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Add exact C3 gather rank-shape obstruction - #1814
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Batch review at Merged to Reviewed scope: All32 consecutive C3 gather windows priced with all source/destination rank increments; exact interval DP certifies every disjoint schedule misses5% even at zero implementation overhead. Concrete16-window relaxed profile is a planning figure, not an admitted gather child. 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. |
Source-bound consolidation receipt (card overlap-receipt, scope refined to one existing integration receipt). Re-derives from Git that all 77 changed paths of the nine reviewed heads (#1805, #1806, #1808, #1810, #1811, #1812, #1814, #1815, #1827) are retained byte-identically in merge 5112234, that no head changed since review, and that all authors are credited in CONTRIBUTORS.md. Records the still-partial ledger dispositions without changing them. No kappa, disposition, closure or frontier change. Aaron Wang, with help from opencode.
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Result
Adds a source-pinned scoped negative result for a three-source, one-destination gather child on the selected width-73 local word. The complete finite domain is every three-consecutive-ADD window in A or B with one common destination, three distinct source registers not equal to the destination, and at least two positive frame climbs across the touched registers.
For each window, the exact value map is
D += c1*S1 + c2*S2 + c3*S3, with source values preserved. The hypothetical child replaces every positive destination and source frame increment with one child of rank equal to their sum. Exact weighted interval scheduling selects 16 of 32 windows, eight rank-12 and eight rank-16 children. This rank-mass-preserving max-saving profile raises the fixed-word ceiling by 1.3641268145%.More strongly, exact per-window saving upper bounds and interval scheduling prove that every allowed schedule leaves the moment above one at 1.05 times the baseline ceiling. The exact positive margin is in
CERTIFICATE.json. This bound gives the gather mechanism zero cost for source collection, copies, adapters, helpers, extra frame handling, restoration, precision and hosting. It is a scoped negative for this consecutive C3 gather family; it does not rule out other arities or schedules, admit a physical supplier, or claim a new kappa.Pins and reproduction
The package records OS-random seed
7a6da0d3a89bdb0425f85454db15342b,complex-mechanisms/complex-rank-shape-decoder, catalogue revision 3, exact base0b1cccf86e2f5132ed286a26ef0a681a495740ea, selected-record and assembly hashes, and compressed/decompressed local-word hashes.SOURCES.jsonpins source blobs at that base. The final exact-gather overlap refresh covered 473 open PRs and 449 Discussions with complete pagination and no warnings; there were no remote matches.Registered commands:
Local verification: exact verifier passed; all seven focused controls passed; package metadata/source-pin checks passed;
git diff --cached --checkpassed. These direct runs used Python 3.14.7. Python 3.12 is not installed in this environment, so the registered Python 3.12 replay was not run locally.Scope and credit
The selected PR1094 construction and inherited obligations are unchanged. The package distinguishes PR1799's one-source/three-destination scatter, the adjacent diagonal rank-16 batching claim, and prior same-source coefficient reuse. Substantial OpenAI Codex assistance is disclosed in
TASK.jsonandREADME.md.