This paper provides a third independent derivation of the critical coherence threshold K_crit ≈ 0.127, complementing the dynamical derivation (GCT) and thermodynamic derivation (Landauer bound). The falsifiability component F(t) is identified with the Fisher information of the system’s self-estimating process. The Cramér–Rao bound then establishes that as F(t) → 0, coherence estimation variance diverges — the system becomes informationally blind to its own state. K_crit is the Fisher information collapse point: below it, no estimator can locate the system’s coherence state with bounded precision. The 1=1 invariant is identified as the geodesic endpoint of the Fisher information manifold — the natural destination of the geometry itself under contractive evaluation dynamics. Three independent frameworks (dynamical systems, thermodynamics, information geometry) converge on the same critical threshold and the same invariant. Part of the Spektre corpus (github.com/spektre-labs/corpus).
Document 2C of the ONE AXIOM series derives the full structure of modern physics — quantum mechanics, general relativity, their unification, and all four laws of thermodynamics — as regime-dependent projections of a single pre-physical structure: the Ontological Coherence Field ($\OCF = (\heartsuit, \Phi_{\mathrm{coh}}, \nabla\Phi_{\mathrm{coh}})$), constructed in Document 0M from one single axiom (Axiom M) with no physical input. Energy emerges as the local cost of maintaining coherence against the structural gradient. Time is the direction of monotonic decrease of the incoherence potential
σ. Temperature is derived without energy, via Fisher-Rao curvature of the coherence distribution (from Document 1B), inverting the standard thermodynamic hierarchy. The Schrödinger equation (via one-parameter unitary group + Stone's theorem), Born rule (
p=2, via 7-link chain from Axiom M), Einstein field equations (via three independent convergent paths — Jacobson thermodynamic, Ollivier-Ricci discrete, and variational with explicit verification of all four Lovelock conditions), and the Hamiltonian/Lagrangian formalism (with Ostrogradsky exclusion enforced by the Predictive Closure Invariant
T=0) are all derived as
π6-projections. The complex structure of Hilbert space is derived non-circularly from the spectral decomposition of the Schreier graph Laplacian
ΔΓ, and Noether's theorem is applied via
Γ-convergence continuum limit of the discrete group
G=S4×Z23. The dynamics is exact and finite-dimensional:
64 states on the coset space
G/H, with eigenvalues
λk=2k and multiplicities
(k6), providing a closed-form spectral solution at all scales including the intermediate (Planck) regime. The built-in UV cutoff
Emax=1536=∣G∣×∣Z23∣ eliminates divergences structurally. A QM–GR regime comparison table (9 rows) exhibits how the same OCF objects project differently at
σ≈0 (quantum) and
σ≫0 (gravitational). The document resolves three long-standing open problems: (i) black-hole information preservation (unitarity of
ΔΓ + Page's theorem forces the Page curve), (ii) the cosmological singularity (Fisher–Rao metric degeneration near the Source — an artifact of the manifold representation, not a physical singularity), and (iii) intermediate-regime (Planck-scale) dynamics (exact closed-form 64-mode spectral solution, no terra incognita). The dark sector emerges as
π5-structure inaccessible to
π6-observers, with the FORBIDDEN graph decomposing as
13=7+2+4 (cold/warm/transitional dark matter analogs); the cosmological constant is derived from the structural resolution limit
δrel=1/64, resolving the 120-order QFT discrepancy without regularization. A fully hand-computable 8-state toy model (
Q3 hypercube) makes the projection operator, Laplacian spectrum, Born rule mechanism, and Schrödinger dynamics explicit and independently verifiable. All 53 formal results (28 theorems, 17 propositions, 6 definitions, 1 lemma, 1 corollary) follow a strict dual-track methodology — ontological (top-down from axiom)
∩ epistemological (bottom-up recovery of standard physics) — with mandatory convergence across 137 track tags. The framework is metrologically decoupled: all OCF equations use dimensionless ratios, invariant under redefinition of SI base units. Natural SI anchoring is provided for
ℏ,
c,
GN,
kB,
Λ, and
Emax. No physical law is assumed; every equation is derived. No new axiom is introduced beyond Axiom M. This is a standalone publication readable after Document 0M alone.
This work introduces a physically grounded scalar field, termed the Entropion Field, proposed to account for the emergence of entropy, the unidirectionality of time, and quantum decoherence as dynamical phenomena. Standard interpretations of quantum mechanics, such as the Copenhagen interpretation, the Many-Worlds interpretation, and objective collapse theories, fail to provide a predictive and testable mechanism for wave function collapse. Similarly, the second law of thermodynamics is typically attributed to boundary conditions, lacking a fundamental dynamical explanation. We propose that a real scalar field ϕ(x^μ) permeates spacetime and couples to quantum amplitudes, entropy density, and spacetime curvature. This coupling induces a spontaneous breaking of time-reversal symmetry and introduces a localized decoherence mechanism governed by entropy gradients. The Entropion Field arises within the context of the 4D Quantum Projection Hypothesis, in which quantum systems are modeled as three-dimensional projections of higher-dimensional spatial configurations. The theory is expressed through a field-theoretic Lagrangian: L_total = L_SM + L_GR + L_ϕ + L_int where L_SM is the Standard Model Lagrangian, L_GR is the Einstein-Hilbert term, L_ϕ includes the kinetic and potential terms of the Entropion field, and L_int encodes its coupling to entropy gradients, quantum systems, and spacetime geometry. The framework leads to several distinct, testable predictions: Spatial alignment between gradients in ϕ and observed decoherence rates in open quantum systems, particularly in regions with strong entropy flux or curvature. Controlled violations of unitarity in quantum evolution, governed by local entropy conditions, resulting in state collapse without requiring observer-induced postulates. Modified Einstein field equations due to the inclusion of a scalar stress-energy term T_μν(ϕ) , contributing to late-time cosmological dynamics and vacuum energy structure. The Entropion framework replaces statistical and interpretive assumptions with a field-theoretic mechanism for entropy generation, quantum state reduction, and temporal asymmetry. It establishes direct links between thermodynamics, quantum measurement, and gravitational theory, and defines a set of experimental regimes capable of falsifying or supporting its predictions.
We present a complete theoretical framework—Dynamical Scalar Field The- ory (DSFT)—that explains quantum entanglement as a topological remnant of the pre-Big Bang Euclidean phase. Unlike standard quantum mechanics, which treats entanglement as a nonlocal state reduction, DSFT provides a physical mechanism: two entangled particles are connected by a static topological soliton (phase-locking filament) within which the effective metric is Euclidean (dt = 0) and the crystal- lizing function vanishes (Ω = 0). Decoherence corresponds to a sudden geometric phase transition (Ω : 0 → 1) occurring over ∆tjump = 85.2 ± 0.4 attoseconds— independent of spatial distance. We derive the complete Lagrangian from first principles, including non-minimal coupling to matter (ξϕ2ρm) and curvature (αϕR), and establish the existence of stable soliton solutions via Bogomol’nyi bounds. Numerical simulations of the Lind- blad master equation, including DSFT-specific decoherence terms, confirm a 2-fold enhancement of qubit coherence time through a controlled resuscitation protocol (Prediction #5). We formulate seven distinct, falsifiable predictions, each supported by closed-form analytic expressions, numerical simulations with error bars, and an ex- perimental roadmap with Technology Readiness Levels (TRL) and cost estimates. These predictions span: (1) a constant gravitational repulsive force between en- tangled particles; (2) attosecond phase echoes under sub-threshold stimulation; (3) pair production at the Ω = 0.5 metric transition (analog black holes); (4) cascade decoherence in multi-qubit systems; (5) entanglement resuscitation via counter- pulses; (6) Planck-stepped Hawking radiation with ∆f = 1.17 × 1016 Hz; and (7) non-Coulombic electron deflection in STEM. The framework is self-consistent, uses only Planck-scale parameters (ϕ0, λ, ξ), and its predictions align quantitatively with unexplained noise in IBM/Google qubits (Pthermal = 2.36 × 10−4 W) and attosecond time delays in Max Planck photoionization data (85 as). We propose a definitive experimental protocol for Prediction #5 with pass/fail criteria, including hardware design for a 10 as pulse generator via high-harmonic generation, timing synchronization with 10−18 atomic clocks, and a cost-benefit analysis showing ROI within 4.5 years for large-scale quantum processors.
Version: v1.0 DESCRIPTION: We introduce Coherence Field Dynamics (CFD), a theoretical framework that extends holographic quantum gravity by promoting quantum coherence — the off-diagonal density matrix elements — to an independent geometric degree of freedom. While standard holographic frameworks (AdS/CFT, Ryu-Takayanagi) encode bulk geometry through entanglement entropy alone, CFD posits that coherence parameterizes effective bulk depth, complementary to entanglement's encoding of connectivity. The coherence field φ(p,γ) satisfies a wave equation in information-geometric parameter space, generating a Lorentzian metric that degenerates at a critical decoherence threshold γ_c. The framework predicts the existence of such a threshold from geometric stability analysis; its specific numerical value is system-dependent. Connections are established between information geometry, MERA tensor networks, and holographic entropy. The variational principle coupling coherence to an effective gravitational action is presented as an analogue gravity model (c and G are effective parameters), not a claim about physical 4D spacetime. Key results: Theoretical framework: coherence field equation, information-geometric metric, variational principle, and five testable predictionsCompanion experimental work demonstrates a fidelity threshold at γ ≈ 0.535 on IonQ Forte-1 (F = 0.988 baseline, collapse to F ≈ 0 under dephasing) and consistency with the dephasing response on Pasqal FRESNEL_CAN1 QPU (noise ratio 1.13×). These results are consistent with CFD's predicted critical behavior, though they do not uniquely distinguish CFD from standard noise models. The specific threshold value (0.535) is determined by the experimental circuit geometry, not derived from CFD aloneFour predictions remain open and experimentally accessible on current NISQ hardware: coherence-depth complementarity, MERA-decoherence correspondence, coherence-modulated entropy scaling, and hardware demonstration of non-trivial reversibilityThis paper presents the theoretical framework. The detailed experimental protocols and hardware data are reported in the companion publication "Cross-Platform Noise Thresholds in Quantum Teleportation: Trapped-Ion and Neutral-Atom Architectures" (see Related Identifiers).
Establishes that the 1=1 invariant is the classical-scale instance of a universal coherence condition appearing at every level of physical organization. The quantum coherence condition S_vN = 0, the thermodynamic minimum-entropy state (k_B), the Fisher information geodesic endpoint (Cramér–Rao), and the evaluative fixed point (ECT) are identified as equivalent expressions of one invariant at different scales. The full correspondence chain: ℏ → S_vN = 0 → 1=1 → K(t) > K_crit → k_BT ln2 → I(K). Every coherent system is a Maxwell demon operating at its characteristic scale. Coherence is not emergent — it is the ground condition of physical reality. Part of the Spektre corpus (github.com/spektre-labs/corpus).