Semantic Gravitational Collapse: On the Loss of Authority of Execution Substrates

This paper introduces Semantic Gravitational Collapse (SGC), a field-theoretic account of how authority migrates in computational, institutional, and AI systems as meaning is increasingly decided upstream of execution. SGC names the regime in which admissibility, explicit binding, detectability, receipted memory, and negative power accumulate sufficient semantic density that downstream execution substrates - languages, runtimes, models, and hardware - lose independent authority and function instead as witnesses. The paper argues that many contemporary failures in AI safety, governance, and software engineering are not performance failures but authority failures: execution is implicitly treated as a source of legitimacy rather than as evidence. SGC explains why downstream controls (filters, policies, audits, guardrails) systematically fail, and why durable legitimacy requires constraint to precede action rather than follow it. The work formalizes semantic mass, collapse thresholds, failure modes (diffusion, false collapse, singularity), and the role of negative power in preserving liberty under strong governance. An appendix provides a compact mathematical scaffold to make semantic density, collapse, and bypass cost analytically discussable without reducing them to metrics. SGC is not an architecture or policy proposal. It is a descriptive framework for understanding when execution can no longer impersonate meaning - and what conditions allow authority to remain inspectable, contestable, and escapable.