{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:BYUZSCFPETCVDLI57HLHRN4NS3","short_pith_number":"pith:BYUZSCFP","canonical_record":{"source":{"id":"1804.10976","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-29T18:41:51Z","cross_cats_sorted":["math.MP","nucl-th"],"title_canon_sha256":"5fafef36dbd47c140637126fb1779f3deb3d9f05bc9fdfad7da2bac5f2a3111a","abstract_canon_sha256":"afd228d88efb4665e6870cd7a29721bc6faf9c4148ffc84186c99f9ce56efed5"},"schema_version":"1.0"},"canonical_sha256":"0e299908af24c551ad1df9d678b78d96de9d0d46b2efa31ffaec6aa8553a0c02","source":{"kind":"arxiv","id":"1804.10976","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.10976","created_at":"2026-05-18T00:00:19Z"},{"alias_kind":"arxiv_version","alias_value":"1804.10976v3","created_at":"2026-05-18T00:00:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10976","created_at":"2026-05-18T00:00:19Z"},{"alias_kind":"pith_short_12","alias_value":"BYUZSCFPETCV","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BYUZSCFPETCVDLI5","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BYUZSCFP","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:BYUZSCFPETCVDLI57HLHRN4NS3","target":"record","payload":{"canonical_record":{"source":{"id":"1804.10976","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-29T18:41:51Z","cross_cats_sorted":["math.MP","nucl-th"],"title_canon_sha256":"5fafef36dbd47c140637126fb1779f3deb3d9f05bc9fdfad7da2bac5f2a3111a","abstract_canon_sha256":"afd228d88efb4665e6870cd7a29721bc6faf9c4148ffc84186c99f9ce56efed5"},"schema_version":"1.0"},"canonical_sha256":"0e299908af24c551ad1df9d678b78d96de9d0d46b2efa31ffaec6aa8553a0c02","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:19.630510Z","signature_b64":"0tdYd5LP9b+O6CWEzIrwCWaZhs9jH5wFeicPONepY5U5e96VW4yXrdlZOAFTaHmwRzErnfJeKCSsMMa5e079Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e299908af24c551ad1df9d678b78d96de9d0d46b2efa31ffaec6aa8553a0c02","last_reissued_at":"2026-05-18T00:00:19.630067Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:19.630067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.10976","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:00:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qeDTPnK6PrULDRmRqMZonPBOqaUQZiGn9P3T5dp1Q626HPiXRIId/wK6vlm9HEOTMWfJmtb8NgLvHcVIiKRcCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T08:11:45.572002Z"},"content_sha256":"e2802533a197a2593251cd4b0434986271706dfc1b9c381fbe2ab3c829ebd8c6","schema_version":"1.0","event_id":"sha256:e2802533a197a2593251cd4b0434986271706dfc1b9c381fbe2ab3c829ebd8c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:BYUZSCFPETCVDLI57HLHRN4NS3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Connection formulas between Coulomb wave functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nucl-th"],"primary_cat":"math-ph","authors_text":"David Gaspard","submitted_at":"2018-04-29T18:41:51Z","abstract_excerpt":"The mathematical relations between the regular Coulomb function $F_{\\eta\\ell}(\\rho)$ and the irregular Coulomb functions $H^\\pm_{\\eta\\ell}(\\rho)$ and $G_{\\eta\\ell}(\\rho)$ are obtained in the complex plane of the variables $\\eta$ and $\\rho$ for integer or half-integer values of $\\ell$. These relations, referred to as \"connection formulas\", form the basis of the theory of Coulomb wave functions, and play an important role in many fields of physics, especially in the quantum theory of charged particle scattering. As a first step, the symmetry properties of the regular function $F_{\\eta\\ell}(\\rho)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10976","kind":"arxiv","version":3},"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":"2026-05-18T00:00:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n04hO7hSzUUzVpLWYpH68+8832Yf/4Mczce0WzyEh2zYetaZbKjpcTFFVcPfGi6SzAutflsKyiNUoav/BPoBCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T08:11:45.572481Z"},"content_sha256":"b9e1377c9201dcfe563549c78fa01d5834ba3d58975d613001cfa0583c0b1fde","schema_version":"1.0","event_id":"sha256:b9e1377c9201dcfe563549c78fa01d5834ba3d58975d613001cfa0583c0b1fde"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BYUZSCFPETCVDLI57HLHRN4NS3/bundle.json","state_url":"https://pith.science/pith/BYUZSCFPETCVDLI57HLHRN4NS3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BYUZSCFPETCVDLI57HLHRN4NS3/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":"2026-05-23T08:11:45Z","links":{"resolver":"https://pith.science/pith/BYUZSCFPETCVDLI57HLHRN4NS3","bundle":"https://pith.science/pith/BYUZSCFPETCVDLI57HLHRN4NS3/bundle.json","state":"https://pith.science/pith/BYUZSCFPETCVDLI57HLHRN4NS3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BYUZSCFPETCVDLI57HLHRN4NS3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BYUZSCFPETCVDLI57HLHRN4NS3","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":"afd228d88efb4665e6870cd7a29721bc6faf9c4148ffc84186c99f9ce56efed5","cross_cats_sorted":["math.MP","nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-29T18:41:51Z","title_canon_sha256":"5fafef36dbd47c140637126fb1779f3deb3d9f05bc9fdfad7da2bac5f2a3111a"},"schema_version":"1.0","source":{"id":"1804.10976","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.10976","created_at":"2026-05-18T00:00:19Z"},{"alias_kind":"arxiv_version","alias_value":"1804.10976v3","created_at":"2026-05-18T00:00:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10976","created_at":"2026-05-18T00:00:19Z"},{"alias_kind":"pith_short_12","alias_value":"BYUZSCFPETCV","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BYUZSCFPETCVDLI5","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BYUZSCFP","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:b9e1377c9201dcfe563549c78fa01d5834ba3d58975d613001cfa0583c0b1fde","target":"graph","created_at":"2026-05-18T00:00:19Z","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 mathematical relations between the regular Coulomb function $F_{\\eta\\ell}(\\rho)$ and the irregular Coulomb functions $H^\\pm_{\\eta\\ell}(\\rho)$ and $G_{\\eta\\ell}(\\rho)$ are obtained in the complex plane of the variables $\\eta$ and $\\rho$ for integer or half-integer values of $\\ell$. These relations, referred to as \"connection formulas\", form the basis of the theory of Coulomb wave functions, and play an important role in many fields of physics, especially in the quantum theory of charged particle scattering. As a first step, the symmetry properties of the regular function $F_{\\eta\\ell}(\\rho)","authors_text":"David Gaspard","cross_cats":["math.MP","nucl-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-29T18:41:51Z","title":"Connection formulas between Coulomb wave functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10976","kind":"arxiv","version":3},"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:e2802533a197a2593251cd4b0434986271706dfc1b9c381fbe2ab3c829ebd8c6","target":"record","created_at":"2026-05-18T00:00:19Z","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":"afd228d88efb4665e6870cd7a29721bc6faf9c4148ffc84186c99f9ce56efed5","cross_cats_sorted":["math.MP","nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-29T18:41:51Z","title_canon_sha256":"5fafef36dbd47c140637126fb1779f3deb3d9f05bc9fdfad7da2bac5f2a3111a"},"schema_version":"1.0","source":{"id":"1804.10976","kind":"arxiv","version":3}},"canonical_sha256":"0e299908af24c551ad1df9d678b78d96de9d0d46b2efa31ffaec6aa8553a0c02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e299908af24c551ad1df9d678b78d96de9d0d46b2efa31ffaec6aa8553a0c02","first_computed_at":"2026-05-18T00:00:19.630067Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:19.630067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0tdYd5LP9b+O6CWEzIrwCWaZhs9jH5wFeicPONepY5U5e96VW4yXrdlZOAFTaHmwRzErnfJeKCSsMMa5e079Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:19.630510Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.10976","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2802533a197a2593251cd4b0434986271706dfc1b9c381fbe2ab3c829ebd8c6","sha256:b9e1377c9201dcfe563549c78fa01d5834ba3d58975d613001cfa0583c0b1fde"],"state_sha256":"52e17a6d2ba0ccec0b1093abe65064c0a482a4fd25a687b054ac91077dbaf4d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PuSIs2txKEylUD3SBec0RR5xGs62ZaUu6eOyi6mZWNP7tBOnKw5MKE3DeTc+GHWtTvN0GH8H67mjab3P3X3ZAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T08:11:45.575977Z","bundle_sha256":"45e1cf99fd462da26cc29b6f6037db74865b841ea2fd2ab0cb182ac793dcc9bb"}}