{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:6CCXCE6VIDQ7D7X5IQRZGUQN7P","short_pith_number":"pith:6CCXCE6V","canonical_record":{"source":{"id":"1907.01812","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-07-03T09:28:54Z","cross_cats_sorted":[],"title_canon_sha256":"b781e156dc41a5855f9c26327a0c34615f818bf1231b8ea904e1f77b44995544","abstract_canon_sha256":"68bb5cdcbb8271bed79011e58b4b49eb820715d9c38213c32e0fcf4ad0375d04"},"schema_version":"1.0"},"canonical_sha256":"f0857113d540e1f1fefd442393520dfbd8f2388fbddc7826ef18445722e3ba51","source":{"kind":"arxiv","id":"1907.01812","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.01812","created_at":"2026-05-17T23:41:16Z"},{"alias_kind":"arxiv_version","alias_value":"1907.01812v2","created_at":"2026-05-17T23:41:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.01812","created_at":"2026-05-17T23:41:16Z"},{"alias_kind":"pith_short_12","alias_value":"6CCXCE6VIDQ7","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"6CCXCE6VIDQ7D7X5","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"6CCXCE6V","created_at":"2026-05-18T12:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:6CCXCE6VIDQ7D7X5IQRZGUQN7P","target":"record","payload":{"canonical_record":{"source":{"id":"1907.01812","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-07-03T09:28:54Z","cross_cats_sorted":[],"title_canon_sha256":"b781e156dc41a5855f9c26327a0c34615f818bf1231b8ea904e1f77b44995544","abstract_canon_sha256":"68bb5cdcbb8271bed79011e58b4b49eb820715d9c38213c32e0fcf4ad0375d04"},"schema_version":"1.0"},"canonical_sha256":"f0857113d540e1f1fefd442393520dfbd8f2388fbddc7826ef18445722e3ba51","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:16.952521Z","signature_b64":"aePu1gj/hV7pHHS7H6JUxwBEoRFWrQmdIlmufyN3yj3qbovUeE8YcK4bBSc5L6eEfYFAc+IrZiV046a02BJ9Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0857113d540e1f1fefd442393520dfbd8f2388fbddc7826ef18445722e3ba51","last_reissued_at":"2026-05-17T23:41:16.951889Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:16.951889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.01812","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:41:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IE1AOCiZNoyFuZ6YN50i+tH06E9D3G4lsIzohGs3UMlgBuALC8gxBBOXveLsZvGO+PaAuO1S9QPUnqTMSa+lBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:38:23.979847Z"},"content_sha256":"b3536aff2a85cb419c9fe9bbc289021e77287b1089e54590ee560ad1171c1170","schema_version":"1.0","event_id":"sha256:b3536aff2a85cb419c9fe9bbc289021e77287b1089e54590ee560ad1171c1170"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:6CCXCE6VIDQ7D7X5IQRZGUQN7P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic expoansions of mathieu-Bessel series. I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"R B Paris","submitted_at":"2019-07-03T09:28:54Z","abstract_excerpt":"We consider the asymptotic expansion of the Mathieu-Bessel series \\[S_\\nu(a,b)=\\sum_{n=1}^\\infty \\frac{n^\\gamma J_\\nu(nb/a)}{(n^2+a^2)^\\mu}, \\qquad (\\mu, b>0,\\ \\gamma, \\nu\\in {\\bf R})\\] as $a\\to+\\infty$ with the other parameters held fixed, where $J_\\nu(x)$ is the Bessel function of the first kind of order $\\nu$. A special case arises when $\\gamma+\\nu$ is a positive even integer, where the expansion comprises finite algebraic terms together with an exponentially small expansion. Numerical examples are presented to illustrate the accuracy of the various expansions. The expansion of the alternat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01812","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:41:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FeA6hcKkwtIZIai6ocGG0jJK/5jY4bjEyrRhxMJDcHeigIS8usKYzr+yuxd9z+cVsAmGVP/PiSPIu1nWvOEBCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:38:23.980460Z"},"content_sha256":"8f002c5452a104a56ad49b583b956acf5b5243026359cba0be3cc2d79e12e8b6","schema_version":"1.0","event_id":"sha256:8f002c5452a104a56ad49b583b956acf5b5243026359cba0be3cc2d79e12e8b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6CCXCE6VIDQ7D7X5IQRZGUQN7P/bundle.json","state_url":"https://pith.science/pith/6CCXCE6VIDQ7D7X5IQRZGUQN7P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6CCXCE6VIDQ7D7X5IQRZGUQN7P/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-10T23:38:23Z","links":{"resolver":"https://pith.science/pith/6CCXCE6VIDQ7D7X5IQRZGUQN7P","bundle":"https://pith.science/pith/6CCXCE6VIDQ7D7X5IQRZGUQN7P/bundle.json","state":"https://pith.science/pith/6CCXCE6VIDQ7D7X5IQRZGUQN7P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6CCXCE6VIDQ7D7X5IQRZGUQN7P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:6CCXCE6VIDQ7D7X5IQRZGUQN7P","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"68bb5cdcbb8271bed79011e58b4b49eb820715d9c38213c32e0fcf4ad0375d04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-07-03T09:28:54Z","title_canon_sha256":"b781e156dc41a5855f9c26327a0c34615f818bf1231b8ea904e1f77b44995544"},"schema_version":"1.0","source":{"id":"1907.01812","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.01812","created_at":"2026-05-17T23:41:16Z"},{"alias_kind":"arxiv_version","alias_value":"1907.01812v2","created_at":"2026-05-17T23:41:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.01812","created_at":"2026-05-17T23:41:16Z"},{"alias_kind":"pith_short_12","alias_value":"6CCXCE6VIDQ7","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"6CCXCE6VIDQ7D7X5","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"6CCXCE6V","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:8f002c5452a104a56ad49b583b956acf5b5243026359cba0be3cc2d79e12e8b6","target":"graph","created_at":"2026-05-17T23:41:16Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider the asymptotic expansion of the Mathieu-Bessel series \\[S_\\nu(a,b)=\\sum_{n=1}^\\infty \\frac{n^\\gamma J_\\nu(nb/a)}{(n^2+a^2)^\\mu}, \\qquad (\\mu, b>0,\\ \\gamma, \\nu\\in {\\bf R})\\] as $a\\to+\\infty$ with the other parameters held fixed, where $J_\\nu(x)$ is the Bessel function of the first kind of order $\\nu$. A special case arises when $\\gamma+\\nu$ is a positive even integer, where the expansion comprises finite algebraic terms together with an exponentially small expansion. Numerical examples are presented to illustrate the accuracy of the various expansions. The expansion of the alternat","authors_text":"R B Paris","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-07-03T09:28:54Z","title":"Asymptotic expoansions of mathieu-Bessel series. I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01812","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b3536aff2a85cb419c9fe9bbc289021e77287b1089e54590ee560ad1171c1170","target":"record","created_at":"2026-05-17T23:41:16Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"68bb5cdcbb8271bed79011e58b4b49eb820715d9c38213c32e0fcf4ad0375d04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-07-03T09:28:54Z","title_canon_sha256":"b781e156dc41a5855f9c26327a0c34615f818bf1231b8ea904e1f77b44995544"},"schema_version":"1.0","source":{"id":"1907.01812","kind":"arxiv","version":2}},"canonical_sha256":"f0857113d540e1f1fefd442393520dfbd8f2388fbddc7826ef18445722e3ba51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0857113d540e1f1fefd442393520dfbd8f2388fbddc7826ef18445722e3ba51","first_computed_at":"2026-05-17T23:41:16.951889Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:16.951889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aePu1gj/hV7pHHS7H6JUxwBEoRFWrQmdIlmufyN3yj3qbovUeE8YcK4bBSc5L6eEfYFAc+IrZiV046a02BJ9Dg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:16.952521Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.01812","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3536aff2a85cb419c9fe9bbc289021e77287b1089e54590ee560ad1171c1170","sha256:8f002c5452a104a56ad49b583b956acf5b5243026359cba0be3cc2d79e12e8b6"],"state_sha256":"da8ffb1d42ab22275d4b1ecf24338b4a18db7b5cdba6f0bed1e7aa656b3e0aec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9rH+9YAbNNy7I3lJBWNIx2uMc28gDyotQGeADLS93/TtK+FqqDGSnWU5Jj//bwhcCQDk20ZGPtf8iprZu+4UAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T23:38:23.983927Z","bundle_sha256":"4459ab8723d1aacb543e61106625a16a932c219a9a84bb5df9324234e9c5dec3"}}