The Stochastic Rupture (SR) framework for objective wave-function collapse is reformulated as a non-equilibrium statistical field theory using the Martin–Siggia–Rose–Janssen–De Domini- cis (MSRJD) path-integral formalism. The SR Langevin equation for the holographic saturation field χ admits an exact mapping to an MSRJD action with a cubic nonlinearity. Dimensional analysis yields an upper critical dimension dc = 4 and a dynamic exponent z = 2. In d = 3 a one-loop renormalization group (RG) analysis reveals a non-trivial infrared-stable fixed point at dimensionless coupling g ∗ = π (exact, of geometric origin). At this fixed point the satu- ration parameter η—previously phenomenological in SR v14–v15 with the empirical window 3 × 10−2 ≲ η ≲ 1—emerges as the expectation value ⟨χ⟩|g ∗ , not a free input. A specific prediction, contingent on the explicit evaluation of the source-renormalization diagram coefficient cS, is η = 2/3 (verified to machine precision under the stated condition). All assumptions are stated explicitly and open theoretical problems are listed
The Stochastic Rupture (SR) framework for objective wave-function collapse is reformulated as a non-equilibrium statistical field theory using the Martin–Siggia–Rose–Janssen–De Domini- cis (MSRJD) path-integral formalism. The SR Langevin equation for the holographic saturation field χ admits an exact mapping to an MSRJD action with a cubic nonlinearity. Dimensional analysis yields an upper critical dimension dc = 4 and a dynamic exponent z = 2. In d = 3 a one-loop renormalization group (RG) analysis reveals a non-trivial infrared-stable fixed point at dimensionless coupling g ∗ = π (exact, of geometric origin). At this fixed point the satu- ration parameter η—previously phenomenological in SR v14–v15 with the empirical window 3 × 10−2 ≲ η ≲ 1—emerges as the expectation value ⟨χ⟩|g ∗ , not a free input. A specific prediction, contingent on the explicit evaluation of the source-renormalization diagram coefficient cS, is η = 2/3 (verified to machine precision under the stated condition). All assumptions are stated explicitly and open theoretical problems are listed
The Stochastic Rupture (SR) framework for objective wave-function collapse is reformulated as a non-equilibrium statistical field theory using the Martin–Siggia–Rose–Janssen–De Domini- cis (MSRJD) path-integral formalism. The SR Langevin equation for the holographic saturation field χ admits an exact mapping to an MSRJD action with a cubic nonlinearity. Dimensional analysis yields an upper critical dimension dc = 4 and a dynamic exponent z = 2. In d = 3 a one-loop renormalization group (RG) analysis reveals a non-trivial infrared-stable fixed point at dimensionless coupling g ∗ = π (exact, of geometric origin). At this fixed point the saturation parameter η—previously phenomenological in SR v14–v15 with the empirical window 3 × 10−2 ≲ η ≲ 1—emerges as the expectation value ⟨χ⟩|g ∗ , not a free input. A specific prediction, contingent on the explicit evaluation of the source-renormalization diagram coefficient cS, is η = 2/3 (verified to machine precision under the stated condition). All assumptions are stated explicitly and open theoretical problems are listed.
We propose a stochastic rupture mechanism for reaction-diffusion systems based on a state-dependent relaxation rate Γeff(χ) = Γ0 −λχ, which vanishes at the critical amplitude χc = Γ0/λ. This modification is exactly equivalent to a renormalization of the nonlinear coupling in the Langevin equation, preserving locality and the full Martin–Siggia–Rose–Janssen–De Dominicis (MSRJD) formalism. We identify the scalar field χ with the local informational saturation ratio χ = SvN/(η IBek) of the Stochastic Rupture (SR) framework [1], where SvN is the local von Neumann entropy and IBek is the Bekenstein bound of the enclosing causal-diamond region. Under the physically motivated condition α = λ/2, we derive—rather than postulate—the satu- ration feedback function F(χ) = (1 − χ) −1 as a direct consequence of the divergence of the zero-momentum field-fluctuation variance at the critical point. We further derive the homogeneous mean-field dynamics χ(t) and recover the rupture-time estimate τSR ∼ η/γ0 for nanoparticle superpositions. An analogy with overclocking and thermal throttling in computational processors provides physical intuition, in- cluding a speculative interpretation of quantum tunneling as time dilation between dynamically distinct regimes. A conceptual experiment using optically levitated nanoparticles to discriminate this framework from standard decoherence is proposed. The renormalization group analysis of this theory and the determination of its universality class are reserved for a companion work.
Stochastic Rupture (SR) proposes that objective wavefunction collapse is triggered when local von Neumann entropy saturates a fraction eta of the holographic Bousso bound on causal-diamond surfaces. The SR network is concretely realized as a simple cubic lattice — square holographic sheets stacked at Planck-scale intervals — whose exact Laplacian spectrum derives the dimensional flow d s: 2 ( UV, holographic ) to 3 ( stacking ) to 4 ( Lorentzian, open ) without free parameters. The framework has two logically independent sectors. The collapse sector is self-contained and makes parameter-free falsifiable predictions. The general SR decoherence rate Gamma SR = Gm squared /(4 h bar sigma x squared ) produces a sigma x to the minus 2 scaling that discriminates SR from CSL (sigma x to the minus 3) and Diósi–Penrose (flat), independently of any free parameters; the definitive test is at MAQRO (10 to the 9–10 to the 10 amu). For GHZ/Bell states on NISQ hardware, the SR-native prediction is tau Bell / tau GHZ is similar to N squared, with a finite-size correction: reliable collapse onset at N stable is approximately equal to 1.25/(1 minus eta ) rather than the theoretical threshold 1/(1 minus eta ). The geometric sector — Newton's law, Einstein equations, spin-2 graviton — is conditional on the IR limit d s to 4 and is presented explicitly as such. Two new structural results reduce the number of free parameters. The bond-percolation threshold of the simple cubic lattice, p c = 0.2488, matches the cosmological structure-suppression parameter e 0 = 0.249 plus or minus 0.035 to within 0.1 %, linking the connectivity transition of the SR network to the S8 tension without a free fit. The restoration rate lambda q, previously unconstrained, is shown to satisfy lambda q/ gamma 0 is approximately equal to 1/ the square root of pi through a three-step geometric argument: vibrating holographic sheets drive saturation fluctuations to the 2D square interface critical point p c=1/2; Bernoulli variance at criticality gives sigma = the square root of 3 /2; three independent propagation channels in 3D then fix lambda q/ gamma 0 = C/ the square root of pi with C is approximately equal to 0.995. The remaining open step — showing the SR interface dynamics belongs to the Model A universality class with additive noise — reduces to a single one-loop RG calculation. The framework makes fourteen falsifiable predictions spanning NISQ processors, MAQRO, LISA, and Euclid, explicitly distinguishing derived results from calibrated parameters and open problems.
This companion collects results of the Stochastic Rupture (SR) framework that are absent from the main paper. Its organising claim is that a single geometric object—the Fisher–Rao metric, unique by Chentsov’s theorem—supplies the pruning rate, the noise, and the barrier of the collapse sector, leaving that sector with no free choice of its own. We derive rather than posit. The barrier V = γ0/(1−χ) is the Fisher transport of the Casini relative entropy, which fixes the inverse-square exponent as the product of a logarithmic divergence and the Chentsov metric; the noise temperature is Teff = ℏγ0/kB, saturating the Feller condition as an identity. We construct the flash map, identifying pruning events with Wright–Fisher fixations: a martingale argument gives P(k) = |ak|², supplying the branch→effect map that Busch’s theorem requires, so that Born becomes a theorem conditional on one hypothesis-and Born exactness becomes equivalent to neutrality of the race, hence falsifiable. That hypothesis, that the quantum phase is the tangent orientation, is promoted to an elimination theorem: of the four compact angular variables the substrate possesses, Wallstrom’s condition leaves exactly one, with Poincar´e–Hopf supplying the integer winding. On the field-theoretic side we concede that friction is a relevant operator and show its coefficient is nevertheless fixed: multiplicative noise vanishes in vacuum, leaving Γ0 = Λ, so the wave regime (z = 1) holds for all observable physics and diffusive scaling is confined to super-Hubble scales. Transverse traceless gravitons preserve areas at linear order and do not inherit the friction; we accordingly retract an earlier gravitational-wave damping estimate and replace it with a polarisation-selective prediction. The MSRJD action, having no free choices, selects Itˆo by covariance and causality; its quantum lift is the Drude–Lorentz bath, satisfying KMS with analyticity strip 1/γ0 and saturating both the Planckian dissipation and Maldacena-Shenker-Stanford chaos bounds. Throughout, the epistemic status of each claim-derived, assumed, or open-is stated in the text. Two founding premises remain declared rather than derived: the master equation itself, and relational parsimony. Results here are internally verified, symbolically or numerically; they have not been subjected to independent review, which we invite.
The Stochastic Rupture (SR) framework postulates that wavefunction collapse is an informational phase transition triggered by the saturation of local holographic entropy bounds. A central corollary of this framework is the emergence of proper time as a function of local informational occupancy: dτ = dt, IPlanck χ, η, Acausal . (1)While previous analyses focused primarily on the collapse regime (χ → 1), this work explores the opposite limit (χ → 0), characteristic of microscopic quantum systems. We propose that the extreme temporal acceleration associated with low informational saturation provides a physical explanation for quantum delocalization. In this picture, the wavefunction describes a temporally generated ensemble of rapidly iterated configurations within a coarse external time slice. Apparent spatial superposition therefore emerges as a relativistic asynchrony between informational proper time and macroscopic coordinate time.
Three independent frameworks propose that wavefunction collapse is a physical process rather than a postulate: the DiósiPenrose (DP) model, the Stochastic Rupture (SR) model, and the emergent-time theory of Lee (2025). We argue that these are not simply alternative theories but occupy distinct levels of a natural hierarchy. Lee establishes the geometric mechanism by which time and collapse emerge from stochastic relaxation of dieomorphism- constraint violations in full general relativity, but provides no local criterion specifying when a particular system collapses. SR supplies exactly this missing criterion: collapse occurs when the local von Neumann entropy approaches the Bousso-bounded informational capacity, SvN → η IBousso. DiósiPenrose appears as the low-saturation operational limit of SR, valid when SvN ≪ η IBousso and gravitational self-energy dominates. The proposed hierarchy is Lee semiclassical limit −−−−−−−−−−−→ SR SvN ≪ ηIBousso −−−−−−−−−−→ DP. We derive the experimental discriminators that distinguish all three models, identify the conjectural steps in the hierarchy that remain to be derived, and discuss how the SR frame- work resolves the Schrödinger cat problem by providing the local informational criterion absent in both Lee and DP.