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 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.
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.
Foundations OTQG & GKSL (Optimal transport Quantum Gravity and GKSL) Architecture (and stress-test (last update) - stress-test v1 ) Pedagogical Guide, Foundations Audit, Uniqueness & Substitutability Analysis, Literature Comparison, and Reading Guidance : A Pedagogical Guide to Understanding the OT–GKSL Architecture See also : Fixed, Driven, and Autonomous Coherent Generators in Quantum Wasserstein Geometry Trajectory compatibility, driven lifting, and model-level invariance in open quantum dynamics --------------------------------------------------------------------------------------------------------------------- Executive Summary: Covariant Extension of Open Quantum Dynamics 1. Framework and Motivation This work formulates a covariant extension of finite-dimensional open quantum dynamics. The primary goal is to decouple coherent evolution from the detailed-balance (quantum-Wasserstein) sector, allowing the effective coherent generator to vary dynamically with the quantum state ρ. Directional Separation: Distinguishes between a global inner derivation and the instantaneous coherent direction it induces at a given density matrix: E_ρ([K]) = -i [K, ρ] Effective Generator Space: At a fixed faithful ρ, components commuting with ρ exert no effect on the state's instantaneous velocity. The space of effective generators is defined as: G_ρ = k / h_ρ ≃ T_ρ O_ρ where k = A_sa / Z(A)_sa, h_ρ = ker(E_ρ), and O_ρ is the unitary orbit of ρ. Core Objective: Because dissipation drives the state across distinct isospectral orbits, the paper addresses how these effective coherent directions should be systematically compared along the evolution trajectory. 2. Geometric Structure and Transport On a regular stratum with a constant orbit type: The Carlen–Maas metric g_OT (associated with a fixed detailed-balance calculus) induces a metric h_ρ on the effective-generator bundle: h_ρ(κ, λ) = g_(OT, ρ)(Θ_ρ κ, Θ_ρ λ) Metric Connection: Orthogonal projection of the Wasserstein Levi-Civita connection yields a metric connection ∇^G. Modeling Postulate: Elevating this connection to a full transport law represents an independent modeling hypothesis rather than an implicit outcome of standard GKSL dynamics. 3. Augmented Dynamical Equations The resulting augmented dynamical system—generally non-linear following projection onto ρ and characterized as GKSL-anchored—is governed by: State Evolution: dρ/dη = Θ_ρ(κ) - K_ρ D F(ρ) + r(ρ, κ) Generator Transport: D^G κ / Dη = J_κ(ρ, κ) 4. Exact Entropy Balance For an entropy functional F(ρ) = D(ρ || π), the coupled system preserves exact entropy balance: dF / dη = - || grad_(g_OT) F ||² + τ_ρ(κ) + D F_ρ [r] where: τ_ρ(κ) = D F_ρ [Θ_ρ κ] and τ_ρ([K]) = i Tr( K [ρ, log π] ) Implication: The standard Carlen–Maas entropy production rate is recovered exactly whenever the coherent and remainder (r) channels are entropy-transverse. 5. Diagnostics and Coarse-Graining Constraints Curvature & Holonomy: The induced connection establishes curvature and holonomy metrics to evaluate coherent-generator transport. Coarse-Graining: Distinguishes between drift, mobility, and connection basicity under reduced scaling. Hidden generator dynamics can obstruct autonomous reduced closure, with holonomy identified as a primary mechanism driving such unobserved variations. 6. Model Verification: Isotropic Depolarizing Qubit An explicit isotropic depolarizing-qubit model isolates three distinct geometric features: Orbit curvature: K_orb > 0 Mixing curvature: K_mix < 0 Connection curvature: R^G (∂_s, U) V = 0 Key Finding: Non-zero ambient quantum-Wasserstein curvature does not inherently imply mixed coherent–dissipative generator holonomy. Orbit-Collapse Obstruction: Passive parallel transport preserves the effective-generator norm ||κ||_h, whereas the coherent fiber collapses at the maximally mixed state (r → 0). This forces the minimal Hermitian representative to scale as: |ω| ~ ||κ||_h / r Under unit-rate depolarization r(η) = r_0 e^(-η), the norm scales as |ω| ~ e^η. Introducing a relaxation law D^G κ / Dη = -γ_κ κ adjusts the asymptotic scaling to e^((1 - γ_κ)η). 7. Core Contribution & Open Benchmarks Primary Value: The key advance lies in the typed coupling of detailed-balance quantum-Wasserstein geometry with state-dependent effective coherent directions, detailing explicit impacts on entropy balance, holonomy diagnostics, nonlinear augmented dynamics, and coarse-grained closure. Physical Interpretations: Applications to non-Abelian gauge fields, Yang–Mills theory, gravitation, or cosmology remain conditional hypotheses. Open Benchmark: Establishing a Gibbs/Davies or higher-dimensional example exhibiting non-zero mixed generator curvature remains an open challenge. 1. Foundations of the Architecture: Foundations |GKSL/Lindblad ; Carlen–Maas ; Jacobson ; Sakharov ; Donoghue ; Lovelock) Establishes the core Einstein-locked OT/GKSL architecture for certified geometric readout and coherence-dependent gravitational sourcing. Optimal-Transport Gravity Trilemma | Identifies the certified operational boundary of geometric readout by proving the fundamental trade-off between temporal resolution, coframe stability, and bridge fidelity. 2. Emergence and Recovery of Classical Physics: Exact Reduced OT/GKSL Equations | Mori–Zwanzig/projection operators ; effective field theory ; Carlen–Maas ; Wilsonian reduction / Demonstrates the controlled recovery of classical Newtonian and gravitational sectors as exact non-linear reductions of the native OT/GKSL state dynamics. Certified Einstein Non-Linear Readout | Lovelock ; Bianchi identities ; Donoghue EFT ; Jacobson thermodynamic gravity// Develops the full non-linear Einstein-locked readout closure for the metric sector. Non-Linear Dynamics and Readout | Dynamical systems, center manifold/effective reduction ; quantum Markov semigroups ; non-linear open-system reductions // Explores the exact reduced non-linear evolution on collective state manifolds. The Seeley–DeWitt Bridge | Seeley–DeWitt heat-kernel ; Vassilevich // Formalizes the operational connection between native state dynamics and the effective classical readout. The SDW Bridge: Composite Brout–Englert–Higgs Dynamics, Spectral Separation, and the Emergent Graviton | Formalizes the emergence of the Brout-Englert-Higgs composite scalar and the spin-2 graviton via the Seeley-DeWitt expansion, strictly preserving the Einstein-Lock. Bridge between QCD and OT/GKSL Readout | Wilson lattice gauge theory ; Gross–Wilczek–Politzer asymptotic freedom ; Kogut–Susskind Hamiltonian lattice gauge theory // Connects the Optimal Transport / GKSL framework to Quantum Chromodynamics, exploring the constitutive bridge and effective low-energy dynamics. 3. The Certified Boundary and Structural Limits: Certified Spacetime Readout on Finite Support: A Unified Temporal and Geometric Boundary | Decoherence / Quantum Darwinism ; quantum reference frames ; finite information bounds ; Jacobson // Unifies the temporal and geometric branches of classical readout into a single certified spacetime problem. Introduces the unified spacetime readout burden and derives the central unified certified-budget inequality, proving that temporal precision, geometric coframe nondegeneracy, and bridge compatibility draw from the same finite entropic and informational resources and cannot be made simultaneously ideal. Certified Causality, Locality, Nonlocality, and Relativity in the Einstein-Locked OT/GKSL Framework | Algebraic QFT/locality ; operational quantum theory ; quantum reference frames ; relativistic causality tests // Determines the exact status of causality, locality, nonlocality, and the principle of relativity within the Einstein-locked OT/GKSL architecture. Shows that causal-local spacetime semantics is a certified readout property rather than a primitive native axiom; proves a patchwise gluing theorem for certified local causal structure; and derives a unified finite-budget inequality showing that temporal precision, geometric certification, bridge admissibility, and overlap compatibility all compete for a single residual causal-local headroom on finite effective support. Entropic Tick Cost and Certified Temporal Readout in the Einstein-Locked OT/GKSL Framework | Demonstrates that classical ticks are finite-resource readout objects extracted from native entropic ordering, rather than primitive background parameters. Decomposes the entropic tick cost into native, extraction, and certification branches, and derives a theorem-level certified temporal budget inequality connecting temporal resolution, finite effective support, and certification margins. Entropic Tick Cost & Spectral Budget | Page–Wootters time ; thermal time hypothesis ; quantum clocks ; Salecker–Wigner bounds // Establishes a theorem-strength certified boundary for classical spacetime by proving a fundamental trade-off between entropic tick resolution, coframe stability, and finite informational budget. Toy Certified Pipeline from Optimal Transport QCD | Provides a protocol-level implementation and scaling model for certified bridge margins. Certified Spectral Boundary from Heat-Kernel Budgets and Entropic Transport in the Einstein-Locked OT/GKSL Framework | Heat-kernel spectral budgets; entropic OT/GKSL transport; certified spectral boundary; Einstein-locked readout. Develops a spectral-geometric control layer for the OT/GKSL framework, where the native heat trace bounds finite spectral resources, the cutoff gap defines a certification margin, and entropic transport controls the drift of readout-support budgets without inducing a state-dependent Einstein–Hilbert kinetic term. Correlation Separation in the Einstein-Locked OT/GKSL Framework | Establishes a theorem-level distinction between native, readout, and causal-local correlations, and reframes the horizon information problem through certifie
We present a development of the RCD program (Radial Coherential Dynamics) in the complex scalar sector of quantum sequential growth of causal sets. The central question is not only how a causal history grows, but how much of the information about HOW IT WAS FORMED can survive when one of its elements is erased without privileging any temporal label. The central result is an exact separation between coherent inheritance and memory of the cut. For the erasure branches a_i (i = 0, …, N−1), define the branch matrix 𝒜_N = N^(−1/2) [a_0, …, a_{N−1}], the uniform register mode |u_N⟩ = N^(−1/2)(1, …, 1), and Q_N = I − |u_N⟩⟨u_N|. The memory matrix M_N = D_mix − D_coh = 𝒜_N Q_N 𝒜_N† ⪰ 0 identifies exactly the memory sector orthogonal to coherent inheritance. Its trace, Tr M_N = (1/2N²) Σ_{i,j} ‖a_i − a_j‖², is the pairwise dispersion of the causally distinct erasure alternatives: relational memory is precisely that dispersion. The Relational Inheritance Bifurcation theorem (BHR-3) shows already at N = 3 that the inherited amplitude can coincide exactly while non-zero memory of the mode of formation persists: Δ₃^coh = 0 together with Ω₃ > 0, where D_mix − D_coh = Ω₃ · [[1, −1], [−1, 1]]. At the exact point r = 1, Ω₃ = 1/294; the reading with the register traced out has spectrum {147/149, 2/149} and visibility 145/149, while the coherent reading remains pure. One and the same observable inheritance can therefore coexist with residual relational information about its formation. The second main result is an exact memory-flow law. On the star family 𝒮_N — an antichain of N−1 elements with one element above all of them — covariant coherent erasure is closed for every N. With p = ε/(t₀+ε), p′ = (N−1) p / N, P := p/N = constant, and the complete coupling trajectory is ε_n = n ε_N / (N + (N−n) ε_N). The memory has rank one, M_N = (N−1)|P|² J with J = [[1, −1], [−1, 1]], so that Ξ := M_N/(N−1) = |P|² J is an exact invariant of the flow, M_{N−1} = M_N − Ξ, and 𝓜_N − 𝓜_{N−1} = 2|P|²: each coarse-graining step transports an exactly determined amount of relational memory. The star spine 𝒮₄ also appears as an exact component of the closure variety of the 4→3 flow. The non-degenerate regular branch C₁₂ is born tangent to this spine and inherits, at leading order, its memory-contraction factor 2/3. The deposit also contains the prior results leading to this structure: absence of a non-trivial scalar fixed point under uniform incoherent erasure (𝔗_mix); absence of a non-trivial fixed point under the uniform coherent superposition (𝔗_coh), which equals the classical PF-0 condition complexified; the need to formulate erasure covariantly by classes; the rational renormalization map on the closure variety; and the minimal register compression, rank D_mix = rank M_N + 1. These results motivate the Principle of Relational Memory of the Cut, dynamical version (PMRC-D): every fundamental physical differentiation that produces causally distinguishable histories must also determine, through a covariant rule, which information of that differentiation remains recorded and which information may interfere coherently. The emerging working thesis is: "The inheritance of a history does not by itself determine the memory of how it was formed." The program remains open toward closed sectors with several independent memory modes and a covariant dynamics capable of transporting those modes under coarse-graining. Exact results are N ≤ 4 except those with closed proofs for all N (the star spine and its flow); the 5→4 step outside 𝒮_N is numerical; the physical universality of PMRC-D remains open. No claim is made about the emergence of time, Mermin's 25 % or the necessity of H > 1 as a law. Deposit contents: RCD Adjudication Record v0.2 (signed Spanish original and English version; the Spanish text prevails), diligence notes 𝔗_mix-0, 𝔗_coh-0/𝔗_flow-0 and BMR-0 (Relational Memory), reproducible code with SHA-256 manifests, and README. Panel Cerezo credits: ChatGPT (formulation of the diligences, BHR-3, PMRC-D, 𝒜QA† form, invariant Ξ, series of C₁₂) and Claude (exact computation, lemmas, curve C and map R, star spine 𝒮_N, cross-verification and drafting), under the direction and adjudication of the principal.
Foundations OTQG & GKSL (Optimal transport Quantum Gravity and GKSL) Architecture (and stress-test (last update) - stress-test v1 ) Pedagogical Guide, Foundations Audit, Uniqueness & Substitutability Analysis, Literature Comparison, and Reading Guidance : A Pedagogical Guide to Understanding the OT–GKSL Architecture See also : Fixed, Driven, and Autonomous Coherent Generators in Quantum Wasserstein Geometry Trajectory compatibility, driven lifting, and model-level invariance in open quantum dynamics --------------------------------------------------------------------------------------------------------------------- Executive Summary: Covariant Extension of Open Quantum Dynamics 1. Framework and Motivation This work formulates a covariant extension of finite-dimensional open quantum dynamics. The primary goal is to decouple coherent evolution from the detailed-balance (quantum-Wasserstein) sector, allowing the effective coherent generator to vary dynamically with the quantum state ρ. Directional Separation: Distinguishes between a global inner derivation and the instantaneous coherent direction it induces at a given density matrix: E_ρ([K]) = -i [K, ρ] Effective Generator Space: At a fixed faithful ρ, components commuting with ρ exert no effect on the state's instantaneous velocity. The space of effective generators is defined as: G_ρ = k / h_ρ ≃ T_ρ O_ρ where k = A_sa / Z(A)_sa, h_ρ = ker(E_ρ), and O_ρ is the unitary orbit of ρ. Core Objective: Because dissipation drives the state across distinct isospectral orbits, the paper addresses how these effective coherent directions should be systematically compared along the evolution trajectory. 2. Geometric Structure and Transport On a regular stratum with a constant orbit type: The Carlen–Maas metric g_OT (associated with a fixed detailed-balance calculus) induces a metric h_ρ on the effective-generator bundle: h_ρ(κ, λ) = g_(OT, ρ)(Θ_ρ κ, Θ_ρ λ) Metric Connection: Orthogonal projection of the Wasserstein Levi-Civita connection yields a metric connection ∇^G. Modeling Postulate: Elevating this connection to a full transport law represents an independent modeling hypothesis rather than an implicit outcome of standard GKSL dynamics. 3. Augmented Dynamical Equations The resulting augmented dynamical system—generally non-linear following projection onto ρ and characterized as GKSL-anchored—is governed by: State Evolution: dρ/dη = Θ_ρ(κ) - K_ρ D F(ρ) + r(ρ, κ) Generator Transport: D^G κ / Dη = J_κ(ρ, κ) 4. Exact Entropy Balance For an entropy functional F(ρ) = D(ρ || π), the coupled system preserves exact entropy balance: dF / dη = - || grad_(g_OT) F ||² + τ_ρ(κ) + D F_ρ [r] where: τ_ρ(κ) = D F_ρ [Θ_ρ κ] and τ_ρ([K]) = i Tr( K [ρ, log π] ) Implication: The standard Carlen–Maas entropy production rate is recovered exactly whenever the coherent and remainder (r) channels are entropy-transverse. 5. Diagnostics and Coarse-Graining Constraints Curvature & Holonomy: The induced connection establishes curvature and holonomy metrics to evaluate coherent-generator transport. Coarse-Graining: Distinguishes between drift, mobility, and connection basicity under reduced scaling. Hidden generator dynamics can obstruct autonomous reduced closure, with holonomy identified as a primary mechanism driving such unobserved variations. 6. Model Verification: Isotropic Depolarizing Qubit An explicit isotropic depolarizing-qubit model isolates three distinct geometric features: Orbit curvature: K_orb > 0 Mixing curvature: K_mix < 0 Connection curvature: R^G (∂_s, U) V = 0 Key Finding: Non-zero ambient quantum-Wasserstein curvature does not inherently imply mixed coherent–dissipative generator holonomy. Orbit-Collapse Obstruction: Passive parallel transport preserves the effective-generator norm ||κ||_h, whereas the coherent fiber collapses at the maximally mixed state (r → 0). This forces the minimal Hermitian representative to scale as: |ω| ~ ||κ||_h / r Under unit-rate depolarization r(η) = r_0 e^(-η), the norm scales as |ω| ~ e^η. Introducing a relaxation law D^G κ / Dη = -γ_κ κ adjusts the asymptotic scaling to e^((1 - γ_κ)η). 7. Core Contribution & Open Benchmarks Primary Value: The key advance lies in the typed coupling of detailed-balance quantum-Wasserstein geometry with state-dependent effective coherent directions, detailing explicit impacts on entropy balance, holonomy diagnostics, nonlinear augmented dynamics, and coarse-grained closure. Physical Interpretations: Applications to non-Abelian gauge fields, Yang–Mills theory, gravitation, or cosmology remain conditional hypotheses. Open Benchmark: Establishing a Gibbs/Davies or higher-dimensional example exhibiting non-zero mixed generator curvature remains an open challenge. 1. Foundations of the Architecture: Foundations |GKSL/Lindblad ; Carlen–Maas ; Jacobson ; Sakharov ; Donoghue ; Lovelock) Establishes the core Einstein-locked OT/GKSL architecture for certified geometric readout and coherence-dependent gravitational sourcing. Optimal-Transport Gravity Trilemma | Identifies the certified operational boundary of geometric readout by proving the fundamental trade-off between temporal resolution, coframe stability, and bridge fidelity. 2. Emergence and Recovery of Classical Physics: Exact Reduced OT/GKSL Equations | Mori–Zwanzig/projection operators ; effective field theory ; Carlen–Maas ; Wilsonian reduction / Demonstrates the controlled recovery of classical Newtonian and gravitational sectors as exact non-linear reductions of the native OT/GKSL state dynamics. Certified Einstein Non-Linear Readout | Lovelock ; Bianchi identities ; Donoghue EFT ; Jacobson thermodynamic gravity// Develops the full non-linear Einstein-locked readout closure for the metric sector. Non-Linear Dynamics and Readout | Dynamical systems, center manifold/effective reduction ; quantum Markov semigroups ; non-linear open-system reductions // Explores the exact reduced non-linear evolution on collective state manifolds. The Seeley–DeWitt Bridge | Seeley–DeWitt heat-kernel ; Vassilevich // Formalizes the operational connection between native state dynamics and the effective classical readout. The SDW Bridge: Composite Brout–Englert–Higgs Dynamics, Spectral Separation, and the Emergent Graviton | Formalizes the emergence of the Brout-Englert-Higgs composite scalar and the spin-2 graviton via the Seeley-DeWitt expansion, strictly preserving the Einstein-Lock. Bridge between QCD and OT/GKSL Readout | Wilson lattice gauge theory ; Gross–Wilczek–Politzer asymptotic freedom ; Kogut–Susskind Hamiltonian lattice gauge theory // Connects the Optimal Transport / GKSL framework to Quantum Chromodynamics, exploring the constitutive bridge and effective low-energy dynamics. 3. The Certified Boundary and Structural Limits: Certified Spacetime Readout on Finite Support: A Unified Temporal and Geometric Boundary | Decoherence / Quantum Darwinism ; quantum reference frames ; finite information bounds ; Jacobson // Unifies the temporal and geometric branches of classical readout into a single certified spacetime problem. Introduces the unified spacetime readout burden and derives the central unified certified-budget inequality, proving that temporal precision, geometric coframe nondegeneracy, and bridge compatibility draw from the same finite entropic and informational resources and cannot be made simultaneously ideal. Certified Causality, Locality, Nonlocality, and Relativity in the Einstein-Locked OT/GKSL Framework | Algebraic QFT/locality ; operational quantum theory ; quantum reference frames ; relativistic causality tests // Determines the exact status of causality, locality, nonlocality, and the principle of relativity within the Einstein-locked OT/GKSL architecture. Shows that causal-local spacetime semantics is a certified readout property rather than a primitive native axiom; proves a patchwise gluing theorem for certified local causal structure; and derives a unified finite-budget inequality showing that temporal precision, geometric certification, bridge admissibility, and overlap compatibility all compete for a single residual causal-local headroom on finite effective support. Entropic Tick Cost and Certified Temporal Readout in the Einstein-Locked OT/GKSL Framework | Demonstrates that classical ticks are finite-resource readout objects extracted from native entropic ordering, rather than primitive background parameters. Decomposes the entropic tick cost into native, extraction, and certification branches, and derives a theorem-level certified temporal budget inequality connecting temporal resolution, finite effective support, and certification margins. Entropic Tick Cost & Spectral Budget | Page–Wootters time ; thermal time hypothesis ; quantum clocks ; Salecker–Wigner bounds // Establishes a theorem-strength certified boundary for classical spacetime by proving a fundamental trade-off between entropic tick resolution, coframe stability, and finite informational budget. Toy Certified Pipeline from Optimal Transport QCD | Provides a protocol-level implementation and scaling model for certified bridge margins. Certified Spectral Boundary from Heat-Kernel Budgets and Entropic Transport in the Einstein-Locked OT/GKSL Framework | Heat-kernel spectral budgets; entropic OT/GKSL transport; certified spectral boundary; Einstein-locked readout. Develops a spectral-geometric control layer for the OT/GKSL framework, where the native heat trace bounds finite spectral resources, the cutoff gap defines a certification margin, and entropic transport controls the drift of readout-support budgets without inducing a state-dependent Einstein–Hilbert kinetic term. Correlation Separation in the Einstein-Locked OT/GKSL Framework | Establishes a theorem-level distinction between nativ
REGISTRATION PREPRINT NOTE This record is the formal abstract (v0.2) announcing the CoherentialHamming Law, a named operational regularity for Hamming-distancecoherence decay in multi-qubit quantum hardware under localindependent dephasing. The full paper — including per-platform experimental tables, sixfigures, methodology section, complete statistical analysis, andreferences list — is in preparation and will be submitted toQuantum (the open journal for quantum science) as primary targetand Physical Review Research as secondary target within 2026 Q2. The theoretical foundations (Hamming Decay Theorem, bridge D_K → d_H)are available in the author's prior work:— P0/GHZ-Bridge v2.0 (DOI: 10.5281/zenodo.19009933)— P1 v1.1 (DOI: 10.5281/zenodo.19020842)— P1-bis v1.0 (March 2026) Raw cross-platform experimental data supporting the validation areavailable in:— GHZ Cross-Platform v4.1 PLATINUM (DOI: 10.5281/zenodo.18307211) This abstract establishes the formal naming and operational framingof the Coherential Hamming Law. The full paper will provide thecomplete experimental and statistical expedient.