On Boundaries of Evidence — Boundary-State Calculus for Typed Observation, Admissible Transfer, and Falsifiable Persistence

Abstract

Version 1.4.0 of a foundational preprint proposing Boundary-State Calculus as a typed mathematical audit calculus for claims that move between scientific descriptions. This release adds a bounded audit of a published Collatz recursive-sufficiency induction, proves replacement zero-density recursively-sufficient sieves, and retains an exact full-enumeration and first-descent receipt for a conditional finite-prefix extension. It leaves the BSC core framework unchanged and retains the operational-channel, electromagnetic, simulation-evidence, and normalized-scale layers. The package contains eleven mathematical fixtures and three deterministic execution receipts. It does not claim a proof of the Collatz conjecture, an independent replay of the external 2^71 base, an official verification record, a shared microscopic theory, physical validation, a derivation of the fine-structure constant, a proof of the Riemann Hypothesis, a complete reference implementation, or peer review.