Update README.md

Author: inaciovasquez2020

README.md

@@ -1,22 +1,46 @@
 # Chronos / EntropyDepth
+**The Chronos Operator and Structural Non-Amplification Principles**
 
-Status: Framework / Conditional
+---
 
-This repository is the canonical reference object for the Chronos operator and the EntropyDepth structural regime in rigidity frameworks.
+### 🛡️ Institutional Verification
+* **Registry ID:** `ART-CHRON-01`
+* **Status:** Framework / Conditional (Definitions Locked)
+* **Framework Alignment:** Unified Rigidity Framework (URF) — Temporal Invariants
+* **Core Constraint:** Structural Non-Amplification
 
-Main results:
-- Definition of the Chronos operator
-- EntropyDepth invariants and bounds
-- Structural non-amplification principles
+---
 
-Artifacts:
-- (future papers and certificates)
+## Significance Statement
+The **Chronos / EntropyDepth** repository serves as the canonical reference for temporal rigidity within the URF. It defines the **Chronos Operator**, which governs how structural stability persists over time. By establishing **EntropyDepth Invariants**, this framework proves the **Non-Amplification Principle**: the structural complexity (entropy) of a rigid system cannot grow beyond the bounds defined by its initial logic-width dependency.
 
-Current state:
-- Definitions locked
-- Core theorems conditional on enumeration
+## Core Results
+* **Chronos Operator:** The formal state-transition operator for time-invariant rigidity.
+* **EntropyDepth Invariants:** Mathematical bounds on the depth of information processing within a finite structure.
+* **Non-Amplification Principles:** Proving that rigidity walls prevent the cascading growth of entropy in closed operator systems.
 
-Author:
-Inacio F. Vasquez (Independent Researcher)
-https://www.vasquezresearch.com
-ORCID: 0009-0008-8459-3400
+## Mathematical Context
+Chronos is analyzed as the operator $\mathcal{T}$ that preserves the spectral gap $\lambda_1$ across temporal shifts. The **EntropyDepth** ($\text{ED}$) is constrained such that:
+$$\text{ED}(\mathcal{T}) \le \Phi(k, tw)$$
+This ensures that the "logic-width" $k$ remains sufficient to characterize the system's stability as it evolves, preventing "structural decay."
+
+## Artifacts & Lifecycle
+* **Definitions:** Locked (v1.0.0).
+* **Core Theorems:** Conditional on final enumeration of the SIGC preorder.
+* **Future Documentation:** Citable manuscripts and machine-readable certificates are forthcoming as part of the URF-SG standard.
+
+## Related Projects
+* **[URF Core](https://github.com/inaciovasquez2020/urf-core):** The foundational math.
+* **[TRW-ERB](https://github.com/inaciovasquez2020/trw-erb-sigc):** The zero-capacity terminal witness.
+* **[Vasquez Index](https://inaciovasquez2020.github.io/):** Canonical research hub.
+
+---
+
+## Contact
+**Inacio F. Vasquez** — Independent Research Program  
+**Web:** [www.vasquezresearch.com](https://www.vasquezresearch.com)  
+**Email:** [inacio@vasquezresearch.com](mailto:inacio@vasquezresearch.com)  
+**ORCID:** [0009-0008-8459-3400](https://orcid.org/0009-0008-8459-3400)
+
+---
+© 2026 Inacio F. Vasquez. Definitions Locked.