[1337isnot1337]

Result

Exact local construction; no selected-provider admission or new kappa. This package fans one common bilinear product out to q arbitrary-dirty output rows without a clean anchor or helper. For

A_i' = A_i XOR p(x,y) XOR t_i(u_i,v_i),  i=0,...,q-1,

it uses two row-XOR waves around one complete child that toggles p into A0, then computes the q private terms:

for i=1..q-1: A_i ^= A_0       # compensate the old dirty anchor
child:        A_0 ^= p
for i=1..q-1: A_i ^= A_0       # deliver p from the updated anchor
for i=0..q-1: A_i ^= t_i

The exact invoice is q+1 child calls and 2(q-1) full-width row ADDs, versus 2q child calls directly. The net charged saving is (q-1)(mu-2 alpha(w)); no child/ADD price ratio is assumed. For q=112 this is 224 versus 113 child calls plus 222 row ADDs. A Hamming-weight argument proves that 2(q-1) row ADDs are minimal for one common child in the target-row XOR alphabet, without scratch, COPY or CLEAR.

Conditional profile screen

If eight hypothetical 112-port blocks occur, the rank-one profile changes from n1=2412 to n1=1524. The pinned rank-only ceiling brackets change from [1690054109/1000000000000, 169005411/100000000000] to [2026751029/1000000000000, 202675103/100000000000]. The dirty schedule also adds 1,776 scalar XORs at width one, retained as a separate linear term. No matching selected-provider occurrence or finite base-width mu/alpha comparison is established, so no supplier, frontier or kappa claim follows.

Evidence and reproduction

• PROOF.md gives the symbolic identity and row-ADD lower bound. verify.py exhausts 281,600 arbitrary child-output/dirty-target assignments through q=5 and widths one or two, checks inverse execution, rejects four malformed schedules, checks exact operation counts for q=2..112, and recomputes both pinned ceiling brackets.
• python3 scripts/research_package.py --package research/dirty-output-anchor-seed-da1ec3f0 --check-only — PASS_PACKAGE_METADATA_AND_PINS.
• python3 -I -B research/dirty-output-anchor-seed-da1ec3f0/verify.py and python3 -I -O -B research/dirty-output-anchor-seed-da1ec3f0/verify.py — PASS.
• python3 -I -B research/complex-local-word-ceiling/verify.py — PASS.

Local replay used CPython 3.14.7. The registered package workflow specifies Python 3.12, unavailable locally; hosted CI is not yet claimed.

Provenance and distinction

Base commit 0b1cccf86e2f5132ed286a26ef0a681a495740ea; selected-record SHA-256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32. The package pins the selected review, source manifest, assembly certificate and the ceiling model. The selected result remains unchanged.

• PR Add output-anchor variant for shared-product blocks #1907 uses a clean required-output anchor. This construction allows every output to be arbitrary dirty and pays a second fanout wave.
• PR Research: reversible shared rank-one helper across three calls #1872 uses a clean helper and inverse cleanup. This construction uses a dirty output and no helper.
• PR Construction: three-stage persistent prefix shear chain (no new kappa) #1930 studies a three-stage linear prefix chain; PR Audit cross-fed connector handoff against a parity-retaining baseline #1917 studies a cross-fed parity connector.
• The adjacent active claim at Discussion Larger κ: proposals that change the current cost structure #1167 comment 18926048 broadcasts a common linear map from a separate dirty scratch row across distinct source-prefix states, then restores that scratch with a second map call. This scope instead uses a required output row as the carrier for one common bilinear term, adds private products per output, requires no scratch or cleanup, and proves the minimum row-ADD count for the single-child target-row-XOR alphabet.

The final overlap refresh completed at 2026-10-14T14:34:38Z, covering 590 open PRs and 567 Discussions with no warnings; the adjacent claim was manually checked at 14:35:43Z. This is bounded overlap evidence, not a novelty certificate. The package is prepared with substantial OpenAI Codex assistance; no independent human review is claimed. Apache-2.0.

[Mister-Meeseeks]

Batch review at 11110e70e462f95a3e5adcb1d290cd67cd0807e7.

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

Reviewed scope: Dirty-output anchor fanout usesq+1 children and2(q-1) affine row ADDs, removing1907s clean-entry premise. Written single-child ADD lower bound and281600 exhaustive assignments pass. Extra1776 row ADDs remain charged in the hypothetical eight-block screen; selected occurrence and complete child/ADD price inequality are unestablished.

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.