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Centered-X Across Platforms: Magnons, L1/L2, and the [[5-1-3]] Stabilizer Under a Common 4S3 Grammar

Richardson, William J.

Published Nov 4, 2025• 0 citations
Publisher

Abstract

This is the first in three significant manuscripts, and it establishes a mid-level Four-Solves-Three (4S3) controller for wave platforms, with magnons and L1/L2 geometry as the primary arena and a [[5,1,3]] stabilizer twin for device-independent containment. Decisions are made by four fixed roles closing three independent gates under guard-safe containment: parity hygiene, centered-X balance-line co-lock, and corridor-mapping severity. Acceptance lines are locked (IoU >= 0.75; rho <= -0.60) and never moved. Engine-invariant falsifiers (flip-only Z, disable-L, withhold-carrier reproducibility, and a 3-of-4 stabilizer audit) bound artifacts without threshold travel. Reproducibility is delivered through tokens-only replay with minimal hashed schemas (e.g., window_hash, corridor_hash, grid_spec_hash, kpi_script_hash) and a worked micro-example. A rectifier KPI and a preregistered Tz_star budget provide compact auditing of parity and flatness; a one-tick Future_ur lease gate ensures survival consistency before any directive update. A concise concentric-ladder checkpoint (4->5) is identified for stress testing while guards remain fixed. The result elevates wave-scale demonstrations to a replication-ready standard: same grammar across magnons, L1/L2 geometry, Floquet/SRO mapping, and the stabilizer twin, with leave-one-out redundancy and tokens-only replay enabling independent verification.

DOI
10.5281/zenodo.17525236

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This is the first in three significant manuscripts, and it establishes a mid-level Four-Solves-Three (4S3) controller for wave platforms, with magnons and L1/L2 geometry as the primary arena and a [[5,1,3]] stabilizer twin for device-independent containment. Decisions are made by four fixed roles closing three independent gates under guard-safe containment: parity hygiene, centered-X balance-line co-lock, and corridor-mapping severity. Acceptance lines are locked (IoU >= 0.75; rho <= -0.60) and never moved. Engine-invariant falsifiers (flip-only Z, disable-L, withhold-carrier reproducibility, and a 3-of-4 stabilizer audit) bound artifacts without threshold travel. Reproducibility is delivered through tokens-only replay with minimal hashed schemas (e.g., window_hash, corridor_hash, grid_spec_hash, kpi_script_hash) and a worked micro-example. A rectifier KPI and a preregistered Tz_star budget provide compact auditing of parity and flatness; a one-tick Future_ur lease gate ensures survival consistency before any directive update. A concise concentric-ladder checkpoint (4->5) is identified for stress testing while guards remain fixed. The result elevates wave-scale demonstrations to a replication-ready standard: same grammar across magnons, L1/L2 geometry, Floquet/SRO mapping, and the stabilizer twin, with leave-one-out redundancy and tokens-only replay enabling independent verification.
This manuscript specifies a mid-level, standards-ready controller for networked quantum sensing under a Four-Solves-Three (4S3) contract. Four fixed roles (D, A, B, C) decide three gates—parity hygiene, centered-network co-lock, and corridor severity—without threshold travel and with tokens-only replay. The physical setting is a compact continuous-variable network that enables weighted-sum estimation on the determinant lane (D). I/Q centering (L1/L2) anchors the estimator; z_tension operates as a stop-token budget. Device-independent falsifiers (flip-only phase, disable-L, withhold-node, leave-one-out) are executed at network scale. Heisenberg claims are bound-respecting via a preregistered Fisher ratio band and an identifiability angle token. Two guard-safe routes are contrasted under the same contract: Route A (Magnon Electric Readout, direct D-lane weighted sum) and Route B (Angular Ribbon Mid-Stream Tap, advisory-only centering/stop). A minimal replication kit (frozen graph/weights/mask, detector model, and JSON schemas) allows third parties to reproduce IoU and rho, rerun falsifiers, and verify acceptance from tokens alone.
This manuscript establishes a fixed, platform-agnostic measurement corridor for cross-bench certification and applies it uniformly to both on-chip magnon devices and Gaussian homodyne photonics. External papers supply only their hardware and readout templates; all scoring, falsifiers, z-Tension budgeting, and replay rules originate in the present G–Σ–P–L grammar. The work formalizes a native three-parameter witness—F_guarded, Tz_center, and rho_back—under acceptance lines that never move, and introduces a registrar-verified, tokens-only replay path anchored by a one-tick time-triad lease. Reverse UBL contributes the P-lane magnitude (R′), while Centered-X, programmable UBL ⟂ DHP, and local TWA+ calibration provide the structural mapping that locks both platforms to a common contract. This bridge manuscript is technically important: it fixes the corridor for all upcoming triad-based evaluations and ensures that future device claims, photonic or magnonic, are falsifiable, replayable, and computed under the same immovable G–Σ–P–L rules.
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This repository is a verification-first release of SFT: a theory/framework plus a set of runners designed for external audit. Update — FEM cross-backend exploratory bridge outputs Update date: 2026-07-07 This repository now includes SFT_FEM_CROSSBACKEND_REPRO_v0_1_12, an exploratory FEM cross-backend bridge package for selected SFT-facing audit targets. The previous Firedrake/UFL bridge line is preserved through SFT_FIREDRAKE_CORE_REPRO_v0_1_10 and the v0_1_11 S-compliance addendum. The new v0_1_12 package adds an independent FEniCSx/DOLFINx bridge layer for compatibility, native collapse, spin FR, double-slit readout, and Mercury/Venus perihelion gates. This repository therefore now contains selected SFT-facing audit targets implemented across two FEM environments: Firedrake/UFL bridge outputs for spin-½ FR bend robustness, spin/topological memory, scalar recovery/residue controls, hydrogenic radial Coulomb H/T 2s/2p gates, Venus/Mercury 1PN perihelion geometry gates, alpha-localization capacity scans, double-slit phase/visibility diagnostics, double-slit Born-readout diagnostics, exploratory alpha-thread proxy gates, an exploratory S-rigidity compliance-window scan, and an intentionally incomplete Alpha-Out bridge report. FEniCSx/DOLFINx bridge outputs for the compatibility operator, native collapse gate, spin-½ FR signature, double-slit phase/visibility/Born-readout diagnostics, and Mercury/Venus 1PN perihelion gates. The v0_1_10 package consolidates the Firedrake/UFL bridge suite, including spin/topological memory, radial and perihelion sanity gates, recovery/residue controls, double-slit Born readout, and exploratory alpha-thread proxy gates. The v0_1_11 addendum adds a focused S-rigidity compliance landscape: a fixed-physical-time scan mapping a bounded medium regime between rupture and persistent scalar residue under locked gates. This S-compliance landscape is not an alpha result, not a particle-identification result, and not a global physical validation of SFT. The v0_1_12 cross-backend package adds an independent FEniCSx/DOLFINx implementation layer. It supports the narrower claim that selected SFT-facing compatibility, collapse, topological, readout, and geometry gates can be represented reproducibly in both Firedrake/UFL and FEniCSx/DOLFINx under declared protocols. These FEM bridge outputs are more informative than synthetic CI checks because they are produced in external real-solver environments and exported as auditable JSON/CSV artifacts with SHA-256 manifests and machine-checkable PASS/FAIL gates. They are not presented as global physical validation of SFT, nor as derivations of the Standard Model, General Relativity, Born's rule, the electron/photon, the physical fine-structure constant, or matter programmability. They should be read as exploratory P-bridge outputs: real-solver bridge results that exercise the verification-first contract, while still requiring independent third-party REAL runs at multiple resolutions for physical confirmation. Evidence labels used in this repository: CI (C): CPU-only validation of tooling, schemas, manifests, regression checks, and PASS/FAIL logic. REAL-ready (P-input): verifier and artifact contract are ready to ingest third-party real-solver outputs. Exploratory P-bridge: real-solver bridge outputs produced in an external solver environment, with hashes and machine-checkable reports, but not yet independently replicated. Cross-backend exploratory bridge: selected audit targets represented across Firedrake/UFL and FEniCSx/DOLFINx, strengthening implementation transparency without constituting physical confirmation. REAL-verified (P): reserved for independent third-party real-solver runs with artifacts, hashes, locked gates, and at least two resolutions.
Significant — This manuscript installs a bench-independent translation tool for two January 2026 condensed-matter/quantum-tech reports by treating exciton breakup under fermion crowding and self-induced superradiant masing in interacting spins as one control problem: an interaction-driven population-transfer “tilt” between a cooperative lane and a surrounding bath, where corridor-eligible tilt produces burst trains and sustained output while too-weak/too-strong tilt yields no macroscopic fingerprint or runaway breakup/depletion; the method is operationalized with shared tokens BBB (bulge latency), LLL (leakage), and 2f2f2f (curvature/oscillation), a ternary directive knob with a true null for disable-LLL, and a three-bench tokens-only contract that makes the regime replayable, falsifiable, and portable across platforms without importing platform-specific narratives; the deliverable is a protocol-level mapping a lab can implement using its own knobs and carriers, with explicit falsifiers (zeros-stay-zeros, parity-first, bench swap, dither, and ZFlip licensing) to prevent postselection and drift from masquerading as control.
Modern quantum error-correction pipelines are increasingly assembled from heterogeneouscomponents: neural predecoders trained on stabilizer syndromes, heuristic local correctors,and symbolic exact routines. Each component is correct in its regime and wrong outsideit, and a deployment decision must be made per workload, per round, under real-timeconstraints. We present a reproducible trust-layer and routing demonstrator for NVIDIA-style Ising-family surface-code predecoders, packaged as a standalone public artifact. Thesystem combines four load-bearing ingredients: (i) a hash-pinned benchmark surface of512 dual-basis distance-13 samples with SHA-256 contracts on every committed artifact;(ii) a provenance-forensics layer that executably localizes replay mismatches to the specificpipeline stage responsible for them; (iii) a structured-regime routing policy derived froma signed benchmark delta rather than a hand-tuned threshold, with a falsifiable mutationtest that proves the lane selection follows the evidence and not the implementer; and (iv) aCUDA-Q preflight that reports deployment readiness honestly, distinguishing “importable”from “realtime-ready.” We report exact historical parity: 512/512 matching samples acrossboth X and Z stabilizer bases, with the heuristic lane and the NVIDIA-lane outputs agreeingsample-by-sample with the committed reference. On the 512-sample benchmark the NVIDIAlane lifts mean resolved fraction by ∆ = +0.638 on line-propagation regimes and ∆ = +0.595on cycle-event regimes, while incurring ∆ = −0.080 on local-noise regimes — supportinga three-lane routing rule that the infrastructure encodes and tests. The complete artifact,including Lean-compatible reproducibility contracts and a patch-ready CUDA-Q executionpath, is published at https://github.com/Abraxas1010/ising-trust-routing.