[unpaidmoon]

Change and mathematical scope

Partial certificate. No new κ and no selected-frontier change. Selected κ stays 0.001672660197076918.

On the parent word research/r439-target-compensation/candidate.json.gz, D is 306 target-to-target gates, 111 helper reads, and 306 target-to-target gates. A compensated restored shear is D = S + P + M + Q + reverse(S), where S is a list of gates h_a ^= h_b and M is the parent middle after columns[b] ^= columns[a].

One such edge preserves every target sum in an abelian 2-group. The dirty value V_a + V_b is cancelled by toggling membership of b on the targets that already name a. The leading transport creates no helper columns, and the trailing transport is the same map, so the executed helper mask E equals the parent's E. The parent has E = K.

The three words from the K-defect tally have this shape (221, 221 and 236 edges). So does the pinned pair control (188 edges), which is the other helper-mixing word. The star word keeps A, scatter and B. The other three change B and C; their forward helper masks were checked equal to the parent's, not deduced from those edits. Five compensated edges outside the searches also keep E. The same edges without the support update change E. The synthetic edge h0 ^= h1, y ^= h0, h0 ^= h1 still names only h0 and delivers h0 + h1.

This is not a replacement K_equals_D contract, not a paid profile, and not a claim that every restored helper program has E = K.

Task and overlap

• Base: bb4bccbf42844d2801487450727c2f63e10d1d0f (canonical CrocSwap/integer-mult-bounds main, priority revision 6).
• Task: bit-helper-contract, scope refined. The card asks for a replacement H2/K interface. This session takes the next question in discussion Handoffs and requests for independent checks #1166 comment 19056041 instead of adopting that interface.
• Item 13 of the chronological open-handoff list on Handoffs and requests for independent checks #1166, after dropping delivered work, open PRs that already do the named next step, and this account's delivered round through Add a typed one-round actual-width H and rounded return. #4123. The twelve earlier items are comments 19021149, 19030049, 19031016, 19032637, 19034066, 19034676, 19035513, 19035716, 19036235, 19037887, 19039339 and 19040062.
• Predecessor: PR Certify the R439 K defect as the D-internal cross-term tally #4115, the K-defect tally, which left the hypothesis open. The words are the existing target-compensation, helper-star and bsection-star packages. PR Research: per-helper-sector census of the literal K_equals_D defect on retained R439 helper-star words (no new kappa) #4092 counted the defect. PR Show that one restored helper edge misses the literal K mask #3533 isolated one unrestored-mask edge.
• Nearest overlap is PR Certify the R439 K defect as the D-internal cross-term tally #4115. This package does not recompute the 17,636-bit sector table. It names the shape that forces E = K and separates the synthetic edge.

Validation

CPython 3.12, standard library, from the repository root:

python3.12 -B scripts/research_package.py --package research/r439-shear-compensation-hypothesis

Observed:

PASS_R439_SHEAR_COMPENSATION words=4 edges=221/221/236/188 parent_E_equals_K=1 descendants_E_equals_K=4 shape=4 one_edge_steps=871 compensated_probe=1 uncompensated_probe=1 synthetic_rejects=1 no_new_kappa
PASS_REGISTERED_RESEARCH_PACKAGE research/r439-shear-compensation-hypothesis outcome=partial

The same line passed under python3 -I -O -Werror -B. Metadata and pin check passed. The one-edge identity is the case split in the README; the verifier evaluates it on all 866 real edges and the five probe edges. Failure controls are the uncompensated probe and the synthetic edge, both required to separate.

Not run: the owner H2 checker, Lean, Docker, a selected cold replay, hosted CI. The B/C edits that preserve K were executed, not structurally classified.

Credit

Parent bracket: target-compensation. Shear assembly and the star and pair-control words: helper-star builder (PR #967) and research/r439-bsection-stars-seed01. PR #3533 for the restored-edge mechanism. PR #4092 (Nick Petalas) for the sector census. PR #4115 for the tally and the open hypothesis.

Prepared by unpaidmoon with substantial AI assistance (Cursor Grok). Apache-2.0. No independent human or proof-kernel review is claimed.

Open next questions

Linked from research/r439-shear-compensation-hypothesis/README.md.

1. Does every later phase-B rewrite with this D bracket preserve K, or only the three checked variants? First step: compare one other pinned B-section word. Blocker: those B and C edits have no structural account here.
2. Which H2 clause still fails once E is read as delivered columns? First step: name the first failing H2_D_frame0_targets_from_helpers read on the star word. Blocker: this package does not rerun that checker.

Workflow feedback (optional)

The released question named the synthetic edge and the three words, so the session could stop at one shape. No separate workflow note.