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

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||²F / (2·2N) 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 Jᵢ = J0·sqrt (Cᵢ·C₈+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.