Self-Certification Is Not Grounding: A Grounding Conservation Law, the AI-Supervising-AI Death Spiral, and the Price of External Anchoring

This paper identifies the certification gap G, the difference between a system's self-certified success probability and its externally checkable success rate. The central claim is a zero-anchor identifiability law for reliable level correction: internal signals may rank outcomes, but without an independent outcome anchor, trusted calibration prior, or external world model, the absolute self-certification level gap cannot be reliably identified and eliminated from self-certification alone. Executable constructed witnesses illustrate the separation between discrimination and level calibration, a shared-prior AI-supervising-AI death spiral, structured-gap tightening, supervision-credit pricing, and an imagine-then-act extension G_img = E[p_img_success]-E[Y_real]; they verify script reproducibility, not real-stack validity. A third application note defines G_img for world-model planning surfaces; named systems such as V-JEPA, OpenVLA, VLA-JEPA, LingBot-VA, VLOA, and WoVR are future targets or neighboring architectures, not current evidence. The package includes a references/collision ledger that assigns neighboring findings on agentic overconfidence, VLA false completion, self-correction limits, MLLM verifier agreement bias, public VLA/world-model architectures, and world-model failure-mode literature to the originating works. The release includes pre-registered attack patches for the two main reviewer attacks plus a public world-model proxy preregistration: all witnesses are constructed, and flip_eff(g) is a modeling assumption until a real stack measures the full binary anchor channel. No real-stack validation, public world-model target result, third-party replication, live deployment, trading edge, or financial claim is made.

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