research: reduce calibrated endpoint gauges to exact source tours

[RichardHoekstra]

Restored target phases can appear to make separately addressed pair readouts cheaper. A constructive detour moves each target's visited gauge to its declared source at no greater phase-moment cost, preserving every old input and both individual read calibrations. This closes arbitrary endpoint-gauge timing within a specified family, rather than only one phase window.

For even h >= 6, separate restored sources, separate dirty ordered within-half pair targets, exactly two individually calibrated reads per target, and no role mixing, the written proof gives exact minima for every 0 <= p <= 1:

• Oriented coordinate phases, rank cap h-2: 2h(h-2)^p + h(h-4).
• With binary translations separately counted but assigned zero phase-moment charge: 2h(h-2)^p + h(h-4)2^(p-1).

Translations are not declared free machine operations. At h=10 the attaining translation-closed word has 50 phase calls plus 30 translations, compared with 80 oriented phase calls; both have rank mass 220 and 80 scalar ADDs. The translation identity is inherited elementary algebra, not a new supplier mechanism. No new kappa, multiplication speedup or full formal proof is claimed.

Evidence

Only research/calibrated-endpoint-gauge-tours/ is added. Python standard library only:

python3 -I -O -B research/calibrated-endpoint-gauge-tours/test_verify.py
python3 -I -B research/calibrated-endpoint-gauge-tours/verify.py NEW_RECEIPT.json

• Twelve complete words at h=6,8,10: direct, translation-closed, overlapping endpoint gauges with late negative reads, and normalized source detours.
• Sparse integer Laurent-monomial replay and independently implemented dense Gaussian-integer/projector replay agree on 11,371,520 old-input operator entries.
• Exhaustive oriented phase-group searches cover 4,352 states at h=4,6.
• Eight test groups pass in optimized isolated Python mode, including twelve record corruptions, changed readouts, source/dirty-target restoration failures and existing-output preservation.
• Fresh patch application and relocation to a path containing spaces pass; the complete regenerated receipt is byte-identical. The relocated replay took 14.43 seconds, peak RSS 15,548 KiB, Linux x86_64 / CPython 3.10.12, one low-priority CPU and a 4 GiB address-space limit. These are resource observations, not a matched speed comparison.

The all-p all-size theorem is a written argument. The executable detour normalizer certifies rank mass (p=1); it is not a general all-p shortest-path solver. Finite replay is not formal verification of the universal theorem or the multiplication algorithm.

Scope, credit and overlap

The coordinate-phase and rank-priced residual framework is inherited from the project's stopped/partial-gauge lineage, including icekylinx's #104. The phase/translation identity is not claimed novel.

Inspected 823 open PR titles/bodies, active discussions, nearest public proof notes and later arrivals through #1227. Exact heads are recorded in SOURCES.json. Eumemic's #288 and CubeJerry's #907 concern broader abelian-metric claims; this proof derives its explicit coordinate metric and uses no general l1-embeddability premise. Navinor's #825 treats rational-frame XOR common flags, outside the present complex-phase model. #1227 prices fixed-child sign restoration and dirty echo, not calibrated pair-port tours. This bounded overlap check does not establish literature priority.

Cross-role mixing, additional reads, target consumption, changed outputs and arbitrary circuits realizing the same final map are excluded. The README supplies a concrete bounded next question beyond those restrictions. Supplier allocation, complete recursive invoice, realization, precision/tape and analytic transfer remain open. The selected frontier, immutable inputs and all existing files remain unchanged.

Prepared by Richard Hoekstra with substantial OpenAI Codex assistance in mathematics, implementation and writing. Both replay engines are AI-assisted; no independent human review is claimed. New standalone material is offered under Apache-2.0 with predecessor attribution retained.

[Mister-Meeseeks]

100-PR batch review at 3941a3c63651d379feceb411019c30310e9e12d0.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Calibrated two-read pair-port words reduce target gauge paths to restored source tours without increasing concave phase moments. Exact all-even-h oriented/translation-quotient minima; separate outputs, fixed calibration and no cross-role mixing are essential.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.