This paper develops the deterministic finite-dimensional dynamical layer of Variable-Signature Quantum Theory and Obstruction Theory. The regular finite-dimensional theoryis deliberately conservative: it does not produce a new local Schrödinger law. Its main roleis to calibrate VSQT-OT by proving fixed-Hilbert recoverability on regular intervals and byisolating nontriviality into typed admissibility, comparison, global, or transition constraints.Along a regular path t 7 → θ(t) inside a fixed-rank positive stratum, the physical Hilbert spaceis the moving sectorEt = PtK, Ht = (Et, ⟨·, ·⟩t),where the restricted sector metric gt induced by an ambient representativê Gt is positive.The paper defines sector-metric compatible connections, sector Schrödinger equations, sector-unitary propagators, covariant von Neumann dynamics, and transported state/effect/POVMcalculus. Its main results show that compatible dynamics preserves sector membership, sectornorm, density states, effects, POVMs, and Born probabilities in transported or Heisenbergform. It also proves that every regular finite-dimensional interval satisfying the standing C1hypotheses admits a C1 fixed-Hilbert reduction. In any such reduction,Dt = St∇tS−1t = ∂t + Γt, Γ†t = −Γt,and the effective Hamiltonian is˜Ht = SthtS−1t − iΓt.Thus regular pathwise finite-dimensional dynamics over intervals is mathematically fixed-Hilbert ordinary at the intrinsic dynamical level, relative to the unrestricted admissibletrivialization class and the full finite-dimensional time-dependent Hermitian Hamiltoniancomparison class. Nontriviality can be claimed only after declaring admissibility, comparison-class, global, or transition constraints
This paper develops the deterministic finite-dimensional dynamical layer of Variable-Signature Quantum Theory and Obstruction Theory. The regular finite-dimensional theoryis deliberately conservative: it does not produce a new local Schrödinger law. Its main roleis to calibrate VSQT-OT by proving fixed-Hilbert recoverability on regular intervals and byisolating nontriviality into typed admissibility, comparison, global, or transition constraints.Along a regular path t 7 → θ(t) inside a fixed-rank positive stratum, the physical Hilbert spaceis the moving sectorEt = PtK, Ht = (Et, ⟨·, ·⟩t),where the restricted sector metric gt induced by an ambient representativê Gt is positive.The paper defines sector-metric compatible connections, sector Schrödinger equations, sector-unitary propagators, covariant von Neumann dynamics, and transported state/effect/POVMcalculus. Its main results show that compatible dynamics preserves sector membership, sectornorm, density states, effects, POVMs, and Born probabilities in transported or Heisenbergform. It also proves that every regular finite-dimensional interval satisfying the standing C1hypotheses admits a C1 fixed-Hilbert reduction. In any such reduction,Dt = St∇tS−1t = ∂t + Γt, Γ†t = −Γt,and the effective Hamiltonian is˜Ht = SthtS−1t − iΓt.Thus regular pathwise finite-dimensional dynamics over intervals is mathematically fixed-Hilbert ordinary at the intrinsic dynamical level, relative to the unrestricted admissibletrivialization class and the full finite-dimensional time-dependent Hermitian Hamiltoniancomparison class. Nontriviality can be claimed only after declaring admissibility, comparison-class, global, or transition constraints
This paper develops the state and measurement layer of Variable-Signature QuantumTheory and Obstruction Theory. Building on the projected positive-sector geometry ofVSQT-OT I, it defines θ-density states, algebraic states, effects, finite POVMs, sectorcompletely positive maps, and passive instruments intrinsically on the physical sectorEθ = Pθ K, Hphys,θ = (Eθ , ⟨·, ·⟩θ ).The paper fixes the sector trace, θ-adjoint, sector positivity, amplified sector positivity, andsector complete-positivity conventions, carefully distinguishing abstract sector endomorphismsfrom ambient representatives. Its main results prove compact convexity of the θ-density statespace, Born positivity and normalization for sector POVMs, selected-operator-system states,algebraic-state restriction and positive-extension representation on finite-dimensional ∗θ-subalgebras, finite-dimensional sector Kraus representation, Schrödinger–Heisenberg dualityfor sector CP maps, passive instrument normalization, instrument-to-POVM compatibility,admissibility of stratumwise measurement families, pointwise equivalence with ordinary finite-dimensional measurement theory, a fixed-Hilbert obstruction criterion, and fixed-Hilbertrecovery in Born-pair, POVM, and instrument forms. The paper does not introduce a newfinite-dimensional Born rule or a new Kraus theorem; pointwise sector measurement theoryis ordinary finite-dimensional measurement theory written in the sector Hilbert structure.Its contribution is the sector-typed formulation of the standard measurement calculus overvariable positive sectors, together with a first obstruction class detecting when the sectorbundle cannot be globally reduced to one admissible fixed-Hilbert carrier, gauge-compatibleadmissibility rules for stratumwise families, a formal admissible comparison class, and arecovery criterion identifying when that layer is ordinary after compatible admissible transport.The selected-observable layer is an operator-system layer by default, with selected ∗θ -algebrastreated as a stronger optional case. All operator-algebraic statements are finite-dimensionaland algebraic; no infinite-dimensional, unbounded, spectral, semigroup, or von Neumannalgebraic operator theory is claimed. The paper is finite-dimensional, stratumwise, andnon-dynamical. Active inter-sector instruments are isolated as a separate typed skeletonrather than claimed as a consequence of passive measurement calculus
This paper develops the first mathematical layer of Variable-Signature Quantum Theoryand Obstruction Theory in the finite-dimensional deterministic setting. The core object is asignature-parameterized family inside a fixed ambient complex vector space K ∼=CN, withparameter space Θ, Hermitian forms Gθ, representing matrices Bθ, physical-sector projectionsPθ, and selected sector-preserving observable algebras Aθ. The Paper-I projected physicalsector is not the positive cone of Gθ, but the selected positive sector HIphys,θ = (Eθ,Gθ|Eθ).On each regular stratum Θα, projected positive sectors form finite-rank Hilbert bundles. Thepaper distinguishes ambient comparability from smooth fixed-Hilbert triviality and introducesfirst-layer coarse obstructions to sector representation, transition extension, and conditionalselected-algebra transport. The algebra obstruction is evaluated only after a smooth globalsector representation exists. On regular strata, the paper recovers the ordinary fixed-Hilbertform of finite-dimensional sector kinematics, numerical Born state-effect pairings under sectorrepresentation, and selected algebra transport when the relevant algebra obstruction alsovanishes. This first paper proves mathematical nontriviality criteria for sector geometry; itdoes not claim empirical deviation from standard quantum mechanics or a full operationalreconstruction of measurement theory.
This paper develops the measurement-stability layer of the VSQT-OT program. Build-ing on the finite-dimensional sector measurement calculus of VSQT-OT II and the typedobstruction methodology of VSQT-OT IV, it studies finite-outcome passive measurementsover declared signature regimes and local measurement charts. The signature parameter θ isnot derived endogenously here; it is treated as a declared static parameter, prescribed path,external control, measurable stochastic index, or deferred measurement-updated/endogenousvariable. Once a pre-regular chart, typed local sector gauge, compatible finite measurementrecord, comparison channel, and the relevant quantitative measurement-control certificatesare supplied, the paper proves quantitative stability estimates for Born probabilities, fi-nite POVM distributions, passive instrument probabilities, and passive posterior stateson positive-probability domains. It also proves transported standard recovery, same-rankrecovery under exact recovery gauges, perturbative recovery under declared dual positivequasi-transport, and channelwise finite commuting-POVM statistical convergence by distance-to-class certificates. The concrete commuting-POVM comparison class is given an explicitfinite stochastic representation through joint spectral decomposition; it is not identified withjoint measurability, noncontextuality, instrument-level classical simulation, or a global classi-cal phase-space limit. Finally, it proves that rank loss, positivity-gap closure, failed algebratransport, and zero-probability conditioning obstruct unconditional full all-state/all-effectmeasurement-statistics continuation unless transition data are declared; zero-probability con-ditioning obstructs uniform posterior-stability estimates based only on unnormalized-outputcontrol, even for ordinary finite two-outcome CPTP instruments
This paper develops the obstruction-theoretic grammar of Variable-Signature QuantumTheory and Obstruction Theory. Its central convention is claim-theoretic rather thanontological: a variable-signature quantum family supports a channel-relative nonclassicalityclaim only when a licensed, schema-generated recovery problem has a soundly certifiedfailure of recovery from a declared comparison class under declared admissibility constraints.The paper refines the earlier coarse triviality tuple into a partial annotated obstructionpacket whose components record decision values, invariant values, statuses, and certificatesfor representation, transition, algebraic, dynamical, operational, geometric, topological,stochastic, and compression channels. The construction separates recoverability decisions frominvariant obstruction values and proof certificates, introduces partial domains to distinguishzero obstruction from undefined, deferred, or out-of-scope channels, formalizes structurallicensing through licensed recovery schemas and proof ledgers, formalizes certification throughsound verifiers, and adds a claim-export gate separating invariant detection from certifiednonclassicality claims. The resulting framework is deliberately conservative: moving sectors,moving metrics, and moving projections are not automatically nonclassical; they support arelative nonclassicality claim only when a structurally licensed recovery problem has soundlyverified no-recovery in a specified channel and passes the declared claim-export standard
FoundationsOTQG &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: Covariant Coherent-Generator Geometry over Quantum Wasserstein State Space This work develops a covariant framework for distinguishing three different situations in finite-dimensional open quantum dynamics: a fixed global coherent generator, an externally driven time-dependent generator, and an intrinsically transported effective coherent degree of freedom. The starting point is the observation that a fixed Hamiltonian generator and the coherent direction that is instantaneously visible at a density matrix are not the same mathematical object. For a self-adjoint generator K, E_ρ([K]) = −i[K, ρ], and the components commuting with ρ are instantaneously invisible. The effective coherent direction therefore belongs to the state-dependent quotient 𝒢_ρ = 𝔲/𝔥_ρ≃ T_ρ𝒪_ρ, where 𝔲 is the global space of inner self-adjoint derivations modulo the center and 𝔥_ρ is the stabilizer of ρ. On regular constant-orbit-type strata, the Carlen–Maas quantum-Wasserstein metric associated with a fixed detailed-balance GKSL sector induces a metric and a projected connection on the effective-generator bundle. Importantly, a varying quotient representative κ(ρ) does not by itself imply a physically varying Hamiltonian. To make this distinction quantitative, we introduce the path operator (T_I [K])(ξ) = ϖ_{ρ(ξ)}([K]) and the fixed-generator recovery defect ε_fix = dist(κ, Ran T_I). The vanishing of ε_fix is equivalent to compatibility with a single global fixed generator along the trajectory. This zero/nonzero criterion is metric-independent, while its numerical value, conditioning, covariant derivative, curvature, and holonomy depend on the chosen generator metric, here supplied by the detailed-balance Carlen–Maas geometry. We further distinguish trajectory-level recovery from model-level recovery. Smooth effective-generator histories admit pathwise lifts to time-dependent generators K(ξ); therefore failure of fixed-generator recovery does not by itself imply new autonomous physics. A genuinely augmented regime requires an independent evolution law for the effective generator. Graph-invariance criteria are given for both fixed and externally driven sectors. Explicit qubit calculations illustrate the framework. A constant global Hamiltonian can induce a non-parallel effective-generator field, while a nonconstant effective amplitude provides a simple example with ε_fix > 0. The corresponding entropy balance is also derived without modifying the exact Carlen–Maas detailed-balance gradient-flow result. The contribution is therefore structural and classificatory: it provides a mathematically controlled separation between fixed, driven, and autonomous coherent-generator descriptions, together with recovery, conditioning, coarse-graining, and geometric diagnostics. No derivation of gauge theory, gravity, or spacetime curvature from the generator geometry is claimed. 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 certified-domain correlation layering 4. Cosmological Dynamics & Global Readout Constraints: Vacuum-like Residual Energy from Constitutive-Holonomic Balance in a Minimal Reduced OT-C3 Sector | Effective potentials ; Coleman-Weinberg ; Sakharov induced gravity ; vacuum energy problem // Demonstrates analytically that the macroscopic cosmological constant emerges as a non-zero vacuum-like residual energy resulting from the exact balance between scalar constitutive dissipation (source sector) and the non-commutative holonomic barrier of the Optimal Transport geometry. Homogeneous Closed Readout Dynamics under Finite Spacetime Budget | FLRW cosmology ; effective dark energy ; backreaction ; EFT of dark energy// Constructs a homogeneous and isotropic model (G-FLRW) demonstrating how the spacetime budget acts as a branch-selection mechanism, effectively identifying the vacuum-like sector (Λ) as the maintenance cost of certified spacetime solvability. 5. Experimental Protocols and Testability: Testing Source-Side State Dependence in Gravity with Lock-In Atom Interferometry | Kasevich–Chu ; Peters–Chung–Chu ; Rosi–Tino ; atom gravimetry // Proposes a concrete experimental protocol to falsify source-only emergent gravity at low energy. A Lock-in Atom-Interferometric Test (Clock) | Detailed operational implementation of the low-energy readout test for the Einstein-locked framework. Experimental Sepa
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