Certify composed scalar centre-source rank for a selected call pair

[adamgall]

Result and scope

Exact scalar-projection certificate for selected forward calls time 0/1 (stage 0, replicas 0/8), on base 0b1cccf86e2f5132ed286a26ef0a681a495740ea. This is not a native centre-path obstruction, new supplier, or κ improvement.

The pair has 704 owner roles per call, 30 shared physical-owner families, and 1,378 initial scalar owner coordinates. The verifier composes both full emitted scalar programs on shared owner variables, snapshots their centre source maps, and checks ordinary endpoint restoration and private-centre clearing.

• Stacked source-map rank: 16; stacked two-panel scatter-output rank: 16.
• Rank remains 16 when restricted to the 224 initial source-data coordinates, so it does not rely on additional hosted dirt information.
• Full first call leaves the second call's scalar source maps unchanged.
• Exact pooled-sum collision: assign (3,-1,2,-1,-1,-1,-1,-1)/4 to owners (0,1,2,3,4,5,6,12), its negative to corresponding owners plus 7168, and zero elsewhere. Centre sources become (e0,-e0); all eight pairwise sums vanish but the required scatter output is nonzero.
• Equal maps and distinct-but-permuted maps both have joint rank eight: map inequality alone is not the obstruction.

The standard linear-information factorization T=RE excludes an eight-scalar-total-only transcript for this projected pair. The artifact's contribution is the exact composed selected source maps and collision witness, not novelty of the rank lemma.

Invoice and limitations

Unchanged two-call centre bill: 16 rank-8 children, 16 COPY, 32 CLEAR, 352 ADD, total 416 listed macros and rank mass 128. All scalar helper restoration is replayed; shared owner dirt is not cloned. No changed hosting/routing/precision schedule is supplied or admitted.

Frame transports and adapters are explicitly projected to identity. This does not prove that projected rank lower-bounds native 512-address operator rank, nor that 128 is a native minimum. The missing native lift and complete history-dependent hosting/precision obligations are documented as Open next questions. No arbitrary-pair census, native retiming exclusion, or full multiplication theorem is claimed.

Files and source binding

Only research/selected-centre-composed-source-rank/ is added: README, task/source/replay manifests, exact receipt and verifier. Archive/member hashes and selected-record bytes are checked. Frozen sources and selected frontier are untouched. The source is the selected 480-helper emitted replay, not the historical 492-helper evidence.

Verification actually run

CPython 3.12.12, Darwin arm64; final commands passed in 2.77 s combined:

uv run --python 3.12 --no-project python -I -B research/selected-centre-composed-source-rank/verify.py --write
uv run --python 3.12 --no-project python scripts/research_package.py --package research/selected-centre-composed-source-rank
uv run --python 3.12 --no-project python -I -O -B research/selected-centre-composed-source-rank/verify.py

Observed:

PASS_SELECTED_PAIR_SCALAR_SOURCE_RANK source_rank=16 scatter_rank=16 data_rank=16 shared_owners=30 rank_mass=128 controls=5
PASS_REGISTERED_RESEARCH_PACKAGE research/selected-centre-composed-source-rank outcome=completed

Five controls: equal-map and distinct-dependent-map ranks, pooled-sum collision, omitted scatter rejection, omitted final-clear rejection. Ordinary replay compares all receipt fields without writing. Required initial ceiling example and lever script also passed; their favorable numbers are not claimed as this result. No full suite/native frame/supplier cold replay was run.

Overlap, credit and coordination

Closest predecessors: #1708 (Cinna Davis/1337isnot1337, forward equal-source fanout), #1748 (ToikY, reverse return and precision guard), #1664 (Andrey Mas/an664, conditional history-span bound), #1684 (single-call cut-rank application), #1829 (adjacent owner/chart identity census). Exact heads are in TASK.json and were targeted-rechecked before publication.

Delta over #1829: propagated source dependencies and complete intervening scalar-call composition on one actual shared-owner pair, rather than treating unequal owner IDs as proof of independent values. Native lifting remains open.

Cached overlap coverage: 539 open PRs and 524 discussion records, complete pagination fetched 2026-10-14 13:09–13:10Z; arbitrary diffs and every closed submission were not searched. No novelty guarantee. Coordination: #1884 .

Credit ctoth's discussion1516, Rohan Arun's #1094 owner placement, Jeremy Kothe's word and the retained compiler/emitter lineage. Prepared by Adam Gall with substantial OpenAI Codex assistance in scoping, proof argument, code, experiments and packaging. Apache-2.0; no independent human proof review claimed.

[Mister-Meeseeks]

Batch review at cc43a233ad989e717c8d46c6398ee50f97f5c0b9.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Full two-call scalar projection propagates1378 physical-owner variables including30 shared helpers; exact16-dimensional source/data/scatter ranks and pooled-sum witness pass.416 centre macros and rank mass128 are unchanged invoices. Identity-projected rank is explicitly not a native-frame lower bound.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.