Foundations of the ρ-diffusion programme: NGFO master identity, Z/p^kZ extension, Q7, and the p-adic anchor
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| Format: | Recurso digital |
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2026
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| _version_ | 1866901368613109760 |
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| author | Niedbala Giraudin, David |
| author_facet | Niedbala Giraudin, David |
| contents | <p>This volume consolidates the foundational layer of an ongoing programme on the diffusion-theoretic moment sequence S_r(1) = [z^r] e (1-z)^{1/z-1} and its rescaled integer companion U_r = (2r)! S_r(1). We establish: (i) the structural identity X_r = (3/(2e)) S_r(1) relating the Laurent coefficients of d_TV(P_{d,p}, Y_d) to moments of ρ via a master generating function (1-z)^{1/z} identity; (ii) an extension framework over Z/p^k Z producing polynomials Q_2, Q_3 encoding the higher-order terms; (iii) a closed-form combinatorial interpretation of U_r via decorated set partitions, resolving Q7; (iv) the diffusion characterisation of ρ(x) = (e/π) sin(πx) e^{H(x)} and a proved p-adic anchor v_p(S_{p-1}) = -1 together with a reduction theorem for v_p(S_p) ≤ 1. Five companion notes are integrated as chapters; cross-references are internal.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19763006 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Foundations of the ρ-diffusion programme: NGFO master identity, Z/p^kZ extension, Q7, and the p-adic anchor Niedbala Giraudin, David diffusion theory p-adic valuations moment sequences generating functions compound Poisson set partitions Wright-Fisher process number theory total variation distance Riemann hypothesis (peripheral) <p>This volume consolidates the foundational layer of an ongoing programme on the diffusion-theoretic moment sequence S_r(1) = [z^r] e (1-z)^{1/z-1} and its rescaled integer companion U_r = (2r)! S_r(1). We establish: (i) the structural identity X_r = (3/(2e)) S_r(1) relating the Laurent coefficients of d_TV(P_{d,p}, Y_d) to moments of ρ via a master generating function (1-z)^{1/z} identity; (ii) an extension framework over Z/p^k Z producing polynomials Q_2, Q_3 encoding the higher-order terms; (iii) a closed-form combinatorial interpretation of U_r via decorated set partitions, resolving Q7; (iv) the diffusion characterisation of ρ(x) = (e/π) sin(πx) e^{H(x)} and a proved p-adic anchor v_p(S_{p-1}) = -1 together with a reduction theorem for v_p(S_p) ≤ 1. Five companion notes are integrated as chapters; cross-references are internal.</p> |
| title | Foundations of the ρ-diffusion programme: NGFO master identity, Z/p^kZ extension, Q7, and the p-adic anchor |
| topic | diffusion theory p-adic valuations moment sequences generating functions compound Poisson set partitions Wright-Fisher process number theory total variation distance Riemann hypothesis (peripheral) |
| url | https://doi.org/10.5281/zenodo.19763006 |