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README.md

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Chronos-EntropyDepth
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# Chronos Certificates
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Information-theoretic limits on refinement and computation.
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Entropy-Depth bounds, structural obstructions, and executable artifacts.
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Overview
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Chronos-EntropyDepth is a core research repository within the Unified Rigidity Framework (URF).
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It formalizes and studies Entropy-Depth as a universal obstruction to fast computation under locality, bounded information flow, and admissible refinement processes.
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The repository contains definitions, constructions, and executable artifacts supporting lower bounds on sequential refinement depth, with applications to SAT, locality-restricted algorithms, and capacity-limited computation.
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This repository is intended to be:
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Audit-ready
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Reproducible
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Structurally minimal
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Consistent with URF admissibility standards
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Core Concept: Entropy-Depth
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Entropy-Depth (ED) measures the minimum sequential depth required for any admissible process to resolve a system with initial entropy ( H(X) ), under bounded per-step information gain.
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Informally:
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Local or bounded-width computation can only extract a constant (or polylogarithmic) amount of information per step.
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High-entropy instances therefore force long sequential depth.
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ED lower bounds translate into intrinsic time lower bounds for large classes of algorithms.
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Chronos is the structural program establishing, amplifying, and certifying these bounds.
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Scope of This Repository
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This repository focuses specifically on:
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Formal definitions of Entropy-Depth
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Chronos amplification mechanisms
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Locality-based obstructions (FOᵏ, WLᵏ, bounded-radius refinement)
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Certified negative results for shallow refinement
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Executable witnesses and verifier-friendly artifacts
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It does not attempt to:
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Solve P vs NP outright
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Enumerate all SAT algorithms
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Replace general complexity-theoretic models
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Instead, it isolates structural limits shared by broad algorithmic classes.
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Repository Structure
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Chronos-EntropyDepth/ ├── docs/ ├── src/ ├── tests/ ├── paper/ ├── STATUS.md └── README.md
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Relationship to URF
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Chronos-EntropyDepth is a downstream instantiation of the Unified Rigidity Framework.
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Upstream:
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https://github.com/inaciovasquez2020/urf-core
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https://github.com/inaciovasquez2020/scientific-infrastructure
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Reproducibility
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All artifacts are deterministic and audit-ready. No generated state is committed.
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Citation
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@manual{Vasquez_Chronos_EntropyDepth_2026, author = {Vasquez, Inacio F.}, title = {Chronos-EntropyDepth: Entropy-Based Structural Limits on Computation}, year = {2026}, url = {https://github.com/inaciovasquez2020/Chronos-EntropyDepth} }
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License
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MIT
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Maintainer
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Inacio F. Vasquez
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Independent Researcher
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Chronos Certification (Defined)
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This repository supports a defined but unreleased certification layer.
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Status:
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Defined
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Not released
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No signed claims
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Scope:
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Structural definitions and bounds only
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Deterministic, audit-ready artifacts
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Non-scope:
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No Clay problem resolution
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No algorithmic prescriptions
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No performance claims beyond EntropyDepth bounds
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This repository is intentionally **certificate-only**. As of tag `chronos-certificates-frozen`, the Chronos depth constants and related artifacts are frozen, cryptographically signed, and treated as canonical. The files `chronos_constants.json` and `Chronos/Cert/ChronosDepthConstants.lean`, together with their corresponding `.minisig` signatures, constitute the complete, verifiable Chronos certificate set. No Chronos theory is developed here: all mathematical definitions, transport lemmas (including the PSH → boundary-overlap conditional), and proofs live upstream in `urf-core`. Any modification to the frozen artifacts requires an explicit unfreeze decision, regeneration of signatures, and a new freeze tag.

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