{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:CUZXLQPN27BV4S6JSAZIRFC6UJ","short_pith_number":"pith:CUZXLQPN","canonical_record":{"source":{"id":"1110.6147","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-27T18:11:46Z","cross_cats_sorted":["math.MP","nucl-th"],"title_canon_sha256":"48bc9d3dec5df55d8028296273e11961a3fdf187b54a7a515b2a60030e25ab29","abstract_canon_sha256":"f8830a71e935768d2ee27c544c8bbfcbb3014bede87167f955ec26b36b67e3c2"},"schema_version":"1.0"},"canonical_sha256":"153375c1edd7c35e4bc9903288945ea257c43e7d1db11231c81f15a86904c23b","source":{"kind":"arxiv","id":"1110.6147","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6147","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6147v1","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6147","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"pith_short_12","alias_value":"CUZXLQPN27BV","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CUZXLQPN27BV4S6J","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CUZXLQPN","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:CUZXLQPN27BV4S6JSAZIRFC6UJ","target":"record","payload":{"canonical_record":{"source":{"id":"1110.6147","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-27T18:11:46Z","cross_cats_sorted":["math.MP","nucl-th"],"title_canon_sha256":"48bc9d3dec5df55d8028296273e11961a3fdf187b54a7a515b2a60030e25ab29","abstract_canon_sha256":"f8830a71e935768d2ee27c544c8bbfcbb3014bede87167f955ec26b36b67e3c2"},"schema_version":"1.0"},"canonical_sha256":"153375c1edd7c35e4bc9903288945ea257c43e7d1db11231c81f15a86904c23b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:09.459362Z","signature_b64":"+vMwinMOq379nhoGb8sRduObqei8vIHPhorLkx5qTOUE2vrv/aF/T+oaAQkqbNH+zA9bouWgYOXhJ7sD82J+CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"153375c1edd7c35e4bc9903288945ea257c43e7d1db11231c81f15a86904c23b","last_reissued_at":"2026-05-18T04:10:09.458666Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:09.458666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.6147","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:10:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LJ0eb9cC+B846k/Ud1c+bmgZ6RvoBpm4jaCt8oWBiQAnVLVcx4PSABzKqBDTyQRNcBISx+mh11HLCwzs07x7Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T14:44:21.512377Z"},"content_sha256":"13839430ad792b2eeb23cc18a5e243785bcac93b90d2cdc8f48c245014465af7","schema_version":"1.0","event_id":"sha256:13839430ad792b2eeb23cc18a5e243785bcac93b90d2cdc8f48c245014465af7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:CUZXLQPN27BV4S6JSAZIRFC6UJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Analytical Evaluation For The Integral Of Two Spherical Bessel Functions With An Additional Exponential And Polynomial Factor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nucl-th"],"primary_cat":"math-ph","authors_text":"R. Mehrem","submitted_at":"2011-10-27T18:11:46Z","abstract_excerpt":"The integrals $\\threej{\\Llo}{\\Llt}{\\Llth} {0}{0}{0}\\,\\int_0^\\infty \\,r^{\\Llth+1}\\,e^{-\\alpha r}\\,j_\\Llo(k_1r)\\, j_\\Llt(k_2r)\\,dr$ and $\\threej{\\Llo}{\\Llt}{\\Llth} {0}{0}{0}\\,\\int_0^\\infty \\,r^{\\Llth+2}\\,e^{-\\alpha r}\\,j_\\Llo(k_1r)\\, j_\\Llt(k_2r)\\,dr$ are evaluated analytically. The result is a finite sum over the associated Legendre function of the second kind."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6147","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:10:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"87eiCoDQRvNMvp3P6o2Dj2BE5vK2xbkMunWkGnr7F87hbkFCI6Ks6HSDf+Ip4/Q17fl/ATA5mFpHYMTxciKBAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T14:44:21.512721Z"},"content_sha256":"1ccf083b26a09eef99af294c551e0bbe6b6c6333409ccf09409af86d777e848f","schema_version":"1.0","event_id":"sha256:1ccf083b26a09eef99af294c551e0bbe6b6c6333409ccf09409af86d777e848f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CUZXLQPN27BV4S6JSAZIRFC6UJ/bundle.json","state_url":"https://pith.science/pith/CUZXLQPN27BV4S6JSAZIRFC6UJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CUZXLQPN27BV4S6JSAZIRFC6UJ/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":"2026-06-29T14:44:21Z","links":{"resolver":"https://pith.science/pith/CUZXLQPN27BV4S6JSAZIRFC6UJ","bundle":"https://pith.science/pith/CUZXLQPN27BV4S6JSAZIRFC6UJ/bundle.json","state":"https://pith.science/pith/CUZXLQPN27BV4S6JSAZIRFC6UJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CUZXLQPN27BV4S6JSAZIRFC6UJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CUZXLQPN27BV4S6JSAZIRFC6UJ","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":"f8830a71e935768d2ee27c544c8bbfcbb3014bede87167f955ec26b36b67e3c2","cross_cats_sorted":["math.MP","nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-27T18:11:46Z","title_canon_sha256":"48bc9d3dec5df55d8028296273e11961a3fdf187b54a7a515b2a60030e25ab29"},"schema_version":"1.0","source":{"id":"1110.6147","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6147","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6147v1","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6147","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"pith_short_12","alias_value":"CUZXLQPN27BV","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CUZXLQPN27BV4S6J","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CUZXLQPN","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:1ccf083b26a09eef99af294c551e0bbe6b6c6333409ccf09409af86d777e848f","target":"graph","created_at":"2026-05-18T04:10:09Z","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":"The integrals $\\threej{\\Llo}{\\Llt}{\\Llth} {0}{0}{0}\\,\\int_0^\\infty \\,r^{\\Llth+1}\\,e^{-\\alpha r}\\,j_\\Llo(k_1r)\\, j_\\Llt(k_2r)\\,dr$ and $\\threej{\\Llo}{\\Llt}{\\Llth} {0}{0}{0}\\,\\int_0^\\infty \\,r^{\\Llth+2}\\,e^{-\\alpha r}\\,j_\\Llo(k_1r)\\, j_\\Llt(k_2r)\\,dr$ are evaluated analytically. The result is a finite sum over the associated Legendre function of the second kind.","authors_text":"R. Mehrem","cross_cats":["math.MP","nucl-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-27T18:11:46Z","title":"An Analytical Evaluation For The Integral Of Two Spherical Bessel Functions With An Additional Exponential And Polynomial Factor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6147","kind":"arxiv","version":1},"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":"sha256:13839430ad792b2eeb23cc18a5e243785bcac93b90d2cdc8f48c245014465af7","target":"record","created_at":"2026-05-18T04:10:09Z","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":"f8830a71e935768d2ee27c544c8bbfcbb3014bede87167f955ec26b36b67e3c2","cross_cats_sorted":["math.MP","nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-27T18:11:46Z","title_canon_sha256":"48bc9d3dec5df55d8028296273e11961a3fdf187b54a7a515b2a60030e25ab29"},"schema_version":"1.0","source":{"id":"1110.6147","kind":"arxiv","version":1}},"canonical_sha256":"153375c1edd7c35e4bc9903288945ea257c43e7d1db11231c81f15a86904c23b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"153375c1edd7c35e4bc9903288945ea257c43e7d1db11231c81f15a86904c23b","first_computed_at":"2026-05-18T04:10:09.458666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:09.458666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+vMwinMOq379nhoGb8sRduObqei8vIHPhorLkx5qTOUE2vrv/aF/T+oaAQkqbNH+zA9bouWgYOXhJ7sD82J+CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:09.459362Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.6147","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13839430ad792b2eeb23cc18a5e243785bcac93b90d2cdc8f48c245014465af7","sha256:1ccf083b26a09eef99af294c551e0bbe6b6c6333409ccf09409af86d777e848f"],"state_sha256":"6162d7e2153874891aade1ba29e88ca57303be7f72ff26ab99d37dad247ba1aa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x4wcaGoT4jt0L0VebLYGu8/y4gd5TF0rvLScz6mC9wl43Q+dMsUjKtxPwkYTXsq67CXSaDP44sHhIJ5DdBZoCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T14:44:21.514590Z","bundle_sha256":"6217c429704cf929b524557f4cc1ebf6fb73d7283659428314493fea1a763c30"}}