{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:XP24XHGOYI7RVS42QFYVUWVLMF","short_pith_number":"pith:XP24XHGO","schema_version":"1.0","canonical_sha256":"bbf5cb9ccec23f1acb9a81715a5aab61734f7253a9fd061b3ce619df113be94f","source":{"kind":"arxiv","id":"1505.06509","version":1},"attestation_state":"computed","paper":{"title":"Exact analytical approach to differential equations with variable coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"Mauro Bologna","submitted_at":"2015-05-16T16:17:47Z","abstract_excerpt":"This paper shows how to build a formal analytical solution for a differential equation of arbitrary order and with variable coefficients. It proofs that the most known approximated solutions for such a problem can be derived from the analytical expression presented in the paper. The formalism can be easily extended to the infinite dimensional case such as the quantum time-dependent Hamiltonian problem."},"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":"1505.06509","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-05-16T16:17:47Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f9825a298c60df6e426942fdd199ef54d9408e4eaee6f4f2d6db1fcefad72fb5","abstract_canon_sha256":"41c95dd00b7d3419f11fd88f49fb3a3093cdb4ea4a717efe460ec14945c01b63"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:44.796486Z","signature_b64":"6jFrg7ghGGWlVtJDwoyv3kn8nmRAoVKTXlqrjlKLn+ds2oTWciqCAxvD5NkAz+NLk1U0YnJ5Feg3TxvEc4btCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbf5cb9ccec23f1acb9a81715a5aab61734f7253a9fd061b3ce619df113be94f","last_reissued_at":"2026-05-18T02:03:44.795967Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:44.795967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact analytical approach to differential equations with variable coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"Mauro Bologna","submitted_at":"2015-05-16T16:17:47Z","abstract_excerpt":"This paper shows how to build a formal analytical solution for a differential equation of arbitrary order and with variable coefficients. It proofs that the most known approximated solutions for such a problem can be derived from the analytical expression presented in the paper. The formalism can be easily extended to the infinite dimensional case such as the quantum time-dependent Hamiltonian problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06509","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":"1505.06509","created_at":"2026-05-18T02:03:44.796045+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.06509v1","created_at":"2026-05-18T02:03:44.796045+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06509","created_at":"2026-05-18T02:03:44.796045+00:00"},{"alias_kind":"pith_short_12","alias_value":"XP24XHGOYI7R","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"XP24XHGOYI7RVS42","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"XP24XHGO","created_at":"2026-05-18T12:29:50.041715+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/XP24XHGOYI7RVS42QFYVUWVLMF","json":"https://pith.science/pith/XP24XHGOYI7RVS42QFYVUWVLMF.json","graph_json":"https://pith.science/api/pith-number/XP24XHGOYI7RVS42QFYVUWVLMF/graph.json","events_json":"https://pith.science/api/pith-number/XP24XHGOYI7RVS42QFYVUWVLMF/events.json","paper":"https://pith.science/paper/XP24XHGO"},"agent_actions":{"view_html":"https://pith.science/pith/XP24XHGOYI7RVS42QFYVUWVLMF","download_json":"https://pith.science/pith/XP24XHGOYI7RVS42QFYVUWVLMF.json","view_paper":"https://pith.science/paper/XP24XHGO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.06509&json=true","fetch_graph":"https://pith.science/api/pith-number/XP24XHGOYI7RVS42QFYVUWVLMF/graph.json","fetch_events":"https://pith.science/api/pith-number/XP24XHGOYI7RVS42QFYVUWVLMF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XP24XHGOYI7RVS42QFYVUWVLMF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XP24XHGOYI7RVS42QFYVUWVLMF/action/storage_attestation","attest_author":"https://pith.science/pith/XP24XHGOYI7RVS42QFYVUWVLMF/action/author_attestation","sign_citation":"https://pith.science/pith/XP24XHGOYI7RVS42QFYVUWVLMF/action/citation_signature","submit_replication":"https://pith.science/pith/XP24XHGOYI7RVS42QFYVUWVLMF/action/replication_record"}},"created_at":"2026-05-18T02:03:44.796045+00:00","updated_at":"2026-05-18T02:03:44.796045+00:00"}