{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CCY25PJKTZF3LRIPM4BYXXGYSK","short_pith_number":"pith:CCY25PJK","canonical_record":{"source":{"id":"1612.07573","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-22T12:27:54Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"a3001ab47df304efc60c37bd6043a3113426e0707303f9a82fcf039a72e46386","abstract_canon_sha256":"4e7523827d075a31d436f36f5c0a189fe124d888b85c8caa4540a7e9d8e5aff1"},"schema_version":"1.0"},"canonical_sha256":"10b1aebd2a9e4bb5c50f67038bdcd892a777c359969052aaa3eeb533bc2d9d2a","source":{"kind":"arxiv","id":"1612.07573","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07573","created_at":"2026-05-18T00:54:09Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07573v1","created_at":"2026-05-18T00:54:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07573","created_at":"2026-05-18T00:54:09Z"},{"alias_kind":"pith_short_12","alias_value":"CCY25PJKTZF3","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CCY25PJKTZF3LRIP","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CCY25PJK","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CCY25PJKTZF3LRIPM4BYXXGYSK","target":"record","payload":{"canonical_record":{"source":{"id":"1612.07573","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-22T12:27:54Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"a3001ab47df304efc60c37bd6043a3113426e0707303f9a82fcf039a72e46386","abstract_canon_sha256":"4e7523827d075a31d436f36f5c0a189fe124d888b85c8caa4540a7e9d8e5aff1"},"schema_version":"1.0"},"canonical_sha256":"10b1aebd2a9e4bb5c50f67038bdcd892a777c359969052aaa3eeb533bc2d9d2a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:09.719018Z","signature_b64":"AF7oPHSBkXUjeL2nhQfc2bMJqfBFn1Hprca0HXzipQButEMPkNgxSHIvm+NrJa9RphZow6fnSY/Va49sDNKNBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10b1aebd2a9e4bb5c50f67038bdcd892a777c359969052aaa3eeb533bc2d9d2a","last_reissued_at":"2026-05-18T00:54:09.718535Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:09.718535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.07573","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":"2026-05-18T00:54:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KN+Z3gSiL97Fl0O9ObtsSj5THwiiTTaPCQDwAWG9s0LFBPgtxnvtDLfu+yrcC127wI54SQskahIKnl990/IPDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T01:41:10.348137Z"},"content_sha256":"c60fc29757e9cce8ee957cf679af855e8b9d8454bf509a308231af6e06fc6e0f","schema_version":"1.0","event_id":"sha256:c60fc29757e9cce8ee957cf679af855e8b9d8454bf509a308231af6e06fc6e0f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CCY25PJKTZF3LRIPM4BYXXGYSK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Confluent Hypergeometric Equation via Fractional Calculus Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Edmundo C. Oliveira, Fabio G. Rodrigues","submitted_at":"2016-12-22T12:27:54Z","abstract_excerpt":"In this paper, using the theory of the so-called fractional calculus we show that it is possible to easily obtain the solutions for the confluent hypergeometric equation. Our approach is to be compared with the standard one (Frobenius) which is based on the ordinary calculus of integer order."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07573","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":"2026-05-18T00:54:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1O4kZYiKlwHWp5OORuhKCysGoN3vaQIp42fDjPxTPvLvLsG6lrtpfVGXE1VhY9nhtWCn6sSb+GPimkaMKia5Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T01:41:10.348856Z"},"content_sha256":"480f303c468f940a418924156f7f7c62d2fad9204130ef33b646e3118e9c06d5","schema_version":"1.0","event_id":"sha256:480f303c468f940a418924156f7f7c62d2fad9204130ef33b646e3118e9c06d5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CCY25PJKTZF3LRIPM4BYXXGYSK/bundle.json","state_url":"https://pith.science/pith/CCY25PJKTZF3LRIPM4BYXXGYSK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CCY25PJKTZF3LRIPM4BYXXGYSK/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":"2026-06-04T01:41:10Z","links":{"resolver":"https://pith.science/pith/CCY25PJKTZF3LRIPM4BYXXGYSK","bundle":"https://pith.science/pith/CCY25PJKTZF3LRIPM4BYXXGYSK/bundle.json","state":"https://pith.science/pith/CCY25PJKTZF3LRIPM4BYXXGYSK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CCY25PJKTZF3LRIPM4BYXXGYSK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CCY25PJKTZF3LRIPM4BYXXGYSK","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":"4e7523827d075a31d436f36f5c0a189fe124d888b85c8caa4540a7e9d8e5aff1","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-22T12:27:54Z","title_canon_sha256":"a3001ab47df304efc60c37bd6043a3113426e0707303f9a82fcf039a72e46386"},"schema_version":"1.0","source":{"id":"1612.07573","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07573","created_at":"2026-05-18T00:54:09Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07573v1","created_at":"2026-05-18T00:54:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07573","created_at":"2026-05-18T00:54:09Z"},{"alias_kind":"pith_short_12","alias_value":"CCY25PJKTZF3","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CCY25PJKTZF3LRIP","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CCY25PJK","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:480f303c468f940a418924156f7f7c62d2fad9204130ef33b646e3118e9c06d5","target":"graph","created_at":"2026-05-18T00:54:09Z","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":"In this paper, using the theory of the so-called fractional calculus we show that it is possible to easily obtain the solutions for the confluent hypergeometric equation. Our approach is to be compared with the standard one (Frobenius) which is based on the ordinary calculus of integer order.","authors_text":"Edmundo C. Oliveira, Fabio G. Rodrigues","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-22T12:27:54Z","title":"Confluent Hypergeometric Equation via Fractional Calculus Approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07573","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:c60fc29757e9cce8ee957cf679af855e8b9d8454bf509a308231af6e06fc6e0f","target":"record","created_at":"2026-05-18T00:54:09Z","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":"4e7523827d075a31d436f36f5c0a189fe124d888b85c8caa4540a7e9d8e5aff1","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-22T12:27:54Z","title_canon_sha256":"a3001ab47df304efc60c37bd6043a3113426e0707303f9a82fcf039a72e46386"},"schema_version":"1.0","source":{"id":"1612.07573","kind":"arxiv","version":1}},"canonical_sha256":"10b1aebd2a9e4bb5c50f67038bdcd892a777c359969052aaa3eeb533bc2d9d2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10b1aebd2a9e4bb5c50f67038bdcd892a777c359969052aaa3eeb533bc2d9d2a","first_computed_at":"2026-05-18T00:54:09.718535Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:09.718535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AF7oPHSBkXUjeL2nhQfc2bMJqfBFn1Hprca0HXzipQButEMPkNgxSHIvm+NrJa9RphZow6fnSY/Va49sDNKNBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:09.719018Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.07573","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c60fc29757e9cce8ee957cf679af855e8b9d8454bf509a308231af6e06fc6e0f","sha256:480f303c468f940a418924156f7f7c62d2fad9204130ef33b646e3118e9c06d5"],"state_sha256":"5d1f17c0179d926d2d8e634b27ed841992d27c6c7b1595d577c2156f5d96d45d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CGw7PVqeqCVQxOCCJocLzvgCD+Jo1OJ9sOXGtfsgeh+T4gvWIBnxOHuMidf768Uc5dgQtGamlh8mu+3CgZPCBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T01:41:10.351949Z","bundle_sha256":"4f64f4bc3830fb83610633f49e8f2fa906f5ad9ed853158e491cca4c77d26cff"}}