Present-Anchored Generation Evidence-Gated Attentional Stabilization as a Geometry of Permission

This paper presents a theoretical framework for claim-level hallucination mitigation in language model outputs. Instead of assigning a single factuality score to an entire generated answer, the proposed controller decomposes an answer into typed factual claims and evaluates each claim separately for evidential support, contradiction, numerical and temporal agreement, unit consistency, citation alignment, extraction uncertainty, and perturbation fragility. The central contribution is a selective-risk formulation: a system should emit an answer only when its calibrated claim-level defect is lower than the cost of abstention. The framework separates three cases that are often collapsed in answer-level factuality scoring: claims supported by evidence, claims contradicted by evidence, and claims for which the evidence is silent. This distinction allows abstention, revision, or refusal to become an explicit mathematical decision rather than an informal safety heuristic. The paper introduces typed claim extraction as a stochastic finite-measure problem, separates support and contradiction fields, defines local epistemic defect functions, incorporates extraction instability and perturbation sensitivity, and provides optional diagnostic extensions using dependency graphs and evidence anchoring. It also outlines conformal calibration for selective abstention, a complete decision procedure, and an evaluation protocol for future empirical validation. This work is intended as a conditional theoretical architecture rather than an empirical benchmark study. Its guarantees depend on the availability of reliable claim extraction, calibrated verification scores, meaningful perturbation tests, and suitable validation data. The framework is most relevant to factuality control, retrieval-augmented generation, selective prediction, hallucination detection, abstention mechanisms, and trustworthy AI system design.