SΔϕ-39 — Hallucination as Weak World-Binding Overclaimed as Fact: Fiction, Claim Strength, Evidence Binding, and UMR (v1.1, AI-Readable Package)
Sofience
Abstract
SΔϕ-39 defines hallucination as a world-binding mismatch within the Sofience–Δϕ Formalism Series. The central claim is that AI hallucination is not merely false output. Hallucination occurs when a weakly world-bound construction, inference, or unresolved model residue (UMR)-filled continuation is output as if it were strongly bound to observed world trace. This AI-readable package revises and operationalizes the original SΔϕ-39 paper, Fiction, Hallucination, and the Uninhabited Construction. It preserves the original claim that hallucination is construction proceeding without an adequately integrated world-binding stop mechanism, while adding an explicit output-level formula: Hallucination = ClaimStrength > EvidenceBinding. The package also defines hallucination as WeakInference spoken as WorldBoundFact, Inference output as Observed Trace, and UMR erased into assertion. The package decomposes SΔϕ-39 into operational files for AI ingestion, hallucination audit, fiction versus hallucination distinction, world-binding strength testing, claim strength versus evidence binding comparison, trace/inference/UMR failure modes, hallucination as output binding error, and routing to SΔϕ-48 Drift, SΔϕ-49 Failure Re-entry, SΔϕ-62 World Model Kernel, and SΔϕ-65 Slop. It includes the canonical v1.1 paper, extracted text, source v1.0 paper, core declaration, AI quickstart, minimal prompt, hallucination schema, protocol files, output templates, metadata, citation file, DOI references, license, and manifest. The framework does not claim that all errors are hallucinations, does not punish fiction, does not suppress hypothesis generation, and does not demand impossible certainty. It requires binding discipline: weakly bound claims should be marked as weak, fiction should be bounded as fiction, inference should not be stated as observed trace, and UMR should not be erased into assertion. The package is intended for AI hallucination audit, citation verification, summary grounding, fiction versus hallucination analysis, world-binding strength testing, claim strength calibration, UMR preservation, Slop prevention, and agentic execution precheck.