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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.19441471 |
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- <p dir="auto">Law III / Part 3</p> <p dir="auto">This paper resolves the third of six fundamental unsolved mathematical laws governing the human brain: the L¹-Integrability Law (Cognitive Energy Bound). It supplies the universal dynamical constraint on the total informational mass of any admissible cognitive state: ‖V_M(x)‖<em>{L¹} < ∞. Building on the Betti Swoosh Law (Part I) and the Cognitive Hamiltonian (Part II), the law derives the closed-form bound enforced by the Anti-Collision Identity (ACI) and the spectral damping operator L</em>{ACI}. An explicit computable upper bound in terms of C_{UFT-F} and the Tamagawa number τ(M) is given, together with a no-singularity theorem that prevents informational collapse.</p> <p dir="auto">This is <strong>Part III</strong> of the six-law series “UFT-F: The Mathematical Structure of Cognition.” It provides the energetic foundation used by all subsequent laws. See Part IV for the holographic pair-correlation and the synthesis paper for the unified wave-motive equation.</p> <p dir="auto"> </p> <p dir="auto">Part 1: https://zenodo.org/records/19440860</p> <p dir="auto">Part 2: https://zenodo.org/records/19441132</p>