Identifying the conditions for a discriminating test of the Specular Field Theory: a diagnostic use of the Barron et al. (2026) operator Loschmidt echo dataset
This working note reports a diagnostic use of the operator Loschmidt echo (OLE) dataset published by Barron et al. (2026). The dataset provides the first hardware measurement of the OLE across a range of scattering strengths, and it is accompanied by a comparison with state-of-the-art classical methods. The classical methods agree with the hardware at small and at large scattering strengths, and disagree with the hardware, and with each other, in the intermediate regime.The origin of this disagreement is left as an open question in the paper. The note does not claim to resolve this open question. It uses the dataset as a diagnostic, in order to identify the conditions that a circuit must satisfy in order to test the Specular Field Theory (SFT) in a discriminating way. The conditions for a discriminating test are independent control of the temporal curvature A, of the entanglement contribution E_ent, and of the baseline curvature A_0. The 56-qubit dataset allows only a partial test: it is approximately in the linear regime (small eta, E_ent approximately constant, A_0 = 0 by construction), and where these linear-regime conditions hold, the data are consistent with the linear structure of the SFT, with a parameter-free ratio prediction that requires no fitting on the data.However, the dataset does not allow independent control of A, E_ent, and A_0, and the comparison at large scattering is therefore not discriminating: the deviation observed there is compatible with the SFT but also with alternative explanations (finite-size effects, noise, deviation from the linear response, trigonometric dependence on eta). The note states explicitly the limitations of the test: visual extraction of the data from the published figure; validity of the exponential approximation at delta = 0.3; choice of the reference measurement; non-independence of the four ratios; constant entanglement contribution assumed but not verified; single set of X-field angles; test of the linear structure only; alternative explanations not excluded; dimensions of A to be stated explicitly. The note concludes that the linear structure of the SFT is tested where the linear-regime conditions are approximately satisfied, and that the specific SFT prediction requires the dedicated protocol described in the companion brief. The comparison with Barron et al. has been used as a diagnostic, not as a confirmation: it has allowed us to identify the conditions that a circuit must satisfy to test the SFT in a discriminating way, and it has shown that the 56-qubit dataset satisfies some of them and not others.
This working note reports a diagnostic use of the operator Loschmidt echo (OLE) dataset published by Barron et al. (2026). The dataset provides the first hardware measurement of the OLE across a range of scattering strengths, and it is accompanied by a comparison with state-of-the-art classical methods. The classical methods agree with the hardware at small and at large scattering strengths, and disagree with the hardware, and with each other, in the intermediate regime.The origin of this disagreement is left as an open question in the paper. The note does not claim to resolve this open question. It uses the dataset as a diagnostic, in order to identify the conditions that a circuit must satisfy in order to test the Specular Field Theory (SFT) in a discriminating way. The conditions for a discriminating test are independent control of the temporal curvature A, of the entanglement contribution E_ent, and of the baseline curvature A_0. The 56-qubit dataset allows only a partial test: it is approximately in the linear regime (small eta, E_ent approximately constant, A_0 = 0 by construction), and where these linear-regime conditions hold, the data are consistent with the linear structure of the SFT, with a parameter-free ratio prediction that requires no fitting on the data.However, the dataset does not allow independent control of A, E_ent, and A_0, and the comparison at large scattering is therefore not discriminating: the deviation observed there is compatible with the SFT but also with alternative explanations (finite-size effects, noise, deviation from the linear response, trigonometric dependence on eta). The note states explicitly the limitations of the test: visual extraction of the data from the published figure; validity of the exponential approximation at delta = 0.3; choice of the reference measurement; non-independence of the four ratios; constant entanglement contribution assumed but not verified; single set of X-field angles; test of the linear structure only; alternative explanations not excluded; dimensions of A to be stated explicitly. The note concludes that the linear structure of the SFT is tested where the linear-regime conditions are approximately satisfied, and that the specific SFT prediction requires the dedicated protocol described in the companion brief. The comparison with Barron et al. has been used as a diagnostic, not as a confirmation: it has allowed us to identify the conditions that a circuit must satisfy to test the SFT in a discriminating way, and it has shown that the 56-qubit dataset satisfies some of them and not others.
This working note presents a quantum circuit test of Specular Field Theory (SFT), a geometric framework in which the scrambling rate of a quantum system is linked to the curvature of a temporal manifold. Using a 5-qubit mirror circuit (Loschmidt echo) with a temporal modulation applied to the single-qubit rotation angles,we establish a quantitative mapping between the circuit modulation parameter (omega) and the temporal curvature (A).We analyze the entanglement contribution (E_ent) as an operational interpolation between the fidelity of recovery (F_rec0) in the bulk and the Shannon entropy (S_Shannon) at the boundary, governed by a sigmoidal transition. The study evaluates the model across three main aspects: Circuit Calibration: The mapping A(omega) is calibrated using baseline circuit constants (A_0 and alpha),establishing a consistent linear response in the bulk. Bulk-Boundary Transition: The transition between bulk and boundary regimes is analyzed using a sigmoidal weighting function, yielding a strong coefficient of determination (R^2 = 0.9974). Blind Prediction & Horizon Regularization: Parameters are calibrated exclusively on the linear bulk (omega <= 0.05), and the regularized formula predicts the scrambling rate in the critical regime (omega >= 0.08) with an average error of 7.93%, utilizing a boundary regularization scale (epsilon) that accounts for temporal volume saturation near the informational horizon (A = 1/2). The note also discusses finite-size scaling (showing the bulk intercept beta vanishing in the thermodynamic limit),directional circuit responses under time reversal (comparing forward and rewind evolutions), and the distinction between exact statevector simulations and future empirical validation on quantum hardware.
The Specular Field Theory (SFT) introduces a minimal geometric extension in which time is endowed with an independent informational geometry, sourced by a scalar coherence field. Informational behaviour is not imposed through system-specific dynamical assumptions, but emerges as a consequence of temporal curvature. The theory identifies three dynamical regimes: a Linear Regime, with linear-response behaviour analogous to fidelity decay under small perturbations; a Critical Scaling Regime, marking the approach to an operational boundary of the temporal geometry; and a Coherent Regime. In the Linear Regime, the SFT yields a falsifiable, parameter-free prediction for the ratio of scrambling exponents between two circuit configurations, testable on current quantum hardware with minimal resources. The Critical Scaling Regime remains an open direction for collaborative investigation. This document establishes the author's priority and paternity over the foundational concepts and structural framework of the SFT, while reserving certain mathematical formulations for collaborative development. It is intended as a conceptual foundation for future research partnerships in informational dynamics, temporal geometry, and quantum scrambling.
In this work we present two contributions: physical hypothesis (SFT) and a verification protocol designed to test it, which by its generic nature can be reused to evaluate any similar field theory. The protocol is built around a structured sequence of artifacts—SCAN, REGION, and REPORT—together with pre-registered gates, schema-validated outputs, and deterministic verification tools. Its purpose is to provide a clear, transparent, and falsifiable framework that allows independent reviewers to assess specific claims without ambiguity. Beyond its role as a verification mechanism, the protocol also functions as a practical research compass. Each module produces explicit PASS or FAIL outcomes tied to well-defined metrics and thresholds. A FAIL is not merely a negative result: it identifies the precise gate, metric, and artifact where the breakdown occurs, offering immediate diagnostic information. This structure enables rapid iteration, guiding model refinement and helping researchers navigate complex hypothesis spaces efficiently. We believe this work aligns well with methodological rigor, openness, and reproducibility. We hope it will be of value to researchers working on computational physics, speculative frameworks, and verification-driven scientific practice. SFT — Structural Field Theory (Docs + Runners) This repository is a verification-first release of SFT: a theory/framework plus a set of runners designed for external audit. Start here: read Doc 0 — Abstract & Orientation for the ontological stance, scope, current limitations, and falsifiable predictions. The key idea is simple: The “vacuum” is treated as a structural medium/field. “Particles” are stable field configurations (discrete in manifestation, continuous in availability). The project is organized so third parties can verify pipelines via PASS/FAIL gates, hash manifests, and schema-validated artifacts. Important: many included datasets are synthetic (C) because this release is built to be verified on CPU-only.Physical end-to-end confirmation requires REAL (P) solver outputs. CI only validates the verification pipeline (CPU-only), not physical validation. REAL-ready: verifiers + artifact contract are in place; can consume third-party real-solver outputs. REAL-verified: a real-solver run has been published with artifacts + hashes and passes the declared gates. Repository structure Doc_01/ ... Doc_14/ The full documentation set (each doc in its own folder). *_CLEANED.zip and runner bundles When a document has an executable verification component, the corresponding zipped runner bundle is included. https://github.com/Xaquer69/sft-theory-and-runners
This document is a working protocol for the minimal experimental test of the Specular Field Theory. It is not a final protocol: it is a starting point for a joint discussion with a scientific or industrial partner. We are seeking a collaboration to define the exact protocol: the choice of the circuit, the mapping of A and E_ent, the choice of delta and of the measurement window, the calibration procedure, and the analysis pipeline. The document describes what we believe is needed, and where we would like the partner's expertise.
Here's what this paper means for actual humans: WHAT THIS IS ABOUT. When you build or use a quantum device, everything rests on knowing what its parts are: which degrees of freedom are "qubit 1," which are "qubit 2." The companion paper ("Forged Frames") showed that simple mathematical criteria cannot certify this; convincing fakes exist. This paper answers the question that result leaves standing: what is the MINIMUM experimental information that genuinely pins down a system's subsystem structure, and when can that information silently fail? WHAT WE FOUND, IN PLAIN TERMS. Four things. (1) EXACT LAWS INSTEAD OF MEASUREMENTS. Any wrong choice of parts must visibly distort the family of unentangled states, and we derive exactly how much, at every system size: closed-form constants (verified to seven decimal places), an explicit error bound, and a surprise. The two natural ways to measure "wrongness" (state distortion versus operator scrambling) turn out to be literally the same measurement, up to a fixed number, whenever the two parts have equal size. Wrongness cannot hide. (2) THE TWO-OPERATION THRESHOLD. You can pin down what your subsystems are by implementing just TWO generic operations and checking their statistics, while a THOUSAND mutually commuting operations tell you nothing at all. Diversity of control, not volume of control, is what fixes what your qubits are. The residual uncertainty is proportional to your measurement tolerance, with a constant we derive exactly and show how to compute in advance, so an experimenter can screen candidate operation pairs and pick a strong one (random pairs are typically several times worse, occasionally catastrophically so). (3) THE ALIASING LIMIT: CERTIFICATION CAN PASS WHILE TELLING YOU NOTHING. If you sample your certification data at special "resonant" times (set by the operations' energy scales), a maximally wrong assignment of subsystems passes the test perfectly. What your qubits are depends on when you looked. We characterize these blind spots exactly (for qubits they are universal and computable in advance; the danger windows shrink with the square root of your tolerance), and the fix costs almost nothing: sample at two different times, at least one away from the resonant set. With that, certification is restored; we prove it exactly and measure it. (4) REAL-LAB BUDGETS. We work out what certification costs in actual measurement shots (the error falls off unusually fast, inversely with the total number of shots rather than with its square root), how hardware noise floors the procedure, and how a simple reference measurement removes that floor to first order. A single seven-row table in the paper is effectively a lab protocol: it shows, condition by condition, which kinds of experimental access identify the subsystem structure (two generic operations: yes; one operation, commuting operations, resonant sampling: no). WHY IT MATTERS. For quantum hardware: this is a concrete recipe for certifying that the qubits you think you have are the qubits you physically have, with explicit tolerances, a sampling-time warning that is a real failure mode on calibrated hardware, and shot budgets. For foundations: the contested question "does physics determine its own subsystems?" gets a quantitative operational answer. Physics determines an operational subsystem CLASS (not one preferred coordinate representation of it), and that class is fixed by two operations sampled at two times, and by nothing less that we tested. WHAT IT OPENS UP. The seven-row identifiability table is a blueprint for a tabletop experiment on any small quantum platform; running it on hardware would move this from simulation to laboratory fact. On the theory side the paper leaves sharply posed open problems: the exact global constants when the two parts differ in size, the number-theoretic structure of long-time sampling (the failure times form a small-divisor hierarchy), and the extension from two parts to many. METHODS NOTE, BECAUSE IT MATTERS FOR TRUST. Every quantitative claim was pre-registered in the companion scripts before its run. The full ledger, including predictions that failed and one published-in-note constant that our own later theory overturned, is an appendix of the paper. All code, data, and working notes are in the deposit, seeded for exact reproduction. WHO AND HOW. A human-AI collaboration: research direction and standards of evidence by Ryan Cardwell (Crystalline Labs); design, code, derivations, and drafting by Claude (Anthropic), including autonomous sessions under the program's pre-registration rules, with adversarial reviews by other AI models incorporated and credited.
We report systematic experimental observation of coherent, topology-dependent inter-horizon correlations in thermofield double (TFD) states implemented on IBM quantum processors. Using a 100-qubit ladder geometry mapped onto the heavy-hex topology of ibm_fez (156 qubits, Heron r2 architecture), we demonstrate signal ratios R_fit spanning 1.2–202.7 across runs/seeds, with best single-seed R_fit = 23.93 (Run #11) and record multi-seed median R_fit = 102.7 (Run #2, 5 seeds, range 63.5–202.7), validated by pre-registered GO/NO-GO criteria across 14 experimental runs spanning January 24-30, 2026. Our experimental framework incorporates two rigorous anti-artifact controls (see Fig. 6-7): (1) SCRAMBLE control applies identical circuit depth with incorrect topology, destroying the signal (reduction factor > 10×); (2) ECHO control (Loschmidt reversal) applies the coupling layer twice, annihilating coherent contributions (reduction factor 8.6-50.5×, consistent with expected finite-size echo saturation for N~50 effective subsystems (see Gorin et al. [14] for saturation plateau theory)). Both controls maintain > 95% local fringe retention, confirming they do not trivially destroy coherence. A critical discovery emerged from our January 30, 2026 validation campaign (see Fig. 5): quantum processor calibration drift can cause signal collapse within less than one hour on hardware with identical offline calibration snapshots. Runs #11-#12 achieved R_fit = 23.93 and 18.4 respectively (GO-1 PASS, GO-3 PASS), while Run #13 executed only 53 minutes later on the same backend collapsed to R_fit = 1.20 (GO-1 FAIL). This finding establishes that offline Health Scores do not reliably predict experimental success, and defines an operational envelope requiring Health > 80% (Grade B or better) for empirically associated with high-probability signal stability. The observed second-harmonic (2ω) dominance in the phase-dependent signal (A₂ω/A₁ω > 40×, R² > 0.99, see Fig. 9) is consistent with theoretical predictions for bilinear left-right correlations. A stride sweep (s = 2-5, see Fig. 4) reveals a signal-coherence trade-off, with s = 3 identified as optimal. Total quantum processor time across all 14 runs: approximately 45 minutes. These results establish a validated, falsifiable experimental framework for probing analog quantum gravity signatures on NISQ hardware, with explicit calibration-conditional bounds. The methodology may provide a validated framework applicable to analog Hawking radiation platforms where topology-controlled correlations play a central role (see Section 5.4). Note: Results demonstrated primarily on IBM ibm_fez; multi-device validation on additional backends is recommended to establish cross-platform generalizability.