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. This is a v1 timestamp-establishing release. A revised journal-targeted version is expected. The combination of Zenodo DOI (institutional anchor) and OpenTimestamps Bitcoin attestation (cryptographic anchor, applied to the release archive prior to upload) provides redundant verification of the release date.