ARR-RN-2026-001·Research Note·2026-01-04

Invalidation Geometry in Short-Horizon Discretionary Signal Systems

· signal classification· invalidation· risk asymmetry
§01

Abstract

A directional conclusion that lacks an invalidation surface is not a research output. We formalise the geometry of invalidation as a codimension-one boundary in the joint space of (price, time, evidence) and derive necessary conditions for its construction prior to signal publication.

§02

Notation / Conceptual Frame

Invalidation set I = { (p, t, e) : f(p, t, e) ≤ 0 } where f encodes price triggers, time decay, and evidence revisions. A signal is admissible only if I is non-empty and finite-measure within the stated horizon.

§03

Commentary

Constructing I before publication enforces discipline: the question is not 'where could I be right' but 'where would I be wrong'. The framework is symmetric across BUY, SELL, and HOLD outputs.

§04

Implications for Research Methodology

Memo synthesis is gated on the existence of a non-empty I. Signals that cannot be falsified within the stated horizon are downgraded to commentary.

§05

Limitations

Boundary specification is itself a modelling choice; sensitivity to f is reported explicitly.

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This note is informational and interpretive. It does not constitute personalized investment advice. Market activity involves risk. Historical analysis and model outputs do not guarantee future results.