{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:6YAICKYGZFZ7HHVVKXBQWYIKOR","short_pith_number":"pith:6YAICKYG","schema_version":"1.0","canonical_sha256":"f600812b06c973f39eb555c30b610a7466d73fb08cd517c08facc7d915f7b657","source":{"kind":"arxiv","id":"1401.7843","version":1},"attestation_state":"computed","paper":{"title":"Random Aharonov-Bohm vortices and some exact families of integrals: Part III","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Stephane Ouvry","submitted_at":"2014-01-30T13:45:44Z","abstract_excerpt":"As a sequel to [1] and [2], I present some recent progress on Bessel integrals $\\int_0^{\\infty}{\\rmd u}\\; uK_0(u)^{n}$, $\\int_0^{\\infty}{\\rmd u}\\; u^{3}K_0(u)^{n}$, ... where the power of the integration variable is odd and where $n$, the Bessel weight, is a positive integer. Some of these integrals for weights n=3 and n=4 are known to be intimately related to the zeta numbers zeta(2) and zeta(3). Starting from a Feynman diagram inspired representation in terms of n dimensional multiple integrals on an infinite domain, one shows how to partially integrate to n-2 dimensional multiple integrals "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1401.7843","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-01-30T13:45:44Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"e8e6522bb6600df20c78fff0b85d18259c3830d84b6e9710a8304e3571bea19d","abstract_canon_sha256":"5978c9b519fbcd1112c94e2a078f6e5b59debd683251655e3f5992003c0002ec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:38.222014Z","signature_b64":"mHuMJRQYZ+dbNFdtTKIr9cTfLPtR77XYGK5CAtPCHAf+vmGB6OFxV5wOqh9R2XS6xCOrDrB3TTY/MHPy+lUlAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f600812b06c973f39eb555c30b610a7466d73fb08cd517c08facc7d915f7b657","last_reissued_at":"2026-05-18T03:00:38.221430Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:38.221430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Random Aharonov-Bohm vortices and some exact families of integrals: Part III","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Stephane Ouvry","submitted_at":"2014-01-30T13:45:44Z","abstract_excerpt":"As a sequel to [1] and [2], I present some recent progress on Bessel integrals $\\int_0^{\\infty}{\\rmd u}\\; uK_0(u)^{n}$, $\\int_0^{\\infty}{\\rmd u}\\; u^{3}K_0(u)^{n}$, ... where the power of the integration variable is odd and where $n$, the Bessel weight, is a positive integer. Some of these integrals for weights n=3 and n=4 are known to be intimately related to the zeta numbers zeta(2) and zeta(3). Starting from a Feynman diagram inspired representation in terms of n dimensional multiple integrals on an infinite domain, one shows how to partially integrate to n-2 dimensional multiple integrals "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7843","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1401.7843","created_at":"2026-05-18T03:00:38.221517+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.7843v1","created_at":"2026-05-18T03:00:38.221517+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7843","created_at":"2026-05-18T03:00:38.221517+00:00"},{"alias_kind":"pith_short_12","alias_value":"6YAICKYGZFZ7","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"6YAICKYGZFZ7HHVV","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"6YAICKYG","created_at":"2026-05-18T12:28:16.859392+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6YAICKYGZFZ7HHVVKXBQWYIKOR","json":"https://pith.science/pith/6YAICKYGZFZ7HHVVKXBQWYIKOR.json","graph_json":"https://pith.science/api/pith-number/6YAICKYGZFZ7HHVVKXBQWYIKOR/graph.json","events_json":"https://pith.science/api/pith-number/6YAICKYGZFZ7HHVVKXBQWYIKOR/events.json","paper":"https://pith.science/paper/6YAICKYG"},"agent_actions":{"view_html":"https://pith.science/pith/6YAICKYGZFZ7HHVVKXBQWYIKOR","download_json":"https://pith.science/pith/6YAICKYGZFZ7HHVVKXBQWYIKOR.json","view_paper":"https://pith.science/paper/6YAICKYG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.7843&json=true","fetch_graph":"https://pith.science/api/pith-number/6YAICKYGZFZ7HHVVKXBQWYIKOR/graph.json","fetch_events":"https://pith.science/api/pith-number/6YAICKYGZFZ7HHVVKXBQWYIKOR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6YAICKYGZFZ7HHVVKXBQWYIKOR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6YAICKYGZFZ7HHVVKXBQWYIKOR/action/storage_attestation","attest_author":"https://pith.science/pith/6YAICKYGZFZ7HHVVKXBQWYIKOR/action/author_attestation","sign_citation":"https://pith.science/pith/6YAICKYGZFZ7HHVVKXBQWYIKOR/action/citation_signature","submit_replication":"https://pith.science/pith/6YAICKYGZFZ7HHVVKXBQWYIKOR/action/replication_record"}},"created_at":"2026-05-18T03:00:38.221517+00:00","updated_at":"2026-05-18T03:00:38.221517+00:00"}