[Matarener]

Requested by Mark

Change and mathematical scope

Documentation-only update to our own package research/centre-nonlinear-fresh-floor (#4417). Its open question 1 ("can a terminal-only consumer avoid forming the internal call-10 query?") is marked as answered, with pointers to the community's later work.

Before: the README and TASK.json list the terminal-only consumer as an open, unpriced contract.

After: the README says that this contract is the centre-free coded word of #4929, and that its terminal repair is already priced. TASK.json moves the question to answered_questions.

The facts recorded:

• With the centre deleted, the call exit is Y <- Y + A X with A = I - R^T R/4, so the terminal repair is R^T R X / 4 = 14PX.
• On the 112 kernel witnesses of centre-history-innovation, R w^p = 0 makes the call-0 repair vanish. At call 10, the routed witnesses 52 phi_p e_p, p in J, give the repair 13 R^T P, which has rank 8 (det P = 32).
• So the terminal map is recoverable in information terms (A^-1 = (A+12I)/13). It still needs 8 fresh dimensions per call, which is rank 144 per 18-call stage.
• fragmentation-ceiling §6.3–6.5 bounds the price at >= 8 f(8) = 63.5989 per call against a budget of 63.5780. Any mix of at-stage and post-hoc decoding costs at least 1144.780 against 1144.404. These bounds are conditional on P-ATOM, owned carriers and fixed main chains.
• The doors that remain lie outside that scope: decoders that read X directly, network-coded carriers, and a typed recursive coded product.

No new κ, theorem or supplier. The verifier and RESULT.json are unchanged.

Task and overlap

Base: ff3cc58e3. Card centre-path-sharing; scope unchanged (bookkeeping of an open question). The nearest work, which this PR only cites: #4929, #4932, #4933, #4940, #4943, #4948, fragmentation-ceiling, coded-port-adapter-ceiling, coded-native-caller, two-stage-coded-terminal, coded-reverse-physical-pair-gap. No other package pins files of this package.

Validation

• python3.12 -B scripts/research_package.py --package research/centre-nonlinear-fresh-floor --check-only → PASS_PACKAGE_METADATA_AND_PINS
• python3.12 -I -B research/centre-nonlinear-fresh-floor/verify.py → PASS_CENTRE_NONLINEAR_FRESH_FLOOR premise=8edf9aec270e packing_best=x1.006721 controls=4 no_new_kappa

The witness facts follow from R w^p = 0 and the stated minor. I also checked them in exact integer arithmetic on the emitted R (112 witnesses, repair ranks 0 and 8) with a local script, which is not added to the package. Windows, CPython 3.12.

Credit

Credit for the coded word, its pricing and the witnesses belongs to the authors of the linked PRs and packages, chiefly Dugongue (#4929), dillona (#4933), the fragmentation-ceiling authors and Jose Manuel (centre-history-innovation). Prepared by Mark (Matarener) with substantial Claude (Anthropic) assistance.

Open next questions

Question 2 (carrier premise) remains open, unchanged. For question 1, the remaining scope is listed in TASK.json answered_questions[0].remaining_scope.

🤖 Generated with Claude Code