Research: first F0 caller six-tape admission audit

[Clear1nsight]

Change and mathematical scope

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

A reachable nonconstant dirty-helper impulse violates the six-tape kernel’s unchanged-grid divisibility premise. The actual child returns (1+i)/2 at address 0 and (-1-i)/2 at address 459. PROOF.md derives the exact index-2^256 divisibility sublattice on the 512-coordinate native slice, and a sufficient one-extra-fractional-bit repair with W=bit_length(M)+4 under component bound M.

This is not a counterexample to #3303’s already finer format: its 71 reserved fractional bits and P+215 width conditionally satisfy this first child’s arithmetic premises. Last-write CLEARs identify an abstract C0/C1 scratch candidate with no new logical field. Separate physical tapes/origins, input encoding/head positions, paid monomials, adjacent L546 -= L561, movement/address/control, helper return and consumer remain unbound. No fully costed connection, physical caller admission, complete supplier or new kappa is claimed. The 512-coordinate slice has identity spectators and is not the full N=2^(73 lambda) payload.

Task and overlap

Explicit assigned continuation; scope refined to this exact admission audit, then narrow and stop. Scientific/refreshed canonical base: 20ecf28, priority revision 6. Current AGENTS.md, autoresearch.md, CONTRIBUTING.md, priorities, selected record and family gate were read. Targeted live PR bodies, QQ16 Discussion index/handoff and canonical package notes were checked. The overlap helper lacked gh, so remote corpus coverage is partial; no exhaustive novelty claim.

Only research/qq16-f0-first-caller/ changes. The separate P112 workflow fix is preserved in fork PR10 and excluded here. Frozen inputs and selected frontier are unchanged. PR3884 tapes.py is retained byte-for-byte with its notice and pre-execution SHA256 check. Scientific head: 12c324c.

Validation

Normal/optimized warning-strict Python 3.12, full RESULT.json comparison, exact 9,894-event witness prefix, all 1,024 Gaussian basis columns, all 16 pair parity classes, 20 dense tape/native cases at widths 5–68, and the existing finer-format witness at width 216 pass. Fifteen test groups include 81 independently calculated signed pairs and source, prefix, recipe, private-scope, receipt, parity, range and ownership failures. Registered replay and read-only Git-free export pass; actual commands/environment/timings and unchanged input hashes are in VERIFICATION.json. Hosted checks are separate.

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 payload/producer/native/selected cold replay, Lean and independent human review are unrun. Elementary parity facts and the inherited kernel are not claimed as new.

Credit

Ali Romman and the QQ16/native lineage; Douglas Colkitt’s joint-query source; Nick Petalas #3270/#3303; Tekalign/PR3017 and Sricharan Vagvala’s native semantics; ToikY #3652 and #3671; Sagar Thakrar #3241/#3377; Dugongue #3394; retained source notices. #3181/#3908 are adjacent results, not independently verified dependencies. Chris R / Clear1nsight with substantial OpenAI ChatGPT assistance. Apache-2.0; no human or formal-kernel acceptance claimed.

Open next questions

Bind the proposed bounded grid and C0/C1 scratch candidate to real physical intervals, then price this child and adjacent ADD including monomials, movement, addressing and return. Before larger construction, check #3908’s fixed-profile consumer-budget assumptions. Unknown costs remain unknown.