection remains open under the explicit interval/origin/movement/consumer obligations in the README. No supplier or frontier claim; no merge or closure performed.

[Clear1nsight]

Closing this duplicate fork review in favour of upstream CrocSwap#3932, published at scientific head 12c324c with the same ten research package files. The publication verification above records passing source-bound replays for both heads. The additional P112 workflow repair is separately submitted upstream in CrocSwap#3885. Keep the upstream PR as the review location; discussion, evidence and branches are retained here. No upstream merge, supplier admission or frontier change is implied.