diff --git a/research/centre-nonlinear-fresh-floor/README.md b/research/centre-nonlinear-fresh-floor/README.md index 0f2520b927..9dc0abbb45 100644 --- a/research/centre-nonlinear-fresh-floor/README.md +++ b/research/centre-nonlinear-fresh-floor/README.md @@ -72,7 +72,8 @@ its constant witness gives a bounded dyadic counterexample but supplies no fixed any regrouping of that mass could gain. - The screen uses the fixed selected local word, 112 ports, the nine-stage template and the coverage law. Changed words, templates or coverage laws are outside it. -- A terminal-only consumer that never forms the internal call-10 query is a changed contract and is not covered. +- A terminal-only consumer that never forms the internal call-10 query is a changed contract and is not covered by + Theorems 1–2. It has since been specified and priced elsewhere; see Open next question 1. ## Reproduce @@ -91,9 +92,18 @@ predecessor digest are rejected. `--write` regenerates `RESULT.json`. Structured in [TASK.json](TASK.json): -1. **Terminal-only consumer.** Can a changed consumer avoid forming the internal call-10 query? First step: - state the complete varying-source-and-target terminal map and test the 112 kernel witnesses of - centre-history-innovation. Blocked by: no priced changed terminal contract. +1. **Terminal-only consumer (answered by later packages, 2026-10-23).** The changed contract is the centre-free + coded word of [#4929](https://github.com/CrocSwap/integer-mult-bounds/pull/4929): with the centre deleted the call exit is + `Y <- Y + A X`, `A = I - R^T R/4`, so the terminal repair is `(I - A) X = 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 (`A w^p = w^p`), while at call 10 the routed + witnesses `52 phi_p e_p`, `p in J`, give repair `13 R^T P` of rank 8 (`det P = 32`). So the terminal map is information- + recoverable (`A^-1 = (A+12I)/13`), but it still needs 8 fresh dimensions per call that no earlier call carries, i.e. rank + 144 per 18-call stage. Its price is already bounded: [fragmentation-ceiling](../fragmentation-ceiling/PROOF.md) §6.3–6.5 + gives at least `8 f(8) = 63.5989` per call against the budget `63.5780`, and any mix of at-stage and post-hoc decoding + at least `18 · 8 f(8) = 1144.780` against `1144.404` (conditional on P-ATOM, owned carriers and fixed main chains). + See also coded-port-adapter-ceiling, coded-native-caller (TERMINAL.md), two-stage-coded-terminal and + coded-reverse-physical-pair-gap. Remaining doors lie outside that scope: decoders that read X directly (no P-ATOM), + network-coded carriers, and a typed recursive product for coded jobs. 2. **Carrier premise.** Does `8d` fresh coordinates force 64 rank-mass units for carriers other than rank-8 channels? First step: price one alternative carrier with its restoration and hosting bill. The screen here caps its ideal gain at +0.67%. diff --git a/research/centre-nonlinear-fresh-floor/TASK.json b/research/centre-nonlinear-fresh-floor/TASK.json index e2e36d0f08..7c941ceeb1 100644 --- a/research/centre-nonlinear-fresh-floor/TASK.json +++ b/research/centre-nonlinear-fresh-floor/TASK.json @@ -57,12 +57,6 @@ "author": "Mark (Matarener)", "ai_assistance": "Substantial Claude (Anthropic) assistance in proof, code and prose; no independent human or formal-kernel review.", "open_questions": [ - { - "question": "Can a terminal-only consumer avoid forming the internal call-10 centre query?", - "why_it_matters": "Both this floor and its predecessor bind the internal query; a changed consumer contract is the remaining route to fewer fresh centre coordinates.", - "first_step": "State the complete varying-source-and-target terminal output map and evaluate it on the 112 kernel witnesses of centre-history-innovation.", - "blocked_by": "No changed terminal contract with priced consumer, restoration and hosting obligations is specified." - }, { "question": "Does the information floor (8d fresh complex coordinates) imply the 64-unit rank-mass charge for carriers other than rank-8 channels?", "why_it_matters": "The step from coordinates to rank mass is the rank-8-per-channel carrier premise of #3918, independent of nonlinearity.", @@ -74,5 +68,13 @@ "canonical_main": "12fa8c5c844be21bfefb38a19503fbd867a11244", "overlap": "Inspected PRs 3075, 3120, 3147, 3151, 3291, 3548, 3873, 3918, 3948, 1888, 785, 888 and packages centre-history-innovation, centre-causal-tangent, *-nonlinear-copy-floor; no nonlinear fresh-observation centre bound found. No novelty guarantee.", "preservation": "Only the new package directory is added." - } + }, + "answered_questions": [ + { + "question": "Can a terminal-only consumer avoid forming the internal call-10 centre query?", + "answer": "Specified later as the centre-free coded word (#4929: exit Y <- Y + A X, A = I - R^T R/4, terminal repair R^T R X/4). On the 112 kernel witnesses the call-0 repair is zero and the call-10 repair has rank 8, so 8 fresh dimensions per call remain (rank 144 per 18-call stage). fragmentation-ceiling section 6.3-6.5 prices any at-stage or post-hoc repair at >= 18*8f(8) = 1144.780 > budget 1144.404, conditional on P-ATOM, owned carriers and fixed main chains.", + "remaining_scope": "Decoders reading X directly (no P-ATOM), network-coded carriers, a typed recursive product for coded jobs.", + "answered_utc": "2026-10-23" + } + ] }