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Prethermal Plateau Unification: Pad Geometry Plus MAP Translation

William J. Richardson

Published Jan 31, 2026• 0 citations
Publisher

Abstract

This critical manuscript addresses a persistent failure mode in prethermal plateau and stability claims: the gap between demonstrating a long-lived dynamical regime and certifying that the regime is usable under fixed, replayable rules. Recent platform results show that structured random driving can suppress heating and extend prethermal lifetimes on many-qubit processors. While these results establish physical existence and controllable lifetime, they do not by themselves certify operational utility or guard against boundary narrative repair. This manuscript extends the earlier pad and triad-of-triads program by applying MAP as a unifying translation layer to prethermal plateau claims. Prior work established the signed-triad ledger, Strong-to-Weak downgrades, STLF refusal discipline, and tokens-only replay as independent enforcement tools. Here, those tools are bound together by MAP and explicitly externalized from the engine, allowing plateau lifetime claims to be evaluated as contract objects rather than as narrative curves. The result is a carry-forward certification spine that preserves earlier triad logic while adding a thermodynamic interpretation of acceptance leakage and a regime-transition marker (ZFlip) suitable for plateau-style datasets. The central contribution of this work is Mapping and Amplification Protocol (MAP), a pad-centered translation layer that externalizes certification logic from the engine and forces enforcement tools to act coherently under a shared coordinate meaning. MAP is not a new physical mechanism and not an optimizer. It is a deterministic translator from tokens to enforcement actions that binds Strong-to-Weak, STLF, Knob, and Sum-of-Zeros to the same declared pad and corridor. By doing so, MAP removes silent degrees of freedom that otherwise allow filtering, tightening, or drift to masquerade as stability. Under MAP, plateau behavior is no longer evaluated by a single flat curve or preferred projection. Instead, claims are promoted, downgraded, or refused through a triad-of-triads contract that separates signed state, windowed pattern fingerprints, and meta-promotion logic. Two independent redundancy cages (view square and ladder square) are enforced via double Four-Solves-Three auditing, blocking majority narratives and forcing disagreement to remain visible. Acceptance recovery is explicitly bounded: any recovered utility must be paid for through declared downgrades rather than repaired into Strong. Within this framework, the manuscript introduces a contract-level thermodynamic separation: what platform studies describe as “heating” is treated here as acceptance leakage in time under a fixed corridor. The quantity TzTzTz is operationalized as a burn-rate proxy that tracks how quickly tension is consumed as trajectories approach refusal, while ZFlipZFlipZFlip marks the first persistent regime transition where the effective plateau description fails. Plateau lifetime is therefore treated as necessary but not sufficient; the resource question is whether the plateau survives under fixed accounting until the flip. The intended outcome is a reusable, platform-independent certification object. MAP and the surrounding contract infrastructure are designed to carry forward across qubit, magnonic, photonic, and hybrid platforms, allowing future plateau datasets to be evaluated without modifying the rule spine. The result is not a critique of platform physics, but a durable method for turning plateau observations into bounded, replayable, and falsifiable objects of record.

DOI
10.5281/zenodo.18437091

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Significant — This work takes the “magnetic sweet spots” story for hole spin qubits and turns it into a standards-ready control program instead of a one-off tuning narrative. The core move is to treat magnetic-field orientation as a first-class coordinate layer and the sweet spots as an extended manifold (not a fragile point), then bind operation to preregistered acceptance lines and replayable tokens so the claim survives drift, device variation, and calibration error rather than being rescued by post hoc selection. The paper explicitly encodes the result as a triad—noise insensitivity, drive efficiency, and orientation—and adds explicit failure sinks (null pressure, drift proxy, yield/SoZ) so borderline regions cannot be laundered into success by averaging. It also blocks the common “one global angle fixes all” misread by proposing a multi-level knob hierarchy (global orientation policy + local gate policies + audit schedules) and a three-bench contract (baseline, stress, portability) so “works on this device today” is separated from “portable and replayable under stress.” The net contribution is a reusable certification wrapper for sweet-manifold operation: it does not change the physics, it changes what is allowed to count as a scalable operating point.
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Foundational — From Two-Dimensional Photon A-to-B Routing to a True Three-Dimensional Pedigree–Transmission–Triad-of-Triads (PTT) Engine. This article develops a three-dimensional custody engine for preserving and comparing correlated records from a cascaded quantum network. Rather than placing the upstream A-side and downstream B-side observations into one shared qudit cell, the engine gives each record its own three-dimensional address, corridor identity, fire history, position count, and sealed route record. A shared Correlation ID and frozen comparison-window number bind the pair without averaging their amplitudes, phases, support fields, typed-zero histories, or native source times. The physical cascade remains unidirectional from A to B. A frozen time-translation rule maps the distinct source times and propagation delay into one correlation window without claiming physically simultaneous qubit fires. Cross-Chain later compares the sealed A-side and B-side records at the signed balance center S = 0. The B-side record may strengthen downstream evidence, but it cannot rewrite the A-side record, the upstream emission history, or the frozen source contract. This preserves paired comparison while enforcing no backward authorship. After a signed direct block, the production engine tests a declared four-route three-dimensional forward-bypass set: two x-y routes and two x-z routes. This selected set does not claim to enumerate every possible corner route in a three-dimensional neighborhood. Each route keeps its own support, direction, timing, phase-facing, and burden record. A successful bypass retains Strong-to-Weak authority because the original direct block remains part of its history. Directional Empty Frames 1 through 3 separate outward reading, burdened return, and terminal stopping authority. EF1 preserves the inward three-dimensional support read while opening the first outward directional witness. EF2 is the Strong-to-Weak and Weaker decision region: a forward-preserving return remains eligible for Strong-to-Weak, while a backward-burdened return becomes eligible for Weaker. EF3 is the outer kill and flattening boundary. It stops further outward movement, forces the bounce through EF2, and keeps the final direction witness at the EF1-EF2 edge rather than allowing hidden support to accumulate at the outer boundary. Typed-zero custody controls which routes may continue. Sign-empty launch failure writes 0T. A signed direct block may form a 0S candidate carrying inherited half-sign continuity. A contacted timeout writes 0S timeout only when inherited sign and support remain demonstrably present through qualified contact; precontact loss remains 0T or the declared failure class. Detour and the Common Detour Reporter activate only after all four declared bypass routes fail while a live signed candidate remains. One logical Reader receives the completed sealed measurement record, including the separate corridor histories, selected bypass, typed-zero fields, Cross-Chain closure bits, and route grade. The Reader may consume multiple tomography settings, detector records, positive operator-valued measurements, or physical channels, but it remains one endpoint authority rather than a replacement for those experimental measurements. A 400,000-cycle Python synthetic reports 90.953 percent Strong-or-Strong-to-Weak route admissibility, 8.795 percent remaining post-route typed-zero burden, and 5.406 percent Reader classification error. Four-route bypass recovery returns 46.150 percent of all cycles to Strong-to-Weak custody, while Detour returns another 11.348 percent. Ten independent seeds, nine stress combinations, and twenty production guardrails test address separation, excluded-corner discipline, time translation, typed-zero routing, no-backflow, Detour activation, Cross-Chain closure, Reader authority, and deterministic counter behavior. The article does not replace the source experiment’s entanglement formation, concurrence measurement, tomography, channel-loss analysis, or hardware calibration. Its contribution is a reusable logical custody engine for preserving two correlated histories, routing them without shared-cell flattening, separating physical, route, and Reader burdens, and producing one auditable endpoint decision.
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