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.
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.
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.
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.
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.
Scope label (load-bearing). Genuinely interacting quantum field theory in flat 1+1 Minkowski space. No gravity: not dynamical, not backreacting, not quantum. This is Exit (a) of Proposition 2 — the coupling axis, isolated from the gravity axis. Archived as Phase VII (with its certification Phase VII-b); not merged into the free-field Minkowski corpus of Phases IV–V, nor into the fixed-curved-background Phase VI. Phase VI closed the fixed-background branch with a structural obstruction (Proposition 2): for a free field on a fixed classical background the state is a functional of the background data, hence so is every modular observable, and grade (ii) is the ceiling — a genuine positive is structurally unreachable there. Exactly two exits survive: (a) genuine interaction, and (b) dynamical gravity. This paper attacks Exit (a), the minimal scope extension: still flat space, no gravity, only the coupling switched on. The object is the interval entanglement Hamiltonian K_A = −log ρ_A in the DMRG/MPS ground state of the mixed-field Ising chain — genuinely interacting, non-integrable, gapped, non-conformal — and the reference is the model's own interacting Bisognano–Wichmann family (identity plus a freely weighted local energy density plus first descendants), never the free stress tensor. The same structural logic caps the attainable outcome at a distinction inside grade (ii): REDUCE (the third verdict extends to coupling) versus IRREDUCIBLE (the first crack of the enclosure). Both were preregistered as publishable and hash-frozen before any production run. Phase VII returned a substantive but uncertifiable result: all four target residuals sit 5–30× below the controls, the residual anti-tracks the coupling, and the co-primary spectral reconstruction echoes a correlation-length ordering — yet the frozen multiplicative threshold (θ = 10 × floor = 1.62) exceeded the maximum response of any bounded foil (≈ 0.45), because the free-control floor was dominated by Jordan–Wigner representation mismatch, an instrument bias ~30× the target signals. The teeth precondition failed by arithmetic, not by physics, and the verdict was left with an asterisk. Phase VII-b removes it: an independently frozen rerun in the model's natural variables (the fermionic Jordan–Wigner-bilinear BW family, whose free-control residual is exactly zero at full range — the calibration the earlier instrument lacked), an additive threshold, and satisfiable contrast teeth. Teeth pass; all four targets lie 8–200× below the certified threshold and below every control, in both representations. Verdict: COLLAPSE (Exit (a)), certified. The interacting entanglement Hamiltonian reduces to the local Bisognano–Wichmann energy density; the reduction is representation-independent, and increasing the coupling makes K_A more BW-local, not less. The strong-coupling axis carries no grade-(ii)-irreducible modular orientation. No grade-(i) claim is made or implied (Proposition 2 forbids it for a fixed-Hamiltonian ground state). The genuine positive, if it exists, is pushed onto Exit (b) — dynamical geometry — named and out of scope here. Preregistration and reproducibility. Both investigations were governed by preregistrations frozen and hashed before any production run — Phase VII: SHA-256(§1–§6) = 5c53a0c0…fc09f (frozen 2026-06-30 22:45:34 UTC); Phase VII-b: SHA-256(§1–§6) = c63f8a10…39d46 — with append-only deviation logs (DEV-1…DEV-6 and DEV-1…DEV-4(VII-b)) below the hash boundary, and cautionary records of the two failed instruments preserved rather than discarded. Code, preregistrations, per-claim ledgers, and all emitted CSV/JSON data: https://github.com/PauDD/Simulador-Fase-VII Continues Phase IV (10.5281/zenodo.21261576), Phase V (10.5281/zenodo.21302338) and Phase VI (10.5281/zenodo.21321084) of the programme Rigidez de la Incidencia Geométrica (Geometric Incidence Rigidity).
This technical note documents the numerical stability of a two-peak (Z-level) interference pattern observed in a fixed 29-qubit quantum circuit. The analysis was performed using the Qiskit AerSimulator backend under controlled conditions, including variations in shot count and phase-parameter offsets. The results demonstrate that the observed interference structure is reproducible, robust against sampling fluctuations, and not dependent on fine-tuned parameter choices. This document does not present a theoretical proof or physical interpretation. Its sole purpose is to provide an empirical numerical reference for the stability and reproducibility of the observed interference pattern, serving as a supporting record for related theoretical and conceptual works by the author. In version v3, the numerical analysis is extended beyond 63 qubits up to 79 qubits by employing reduced statistical descriptors rather than full state-space representations. This extension demonstrates that the observed Z-level interference stability persists under scalable statistical evaluation, without requiring exponentially growing state-vector simulations. Additional clarification The reported “Z-level progress” refers to an internal, relative coverage metric within the author’s numerical stability framework. It is not a physical completeness measure, nor a claim of global optimality. Earlier high-percentage stability values (e.g. 95–98%) correspond to local robustness indicators such as sampling consistency, seed invariance, and phase-noise tolerance within fixed parameter windows. The lower percentage reported here reflects a stricter, global aggregation across multiple independent stability dimensions. This distinction is intentional and avoids conflating local robustness with global domain coverage. This work reports a numerical stability certificate for X–Z basis statistical divergence measures obtained in controlled simulations. A multiscale grid and zoom analysis identifies a non-trivial stable phase-offset interval (pj ∈ [0.038, 0.052]) in which total variation distance, Shannon entropy, and directed Kullback–Leibler divergences remain reproducible under changes in sampling depth, random seed, and numerical resolution. A persistent directional asymmetry between KL_XZ and KL_ZX is numerically observed across all tested scales. This document reports numerical results only and does not claim physical realization, theoretical proof, or universal validity. Interpretational note: The absence of a direct Lorentz-covariant or gauge-field embedding should not be interpreted as a deficiency of the numerical results, but as a limitation of applying classical spacetime questions to an emergent, resonance-based stability structure. The reported Z-level behavior constrains the space of viable physical interpretations rather than completing one.
Two established results have never been composed. The fidelity susceptibility of a quantum state to a Hamiltonian parameter equals one quarter of its quantum Fisher information, F_Q = 4·chi_f; and an exact calculation in the Rosenzweig-Porter (RP) ensemble shows that eigenfunction fidelity susceptibility is enhanced in the fractal non-ergodic-extended phase (Skvortsov, Amini and Kravtsov, PRB 106, 054208, 2022). Composed, they make the eigenvector fractal dimension D2 — until now a diagnostic of localization physics — an operational metrological figure of merit: along the RP fractal phase, at fixed distance from criticality and for field-like (local) couplings to the sensed parameter, the finite-size enhancement exponent of the quantum Fisher information over the ergodic reference is 1 − D2. We confirm this in-house under preregistered criteria on the generalized-RP ensemble with D2 measured from inverse-participation-ratio scaling (not assumed): enhancement = 1 − D2 within 0.15 at 4/4 interior points of the phase (deviations 0.009–0.078; correlation 0.996). Two further preregistered experiments fix the criterion's boundaries: geometric fractality alone — a disorder-free Sierpinski-gasket lattice with certified eigenpairs and degenerate-multiplet treatment — shows no effect (enhancement −0.12; the RP formula does not extend), while critical power-law banded random matrices extend the law at all three tested bandwidths (deviations 0.016–0.064). The criterion is therefore: multifractal eigenstates of random ensembles, sensed through local couplings — randomness, not fractal geometry, is the missing ingredient, and an operator-structure scope law (diagonal inherits; short-range inherits once its range fits the fractal support; collective and dense couplings are D2-blind) gives the design rule. On the platform side we construct — because it cannot be cited — the minimal model that carries the physics onto cold atoms: an interacting tilted+disordered lattice in which the tilt is only the sensed parameter (the bare Wannier-Stark ladder is integrable, so sourcing RP statistics from gravity would be immediately refutable) and the dense RP-like spectrum comes from interactions and disorder. A preregistered coexistence test on the interacting t–V chain finds a textbook ergodic-to-localized crossover whose typical susceptibility peaks at the crossover's ergodic edge — not mid-crossover — with the predicted heavy x^−2 tail (Hill index 1.96–2.04) in the chaotic regime and estimator-dependent rare-event gains inside the crossover. The platform statement is scoped accordingly, and one instrument caveat is stated up front: this attaches to lattice/Bloch gravimetry, not to free-fall light-pulse interferometry. Tier-2 throughout: a shared random-matrix description with preregistered numerical evidence, not a hardware claim.