Research
Status:[EXA]Exact result
Theorems and Exact Results
Mathematical Rigor with Explicit Hypotheses and Claim Ceilings
Executive Summary (Plain English)
A rigorous catalog of the primary theorems established across the Foundations Audit corpus, including the Fisher-Clock Correspondence, Network Synchronization, Paired-Expansion Nondefinability, Quantum Darwinism Survival, and Sector-Family Lieb-Robinson Envelopes.
Evidence Class: Analytic Theorem·Scope: Catalog of primary exact and restricted theorems
Last Audited: 2026-09-18
Claim Boundary & Exclusions Audit
What Is Claimed (Within Scope)
- •Dynamical-Time / Fisher-Clock Correspondence Theorem (FA-LRT-01).
- •Network Loop Holonomy Synchronization Theorem (FA-LRT-01).
- •Paired-Expansion Nondefinability Theorem (FA-AUTH-01).
- •Quantum Darwinism Channelwise Survival Theorem (FA-QD-ST-01).
- •Objectivity vs. Causal Nonseparability Independence Theorem (FA-QD-PRXQ-01).
- •Postselection Average-Gain Identity & Universal Budget Theorem (FA-QD-PS-01).
- •Lieb-Robinson Sector-Family Envelope Theorem (FA-CB-02).
What Is NOT Claimed (Prohibited Inferences)
- •No theorem may be generalized beyond its declared dimensional, algebraic, or carrier hypotheses.
Technical Exposition & Formulation
Every theorem entry contains the verbatim mathematical statement, required hypotheses, proof sketches, complete carrier declarations, and explicit exclusion boundaries.
Assumptions & Input Data
- Standard operator-algebraic and information-theoretic frameworks.
Declared Complete Carrier (K3)
Declared in each respective theorem.
Source Provenance & Verification Hashes
FA-SYN-01CONTROLLING
ETP_Final_Synthesis_Draft-20...
SHA-256:02a884082f...00f608ff
Corpus DetailsChallenge This Claim Ceiling
Identified an unstated carrier or a counterexample? Submit a formal challenge.