RENASCENT-Q Theory: presence, non-presence, and the bound. The unified explanation, with Analytical Supplement (Lean 4), 9 October 2026

This record deposits two files of 9 October 2026. The article is the unified explanation of RENASCENT-Q Theory: presence, non-presence, and the bound. The analytical supplement is the arithmetic that sustains that explanation. Together they are the account written for the book Negentropic Consciousness..a tale from timeless memories. They carry five deposits and do not replace them, and they do not refute them. The five offices stay where they were published. The Eternity Theorem, v.37 (doi:10.5281/zenodo.23095017), owns the place and the no-place, and the conservation of information on Maya Space. Maya Spectral Theory, v.3 (doi:10.5281/zenodo.23173831), owns the well {9, 16, 21, 24}κ² and the floor 25κ². The Eternal Information Formula, v.11 (doi:10.5281/zenodo.23174809), owns the bill: W ∈ {0, 2}, a completed cycle at η = 2π, and a retained contrast χ ∈ {0, 1} that is not a value of W. Maya Theorems, v.6 (doi:10.5281/zenodo.23172977), owns the relay: the thirteenth checks and does not spend. RENASCENT-Q, v.53 (doi:10.5281/zenodo.23171814), owns the host: intelligence selects, thought retains, will lies between thought and comprehension, and consciousness can spend the contrast. Eternity, in this account, is the availability of geometric information and of potentials: no time, no distance, no entropy, and not a mind, or a personalized divinity. Maya Space is the temporary buffer in which that availability becomes a presence. The bound throughout is implication without identity. Both factors of a pair are implied in the unsigned middle, and the middle is identical with neither. What the theorems separate is an office: a letter can remain available before any hire, and that availability is not the bill, not the tide, and not a boson. The name “fifth influence” is the name of that office, read as a feature of nature. The separation is what is proved. The name is not a certificate, and a detector does not assign it a probability. A wave from merging black holes and a spontaneous moment in a cold crystal make the suspicion visible. They do not install the name. Gravity is read as a relation that maintains and, when the relation changes, communicates. The Einstein equation is displayed so that this refusal has an object. No term is added to it, and the mechanics of the article do not start from it. Two later readings use the same bound and add no office. An unjoined integer is not an atom of the well: 9, 16, 21, and 24 are not prime, and a class modulo 4 is not a certificate of primality. Two squares rotated by a prime number of degrees share side, spectrum, and the two radii, and they are not one placed figure. Fermat’s theorem on primes that are sums of two squares is cited and is not proved. A gradient flow and one Euler step share the sign of decrease and are not one motion. The evolution that keeps a norm is not that decrease. A power t^(−α) does not follow from the sign. The supplement records what Lean 4.24.0 checks and what it does not. MayaEternity.Sustain cites certificates already proved in Algebra, Hire, Vertex, and Buffer, and adds the detuning and two reported ranges. MayaEternity.Deficit checks the flat ledger as rationals. MayaEternity.Descent checks the prime angle and the shared sign. MayaEternity.Analysis checks the derivative along the flow, the Lipschitz remainder, the strict Euler step when the step is short and positive, and the norm kept by a self-adjoint step. Lake reported 3142 jobs for the build of these four targets. That figure counts dependencies replayed. It is not a count of theorems. There is no sorry and no new axiom. If a theorem cited by Sustain were erased, Sustain would not build. Erasing a theorem of Descent or Analysis would break that module and would leave Sustain standing. The fifth influence, the no-present cat as availability, the will of a host, and the biological step remain hypotheses of the article. They are not certificates of the supplement. The deposit does not answer why a buffer is required. It does not make presence a person. It does not disclose the device of USPTO Provisional Application No. 63/984,236. MSC 2020: 81Q10, 82C10, 94A17, 58J50, 83C05, 92B05 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. 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: [email protected] 09 October 2026