Claim or Refuse: A Threshold-Free Structural Operator and the Law of Edges in Text Continuation

Abstract

Generative systems imagine fluently and verify poorly; the gap is calledhallucination. We present a measured study of the opposite trade-off: astructural operator (the novum library, companion paperdoi:10.5281/zenodo.21807980) that generates only what the structure of itsuniverse demands, refuses everywhere else, and never asserts content it cannotground. The material is five raw public-domain texts: Wittgenstein'sTractatus, Spinoza's Ethics and Political Treatise, Pascal's Pensees, andNietzsche's Beyond Good and Evil, with perception delegated to ordinary MLtooling. Four things are measured. The operator selects the structurally true encodingout of a mechanically generated pool without hints, while a chance-correcteddependence criterion (AMI) peaks on tautologies and never scores the trueencoding above chance. It recovers 1,245 of 1,245 deleted units exactly, withzero spurious demands. It raises demands beyond the text only where somethingis genuinely missing: four demands on the Tractatus match exactly the fourpropositions absent from the book, and every other demand ever raised tracedto a real data defect, six catches in all, including a Project Gutenbergmisprint and an edition truncation. And it claims continuations past the edgeof a text in a bounded, named, refutable form. A sweep of 1,985 truncation points yielding 9,585 edge claims gives athree-way law of edges. Edge claims are true in the archive at transmissioncuts (97.8% of 6,604 claims). They are false at authorial endings (11/11 atthe two content-closed endings). And they are true in intention yet foreverempty in the archive at world cuts, witnessed twice: the death-truncatedPolitical Treatise, where the operator's surviving claims all point past XI.4,exactly where the work historically breaks off, and the Pensees' canon, anapology death left unassembled. A selective-prediction baseline with a swept confidence gate reaches theoperator's calibration point only with its gate disabled; the discriminatingpower is the structural bracket, not a threshold. A three-round protocol inwhich LLMs reason about the operator's claims, with a blind genus judge thatindependently caught a numbering shift between editions, shows how the twohalves, structural claiming and content judging, compose into generation witha reality check.