OUF (Information–Observer Unified Framework) series, Papers I–V, preprint v1.0. The series reconstructs physics from operational axioms: Paper I derives the measurement formalism as a theorem; Paper II recasts the equations of quantum mechanics in dual-real information form; Paper III develops detector–recorder systems as quantum channels; Paper IV derives the readout-channel thermal spectrum; Paper V rebuilds open quantum systems and quantum-engine laws from settlement. Remaining papers of the series will be added in a later version. License: CC BY 4.0.
OUF (Information–Observer Unified Framework) series, Papers I–V, preprint v1.0. The series reconstructs physics from operational axioms: Paper I derives the measurement formalism as a theorem; Paper II recasts the equations of quantum mechanics in dual-real information form; Paper III develops detector–recorder systems as quantum channels; Paper IV derives the readout-channel thermal spectrum; Paper V rebuilds open quantum systems and quantum-engine laws from settlement. Remaining papers of the series will be added in a later version. License: CC BY 4.0.
This paper closes three theoretical gaps that remained open in the Krylov-based quantum channel authentication framework developed across Papers 1-8 of this series. Physical Bridge (Theorem 1): I derive a formal proof that the QBER autocorrelation is proportional to the operator autocorrelation, C_QBER(τ) = α(N) · C_op(τ), establishing the connection between Krylov theory and observable measurement statistics (numerically confirmed with Pearson r = 0.9997). Physical One-Way Function (Theorem 2): I prove that the Krylov fingerprint map constitutes a physical one-way function with three independent hardness sources: (I) unconditional information-theoretic exponential ill-conditioning of the inverse moment problem (κ_n ~ 32^n), (II) complexity-theoretic reduction to Hamiltonian learning, and (III) physical irreversibility of scrambling dynamics (t_rec ~ 10^765). Hardness source I is unconditional and provides post-quantum security. Universality (Theorem 3): I establish the universality of the detection framework through systematic numerical verification across 8 Hamiltonian families and 10 perturbation types, achieving 8/8 families and 10/10 perturbation types at the physically relevant distance d = 1. All three results are detector-agnostic: they characterize the Krylov framework itself, independent of the specific detection algorithm applied to the Lanczos coefficients. Paper 9 in the Krylov QKD series. See also: qkd-krylov-detector on GitHub.
We develop a unified, operational, and falsifiable framework for quantum communication, quantum networks, and quantum cryptography as a conservative extension of three physical axioms: microscopic ontic definiteness with finite localization, the physical reality of the spacetime–vacuum substrate, and persistent causal retarded source–response coupling. Quantum states, density operators, entanglement, channels, and information are treated as mathematical or operational representations rather than additional fundamental ontologies. The framework derives completely positive trace-preserving maps from unitary system–environment dynamics and examines Kraus, Choi, Liouville, Stinespring, complementary-channel, and process-tensor representations. It establishes explicit interfaces for initial system–environment correlations, non-Markovian memory, channel discrimination, diamond-norm certification, and causal multitime processes. Classical, quantum, private, and entanglement-assisted capacities are distinguished from finite-blocklength and resource-normalized throughput. Optical-fiber, free-space, atmospheric, satellite, deep-space, microwave, atomic, spin, and continuous-variable links are incorporated through complete source–channel–receiver–detector forward models. Quantum networks are formulated as stochastic renewal, memory, swapping, purification, routing, and queueing systems subject to cut-set bounds, decoherence, synchronization error, congestion, latency, and energy constraints. For quantum key distribution, the security chain proceeds from source characterization and parameter estimation through smooth min-entropy, entropic uncertainty, error correction, authentication, privacy amplification, and composable key certification. BB84, decoy-state, entanglement-based, measurement-device-independent, device-independent, and continuous-variable protocols are treated with explicit finite-size and assumption boundaries. The theory preserves operational no-signaling, finite propagation speed, passivity, and complete energy accounting. Every performance or security claim requires independent calibration, nuisance covariance, held-out prediction, finite-sample validation, matched classical comparison, and an explicit rejection criterion. **Keywords** Quantum communication; quantum channels; quantum networks; quantum cryptography; quantum key distribution; open quantum systems; channel capacity; continuous-variable communication; quantum repeaters; process tensors; non-Markovian dynamics; composable security; finite-key analysis; no-signaling; detector forward models; experimental identifiability.
Holographic Information Ontology Framework (HIOF) — Spirit-Diagram Theorem · Emergence Equation Series (OTE·ME) Overview The Holographic Information Ontology Framework (HIOF) — Spirit-Diagram Theorem, Emergence Equation Series(abbreviated OTE·ME, from the Chinese 靈圖定理—顯現方程) is an eleven-paper theoretical series that reconstructs physical cosmology, decoherence, and cosmic-scale dynamics on an informational rather than a purely material substrate. The series replaces the classical spacetime block with the subjective information unit as its basic ontological primitive, and formalises the resulting dynamics through three coupled variables — entanglement (E), relational structure (R), and the field medium (ϕF) — governed by a unified transaction–recognition operator. The series begins from a methodological argument for observation-boundedness and the principle of simplest cause (Paper 0), develops the formal mathematical and geometric apparatus of the framework (Papers 1–2), applies it to reinterpret quantum decoherence, matter, and the two historical "clouds" of classical physics (Papers 3–5), extends it to cosmological closure and cross-scale singularity dynamics (Paper 6), positions it against competing research programmes such as causal set theory and the Page–Wootters mechanism (Paper 7), and derives concrete, falsifiable predictions (Paper 8). Paper 9 develops white-hole information re-injection as a mechanism for effective cosmic expansion. Paper 10, added subsequently to the original nine-paper arc, supplies the series' axiomatic foundation for consciousness and consensus — the Observation Postulate and the Panexperiential Postulate — resolving the problem of other minds and the combination problem within the framework's own transactional vocabulary. Series Structure Paper Title Core Content 0 Observation-Boundedness and the Simplest Cause Verification paradox; simplicity as inference to the best explanation; methodological foundation 1 From the Block to Information Subjective information unit; E, R, ϕF; observation postulate; panexperientialism 2 The Nonlinear Information Manifold Formal geometrisation of E, R, ϕF; curvature as informational tension 3 Deconstructing Decoherence Decoherence as informational settlement 4 Beyond the Matter Barrier Matter as a boundary condition of information flow 5 Deconstructing the Two Clouds Classical clouds of physics reframed through HIOF 6 Singularity Decoupling and Cross-Scale Closure Cosmological closure; singularities as decoupling events 7 Theoretical Comparison and Framework Positioning HIOF vs. causal set theory, Page–Wootters mechanism 8 Verification and Testable Predictions Falsifiable predictions derived from HIOF 9 White-Hole Information Injection and Effective Cosmic Expansion Re-injection dynamics; expansion as informational output 10 The Observation Postulate and the Consensus Recognition Mechanism Axiomatic foundation of consciousness and consensus Keywords holographic information ontology; observation postulate; panexperientialism; decoherence; information manifold; causal ledger; cosmic information; consensus recognition; combination problem; transaction–recognition operator; theoretical cosmology Author Wai-Hung Tam (Pan)Independent ResearcherORCID: 0009-0002-7789-8464Email: panxtam@protonmail.com Citation format Tam, W.-H. (Pan). (2026). Holographic Information Ontology Framework — Spirit-Diagram Theorem, Emergence Equation Series (Papers 0–10).
Introduction. Operational quantum logic: An overview B. Coecke, et al. I: Algebras. Algebraic aspects of orthomodular lattices G. Bruns, J. Harding. Observables in the logico-algebraic approach P. Ptak. Test spaces and orthoalgebras A. Wilce. Representations on unigroups D.J. Foulis. Free extensions of group actions, induced representations, and the foundations of physics D.J. Foulis, A. Wilce. II: Categories. Short introduction to enriched categories F. Borceux, I. Stubbe. Operational Galois adjunctions B. Coecke, D. Moore. Operational axiomatics and compound systems F. Valckenborgh. Quantales J. Paseka, J. Rosicky. III: Languages. Quantales and observational semantics P. Resende. Quantum languages S. Gudder. Indices. Concept index. Citation index.
Holographic Information Ontology Framework (HIOF) — Spirit-Diagram Theorem · Emergence Equation Series (OTE·ME) Overview The Holographic Information Ontology Framework (HIOF) — Spirit-Diagram Theorem, Emergence Equation Series(abbreviated OTE·ME, from the Chinese 靈圖定理—顯現方程) is an eleven-paper theoretical series that reconstructs physical cosmology, decoherence, and cosmic-scale dynamics on an informational rather than a purely material substrate. The series replaces the classical spacetime block with the subjective information unit as its basic ontological primitive, and formalises the resulting dynamics through three coupled variables — entanglement (E), relational structure (R), and the field medium (ϕF) — governed by a unified transaction–recognition operator. The series begins from a methodological argument for observation-boundedness and the principle of simplest cause (Paper 0), develops the formal mathematical and geometric apparatus of the framework (Papers 1–2), applies it to reinterpret quantum decoherence, matter, and the two historical "clouds" of classical physics (Papers 3–5), extends it to cosmological closure and cross-scale singularity dynamics (Paper 6), positions it against competing research programmes such as causal set theory and the Page–Wootters mechanism (Paper 7), and derives concrete, falsifiable predictions (Paper 8). Paper 9 develops white-hole information re-injection as a mechanism for effective cosmic expansion. Paper 10, added subsequently to the original nine-paper arc, supplies the series' axiomatic foundation for consciousness and consensus — the Observation Postulate and the Panexperiential Postulate — resolving the problem of other minds and the combination problem within the framework's own transactional vocabulary. Series Structure Paper Title Core Content 0 Observation-Boundedness and the Simplest Cause Verification paradox; simplicity as inference to the best explanation; methodological foundation 1 From the Block to Information Subjective information unit; E, R, ϕF; observation postulate; panexperientialism 2 The Nonlinear Information Manifold Formal geometrisation of E, R, ϕF; curvature as informational tension 3 Deconstructing Decoherence Decoherence as informational settlement 4 Beyond the Matter Barrier Matter as a boundary condition of information flow 5 Deconstructing the Two Clouds Classical clouds of physics reframed through HIOF 6 Singularity Decoupling and Cross-Scale Closure Cosmological closure; singularities as decoupling events 7 Theoretical Comparison and Framework Positioning HIOF vs. causal set theory, Page–Wootters mechanism 8 Verification and Testable Predictions Falsifiable predictions derived from HIOF 9 White-Hole Information Injection and Effective Cosmic Expansion Re-injection dynamics; expansion as informational output 10 The Observation Postulate and the Consensus Recognition Mechanism Axiomatic foundation of consciousness and consensus Keywords holographic information ontology; observation postulate; panexperientialism; decoherence; information manifold; causal ledger; cosmic information; consensus recognition; combination problem; transaction–recognition operator; theoretical cosmology Author Wai-Hung Tam (Pan)Independent ResearcherORCID: 0009-0002-7789-8464Email: panxtam@protonmail.com Citation format Tam, W.-H. (Pan). (2026). Holographic Information Ontology Framework — Spirit-Diagram Theorem, Emergence Equation Series (Papers 0–10).