Constraint-Realism Without Correspondence: A Four-Path Closure Argument and Its Application to the Dimensional Signature of Presentation

This work establishes that, in any human cognitive system operating through symbols, ontological-correspondence proof — claims of the form "X must be Y in reality itself" — is structurally unrealizable. The result is
  constitutive, not epistemic: the four routes by which such a proof might proceed (pure deduction, empirical observation, physical-stability mechanism, and external verification) are independently closed. From this
  Four-Path Closure, a unique stable philosophy-of-science position is forced: constraint-realism without correspondence — constraint that is real, cumulative, and auditable, derived from the pre-symbolic invariance of
  the referent plus an operational audit rule, but without re-importing correspondence. This middle position is empirically distinguished from scientific realism, van Fraassen's constructive empiricism, and post-modern
  relativism.

  The constructive replacement for impossible ontological proof is given a precise relational form: the signature-consistency relation, written X ⊢_sig Y, defined as Y being the unique notation position at which the
  functional desiderata read off X remain jointly satisfiable. Applied as a case study to the question of why presented experience has a 3+1 dimensional signature, this relation yields a deflationary derivation that
  converges along functional and topological (codimension-2) routes, claiming neither logical necessity nor physical-mechanism dependence.

  The work includes a methodologically novel originality demarcation: the master argument was put to two independent frontier large language models (one English-language in pure-reasoning mode, one Chinese-language in
  search-augmented mode, with project-specific terminology removed from the prompts). Convergent result across both models and across asymmetric test conditions: the general impossibility argument and the
  structural-vs-epistemic distinction are now AI-reachable; the subject-side reflexive closure (as derivation rather than assertion), the middle position as logical consequence of impossibility, the precise definition
  of ⊢_sig, and the Four-Path Closure as structural stitch — these four are not. Full prompts, raw transcripts, grading rubric, and test-condition disclosure are included.

  The release contains the field-facing paper (English and Chinese), the Expression Boundary Principle appendix containing the Four-Path Closure Theorem, the originality assessment with AI-test documentation, the
  application to a structural-realism program (the S_α / inverse-presentation framework), a self-assessment of worth under AI-era discipline, and reading guides.

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