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1 | | -Chronos-EntropyDepth |
| 1 | +# Chronos Certificates |
2 | 2 |
|
3 | | -Information-theoretic limits on refinement and computation. |
4 | | -Entropy-Depth bounds, structural obstructions, and executable artifacts. |
5 | | - |
6 | | -Overview |
7 | | - |
8 | | -Chronos-EntropyDepth is a core research repository within the Unified Rigidity Framework (URF). |
9 | | -It formalizes and studies Entropy-Depth as a universal obstruction to fast computation under locality, bounded information flow, and admissible refinement processes. |
10 | | - |
11 | | -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. |
12 | | - |
13 | | -This repository is intended to be: |
14 | | - |
15 | | -Audit-ready |
16 | | -Reproducible |
17 | | -Structurally minimal |
18 | | -Consistent with URF admissibility standards |
19 | | -Core Concept: Entropy-Depth |
20 | | - |
21 | | -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. |
22 | | - |
23 | | -Informally: |
24 | | - |
25 | | -Local or bounded-width computation can only extract a constant (or polylogarithmic) amount of information per step. |
26 | | -High-entropy instances therefore force long sequential depth. |
27 | | -ED lower bounds translate into intrinsic time lower bounds for large classes of algorithms. |
28 | | -Chronos is the structural program establishing, amplifying, and certifying these bounds. |
29 | | - |
30 | | -Scope of This Repository |
31 | | - |
32 | | -This repository focuses specifically on: |
33 | | - |
34 | | -Formal definitions of Entropy-Depth |
35 | | -Chronos amplification mechanisms |
36 | | -Locality-based obstructions (FOᵏ, WLᵏ, bounded-radius refinement) |
37 | | -Certified negative results for shallow refinement |
38 | | -Executable witnesses and verifier-friendly artifacts |
39 | | -It does not attempt to: |
40 | | - |
41 | | -Solve P vs NP outright |
42 | | -Enumerate all SAT algorithms |
43 | | -Replace general complexity-theoretic models |
44 | | -Instead, it isolates structural limits shared by broad algorithmic classes. |
45 | | - |
46 | | -Repository Structure |
47 | | - |
48 | | -Chronos-EntropyDepth/ ├── docs/ ├── src/ ├── tests/ ├── paper/ ├── STATUS.md └── README.md |
49 | | - |
50 | | -Relationship to URF |
51 | | - |
52 | | -Chronos-EntropyDepth is a downstream instantiation of the Unified Rigidity Framework. |
53 | | - |
54 | | -Upstream: |
55 | | - |
56 | | -https://github.com/inaciovasquez2020/urf-core |
57 | | -https://github.com/inaciovasquez2020/scientific-infrastructure |
58 | | -Reproducibility |
59 | | - |
60 | | -All artifacts are deterministic and audit-ready. No generated state is committed. |
61 | | - |
62 | | -Citation |
63 | | - |
64 | | -@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} } |
65 | | - |
66 | | -License |
67 | | - |
68 | | -MIT |
69 | | - |
70 | | -Maintainer |
71 | | - |
72 | | -Inacio F. Vasquez |
73 | | -Independent Researcher |
74 | | - |
75 | | -Chronos Certification (Defined) |
76 | | - |
77 | | -This repository supports a defined but unreleased certification layer. |
78 | | - |
79 | | -Status: |
80 | | - |
81 | | -Defined |
82 | | -Not released |
83 | | -No signed claims |
84 | | -Scope: |
85 | | - |
86 | | -Structural definitions and bounds only |
87 | | -Deterministic, audit-ready artifacts |
88 | | -Non-scope: |
89 | | - |
90 | | -No Clay problem resolution |
91 | | -No algorithmic prescriptions |
92 | | -No performance claims beyond EntropyDepth bounds |
| 3 | +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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