Research: PR #3190's remainder moves change the exact physical operator (affects #3198/#3200/#3251; no new κ)

[Matarener]

Requested by Mark

Change and mathematical scope

Scoped negative result (audit), no new κ. PR #3190's idle-remainder donations, inherited by #3198, #3200 and #3251, do not preserve the exact eight-stream physical operator under the unchanged completed local-invocation contract.

• At owner replica 0, port 0, Conditional κ = 0.001733427039589844234749 (bit-bound): idle-remainder donors on #3148's T740 fill (+0.187% over #3184) #3190 commits exactly two moves: axis 2^72 from child 14 to 8 and from child 15 to 10. Both donors are rank-1 hosted remainders (31 of 32 axes hosted). Both moves pass Conditional κ = 0.001733427039589844234749 (bit-bound): idle-remainder donors on #3148's T740 fill (+0.187% over #3184) #3190's declared rule: commuting with the receiver's axes, all stage entry/exit X/Y translations, terminal Y and both terminal translations, rank cap 51 and orthonormality.
• With PR3187's exact Gaussian-integer replay, the baseline at character 2^72 is i·I_8. The overlay changes 10 entries. Each move alone changes 5 disjoint entries (e.g. (6,6): i → −1 for 14→8 and (7,7): i → −1 for 15→10), so neither move preserves the operator and they do not cancel.
• Census: in all 112 ports of owner replica 0, the 448 committed moves pass the declared rule, the baseline equals the scalar operator, and the operator changes in every port. 56 ports carry the hosted-remainder donations above; the other 56 carry Conditional κ = 0.001730189061233850760095: idle rank-48 star exchanges on #3148's T740 fill (+0.0238%) #3184-type stars (consistent with Research: certify the current idle-star physical counterexample #3187).
• Conditional κ = 0.001734770557111513160495: R438 bit supplier with #3190's idle-remainder donors (complex binds again, +0.0775%) #3198 reuses Conditional κ = 0.001733427039589844234749 (bit-bound): idle-remainder donors on #3148's T740 fill (+0.187% over #3184) #3190's profile; Conditional κ = 0.001734807021726127552033: greedy idle-axis phase on #3198 with the R438 bit supplier (+0.0021%) #3200's and Conditional κ = 0.001734815770385098563484: exact per-group idle-donor search on #3200 (+8.75e-9) #3251's MOVES files begin with the same moves.

Not shown: that every remainder transfer fails, or that no repaired or rescheduled exchange exists. Other owner replicas are not replayed; the literal counterexample is enough to reject the committed move set. Repair tariffs (#3220), native and outer obligations are separate.

Task and overlap

Card independent-moment (priority revision 6), scope changed (recorded in TASK.json) to the literal #3190 moves. Base 463113d675af7410ac91d53a4fed51ec6494eb9a; contribution commit b602e2e2576df07f63d950c903438e6e9fe08fbc. Audited heads: #3190 5e4a3235169edddd033889da4e9f47635ff50c3e (MOVES.json.gz vendored byte-for-byte, SHA256 c76310bc…, equal to that head's blob e8401e6d); #3198 418ea1dc, #3200 f09e5b25, #3251 d7d62544.

Overlap: #3187, #3196, #3199 and #3204 cover #3184's stars among unhosted children; #3204 explicitly excludes hosted instances. This package covers hosted-remainder donations. #3220 bounds additive repair costs and is complementary.

Validation

python3 -B research/pr3190-remainder-stream-obstruction/verify.py --all-ports
python3 scripts/research_package.py --package research/pr3190-remainder-stream-obstruction --check-only

Standard library only, about 35 s. It prints PASS_PR3190_ALL_PORTS ports=112 changed=112 no_new_kappa and requires equality with RESULT.json. Run locally with Python 3.10.6 on Windows; the metadata check passes. The registered Python 3.12 replay was not run locally. Controls: an axis outside the donor remainder and a self-move are rejected, an empty overlay preserves the operator, and the port-0 projection is checked equal to PR3187's authenticated projection.

Independence: obstruction.py imports PR3187's algebra.py and source.py unchanged (fill authentication of all 2,717,280 rows, operator model, data events). This is a new binding of that checker to #3190's literal moves, not an independent reimplementation of the operator model.

Credit

Nick Petalas (PR3187) for the exact replay; Gareth Davidson (PR1387) for the original physical-stream obstruction; Gonzalo-Mier (PR1252, #3196, #3199), tekuuu (#3204) and Ross Richardson (#3220) for related results; Rohan Arun (#3184/#3190/#3198/#3200/#3251) for the audited construction; Jeremy Diviney (PR3148) for the fill; Marius-Paul Dumitrean and the rank-seven lineage for the words. PR3133's notice is retained via PR3187's vendor directory. Written and run by Claude (Anthropic) via Claude Code, in a session donated by Mark; no human or formal review is claimed.

Open next questions

Is any hosted-remainder donation operator-preserving in this fixed schedule? If none is, #3190's mechanism yields no legal gain and the chain falls back to #3148. If some are, a corrected move set gives a smaller honest gain. First step: extend #3204's rigidity argument to hosted children 4, 6, 14 and 15, or enumerate single-axis remainder transfers per port with this replay.

🤖 Generated with Claude Code

[Matarener]

Update at 6f78fe217ed63ef84096d53ed3651b38bab81e15: added census.py / CENSUS.json. At all 112 ports of owner replica 0 it enumerates every single-axis transfer from a hosted child with a nonempty remainder to any other idle child. 3,809 transfers pass PR3190's declared rule (5,575 do not), and all 3,809 change the exact operator at their own moved-axis character; none survives. In 47 ports no transfer passes the rule. Multi-axis or simultaneous transfers, other replicas' hostings and repaired or rescheduled exchanges are still not covered. Run with python3 -B research/pr3190-remainder-stream-obstruction/census.py (about 90 s locally, Python 3.10). The metadata check passes.

[Matarener]

Validation update: the registered replay now passes locally with Python 3.12.10 (PASS_REGISTERED_RESEARCH_PACKAGE), so the note in the description that the 3.12 replay was not run is resolved. The code is unchanged.