Program update: entropy route formally closed; pivot to communication complexity

Author: inaciovasquez2020

README.md

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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.
 
 This project relies on shared tooling and reproducibility infrastructure provided by the scientific-infrastructure repository; it contains domain-specific research code only.
+
+---
+
+## Program Update (Entropy Route Closed)
+
+The clause-transcript entropy approach to resolution lower bounds
+has been formally closed (see chronos-urf-rr).
+
+Support-symmetric and linear entropy functionals
+cannot capture resolution hardness.
+
+Active direction:
+Communication Information Complexity of Search_F.
+
+See:
+chronos-urf-rr/manuscripts/communication_information_reduction
+chronos-urf-rr/manuscripts/tseitin_ic_lower_bound
+
+---