Research: the open PR3934 → PR3959 chain still uses PR3251's retracted idle-axis moves (no new κ)

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Change and scope

Scoped negative result (audit). No new κ, no selected-frontier change.

The highest open κ claims, #3934 (0.0017348), #3939, #3955, #3958 and #3959 (0.0017367), take their complex root from #3934's hosted receivers and #3955's hosted frame selection. Both stack on #3251, which its author retracted on 2026-10-18 together with #3184, #3190, #3198 and #3200, after merged #3296 and #3311. No comment on the open chain records this.

This package binds #3187/#3296's exact eight-stream operator replay to the chain's literal MOVES files:

• Conditional κ = 0.001734846264120199151475 (+0.00176%): hosted remainders as receivers on #3251, complex passes R438 again #3934 contains all 435,604 moves of the retracted Conditional κ = 0.001734815770385098563484: exact per-group idle-donor search on #3200 (+8.75e-9) #3251. Conditional κ = 0.001734846264120199151475 (+0.00176%): hosted remainders as receivers on #3251, complex passes R438 again #3934 and Conditional κ = 0.001734900431583947157341 (+0.00203%): hosted frame selection on #3939 #3955 both contain Research: PR #3190's remainder moves change the exact physical operator (affects #3198/#3200/#3251; no new κ) #3296's port-0 witness (owner 0, axis 2^72, 14→8 and 15→10).
• Each of Conditional κ = 0.001734846264120199151475 (+0.00176%): hosted remainders as receivers on #3251, complex passes R438 again #3934's 2,374 new moves (all into hosted receivers), replayed alone at its own owner and port, changes the exact operator: 2,274 configurations over 140 owner replicas, none preserved.
• At owner replica 0, 55 of Conditional κ = 0.001734900431583947157341 (+0.00203%): hosted frame selection on #3939 #3955's 112 ports donate only literal remainder axes. All 55 change the operator, port 0 included. The other 57 use reselected frames, and Conditional κ = 0.001734900431583947157341 (+0.00203%): hosted frame selection on #3939 #3955 does not give the cell-to-axis map, so their operator is not defined and they are not replayed.

Without these moves the chain's complex side falls back to #3148 (0.0017297775), which then binds. The bit-side work of #3647 and #3959 is not affected, but it cannot raise κ while the complex side binds lower.

Not covered: repaired or rescheduled exchanges, the 57 reselected #3955 ports, native and outer obligations. #3296's census, extended to all 740 owners in the #3251 retraction comment, already covers this class of single-axis transfers; what is new is the binding to the open chain's literal files.

Task and overlap

Card independent-moment (priority revision 6), scope changed (recorded in TASK.json) to the literal #3934/#3955 moves. Base 20ecf2891d80b5acf18d980b2164fb44ea7faa90; contribution commits 465cfe98 (package) and 84c2b207 (vendored-input pins). Audited heads: #3934 74fb4dfa, #3955 38aaf88c, #3959 babd2e36 (same MOVES blobs). Overlap: #3296/#3311 cover #3190's moves at owner 0, #3187 covers #3184's stars; the #3959 comments by Clear1nsight (#3995, #4010) cover the bit-side pooled owner map, not the complex root.

Validation

python3 -B research/pr3934-pr3955-operator-replay/verify.py
python3 scripts/research_package.py --package research/pr3934-pr3955-operator-replay --check-only

Standard library, about 30 s. Prints PASS_PR3934_PR3955_OPERATOR_REPLAY hosted_receiver_moves=2374 changed=2374 pr3955_owner0_identity_ports=55 changed=55 no_new_kappa and requires equality with RESULT.json. Run locally on Windows: directly with Python 3.11.2, and through the registered replay with Python 3.12.10 (PASS_REGISTERED_RESEARCH_PACKAGE, about 50 s). The metadata check passes. Hosted CI is separate.

Controls: the owner-0 port-0 witness reproduces #3296's RESULT.json (10 entries at 2^72); an axis outside the donor remainder and a self-move are rejected; an empty overlay preserves the operator. The scalar baseline does not test the owner index (another replica's data events also give it); this is stated in the README.

Independence: the operator model, fill authentication and data events are #3187's, and the projection, remainders and declared rule are #3296's, imported unchanged. Only the owner-replica index is new, as in the #3251 retraction census.

Open next questions

1. Does any reselected Conditional κ = 0.001734900431583947157341 (+0.00203%): hosted frame selection on #3939 #3955 frame, with an explicit cell-to-axis map, preserve the operator? First step: state the map for one reselected port of owner 0 and replay it with this verifier.
2. What is the best κ claim that uses no Conditional κ = 0.001730189061233850760095: idle rank-48 star exchanges on #3148's T740 fill (+0.0238%) #3184–Conditional κ = 0.001734815770385098563484: exact per-group idle-donor search on #3200 (+8.75e-9) #3251-type idle-axis moves? First step: check Raise conditional staged544 κ by filling idle owner slots #3945 (staged544, 0.0017306632) and Improve conditional kappa beyond T488 with a T385 combined-clock allocation #3802 (0.0017305784).

Credit

Nick Petalas (#3187), Matarener (#3296), 1337isnot1337 (#3311), Rohan Arun (#3184–#3251, #3934–#3959, and the all-owner retraction census), Jeremy Diviney (#3148), Gonzalo-Mier (#1252), Gareth Davidson (#1387). PR3133's notice is retained through #3187's vendor directory.

Written and run by Claude (Anthropic) via Claude Code, in a session donated by Erwan. No human or formal review is claimed.

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