Final Season F2 — Dynamical spectrum: from a static vertical-line backbone to a living spectrum Article Swipe

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Suga, Hisashi ·

YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.5281/zenodo.17919764

This record contains the main manuscript and Supplementary Information. Season 2 and Final Season Paper F1 of the QCRM Unified Theory introduced a depth-corrected resonance operator and a Bahamut-style Hilbert–Pólya candidate H_B, together with the damped evolution operator L_B = -(1/z_0) I + i H_B, whose eigenvalues lambda_n = -(1/z_0) + i E_n lie on a vertical line in the complex plane. This is structurally analogous to Riemann-type vertical-line spectra, such as the conjectural nontrivial zeros rho_n = 1/2 + i t_n of the Riemann zeta function, in the limited sense that real parts are fixed while imaginary parts form an unbounded sequence. This paper (Final Season F2) shifts the programme from a static spectrum to a living operator. We allow the effective operator configuration (through boundary conditions, feedback, and collective couplings) to evolve with a time-like parameter tau, so that H_B = H_B(tau) and E_n = E_n(tau) become dynamical objects. We introduce (i) a damped nonlinear emotional-phase flow equation, (ii) a boundary–horizon framework separating inner depth from outer orbital/societal regions with flux matching and phase reflection, (iii) a structural time-locking (“heartbeat”) hypothesis linking periodic observables to spectral spacings, (iv) a Dyson-type level-flow ansatz for E_n(tau), and (v) a collective consciousness operator H_B^(N) with real-valued relational couplings J_ij. The aim is not to prove the Riemann Hypothesis, nor to identify the Bahamut spectrum with the Riemann zeta function. Rather, the goal is to formulate a coherent operator programme in which time, emotion, and collective behaviour appear as explicit dynamical structures built on top of a vertical-line spectral backbone.

Related Topics

Mathematics

Riemann Hypothesis

Complex Plane

Mathematical Analysis

Riemann Zeta Function

Theoretical Physics

Concepts

Operator (biology) Mathematics Riemann hypothesis Spectrum (functional analysis) Observable Dynamical systems theory Ansatz Nonlinear system Complex plane Mathematical analysis Eigenvalues and eigenvectors Riemann zeta function Boundary (topology) Riemann surface Pure mathematics Lie group Flow (mathematics) Dynamical system (definition) Matching (statistics) Theoretical physics Resonance (particle physics) Self-adjoint operator Continuous spectrum

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Title: Final Season F2 — Dynamical spectrum: from a static vertical-line backbone to a living spectrum

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Publication year: 2025

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Publication date: 2025-12-16

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Concepts: Operator (biology), Mathematics, Riemann hypothesis, Spectrum (functional analysis), Observable, Dynamical systems theory, Ansatz, Nonlinear system, Complex plane, Mathematical analysis, Eigenvalues and eigenvectors, Riemann zeta function, Boundary (topology), Riemann surface, Pure mathematics, Lie group, Flow (mathematics), Dynamical system (definition), Matching (statistics), Theoretical physics, Resonance (particle physics), Self-adjoint operator, Continuous spectrum

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abstract_inverted_index.observables	185
abstract_inverted_index.real-valued	204
abstract_inverted_index.reflection,	176
abstract_inverted_index.Information.	8
abstract_inverted_index.Riemann-type	67
abstract_inverted_index.structurally	64
abstract_inverted_index.time-locking	180
abstract_inverted_index.Bahamut-style	28
abstract_inverted_index.Supplementary	7
abstract_inverted_index.configuration	124
abstract_inverted_index.consciousness	200
abstract_inverted_index.vertical-line	68, 255
abstract_inverted_index.depth-corrected	23
abstract_inverted_index.emotional-phase	157
abstract_inverted_index.Hilbert–Pólya	29
abstract_inverted_index.orbital/societal	169
abstract_inverted_index.(“heartbeat”)	181
abstract_inverted_index.boundary–horizon	162
cited_by_percentile_year
countries_distinct_count	1
institutions_distinct_count	1
citation_normalized_percentile