Maintenance update, 27 May 2026. This version corrects bibliographic metadata after a source re-check against arXiv, Crossref/CiNii, and Zenodo API records. Corrects the PSWF Part III reference: the 1962 Bell System Technical Journal article is by H. J. Landau and H. O. Pollak, not by D. Slepian; the bibliography key is now LandauPollak1962 and the source is cited explicitly in the eigenvalue plateau paragraph. Updates the three related Zenodo companion titles to their current concept-record titles and keeps their claim status conditional. No new theorem, RH proof, MS2 proof, or Even-Dominance claim is introduced. Expository companion paper to three Riemann-Hypothesis-related preprints by the same author. The note bridges the classical Slepian–Pollak (1961) prolate spheroidal wave function theory to Fact 6.4 of Connes' 2026 spectral programme (arXiv:2602.04022), spelling out the parameter identification c = 2πΛ and the strip-uniform Fourier convergence rate that the Connes programme uses as an external analytical input. What this paper does. Modernises Slepian–Pollak Theorem 1 in current notation. Identifies the Connes-side parameter c = 2πΛ (Footnote 19 of Connes 2026) explicitly. Documents the Fact 6.4 normalisation ledger (variable / Fourier convention / PSWF bandwidth / eigenfunction normalisation / Hermite–Weber regime / strip line / constants / boundary box) as an audit-trail-ready table. Provides a strip-line rate ladder (real-axis PSWF approximation → bulk/edge/tail separation → strip continuation → closed substrip) so that a real-axis statement is not confused with a strip statement. Records the diagnostic outcome of the earlier (abandoned) Route-A attempt: the raw-L² Hurwitz passage is structurally blocked (archimedean tail boundary exponent α = 0, m = 1 prime-Dirac tail divergent), and operator-norm topology via spectral realisation (= Branch B in the parent landscape) is identified as the only viable replacement. What this paper does NOT do. It does not prove the Riemann Hypothesis. It does not close Connes' MS2 / §6.6(b) gap. It does not derive Even Dominance from PSWF concentration. It does not treat the numerical proximity of kλ and θx as an analytical substitute for the remaining Connes step. It does not mark Zookeeper / Landscape / EvenDom dependencies as resolved. Boundary box. This is a bibliography- and convention-service paper for the spectral Riemann community. The substantive RH-related conditional reductions are pursued in three companion preprints by the same author: 10.5281/zenodo.19035640 — Landscape: audit-trail mother paper of all known routes (live, dormant, dead, external). 10.5281/zenodo.19764771 — Even Dominance Proof: standalone extraction of Branch A (A1–A8 reduction, conditional on the Asymptotic Variational Gap Conjecture). 10.5281/zenodo.19673126 — Zookeeper: standalone CCM microcluster programme of Branch Z (conditional on the three C2ca-inputs plus fixed-waterline outer gap). The Fact-6.4-relevant convergence statement is used in all three companion papers as an external analytical input from Connes 2026; this expository note makes that input transparent. Author. Lukas Geiger, Independent Researcher, Bernau, Germany. ORCID: 0009-0005-7296-1534. License. Creative Commons Attribution 4.0 International (CC-BY-4.0). AI Disclosure. Generative AI systems (Claude, Anthropic; Gemini, Google DeepMind; GPT/Codex, OpenAI) were used as non-authorial tools for literature aggregation, notation cross-checking, expository drafting support, and LaTeX/PDF quality assurance. They are not authors, co-authors, acknowledgement recipients, sources of ground truth, or independent validators. The author conceived the research direction, provided the domain expertise, exercised final editorial authority, and bears full and sole scholarly responsibility. ```
Lukas Geiger (Sat,) studied this question.