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Map every source row to its whole complement invocation and child input slot without expanding replicas - #7348
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…ut slot without expanding replicas
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Result
Construct exact inverse row-to-complement-invocation/slot mapping by true job-rank bucket. With S_s fresh sources and replication a, x=b*S_s+j and divmod(x,B_(N-s)) pick the whole child call; s=N receives NoComplement.
Novelty and predecessors
#4507/#5071 already give batch factors; this identifies individual source fields and handles cross-replica batches without expanding all occurrences.
Verification
26 author flows, 1,334 replicated rows; independent 22 flows/3,900 rows/11 controls. Run python3 -I -W error -B research/source-complement-port-index/verify.py.
Limits and kappa
Logical metadata, not physical gather/return or supplied smaller native programs. No new kappa; 0.00363005817 remains conditional.
Credit
Prepared for @CubeJerry with substantial OpenAI assistance; credit predecessor authors and PRs as detailed in the package.
Full proof, reproducibility, negative controls and provenance: https://github.com/CubeJerry/integer-mult-bounds/tree/bd63147b1a193f68b5713e5814ac3b2c743beff8/research/source-complement-port-index