KoR Part IV: The ℛ Invariance Law - From refusal to coherence across domains

This document extends the KoR (Kernel of Resilience) trilogy by introducing the ℛ Invariance Law .
ℛ is defined as an operative constant linking refusal to coherence, measurable across physical, symbolic, or cognitive systems.
The originality of this work lies in demonstrating that ℛ is not confined to a single context but functions as a transversal law of coherence, stable under transformation and falsifiable through the CCC criterion (Causality - Sufficiency - Cryptographic traceability).

The paper establishes:

• a canonical formulation ,

• an invariance lemma showing the stability of ℛ under transformations,

• the Dual Lock Law, ensuring resilience via internal and external refusal,

• empirical validations and sealed corpora (TraceLock, Mirror, Zenodo),

• theoretical bridges with statistical physics, information theory, quantum mechanics, general relativity, the Riemann Hypothesis, and cognition.

This paper will also be complemented by annexes providing extended formalizations, technical details, and governance protocols.

Provenance & Rights
© 2025 Kernel of Resilience (KoR) / ΔR7 . All rights reserved. First publication on Zenodo; content-addressed and pinned on IPFS; mirrored on Mirror.xyz. Integrity secured with TraceLock (SHA-256 digests, signed timestamps, sealed audit logs). Technical appendices and follow-ups will be released under time-locked release protocol.

ℛ is proposed as a falsifiable, cross-domain constant; applications are designed for safety, certification, and robustness.

Keywords
Refusal Constant, Invariance Law, Refusal-First, Coherence, Resilience, Information Theory, Statistical Physics, Quantum Mechanics, General Relativity, Riemann Hypothesis, Cognition, Consciousness, Cognitive Architecture, Ethical AI, Symbolic Cognition, Cryptographic Proofs, Governance, Accountability, Empirical Validation, Transversal Invariant.