|
1 | | -# Chronos-EntropyDepth |
| 1 | +Chronos-EntropyDepth |
2 | 2 |
|
3 | | -**Information-theoretic limits on refinement and computation.** |
4 | | -**Entropy-Depth bounds, structural obstructions, and executable artifacts.** |
| 3 | +Information-theoretic limits on refinement and computation. |
| 4 | +Entropy-Depth bounds, structural obstructions, and executable artifacts. |
5 | 5 |
|
6 | | ---- |
| 6 | +Overview |
7 | 7 |
|
8 | | -## Overview |
9 | | - |
10 | | -**Chronos-EntropyDepth** is a core research repository within the **Unified Rigidity Framework (URF)**. |
11 | | -It formalizes and studies *Entropy-Depth* as a universal obstruction to fast computation under locality, bounded information flow, and admissible refinement processes. |
| 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. |
12 | 10 |
|
13 | 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. |
14 | 12 |
|
15 | 13 | This repository is intended to be: |
16 | | -- Audit-ready |
17 | | -- Reproducible |
18 | | -- Structurally minimal |
19 | | -- Consistent with URF admissibility standards |
20 | | - |
21 | | ---- |
22 | 14 |
|
23 | | -## Core Concept: Entropy-Depth |
| 15 | +Audit-ready |
| 16 | +Reproducible |
| 17 | +Structurally minimal |
| 18 | +Consistent with URF admissibility standards |
| 19 | +Core Concept: Entropy-Depth |
24 | 20 |
|
25 | | -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. |
| 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. |
26 | 22 |
|
27 | 23 | Informally: |
28 | | -- Local or bounded-width computation can only extract a constant (or polylogarithmic) amount of information per step. |
29 | | -- High-entropy instances therefore force *long sequential depth*. |
30 | | -- ED lower bounds translate into intrinsic time lower bounds for large classes of algorithms. |
31 | 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. |
32 | 28 | Chronos is the structural program establishing, amplifying, and certifying these bounds. |
33 | 29 |
|
34 | | ---- |
35 | | - |
36 | | -## Scope of This Repository |
| 30 | +Scope of This Repository |
37 | 31 |
|
38 | 32 | This repository focuses specifically on: |
39 | 33 |
|
40 | | -- Formal definitions of Entropy-Depth |
41 | | -- Chronos amplification mechanisms |
42 | | -- Locality-based obstructions (FOᵏ, WLᵏ, bounded-radius refinement) |
43 | | -- Certified negative results for shallow refinement |
44 | | -- Executable witnesses and verifier-friendly artifacts |
45 | | - |
46 | | -It does **not** attempt to: |
47 | | -- Solve P vs NP outright |
48 | | -- Enumerate all SAT algorithms |
49 | | -- Replace general complexity-theoretic models |
50 | | - |
51 | | -Instead, it isolates *structural limits* shared by broad algorithmic classes. |
52 | | - |
53 | | ---- |
| 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: |
54 | 40 |
|
55 | | -## Repository Structure |
| 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. |
56 | 45 |
|
57 | | -Chronos-EntropyDepth/ |
58 | | -├── docs/ |
59 | | -├── src/ |
60 | | -├── tests/ |
61 | | -├── paper/ |
62 | | -├── STATUS.md |
63 | | -└── README.md |
| 46 | +Repository Structure |
64 | 47 |
|
65 | | ---- |
| 48 | +Chronos-EntropyDepth/ ├── docs/ ├── src/ ├── tests/ ├── paper/ ├── STATUS.md └── README.md |
66 | 49 |
|
67 | | -## Relationship to URF |
| 50 | +Relationship to URF |
68 | 51 |
|
69 | | -Chronos-EntropyDepth is a downstream instantiation of the **Unified Rigidity Framework**. |
| 52 | +Chronos-EntropyDepth is a downstream instantiation of the Unified Rigidity Framework. |
70 | 53 |
|
71 | 54 | Upstream: |
72 | | -- https://github.com/inaciovasquez2020/urf-core |
73 | | -- https://github.com/inaciovasquez2020/scientific-infrastructure |
74 | 55 |
|
75 | | ---- |
| 56 | +https://github.com/inaciovasquez2020/urf-core |
| 57 | +https://github.com/inaciovasquez2020/scientific-infrastructure |
| 58 | +Reproducibility |
76 | 59 |
|
77 | | -## Reproducibility |
| 60 | +All artifacts are deterministic and audit-ready. No generated state is committed. |
78 | 61 |
|
79 | | -All artifacts are deterministic and audit-ready. |
80 | | -No generated state is committed. |
| 62 | +Citation |
81 | 63 |
|
82 | | ---- |
| 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} } |
83 | 65 |
|
84 | | -## Citation |
85 | | - |
86 | | -@manual{Vasquez_Chronos_EntropyDepth_2026, |
87 | | - author = {Vasquez, Inacio F.}, |
88 | | - title = {Chronos-EntropyDepth: Entropy-Based Structural Limits on Computation}, |
89 | | - year = {2026}, |
90 | | - url = {https://github.com/inaciovasquez2020/Chronos-EntropyDepth} |
91 | | -} |
92 | | - |
93 | | ---- |
94 | | - |
95 | | -## License |
| 66 | +License |
96 | 67 |
|
97 | 68 | MIT |
98 | 69 |
|
99 | | ---- |
| 70 | +Maintainer |
100 | 71 |
|
101 | | -## Maintainer |
102 | | - |
103 | | -Inacio F. Vasquez |
| 72 | +Inacio F. Vasquez |
104 | 73 | Independent Researcher |
105 | 74 |
|
106 | | -## Chronos Certification (Defined) |
| 75 | +Chronos Certification (Defined) |
107 | 76 |
|
108 | 77 | This repository supports a defined but unreleased certification layer. |
109 | 78 |
|
110 | 79 | Status: |
111 | | -- Defined |
112 | | -- Not released |
113 | | -- No signed claims |
114 | 80 |
|
| 81 | +Defined |
| 82 | +Not released |
| 83 | +No signed claims |
115 | 84 | Scope: |
116 | | -- Structural definitions and bounds only |
117 | | -- Deterministic, audit-ready artifacts |
118 | 85 |
|
| 86 | +Structural definitions and bounds only |
| 87 | +Deterministic, audit-ready artifacts |
119 | 88 | Non-scope: |
120 | | -- No Clay problem resolution |
121 | | -- No algorithmic prescriptions |
122 | | -- No performance claims beyond EntropyDepth bounds |
| 89 | + |
| 90 | +No Clay problem resolution |
| 91 | +No algorithmic prescriptions |
| 92 | +No performance claims beyond EntropyDepth bounds |
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