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ouroboros-pasterski-research-program / references /run_sabrina_celestial_recursion_pde_generating_function.json
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Publish private Ouroboros Pasterski research program for review
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{
 "kernel": "run_sabrina_celestial_recursion_pde_generating_function",
 "role": "post-computation assertion only",
 "schema": "ouroboros_scientific_reference_assertion_v1",
 "scientific_payload": {
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 }
 ],
 "resummed_pde_kernel": "1/((1+Omega*a*x)*(1+Omega*b*x))",
 "symbolic_recurrence_residuals_p0_to_p5": [
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 },
 "claim_boundary": {
 "capabilities_removed": [],
 "convergence_beyond_formal_series_proved": false,
 "free_operator_commutativity_asserted": false,
 "non_mhv_sector_proved": false
 },
 "exact_checks": {
 "archive_hash_matches": true,
 "coincident_limits_exact": true,
 "complete_homogeneous_sum_present": true,
 "distinct_divided_differences_exact": true,
 "exponential_shift_seed_present": true,
 "member_hash_matches": true,
 "p_indexed_tower_present": true,
 "rational_generating_function_exact": true,
 "rational_witnesses_exact_through_p12": true,
 "source_blocks_match": true,
 "symbolic_second_order_recurrence_exact": true,
 "taylor_seed_present": true
 },
 "paper": {
 "arxiv_id": "2208.11635",
 "title": "Celestial Recursion"
 },
 "result_version": "sabrina_celestial_recursion_pde_generating_function_v1",
 "source_evidence": {
 "archive_sha256": "bb41217149756d1b5a56ca91fd7a5c99c511d0be8b8e54f15c900914c712bd77",
 "block_hashes": {
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 "shift_taylor_seed": "cf5e7223ab84469191344fea116685d7c771dfc6ac5f485d811224cd54a25f5c"
 },
 "checks": {
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 "exponential_shift_seed_present": true,
 "member_hash_matches": true,
 "p_indexed_tower_present": true,
 "source_blocks_match": true,
 "taylor_seed_present": true
 },
 "member_sha256": "2774400bc31506d0693cc7c189a7618ee8d7ae8983b96d8fb8cb4d4f427dd650"
 },
 "status": "complete",
 "theorem": {
 "coefficient_closed_form": "S_p(a,b)=sum_(l=0)^p a^(p-l)b^l=(a^(p+1)-b^(p+1))/(a-b)",
 "coincident_limit": "the removable a=b limit is S_p(a,a)=(p+1)a^p",
 "generating_function": "sum_(p>=0) S_p x^p=1/((1-ax)(1-bx))",
 "pde_resummation": "the termwise Taylor identities resum on the amplitude to exp(xD)A=A/((1+Omega*a*x)(1+Omega*b*x))",
 "recurrence": "S_(p+2)=(a+b)S_(p+1)-ab S_p"
 }
 },
 "scientific_payload_sha256": "94cf744ae42b66c5db61c4d853a7867562d928a7eb80e7cc3297657eb8fcf1cd"
}