Spectral Coherence on the Developmental Attractor
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2026
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| _version_ | 1866901186106359808 |
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| author | Moser, Robert |
| author_facet | Moser, Robert |
| contents | <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]"><strong>Paper 3 — Description (plain text, paste-safe):</strong></p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">A temporal spectral coherence theorem for the developmental flow restricted to its global attractor. The discrete developmental flow of Developmental Geometry (Books 5, 6, 8, 9), shown to possess a unique global attractor A_dev in the companion Global Attractor paper, induces a Koopman semigroup U(t) for t >= 0 on the Banach space C(A_dev) of continuous functions on the attractor via composition with the flow. Under strong operator continuity, classical Kato perturbation theory gives continuity of Riesz projections associated with isolated spectral components. The main theorem shows that the number of isolated spectral components — the coherence index |J| — is invariant under the flow, providing a stable spectral skeleton for the long-time behavior of the developmental system.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">The Koopman spectral theory developed here is conceptually distinct from the Bochner Laplacian spectral theory of Book 11: the two operators act on different function spaces (C(A_dev) versus L^2(TM, g_D)) and capture different structural features (dynamical versus geometric). The relationship between the two spectra is an open direction.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">The result forms part of the analytic foundation for Paper 4 (Convergence of the Developmental Euler Product) and the Developmental Zeta Function paper.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19699935 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Spectral Coherence on the Developmental Attractor Moser, Robert developmental geometry global attractor Koopman operator spectral decomposition dissipative semigroup rank‑2 decomposition discrete dynamical systems spectral coherence multiplicative structure <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]"><strong>Paper 3 — Description (plain text, paste-safe):</strong></p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">A temporal spectral coherence theorem for the developmental flow restricted to its global attractor. The discrete developmental flow of Developmental Geometry (Books 5, 6, 8, 9), shown to possess a unique global attractor A_dev in the companion Global Attractor paper, induces a Koopman semigroup U(t) for t >= 0 on the Banach space C(A_dev) of continuous functions on the attractor via composition with the flow. Under strong operator continuity, classical Kato perturbation theory gives continuity of Riesz projections associated with isolated spectral components. The main theorem shows that the number of isolated spectral components — the coherence index |J| — is invariant under the flow, providing a stable spectral skeleton for the long-time behavior of the developmental system.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">The Koopman spectral theory developed here is conceptually distinct from the Bochner Laplacian spectral theory of Book 11: the two operators act on different function spaces (C(A_dev) versus L^2(TM, g_D)) and capture different structural features (dynamical versus geometric). The relationship between the two spectra is an open direction.</p> <p class="font-claude-response-body break-words whitespace-normal leading-[1.7]">The result forms part of the analytic foundation for Paper 4 (Convergence of the Developmental Euler Product) and the Developmental Zeta Function paper.</p> |
| title | Spectral Coherence on the Developmental Attractor |
| topic | developmental geometry global attractor Koopman operator spectral decomposition dissipative semigroup rank‑2 decomposition discrete dynamical systems spectral coherence multiplicative structure |
| url | https://doi.org/10.5281/zenodo.19699935 |