Mathine — Evidence In, Trust Out

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

Mathine: Proof-to-Pipeline Bridge Contract Machine
Link: https://doi.org/10.5281/zenodo.18406162

Scientific claims often fail in practice not because the mathematics is wrong, but because the bridge from proof to measurement is undeclared. A theorem is proven over 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 pragmatic fix: treat falsifiability as an executable interface. Instead of leaving “how to test the claim” as prose, it becomes an API endpoint—an operational gateway that evaluates the claim under a declared regime and produces an auditable outcome.

The core artifact is Falsifiers as Endpoints in a Nature API: a discovery gateway where each endpoint is a versioned contract. The endpoint ingests (i) data and (ii) instrument + pipeline metadata, applies explicit observation operators, follows a declared resolution ladder, and evaluates the claim inside a tolerance corridor ε. The endpoint returns a decision—PASS / FAIL / INCONCLUSIVE—while emitting a replayable certificate that captures thresholds, evidence, confounder assumptions, and rollback triggers.

Two control knobs govern tempo and safety. Heat controls exploration pressure (measure more aggressively when uncertainty or drift rises). Gate controls preference/compliance pressure (restrict action when obligations tighten). Together, they let the system increase measurement intensity when reality is moving, and increase restraint when the cost of false closure rises.

To make the bridge explicit, the paper defines a minimal Bridge Contract schema: a compact mapping from proof objects to pipeline objects, including admissible transforms, resolution commitments, and decision rules. It also classifies falsifiers into practical families—bandwise, cross-mode, cross-measure, and trajectory-based—so the same interface discipline can span heterogeneous phenomena without collapsing everything into a single test.

The result is a deployable pattern for “Tier-1 by construction”: a claim becomes admissible only when it can be falsified operationally, audited reproducibly, and swapped safely under drift without collapsing backward compatibility.