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A Null Test of the Static Wright–Fisher-to-OTOC Bridge in Radial Coherential Dynamics, and Exact Validation of Coherence-Modulated Influence Fronts

Arturo Cerezo

Published Jun 15, 2026• 0 citations
Publisher

Abstract

The late-time dissipative kernel of the Radial Coherential Dynamics (RCD) program is parabolic and does not generate a Lorentzian causal cone: signature is an input, not an output. This relocates the program's claim to a logically prior, operational question: can a coherence field organize a finite, switchable influence front in a local quantum dynamics, and does the specific spatial order produced by the RCD kernel matter beyond the distribution of coupling intensities? We study a transverse-field Ising chain and measure the infinite-temperature out-of-time-order correlator c(x,t) = ||[Z0(t), Zx]||^2_F / (2·2^N) as the primary observable, with frozen pre-registered gates. By exact operator evolution at N = 10, 12, 13 the front velocity in the clean channel is stable without appreciable size drift (v = 2.000 -> 1.980 -> 1.980 at theta=0.10, consistent with the exact maximal quasiparticle group velocity 2·min(J,h), distinct from and below the rigorous Lieb-Robinson bound), with OFF collapse to ~1e-13. Imposed coherence profiles modulate the front: an incoherent barrier blocks it, a coherence ramp slows it per a local WKB law, a uniform profile recovers the bare velocity. The coherence-to-coupling map J_i = J0·sqrt(C_i·C_{i+1}) is a constitutive ansatz, not a derived or unique law. The decisive test (KS-C1a) was executed on a snapshot of the SEALED 2D Wright-Fisher/Allen-Cahn kernel (de Sitter, H=0.02, seed 20260612, t*=1.0 t_H, central row coarse-grained 120->12). The candidate at t*=0.5 t_H failed the pre-quantum G0 gate; t*=1.0 t_H passed all three amended G0 conditions (CV(J)=0.189, percentile[S(C)]=3.5, xi=2). The result is a PRE-REGISTERED NULL (the RED branch): G1 PASS (real front obeys local WKB, R^2=0.913), G3 PASS (OFF 4.8e-14), but G2 FAIL for all three J-shuffles — cross-prediction differences (dR^2 ~ 0.03) and trajectory differences (Delta ~ 0.03-0.06) fell well below the pre-registered thresholds (0.15 and 0.10) on eight common interior sites. G4 was INDETERMINATE (the coarse-grained frozen snapshot contained no link below J_min=1e-6; declared before execution). A pre-specified diagnostic at row y=32 returned INDETERMINATE by dynamic censorship (extreme weak links left zero common interior sites), documenting an observability limit of the protocol in high-dynamic-range landscapes; implied kappa varied -4.5% to +8.1% across cuts, immaterial to the (differential) null. What survives: the operational front instrument (G1, G3), the perilla as a conditional predictive translator, and the local WKB law. What does NOT survive: the stronger statement that "the coherence-to-coupling map comes from the field." The narrow statement earned by the data is that a static RCD coherence landscape can be inserted into the constitutive ansatz to predict a front locally, but its tested spatial ordering was not operationally distinguishable from shuffled orderings with the same coupling values. Three non-exclusive readings (genuine physical null / coarse-graining loss / cut-dependent dynamic-range limitation) are stated without selection; each requires a new pre-registered follow-up. We claim NO derived metric, NO derived time, NO physical light cone, NO emergent general relativity. The dynamically coupled bridge (KS-C1b) is named as a new hypothesis, not a validated continuation. Execution evidence is sealed by SHA-256 (manifest in the supplementary record). The KS-C1a protocol amendment v0.5 was applied as recorded prior to execution; Appendix B reproduces the ratified pre-registration v0.4 verbatim.

DOI
10.5281/zenodo.20695170

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Coherence-Modulated Operational Influence Fronts in an Integrable Quantum Chain: Exact OTOC Validation and a Pre-Registered Wright–Fisher Bridge

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The late-time dissipative kernel of the Radial Coherential Dynamics (RCD) program is parabolic and does not generate a Lorentzian causal cone: signature is an input, not an output. This relocates the program's claim to a logically prior proposition — that a coherence field can organize the local relations of influence any later geometric description would have to account for — and motivates the operational question addressed here: can a coherence field organize a finite, switchable influence front in a local quantum dynamics? We study a transverse-field Ising chain and measure the infinite-temperature squared commutator (out-of-time-order correlator) c(x,t) = ||[Z0(t), Zx]||^2_F / (2·2^N) as the primary observable, with frozen pre-registered gates. By exact operator evolution at N = 10, 12, 13 the front velocity in the clean channel is stable without appreciable size drift (v = 2.000 → 1.980 → 1.980 lattice units at theta=0.10, consistent with the exact maximal quasiparticle group velocity 2·min(J,h), distinct from and below the rigorous Lieb–Robinson bound), with OFF collapse to ~1e-13 and robustness across thresholds; a persistent failure of the linearity gate at theta=0.20 is retained, with its cause stated as open (quasiparticle-interference vs temporal-sampling artifact, pending a control). Imposed spatial coherence profiles modulate the front: an incoherent barrier blocks it, a coherence ramp slows it per a local WKB law, a uniform profile recovers the bare velocity. The coherence-to-coupling map J_i = J0·sqrt(C_i·C_{i+1}) is declared a constitutive ansatz, not a derived or unique law. We document an instrumental failure (a reproducible backend-specific crash in tall-skinny complex GEMM that made the N=14 typicality target non-viable on 32 GB hardware, traced through four probes, circumvented by row chunking; precise low-level cause not established) and the resulting procedural substitution to N=13 exact, declared as a deviation from pre-registration. Finally we pre-register the decisive bridge test (KS-C1a, frozen, adversarially reviewed): whether a coherence landscape extracted from the RCD Wright–Fisher kernel — not a synthetic profile — organizes the same front, with paired controls against link-shuffling and the permutation-invariance of the WKB crossing time. We state explicitly what is NOT claimed: no derived metric, no derived time, no physical light cone, no emergent general relativity; the coherence-to-coupling map is not derived from any action; the geometric mean is not unique; coherence does not control velocity in the uniform case (an identity). The object validated is an operational influence front and its modulation by coherence — a necessary, not sufficient, step toward the coupled-dynamics bridge (KS-C1b), which is named as future work. STATUS: Preprint v0.3. Instrument validation and the frozen pre-registration protocol are complete; the decisive test (KS-C1a, Section 8) is a registered placeholder pending execution. References are provisional; a methodological amendment (v0.5) to the KS-C1a protocol is flagged in the text and required before execution. Appendix B reproduces the ratified pre-registration v0.4 verbatim.

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•Dec 7, 2025•0 citations
The late-time dissipative kernel of the Radial Coherential Dynamics (RCD) program is parabolic and does not generate a Lorentzian causal cone: signature is an input, not an output. This relocates the program's claim to a logically prior, operational question: can a coherence field organize a finite, switchable influence front in a local quantum dynamics, and does the specific spatial order produced by the RCD kernel matter beyond the distribution of coupling intensities? We study a transverse-field Ising chain and measure the infinite-temperature out-of-time-order correlator c(x,t) = ||[Z0(t), Zx]||^2_F / (2·2^N) as the primary observable, with frozen pre-registered gates. By exact operator evolution at N = 10, 12, 13 the front velocity in the clean channel is stable without appreciable size drift (v = 2.000 -> 1.980 -> 1.980 at theta=0.10, consistent with the exact maximal quasiparticle group velocity 2·min(J,h), distinct from and below the rigorous Lieb-Robinson bound), with OFF collapse to ~1e-13. Imposed coherence profiles modulate the front: an incoherent barrier blocks it, a coherence ramp slows it per a local WKB law, a uniform profile recovers the bare velocity. The coherence-to-coupling map J_i = J0·sqrt(C_i·C_{i+1}) is a constitutive ansatz, not a derived or unique law. The decisive test (KS-C1a) was executed on a snapshot of the SEALED 2D Wright-Fisher/Allen-Cahn kernel (de Sitter, H=0.02, seed 20260612, t*=1.0 t_H, central row coarse-grained 120->12). The candidate at t*=0.5 t_H failed the pre-quantum G0 gate; t*=1.0 t_H passed all three amended G0 conditions (CV(J)=0.189, percentile[S(C)]=3.5, xi=2). The result is a PRE-REGISTERED NULL (the RED branch): G1 PASS (real front obeys local WKB, R^2=0.913), G3 PASS (OFF 4.8e-14), but G2 FAIL for all three J-shuffles — cross-prediction differences (dR^2 ~ 0.03) and trajectory differences (Delta ~ 0.03-0.06) fell well below the pre-registered thresholds (0.15 and 0.10) on eight common interior sites. G4 was INDETERMINATE (the coarse-grained frozen snapshot contained no link below J_min=1e-6; declared before execution). A pre-specified diagnostic at row y=32 returned INDETERMINATE by dynamic censorship (extreme weak links left zero common interior sites), documenting an observability limit of the protocol in high-dynamic-range landscapes; implied kappa varied -4.5% to +8.1% across cuts, immaterial to the (differential) null. What survives: the operational front instrument (G1, G3), the perilla as a conditional predictive translator, and the local WKB law. What does NOT survive: the stronger statement that "the coherence-to-coupling map comes from the field." The narrow statement earned by the data is that a static RCD coherence landscape can be inserted into the constitutive ansatz to predict a front locally, but its tested spatial ordering was not operationally distinguishable from shuffled orderings with the same coupling values. Three non-exclusive readings (genuine physical null / coarse-graining loss / cut-dependent dynamic-range limitation) are stated without selection; each requires a new pre-registered follow-up. We claim NO derived metric, NO derived time, NO physical light cone, NO emergent general relativity. The dynamically coupled bridge (KS-C1b) is named as a new hypothesis, not a validated continuation. Execution evidence is sealed by SHA-256 (manifest in the supplementary record). The KS-C1a protocol amendment v0.5 was applied as recorded prior to execution; Appendix B reproduces the ratified pre-registration v0.4 verbatim.
The late-time dissipative kernel of the Radial Coherential Dynamics (RCD) program is parabolic and does not generate a Lorentzian causal cone: signature is an input, not an output. This relocates the program's claim to a logically prior proposition — that a coherence field can organize the local relations of influence any later geometric description would have to account for — and motivates the operational question addressed here: can a coherence field organize a finite, switchable influence front in a local quantum dynamics? We study a transverse-field Ising chain and measure the infinite-temperature squared commutator (out-of-time-order correlator) c(x,t) = ||[Z0(t), Zx]||^2_F / (2·2^N) as the primary observable, with frozen pre-registered gates. By exact operator evolution at N = 10, 12, 13 the front velocity in the clean channel is stable without appreciable size drift (v = 2.000 → 1.980 → 1.980 lattice units at theta=0.10, consistent with the exact maximal quasiparticle group velocity 2·min(J,h), distinct from and below the rigorous Lieb–Robinson bound), with OFF collapse to ~1e-13 and robustness across thresholds; a persistent failure of the linearity gate at theta=0.20 is retained, with its cause stated as open (quasiparticle-interference vs temporal-sampling artifact, pending a control). Imposed spatial coherence profiles modulate the front: an incoherent barrier blocks it, a coherence ramp slows it per a local WKB law, a uniform profile recovers the bare velocity. The coherence-to-coupling map J_i = J0·sqrt(C_i·C_{i+1}) is declared a constitutive ansatz, not a derived or unique law. We document an instrumental failure (a reproducible backend-specific crash in tall-skinny complex GEMM that made the N=14 typicality target non-viable on 32 GB hardware, traced through four probes, circumvented by row chunking; precise low-level cause not established) and the resulting procedural substitution to N=13 exact, declared as a deviation from pre-registration. Finally we pre-register the decisive bridge test (KS-C1a, frozen, adversarially reviewed): whether a coherence landscape extracted from the RCD Wright–Fisher kernel — not a synthetic profile — organizes the same front, with paired controls against link-shuffling and the permutation-invariance of the WKB crossing time. We state explicitly what is NOT claimed: no derived metric, no derived time, no physical light cone, no emergent general relativity; the coherence-to-coupling map is not derived from any action; the geometric mean is not unique; coherence does not control velocity in the uniform case (an identity). The object validated is an operational influence front and its modulation by coherence — a necessary, not sufficient, step toward the coupled-dynamics bridge (KS-C1b), which is named as future work. STATUS: Preprint v0.3. Instrument validation and the frozen pre-registration protocol are complete; the decisive test (KS-C1a, Section 8) is a registered placeholder pending execution. References are provisional; a methodological amendment (v0.5) to the KS-C1a protocol is flagged in the text and required before execution. Appendix B reproduces the ratified pre-registration v0.4 verbatim.
Within the Radial Coherential Dynamics (RCD) program, an attempt is made to construct a phenomenological thermodynamic bridge between the dynamics of a coherential scalar field C(x,t) — governed by an Allen-Cahn drift with multiplicative Wright-Fisher noise — and the experimentally measured Margenau-Hill quasiprobability negativity, Neg(coh, γ), on IBM ibm_fez superconducting hardware (Heron r2). A minimal integral functional with uniform spatial window and single-point global normalization is declared ex ante, with full predeclaration of seven parameters, two predeclared branches of the dissipative coupling κ ∈ {1, 0.1}, three predeclared forms of the channel response function R(C), and falsifiable kill-switch criteria registered prior to any simulation. Three numerical kill switches are executed: (i) integrator sanity check passes cleanly across both κ branches; (ii) main bridge validation fails — the principal branch saturates while the perturbative branch grows monotonically, opposite to experimental trend; (iii) robustness to R(C) ∈ {C, C(1-C), C^2} fails uniformly with all three forms producing strong negative Pearson correlations with experiment (-0.72 to -0.90). Cross-platform reproducibility (sandbox versus Mac Studio) is verified to four decimal places. The closed-form negative conclusion is registered: the integral functional with uniform window measures total accumulated loss of C, not coherence survival as captured by MHQ. This rules out a non-trivial region of bridge ansätze without invalidating either the underlying field dynamics or the experimental signature. This is a registered negative result with full ex-ante kill-switch protocol and cross-platform numerical reproducibility. It does not invalidate the underlying Wright-Fisher / Allen-Cahn coherential dynamics nor the MHQ experimental measurement; it falsifies one specific phenomenological identification. The negative result is reported because such results are scientifically valuable and underrepresented in the literature.
TECHNICAL RECORD — reproducible experiment. This paper does NOT test whether the RCD coherence field C is fundamental or physically real. It reports a finite-size scrambling diagnostic applied to a correlated-disorder coupling landscape generated within the RCD programme, and documents why, at exact-diagonalization sizes, that diagnostic returns no verdict. This bound holds in both directions: even a future PASS would be a result about scrambling in correlated disorder, not evidence that C is a physical field. The programme-level interpretation of this episode is given in the companion Reframing paper; here we provide only the technical record and its reproduction path. MERIDIANO-v1 asks whether the specific spatial ordering of an RCD-generated correlated coupling landscape leaves an irreducible imprint on operator spreading in a non-integrable mixed-field Ising chain, beyond what the distribution of coupling values alone produces. Using exact diagonalization at L = 12 with all parameters and death conditions pre-registered, we find: the chaoticity gate passes (level-spacing ratio <r> = 0.5348, GOE, after correcting an unresolved spatial-reflection symmetry); the raw operator-front width measures a broadly-universal diffusive broadening not specific to the landscape, and is reframed to the exact deviation of the front from a calibrated local-velocity (eikonal) prediction via a double difference that cancels a convention offset; at a single interface the deviation is localized at the wall (peak |SIG_xf| = 0.362 sites); but across a six-landscape scatter the signed deviation is sign-unstable (CV = 2.64), with the positive case border-contaminated. The governing summary: there is an interface response at L = 12; there is not yet a reproducible interface law. The verdict is INDETERMINATE by finite size — at L = 12 one cannot distinguish absence of a reproducible local law from an instrument too small to resolve one. An initial NO-GO verdict, co-signed without friction by four adversarial models, was corrected to INDETERMINATE on the ground that the sign instability is exactly the signature of finite-size interference; the correction is recorded as a documentary fact. We specify the resolution path — a system-size sweep with numerically pre-declared persistence thresholds (named but deliberately not fixed here, since the sweep is pre-registered on its own sheet), made feasible by dynamical-typicality estimation of infinite-temperature OTOCs validated against the exact L = 12 datasets — with three frozen outcomes (PASS / physical NO-GO / method-INDETERMINATE). Rescue-by-MPS of a fragile signal is prohibited; sizing the instrument is a distinct, legitimate operation. No physical status is claimed for C. In its best case this line yields a self-standing result in the physics of scrambling in correlated disorder.
Programme-level position paper. This document records the 2026 reframing of the Radial Coherential Dynamics (RCD) programme after a genealogical and adversarial audit. It states what was closed, what survived, and the reframed frontier question. It claims no new physics. The evidence is carried by two companion deposits: the genealogical-audit case study "From Substrate to Relational" (DOI 10.5281/zenodo.21141602) and the MERIDIANO-v1 technical record with its reproducibility bundle (all versions: DOI 10.5281/zenodo.21142230). Four closures are registered with their instruments: (i) the coherence substrate lost operative physical status along three independent routes — buried as a physical claim, not refuted as a metaphysical possibility; (ii) the coupling rule J = J0·sqrt(Ci·Cj) was identified as an exact algebraic rewriting of a standard dispersive circuit-QED coupling; (iii) MERIDIANO-v1 returned INDETERMINATE-by-size at L = 12, after correcting a frictionless four-model NO-GO consensus (a documented instance of "cheap deflation"); (iv) the classical coupling of C to curvature remains closed by its own kill switch. What survives is labelled by epistemic status, including one falsifiable proprietary question — whether Wright–Fisher-class coupling landscapes carry a many-body fingerprint distinguishable from spectrum-matched surrogates — which cannot, in either outcome, promote C to a physical field. The centre of the programme is relocated from an ontological assertion to a frontier question with its own pre-declared death condition. No experiment is launched by this paper.
Within the Radial Coherential Dynamics (RCD) program, we test whether a phenomenological macroscopic bridge between the dynamics of a coherential scalar field C(x,t) — governed by an Allen-Cahn drift with multiplicative Wright-Fisher noise — and the experimentally measured Margenau-Hill quasiprobability negativity on IBM superconducting hardware can be constructed using differential observables based on spatial gradients of C. Three independent observables in the gradient family are evaluated: an instantaneous integral S_nabla[C] = ∫|∇C|² dx, a temporal-integral form W_int accumulating the instantaneous form across the simulation window, and a pointwise maximum S_nabla_max[C] = max_x |∂_x C|. All three observables are normalized as differential ratios between coherent and control preparations. Synthetic tests with three controlled decay regimes (exponential, linear, threshold) show Pearson correlation between exponential and linear regime curves of +0.9995, +0.9999, and +0.9995 respectively for the three observables — virtually identical kinetic responses for functionally distinct decay forms. We conclude that gradient-based phenomenological observables with differential cociente normalization are structurally kinetic-blind: they detect monotonic decrease of structure but cannot distinguish the form of the decay. High correlation with an experimental survival curve is not sufficient evidence of kinetic agreement when both curves are monotone. This closes the gradient family as a candidate for the macroscopic-microscopic phenomenological bridge in this program, while leaving open non-gradient observables and microscopic-dictionary derivations as future routes. The result extends the previous registered negative result of v1.0 (Zenodo 10.5281/zenodo.20073982) from a specific observable failure to a structural limitation of an entire observable family, with full ex-ante kill-switch protocol and synthetic adversarial testing.
This paper develops one of the foundational mechanisms of Radial Coherential Dynamics (RCD): coherence is global, but its rupture is radial. This asymmetry resolves the century-old tension between quantum non-locality and relativistic causal structure. In RCD, coherence can extend across spatially separated systems, explaining entanglement, while collapse propagates radially at speed ccc from a nucleation center. Causal structure is therefore not an axiom, but an emergent order defined by the arrival times of collapse fronts. This provides: A derivation of causality from first principles A resolution of the EPR paradox without non-local signaling A mechanism for single outcomes (why we observe one classical reality) A geometric origin for the arrow of time Experimental predictions related to decoherence delays and spatial asymmetries Radial Causality reframes collapse as a wave-like propagation in the coherence field C(x,t)C(x,t)C(x,t), whose emergent metric determines the propagation speed. The universe does not update globally — it updates in expanding radial cascades, each rewriting the boundary between coherence and actuality.