Falsifiers as Endpoints in the Nature API: Declaring the Bridge Between Math and Physics

Scientific claims often fail not because the mathematics is wrong, but because the bridge from proof to measurement is undeclared. A theorem is proven on an internal object; the world is observed through instruments, pipelines, and resolution choices that silently redefine what “the claim” even means. This paper proposes a practical remedy: treat falsifiability as an executable interface. We introduce Falsifiers as Endpoints in a Nature API — a discovery gateway that operationalizes claims as versioned contracts with explicit observation operators, declared resolution ladders, and bounded decision rules. Each endpoint ingests data plus instrument and pipeline metadata, evaluates a claim under a declared tolerance corridor (ε), and returns a decision (PASS/FAIL/INCONCLUSIVE) while emitting a replayable certificate capturing thresholds, evidence, confounder assumptions, and rollback triggers. The gateway governs tempo through two control knobs: Heat (exploration pressure) and Gate (preference/compliance pressure), enabling systems to measure more when drift rises and to restrict action when obligations tighten. We define a minimal Bridge Contract schema that makes the proof-to-pipeline mapping explicit, and we classify falsifiers into bandwise, cross-mode, cross-measure, and trajectory-based families. The result is a deployable pattern for “Tier-1 by construction”: claims become admissible only when they can be falsified operationally, audited reproducibly, and swapped safely under drift without collapsing backward compatibility.