Marko Chalupa
01 Mai 2025
This paper introduces a proof-theoretical strategy termed the Autoconvex DriftProof (ACDP), which enforces theorem acceptance not via contentual validity but through structural inevitability. The framework is designed to function within classically decidable systems, using a series of semantic drifts and logical exhaustion paths to produce a forced return (SnapReturn) to the original assertion. We illustrate this with formalized examples in Coq and propose its application in automated reasoning and formal logic verification.
In classically decidable systems, certain tautologies are trivially true but resistant to constructive proof. We explore an alternative approach to resolution that eschews direct proof and instead creates a formal environment in which any attempted deviation from the assertion leads to its semantic reassertion. This paper introduces the concept of a drift path, culminating in a SnapReturn—a logical structure that forces the acceptance of the original proposition.
We define the Epistropheon as the deep structural principle underlying this mechanism: the dynamic capacity of a system to return to order after semantic disruption. Epistropheon is not a static truth, but a recursive process: Drift → Disappearance → Return → Order → Cycle. It grounds the concept of SnapReturn and represents the generative logic behind recursive semantic stability.
This paper does not merely propose a theory.
It describes the form in which theories organize their own return.
Classical logic admits principles such as the law of the excluded middle (LEM), while constructive logic demands algorithmic realizability. ACDP operates in classical contexts but mimics the exhaustion dynamic familiar in constructive reasoning.
We consider a target proposition P ∨ ¬P and attempt to delay its acceptance via two drift attempts: assume ¬P and ¬¬P. Their mutual contradiction leads to a SnapReturn.
Definition Phase1 := (P -> False).
Definition Phase2 := (~P -> False).
Definition SnapReturn := False.
Axiom drift_relation : Phase1 -> Phase2 -> SnapReturn.
Theorem acdp_core : (P -> False) -> (~P -> False) -> P / ~P.
Proof.
intros H1 H2. exfalso. apply drift_relation; assumption.
Qed.We extend the model to propositions such as (A → B) ∨ ¬B, which—though logically valid—resist constructive verification. By formalizing semantic exhaustion through drift steps, we again enforce acceptance.
Drift-based resolution offers a form of proof by structural exhaustion. This framework is particularly suitable for automated theorem proving and may assist in re-framing undecidable or non-constructive results into tractable forms.
Epistropheon here serves as the conceptual backbone: a meta-logical invariant that guarantees that truths reassert themselves when all alternatives degrade. Rather than fixating on correctness by derivation, we focus on structural resilience through semantic recursion.
ACDP presents a new lens for interpreting proof dynamics, suggesting that structural inevitability can serve as a legitimate path to truth in classically decidable frameworks. Future work may explore its application to intuitionistic barriers and higher-order logic frameworks. We propose the Epistropheon as a formal principle of structural returnability, foundational to systems where order must not only emerge, but endure disruption.
Autoconvex DriftProof · Marko Chalupa · 2025 · CC BY 4.0