ramanujan-challenge/experiments/ramanujan_28/submission/certificates/p28_full_closure_certificate.PASS.txt
Codex 437b439c6c feat(p28): close exact Ramanujan 2.8 limit
Portable proof handoff intended for verified mirror base 1229ab9e61bee936cb1a29c0693ee56922d2d908.
2026-07-31 14:30:10 +09:00

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2.2 KiB
Text

During evaluation of In[1]:= PASS: authoritative matrix is the exact tail differential gauge
During evaluation of In[1]:= PASS: the compact denominator seed is a horizontal adjoint row
During evaluation of In[1]:= PASS: base terminating polynomial
During evaluation of In[1]:= PASS: horizontal elimination gives the terminating 4F3 operator
During evaluation of In[1]:= PASS: the scalar step operator has only z-degrees zero and one
During evaluation of In[1]:= PASS: constant-term normalization recurrence
During evaluation of In[1]:= PASS: generic all-n terminating contiguity coefficient
During evaluation of In[1]:= PASS: terminating top-coefficient boundary
During evaluation of In[1]:= PASS: tail gauge selects the exponent-zero analytic solution
During evaluation of In[1]:= PASS: nonterminating kernel normalization and exact contiguity
During evaluation of In[1]:= PASS: binomial jet converts K_0 to the CM first jet
During evaluation of In[1]:= PASS: compact denominator row reduces to the 3F2 operator
During evaluation of In[1]:= PASS: exact CM-error seed annihilation constant
During evaluation of In[1]:= PASS: regularized transfer has rank one at x=0
During evaluation of In[1]:= PASS: regularized determinant has exact x-adic order three
During evaluation of In[1]:= PASS: Smith valuations are exactly (0,1,1,1)
During evaluation of In[1]:= PASS: regular annihilator transfer gains one power of x
During evaluation of In[1]:= PASS: balanced characteristic polynomial is the authoritative quartic
During evaluation of In[1]:= PASS: characteristic quartic is irreducible
During evaluation of In[1]:= PASS: Rouche separation has three roots in the unit disk
During evaluation of In[1]:= PASS: limiting first-coordinate cyclic frame is invertible
During evaluation of In[1]:= PASS: dominant left eigenvector has four nonzero coordinates
During evaluation of In[1]:= PASS: consolidated exact hypergeometric-closure certificate
During evaluation of In[1]:= M_N K_(N+1)=K_N with kappa_(n+1)/kappa_n=-(6n+1)(6n+5)/(576n^2(2n+1)^2)
During evaluation of In[1]:= P_n(z)[[1]]/a_n = 4F3(-n,-n-1/6,-n-1/2,-n-5/6;1-2n,1-2n,1-2n;z)
During evaluation of In[1]:= a_(n+1)/a_n = 576 n^2 (2n+1)^2/((6n+1)(6n+5)), a_1=18
Out[1]= Null