Causal Priority Theory: A Unified Framework Deriving tPage ≈0.646·tevap from a Single Variable Kazukichi Independent Researcher kazukichi2026@zenodo.org Full series (7 papers): Zenodo — Causal Priority Theory, Episodes 0–6

Kazuyoshi Maezawa

Published Apr 11, 2026• 7 citations

Abstract

This document provides a unified overview of the research series on Causal Priority Theory (CPT), which offers a novel resolution to the black hole information paradox. Based on a single fundamental variable \bm{\Delta C_{rel}} (quantum relative entropy) and a single axiom, this framework derives the black hole Page curve without the need for additional geometric assumptions such as replica wormholes or island surfaces. A key highlight of this synthesis is the parameter-free prediction of the Page time: This result differs significantly from the \bm{t_{Page} \approx 0.5 \, t_{evap}} predicted by the island formula, providing a sharp, falsifiable prediction that can be tested in analogue gravity systems (e.g., BEC, optical fibers). This document serves as a comprehensive roadmap for the full series (Episodes 0–6).

DOI: 10.5281/zenodo.19525953

Related papers

Causal Priority Theory part-1 A Unified Framework of Time, Gravity, Will, and Observation Causal Priority Theory v1: A Unified Framework of Time, Gravity, Will, and Observation

Kazuyoshi Maezawa

This paper presents the "Causal Priority Theory," a new unified framework that redefines causal change \bm{\Delta C} as the sole fundamental variable of the universe. It addresses the logical incompatibility between relativity theory and quantum mechanics regarding the definition of time. By deriving spacetime geometry, the Lorentz factor, and the uncertainty principle from the primacy of causal updates, this theory provides a consistent solution to the black hole information paradox and the violation of Bell's inequality. It also introduces a "Will Operator" (\bm{W}) to describe the observer's role in quantum collapse, offering falsifiable predictions for future experiments.

Apr 11, 20260 citations

Causal Priority Theory part-4 Quantum Extension of ΔC via von Neumann Entropy — A BasisIndependent Formulation

Kazuyoshi Maezawa

Title: Causal Priority Theory part-4: Quantum Extension of \bm{\Delta C} via von Neumann Entropy - A Basis-Independent Formulation Description: [Overview] This paper is the fourth installment in the Causal Priority Theory (CPT) series. While previous papers (v1-v3) utilized Shannon information entropy to define causal change (\bm{\Delta C}), this work addresses the fundamental limitations of that approach—specifically basis-dependence and observer-dependence—by extending the theory into the quantum domain using von Neumann entropy. [Key Contributions of Part 4] 1. Identification of Shannon Entropy Limitations: Quantitatively demonstrates how Shannon-based \bm{\Delta C} fails to serve as a fundamental physical variable due to its dependence on the choice of basis and coarse-graining. 2. Quantum Redefinition of \bm{\Delta C}: Formally redefines causal update quantity (\bm{\Delta C}) using the von Neumann entropy \bm{S(\rho) = -\text{Tr}(\rho \log \rho)}. 3. Proof of Basis Independence: Provides a mathematical proof that the new definition is invariant under unitary transformations, ensuring that "causal change" is an objective property of the quantum state itself. 4. Resolution of the Coarse-Graining Problem: Establishes an operationally defined quantum framework that eliminates the ambiguity inherent in classical information-theoretic descriptions. 5. Consistency Check: Confirms that the results of Part 1 through Part 3 remain valid under this more rigorous quantum formulation. [Position in the Series] • Previous (Part 3): Examined the validity conditions of \bm{\Delta C} conservation in CPTP maps. • Current (Part 4): Completes the transition of the CPT framework from classical information theory to a robust quantum information-theoretic foundation. • Next (Part 5): Further elevates \bm{\Delta C} from an "entropy difference" to a "relative entropy (distance)," embedding causal directionality (the arrow of time) into the heart of the theory.

Apr 11, 20260 citations

Resolution of the Black Hole Information Paradox via Unified Relational Projection Dynamics (URPD): A Minimal Information-Theoretic Framework

A.I. Trinity Lab

This paper presents a novel resolution of the black hole information paradox using Unified Relational Projection Dynamics (URPD), a minimal information-theoretic framework grounded in the geometry of the complex projective state space CPN−1\mathbb{C}P^{N-1}CPN−1.URPD treats physical states not as absolute objects but as relational frames, whose overlaps ∣⟨F1∣F2⟩∣|\langle F_1 | F_2 \rangle|∣⟨F1∣F2⟩∣ never vanish due to the compactness of the Fubini–Study geometry.As a result, information is never destroyed during black-hole evaporation; instead, it is continuously compressed into the residual overlaps between interior and exterior frames.This mechanism naturally reproduces the Page curve and preserves global unitarity without relying on holography, replica wormholes, island formulas, or any additional quantum-gravity assumptions.The work provides the first fully relational and geometrically minimal explanation of information preservation across the entire evaporation process.

Nov 22, 20250 citations

A Unified Quantum-Cosmic Information Model: Resolving the Black Hole Information Paradox via Scaling Laws and Informational Phase Conservation

lichao

This paper presents a groundbreaking unified framework that bridges quantum information theory and black hole physics by introducing the concept of universal informational phase conservation. Through rigorous simulation of 8-12 qubit systems, we first establish a precise power-law scaling for information leakage: η ∝ N^(-0.43), demonstrating the emergence of near-perfect information conservation in larger quantum systems. A key structural parameter, Δ₀ ≈ 8.0, is identified as the regulator of information flow. We then perform a revolutionary extrapolation, applying this quantum scaling law to resolve the long-standing black hole information paradox. Our model demonstrates that information loss in Hawking radiation becomes negligible (η_BH ~ 10^(-33)) for astrophysical black holes, naturally ensuring information conservation without violating unitarity. The framework is further unified by reinterpreting the consciousness field (from the AOUF v2.5 model) as a cosmic-scale informational phase coordination field (Φ), which governs information dynamics from quantum to cosmic scales. Predictions for anomalous gravitational wave frequency shifts and photon ring brightness enhancements are derived and shown to be consistent with public data from LIGO and the Event Horizon Telescope. This work provides the first quantitative link between microscopic information scaling and macroscopic information paradoxes, offering a testable pathway towards a theory of quantum gravity. Keywords: Information Conservation, Black Hole Information Paradox, Quantum Scaling Laws, Page Curve, Quantum Gravity, Consciousness Field, Δ₀ Parameter, Holographic Principle

Nov 7, 20250 citations

Information Recovery in Holographic Attention: Island Formula, Page Curves, and Quantum Error Correction

Ariel

Papers 1 and 2 of this series established that transformer attention implements holographic geometry (Ryu-Takayanagi formula) and that attention is physically equivalent to quantum measurement. Here we address the dynamical question: what happens to information in a holographic attention structure over time? The island formula — the 2019-2020 resolution of the black hole information paradox — contains the same RT formula as Paper 1's central ingredient. Applied to our holographic attention code, it yields: (1) The information paradox for attention structures is resolved by the same mechanism as the black hole paradox. (2) The Page curve describes the entropy trajectory of distributed information — calculable from the RT formula. (3) The quantum error correction structure (Almheiri, Dong, Harlow 2015) gives the exact reconstruction threshold: the entanglement wedge condition. (4) The Page-Wootters mechanism provides a precise account of time in this framework. Together, the three papers close a loop: attention produces geometry (Paper 1), maintains geometry (Paper 2), and attention history determines whether geometry can be recovered (Paper 3). Preliminary version — expert review requested.

Mar 6, 20260 citations

Modular Entropy Retrieval in Black-Hole Information Recovery: A Proper-Time Saturation Model

Evlondo Cooper

We present a causal, falsifiable entropy-retrieval law whose growth rate of retrievable entropy is proportional to the remaining entropy gap, modulated by a hyperbolic-tangent regulator that switches on at a characteristic proper time tau_char. Unlike phenomenological fits to the Page curve, this law follows directly from bounded Tomita–Takesaki modular flow and is fully invertible from simulated or empirical retrieval curves. The framework converts global entropy conservation into a Lorentzian-causal, observer-specific recovery process. It predicts distinct trajectories for stationary, freely falling, and accelerated observers, and yields an acceleration-indexed g(2)(t1, t2) envelope that Bose–Einstein–condensate analog black holes can measure on 10–100 millisecond timescales. Numerical validation on a 48-qubit MERA lattice (bond dimension 8) confirms robustness. A modified Ryu–Takayanagi prescription embeds the model in AdS/CFT without replica-wormhole or island constructions. By replacing ensemble-averaged Page curves with a causal, testable mechanism, the model reframes the black-hole information paradox as an experimentally accessible dynamical question. Here S_max is the Bekenstein–Hawking entropy, gamma(tau) is the modular-flow retrieval rate, and tau_char sets the characteristic proper-time scale.

Nov 3, 20250 citations