Scoped negative result: PR589's bit word is exactly transport-locally optimal (no new kappa)

research/bit589-transport-atlas/README.md

@@ -0,0 +1,78 @@
+# PR589's bit word is exactly transport-locally optimal (scoped negative result, no new kappa)
+
+**Claim.** Keep PR589's gate multiset, operands, scatter, start/final frames, D, the
+rebuilt literal-reverse C, and the retained totals' COPY frames (decoder constant 63)
+fixed. Then no **transport** — relocating one elementary addition `r += s` to any
+position inside its exact commutation window at any legal catalogue frame (or the
+closure frame of the slot bounds) — lowers the moment `Σ_d n_d·d·(64/d)^c` of the
+local paid profile at the exact bit saving `c = 1733427039589844234749/10^24`.
+The same holds for every pair of simultaneous transports sharing a register.
+PR589's own gain came from two transports, and its tuner (`../e8-bit-p111-tuned/tune/`)
+reached the word by greedy single moves with **floating-point** chain fees at the
+rounded exponent `a = 0.001733`, making no optimality claim. `bit589-frame-optimum`
+proved the word exactly frame-optimal with the gate sequence fixed and stated that
+future bit headroom on this word must come from gate-order or structural changes.
+This closes the gate-order part of that question exactly and independently.
+
+**Scope: no new kappa.** The selected assembly binds on the complex primitive
+(`a_c = 0.0016754627 < a_b = 0.0017334270`, bit slack 3.46%); no bit-supplier change
+can raise the selected kappa at this base. As in `bit589-frame-optimum` and
+`bit589-width-packing`, the contribution is bit headroom / door closure.
+
+## Method (`atlas.py`, standard library only, independent of the contributor tuner)
+
+1. **Exact objective.** The pinned moment engine
+   (`../complex-k492-owner-repair/vendor/multicold/engines/base_two_moment.py`,
+   sha256 `aee70c24…`) gives outward rational bounds for `d·(64/d)^c` at the exact c;
+   no float decides a comparison. The scored quantity is the full per-register
+   frame-chain cost (D, A, B, C, final) plus scatter tops, which reproduces the
+   replay paid profile `{1:1323, 2:1342, 3:79, 4:44, 5:102, 6:11, 7:19}` exactly —
+   this also repairs the tuner's section-local model, which double-counts the
+   last-A-to-first-B climb and ignores D.
+2. **Moves.** For each of the 2130 A and 934 B elementary additions: exact
+   commutation window, context-constant slots, feasible catalogue frames between the
+   operand bounds (plus the closure frame), COPY-frame preservation on retained
+   totals, and full-chain nesting. 3411 distinct slot-bound pairs.
+3. **Simultaneity.** Transports on disjoint register pairs are independent (chain
+   costs decompose per register), so with no improving single transport no disjoint
+   simultaneous move improves either. The remaining coupling is shared registers:
+   every pair of movable transports sharing a register is enumerated with all
+   frame/slot choices. Full components are one 1924-op giant (A) and five
+   ~200-op giants (B) — combinatorially out of reach; see Limitations.
+4. **Legality cross-check.** Sample moves of each outcome class are applied to the
+   word, C rebuilt, and replayed exactly (nested frames, F2 endpoint); the replayed
+   profiles match the chain-model predictions.
+
+## Result (`result.json`)
+
+| class | A | B |
+|---|---|---|
+| elementary additions | 2130 | 934 |
+| legal non-home single placements | 5830 | 3561 |
+| same paid profile | 5580 | 3226 |
+| strictly worse (exact) | 250 | 335 |
+| **improving** | **0** | **0** |
+| smallest strict loss | 8.00e−6 | 1.94e−3 |
+| shared-register pairs / combos scored | 13673 / 225152 | 6006 / 218448 |
+| **improving pairs** | **0** | **0** |
+
+No comparison was left unresolved by the rational bounds. The 8 replay spot-checks
+(4 same-profile, 4 strictly-worse) reproduce the predicted profiles.
+
+## Limitations
+
+- Simultaneity is certified for pairs, not for triples or larger shared-register
+  sets (giant components); a superadditive triple is not excluded.
+- Steinberg 3→2 substitutions and other structural changes are a different move
+  class, out of scope here (frames alone: `bit589-frame-optimum`).
+- Cross-section simultaneous moves (one A, one B transport on a shared register)
+  are not enumerated; they couple only through the single last-A-to-first-B climb.
+
+## Reproduce
+
+```sh
+bash research/bit589-transport-atlas/verify.sh   # ~70 s; last line PASS_BIT589_TRANSPORT_ATLAS
+```
+
+Python 3.11+, standard library only (CPython 3.12 used). Base commit
+`bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. Seed 10 (bit supplier track).