Boundary-Trace Fixation under Admissibility

Description

Title:
Boundary-Trace Fixation under Admissibility: Forced Environmental Coupling as the Final Role-Anchor Asymmetry

Summary

This paper establishes the Fixation Theorem for admissible construction systems: a unique role-anchor assignment exists if and only if a boundary-trace asymmetry exists; otherwise, fixation is impossible.

The result is derived within the AASC (Admissible Construction under Standing Constraints) framework and closes the reference-formation problem under internal non-selectivity.

Core result (Fixation Theorem)

• In outcome-complete, internally non-selective construction systems, no admissible internal selector can uniquely fix a role-anchor.
• All admissible asymmetry sources reduce to a normal form:
  • internal invariants
  • indexical markers
  • boundary-trace coupling
• When internal and indexical asymmetries are unavailable or symmetry-saturated, boundary-trace coupling is forced.
• A unique role-anchor exists if and only if a boundary-trace asymmetry exists.

Key contributions

• Formal definition of boundary traces as invariant, admissible, non-generative, standing-preserving predicates.
• Fixation operator (fail-closed): produces a unique anchor or returns impossibility.
• Asymmetry source normalization theorem with explicit collapse of competing proposals.
• Exhaustion theorem establishing boundary-trace coupling as the final admissible asymmetry.
• No-go results:
  • no internal selector under non-selectivity
  • no symmetry-breaking under coupling saturation
  • no post-selection or posterior repair of fixation
• Minimal structural witness demonstrating executable fixation without reliance on prediction, inference, or outcome-based criteria.

Interpretation

Fixation cannot arise from internal structure, inference, or outcome comparison when admissible symmetry is present.
Instead, it must arise from standing-preserving boundary coupling, represented internally as invariant trace structure.

Environmental coupling is therefore not heuristic or interpretive—it is structurally forced under admissibility constraints.

Role in the AASC corpus

This paper provides the fixation layer of the AASC system. It completes the chain:

• admissibility
• standing
• invariance
• non-selectivity
• asymmetry exhaustion
• fixation (this paper)

and serves as the canonical result governing reference formation, role-anchor assignment, and measurement anchoring across downstream domains.

Scope

• Constructional (non-inferential) framework
• Fixed-domain admissibility and standing
• No reliance on probabilistic, causal, or semantic primitives
• Applies to any system satisfying outcome-completeness and internal non-selectivity

This paper is downstream of:

1. Minimal Conditions for Admissible Construction

2.  The Structure of Admissibility