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.
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.
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.
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.
We demonstrate empirically the construction-level blindness of the standard Two-Point Measurement (TPM) protocol to coherence in quantum thermodynamic entropy production: TPM applied to coherent and population-matched diagonal states yields total variation TV_max = 0.006 across 16,384 shots, statistically indistinguishable. We establish the Margenau–Hill quasiprobability (MHQ) as the operational witness of coherent thermodynamic signature where TPM fails by construction. The MHQ protocol is implemented via Hadamard-test interferometry with controlled energy phases (CRZ) and amplitude-damping channel dilation (CRY+CX), and validated against four mandatory Kraus consistency tests at machine precision (~10^-16). We present the first complete empirical survival curve of a coherent thermodynamic witness in commercial NISQ quantum hardware. Eleven independent jobs executed on IBM ibm_fez (Heron r2 architecture, 156 qubits) across six dissipation values gamma in {0.05, 0.10, 0.15, 0.20, 0.25, 0.30} reveal three structured regions: sustained ignition (gamma ≤ 0.20, SNR_diff = 3.5–5.6 with replication), edge transition (gamma = 0.25, SNR_diff = 3.2), and practical extinction (gamma = 0.30, SNR_diff = 1.46). The survival frontier is empirically localized at gamma_crit in (0.25, 0.30). Diagonal control yields exactly zero negativity in all eleven hardware runs — including the practical-extinction regime — establishing the witness signal as coherence-specific rather than channel-induced or systematic-error artifact. Topological robustness is confirmed across three distinct qubit layouts. Cross-platform replication on IonQ, Rigetti, and IQM remains pending administrative resolution of AWS Braket access. A direct quantitative mapping to the Francica–Goold–Plastina Xi remains an open theoretical question. This is the preprint version of the manuscript submitted to Physical Review X Quantum (April 2026). Raw experimental data and source code are publicly available on Zenodo at DOI: 10.5281/zenodo.19801980 under the Creative Commons Attribution 4.0 International license. Released under CC-BY 4.0.
Methodological position paper on the treatment of the arrow of time in coherence-based theoretical programs. After the structural closure of the macroscopic phenomenological bridge between the coherence field C(x,t) and Margenau-Hill negativity (Zenodo DOI 10.5281/zenodo.20073982 and 10.5281/zenodo.20077155, May 2026), this paper articulates the architectural identification dt = -dC/Γ, the effective coherence-entropy bridge, and the four-fold epistemic filter (derivation, bound, approximation, correlation) adopted as universal pruning criterion. Includes methodological implications for AI-assisted theoretical programs: the five-element requirement for operational claims and the two-threshold rule for speculative sessions.
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.