On Decision-Valued Maps and Representational Dependence

TL;DR

The paper addresses how discrete decisions produced by analytical pipelines depend on representation and how to certify reuse across representations. It introduces the decision-valued map $f: \mathcal{R} \to \mathcal{D}$ and DecisionDB for logging, deterministic replay, and post-hoc audits of representation-dependent decisions. Contributions include a five-stage representational sweep protocol, a content-addressed provenance schema with five tables, and an empirical graph-routing demonstration of persistence regions and fractures. The work enables mechanically checkable decision reuse and highlights limitations and future extensions to broader domains and denser sweeps.

Abstract

A computational engine applied to different representations of the same data can produce different discrete outcomes, with some representations preserving the result and others changing it entirely. A decision-valued map records which representations preserve the outcome and which change it, associating each member of a declared representation family with the discrete result it produces. This paper formalizes decision-valued maps and describes DecisionDB, an infrastructure that logs, replays and audits these relationships using identifiers computed from content and artifacts stored in write-once form. Deterministic replay recovers each recorded decision identifier exactly from stored artifacts, with all three identifying fields matching their persisted values. The contribution partitions representation space into persistence regions and boundaries, and treats decision reuse as a mechanically checkable condition.

Figures (3)

• Figure 1: Evaluation protocol for a decision-valued map. A single arena, consisting of a data snapshot and a computational engine, is reused across evaluation. Representations drawn from a declared family are varied within this arena and evaluated independently. Agreement of decision identifiers across representations indicates persistence of decision identity; a change in identifier indicates a boundary induced by representational variation alone.
• Figure 2: DecisionDB relational schema. Five tables form a content-addressed provenance chain. Foreign-key arrows indicate the direction of referential dependency, linking representations to their parent snapshot, engine runs to the representation consumed, the decision map table to representations, runs and decision identities.
• Figure 3: Identity persistence and fracture structure for the two representation parameters. The neighbor weight parameter spans a single persistence region in which both tested values produce Decision A, indicating decision identity is stable across this range. The second-order weight parameter spans two regions separated by a fracture, where decision identity changes from Decision A to Decision B between the values 0.25 and 0.5. The exact threshold is not resolved by this two-point sample.