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Substrate Stability Under Persistent Disagreement: Structural Constraints for Neutral Ontological Substrates

Denise M. Case

TL;DR

This paper analyzes how to design ontologies that function as neutral substrates for interoperability under persistent disagreement. Under explicit neutrality and stability constraints, it proves a conditional lower bound: any such substrate must realize at least $6$ distinct identity-and-persistence regimes, and a construction with exactly six suffices to support accountability without embedding causal or normative commitments. The result is framed as a design constraint within a specific optimization space, not a universal ontology proposal, and it highlights how stability and externalized interpretation constrain representation. The work further connects to existing ontological frameworks, ontology exchange, and data-sharing principles, offering a diagnostic tool and a concrete six-regime blueprint for building neutral substrates in contested domains.

Abstract

Modern data systems increasingly operate under conditions of persistent legal, political, and analytic disagreement. In such settings, interoperability cannot rely on shared interpretation, negotiated semantics, or centralized authority. Instead, representations must function as neutral substrates that preserve stable reference across incompatible extensions. This paper investigates the structural constraints imposed on ontological design by this requirement. Building on a neutrality framework that treats interpretive non-commitment and stability under extension as explicit design constraints, we ask what minimal ontological structure is forced if accountability relationships are to remain referable and comparable under disagreement. Minimality here is not mere parsimony: a reduction is admissible only if it does not reintroduce stability-critical distinctions as hidden roles, flags, or contextual predicates. We establish a conditional lower-bound result: any ontology capable of supporting accountability under persistent disagreement must realize at least six distinct identity-and-persistence regimes. We further show that a construction with exactly six such regimes is sufficient to satisfy the stated requirements without embedding causal or normative commitments in the substrate. The result is not a proposal for a universal ontology, but a constraint on what is possible when neutrality and stable reference are treated as non-negotiable design goals.

Substrate Stability Under Persistent Disagreement: Structural Constraints for Neutral Ontological Substrates

TL;DR

This paper analyzes how to design ontologies that function as neutral substrates for interoperability under persistent disagreement. Under explicit neutrality and stability constraints, it proves a conditional lower bound: any such substrate must realize at least distinct identity-and-persistence regimes, and a construction with exactly six suffices to support accountability without embedding causal or normative commitments. The result is framed as a design constraint within a specific optimization space, not a universal ontology proposal, and it highlights how stability and externalized interpretation constrain representation. The work further connects to existing ontological frameworks, ontology exchange, and data-sharing principles, offering a diagnostic tool and a concrete six-regime blueprint for building neutral substrates in contested domains.

Abstract

Modern data systems increasingly operate under conditions of persistent legal, political, and analytic disagreement. In such settings, interoperability cannot rely on shared interpretation, negotiated semantics, or centralized authority. Instead, representations must function as neutral substrates that preserve stable reference across incompatible extensions. This paper investigates the structural constraints imposed on ontological design by this requirement. Building on a neutrality framework that treats interpretive non-commitment and stability under extension as explicit design constraints, we ask what minimal ontological structure is forced if accountability relationships are to remain referable and comparable under disagreement. Minimality here is not mere parsimony: a reduction is admissible only if it does not reintroduce stability-critical distinctions as hidden roles, flags, or contextual predicates. We establish a conditional lower-bound result: any ontology capable of supporting accountability under persistent disagreement must realize at least six distinct identity-and-persistence regimes. We further show that a construction with exactly six such regimes is sufficient to satisfy the stated requirements without embedding causal or normative commitments in the substrate. The result is not a proposal for a universal ontology, but a constraint on what is possible when neutrality and stable reference are treated as non-negotiable design goals.
Paper Structure (40 sections, 3 theorems)

This paper contains 40 sections, 3 theorems.

Table of Contents

  1. Introduction: Structure Under Disagreement
  2. Assumptions, Neutrality, and Optimization Criterion
  3. Persistent Disagreement and Uncoordinated Extension
  4. Neutrality Constraint
  5. Stable Reference Requirement
  6. Optimization Criterion
  7. Structural Requirements for Accountability Substrates
  8. R1: Stable Identity and Persistence
  9. R2: Obligation-Bearing Capacity
  10. R3: Normative Reference Without Execution
  11. R4: Time-Indexed Occurrence
  12. R5: Applicability and Scope
  13. R6: Descriptive Indicators Without Causal Commitment
  14. Summary
  15. Necessity: A Lower Bound on Ontological Structure
  16. ...and 25 more sections

Key Result

Lemma 4.1

Under the assumptions of Section sec:assumptions, no ontology whose stable partition contains fewer than six distinct identity-and-persistence regimes can satisfy the representational requirements of accountability while remaining neutral and stable under incompatible extension.

Theorems & Definitions (6)

  • Lemma 4.1: Necessity of distinct regimes
  • proof : Proof sketch
  • Proposition 5.1: Sufficiency of six regimes
  • proof
  • Theorem 6.1: Tightness of the six-regime bound
  • proof