Maya Spectral Theory (v.3): the well, the organ of the Laplacian, the odd sector, and the work identity of an oval cycle, with Analytical Supplement (Lean 4)

Abstract

Maya Spectral Theory is the spectral geometry of Maya Space, M^{1,11} = R^{1,1} ×_w F^{10}, and the spectral engine the other papers inherit. They do not replace this spectrum, and they do not enlarge it. v.2 (doi:10.5281/zenodo.22820807) remains the last published organ. v.3 does not add an eigenvalue. After Liouville, the fibre-zero organ is the Pöschl–Teller well of weight 4, H_geom = −∂_r² + V_eff, V_eff = 25 − 20 sech² r (κ = 1). The point spectrum is {9, 16, 21, 24}. Local negentropy is 4. The essential spectrum is [25, ∞), van Hove type 0. Kay–Moses writes the radial warp from those four atoms in the reflectionless class. The odd sector is {16, 24}, with Clark node k = ±√3. What v.3 records is the ownership of that organ against the records of 5 October 2026. The four atoms are the fibre-zero face of the well. They are not a face of the pentagonal deck Z_5 × Z_5, and 24κ² is not the square faces of a tesseract. There is no fifth L² atom. A disposition read at the flare is not an eigenvalue of this operator. The Eternity Theorem v.37 owns the place and the no-place. The Formula v.11 reads W and Q. Maya Theorems v.6 is the containment ledger, cited as a probable possibility and not as a verified extension of these operators. RENASCENT-Q v.53 is the metabolism. Consciousness is not a claim of this spectrum. The analytical supplement is the Lean 4 certificate of that organ: the four atoms, the floor at 25, the odd sector, the occupancy filter, the crystal split 10+2+1, and the operator algebra of the offices. Reed–Simon, Kato–Rellich, Persson, and Kay–Moses remain named axioms. There is no sorry. The listing adds no fifth atom and does not identify the organ with the zeros of ξ. v.3 does not replace the v.2 certificate. This record does not prove the Riemann Hypothesis. It does not disclose the device of USPTO Provisional Application No. 63/984,236. Acknowledgments.The conceptual architecture, the scientific structure, the strategical complexities, the intellectual development and property of this work, are the author’s own.Federico Maya is not academically credentialed as mathematician, physicist or astrophysicist. The work was nonetheless developed from more than 30 years of the self-taught practice of science: the method, the literature, the curiosity and the independent research. Without that scientific and intellectual capacity, no artificial intelligence or language model would write or developed by itself any of the arguments, concepts and formulations divulged.As with the human brain, logic expands from analogies, strategic meaning, experience, controlled improvisation, ponderable knowledge, inspiration and consciousness.Large language models, in particular Grok (xAI), have assisted the author in accelerating the findings of accurate solutions for questions in academic form by providing mathematic, geometric and physics options of formulations, derivations, provisional documentation, certificates, and the written discipline for offices.That assistance was real and is gratefully acknowledged; it does not mean authorship but, in some sense, companionship. Artificial intelligence does not replace a researcher; it can expand the reach of one.The present corpus is offered as evidence of that orchestration: a human scientific capacity, not institutionally titled in those fields, working with an instrument that, used in the service of research, computation, learning and extended thinking, can be instrumental and inspiring for human, technological and scientific development. In Honor of.This work is dedicated to my family: Rosanna María Mauro de Maya, dear wife; Valentina María Maya, dear daughter; and Juan Federico Maya, dear son. MSC. 34L40, 47A10, 47B25, 81Q10, 81U40, 58J50, 82C10 Intellectual Property Notice: The mathematical frameworks, equations, and topological architectures detailed in this manuscript are currently protected under United States Patent and Trademark Office (USPTO) Provisional Application No. 63/984,236, titled "System and Method for Topological-Negentropic Quantum Control via Zeta-Manifold Resonance. (ZN-11 Technology)." All commercial engineering and intellectual rights are strictly reserved and protected by Federal and International Law. Federico MayaIndependent Researcher, San José, Costa Rica ORCID: 0009-0002-3837-7543email: fedemaya@gmail.com 05 October 2026