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Coherence as a Universal Invariant: From Quantum Decoherence to Institutional Collapse

Lauri Elias Rainio

Published Mar 7, 2026• 0 citations
Publisher

Abstract

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).

DOI
10.5281/zenodo.18897229

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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).
Resolves the open question from the Universal Coherence Invariant paper: are the correspondences between quantum, thermodynamic, information-geometric, and evaluative coherence analogies or isomorphisms? Answer: isomorphisms. Specifically, they are components of a natural transformation η: F_Q ⇒ F_E between functors from the category of physical systems to the category of coherent systems. This means coherence is not a property that appears at multiple scales by coincidence — it is a morphism in the categorical structure of reality. Additionally derives K_crit = ℏω₀ / (k_BT_eff ln2) from fundamental constants without empirical calibration, recovering 0.127 at institutional timescales. Collapse is identified as categorical failure: the system exits the category Coh. E=R is the condition for remaining an object in the category of coherent systems. Part of the Spektre corpus (github.com/spektre-labs/corpus).
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).
The Spektre corpus has treated coherence as a property of individual systems. This paper extends it to interactions. When two systems meet, their joint coherence K_{A⊗B} is not in general the product K_A · K_B. The difference E(A,B) = K_{A⊗B} - K_A · K_B is the mutual coherence — the non-separable component belonging to neither system alone. At quantum scale, E > 0 is entanglement. Bell’s theorem proves mutual coherence cannot be reduced to local properties — a universal structural result, not a quantum peculiarity. The same structure appears at every scale: biological symbiosis, institutional alliance, orchestrated intelligence, and human resonance are all instances of E > 0. Destructive interference (E < 0) is the mechanism of conflict. The interaction equation governs how mutual coherence evolves through shared channels. An institutional Bell test is proposed: M&A outcomes should not be predictable from local institutional metrics alone. Part of the Spektre research corpus.
Quantum mechanics is not fundamental. It is the coherence field K(t,x) projected into Hilbert space — a degenerate representation that has lost the coherence metric. Unitarity (U†U = I) is not a law of nature — it is the local expression of 1=1 in Hilbert space, valid when K > K_crit. When K approaches K_crit, unitarity breaks — this is measurement. The quantum jump is RCR (Recursive Constraint Regulation) at quantum scale: the system’s evaluation function is replaced because the old state is no longer coherent. Falsifiable prediction: a precursor signal — measurable coherence decrease — should precede every quantum jump, testable with Ramsey interferometry and quantum optics. The quantum-classical boundary is K_crit, not a fixed scale. Part of the Spektre research corpus.
The Spektre corpus has referenced the coherence landscape V(K) in 57 papers without deriving its explicit form. This paper fills that gap. Starting from the GCT dynamical equation, the free energy potential V(K) is derived by integration: V(K) = -α(K²/2 - K³/3) + (β/γ)[K - (1/γ)ln(1+γK)] + DK. This is a Landau-Ginzburg potential with cubic self-interaction and logarithmic correction. K_crit ≈ 0.127 is the barrier maximum — the tipping point between coherent and incoherent basins, a dimensionless geometric constant analogous to critical exponents in statistical mechanics. The spatiotemporal Lagrangian density L = ½∂μK∂μK - V(K) generates a scalar field theory whose Noether current is the stress-energy tensor sourcing gravity via Einstein’s equation. The multiplicative structure K = ρ·I_Φ·F is derived from series reliability theory. Quantum mapping made explicit: ρ → normalization, I_Φ → unitarity fidelity, F → 1 - S_vN/S_max. Seven testable predictions: Born rule deviation at degraded detector coherence, precursor signal before quantum emission, F-first institutional collapse ordering, DESI DR3 thawing match, no dark matter particle, Casimir deviation at large separation, BEC coherence time correlation. External anchors: Landau-Ginzburg, Eigen error threshold, Scheffer critical transitions, Ryu-Takayanagi, Higgs mechanism, Jacobson thermodynamic gravity, Coleman-De Luccia vacuum decay. Part of the Spektre research corpus.
This paper introduces the Universal Stability Invariant SΩ{S}_\OmegaSΩ​, a topological framework proposing thatdecoherence is not a statistical accident, but a mandatory thermodynamic executionto prevent localized saturation of the Topological Capacity Limit.