{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:4MTIR7INT77YTWQEYSQN5BGDNC","short_pith_number":"pith:4MTIR7IN","schema_version":"1.0","canonical_sha256":"e32688fd0d9fff89da04c4a0de84c3688b9a8cfc7483a3d27342722329e6e209","source":{"kind":"arxiv","id":"1212.5417","version":1},"attestation_state":"computed","paper":{"title":"Program Verification in the presence of complex numbers, functions with branch cuts etc","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"David Wilson, James H. Davenport, Matthew England, Russell Bradford","submitted_at":"2012-12-21T12:35:51Z","abstract_excerpt":"In considering the reliability of numerical programs, it is normal to \"limit our study to the semantics dealing with numerical precision\" (Martel, 2005). On the other hand, there is a great deal of work on the reliability of programs that essentially ignores the numerics. The thesis of this paper is that there is a class of problems that fall between these two, which could be described as \"does the low-level arithmetic implement the high-level mathematics\". Many of these problems arise because mathematics, particularly the mathematics of the complex numbers, is more difficult than expected: fo"},"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":"1212.5417","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2012-12-21T12:35:51Z","cross_cats_sorted":[],"title_canon_sha256":"92d7e9d16dba9ba84c88e828b40893ce024497c67e8ef30a995a090af1e9b8bf","abstract_canon_sha256":"bcf7d34624de74a27e4ac58bac9e4464349c70a76a2659dd4f5144fcd2a33557"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:27.221424Z","signature_b64":"x5m7H1Y+BX6RY/b85gIoVeMo6WixVczl35N/tBzohFRAwyD3L1EUqKdRroqZ40gkQWIxBo/BWf8bFi9Ni+gCDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e32688fd0d9fff89da04c4a0de84c3688b9a8cfc7483a3d27342722329e6e209","last_reissued_at":"2026-05-18T02:53:27.220635Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:27.220635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Program Verification in the presence of complex numbers, functions with branch cuts etc","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"David Wilson, James H. Davenport, Matthew England, Russell Bradford","submitted_at":"2012-12-21T12:35:51Z","abstract_excerpt":"In considering the reliability of numerical programs, it is normal to \"limit our study to the semantics dealing with numerical precision\" (Martel, 2005). On the other hand, there is a great deal of work on the reliability of programs that essentially ignores the numerics. The thesis of this paper is that there is a class of problems that fall between these two, which could be described as \"does the low-level arithmetic implement the high-level mathematics\". Many of these problems arise because mathematics, particularly the mathematics of the complex numbers, is more difficult than expected: fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5417","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":"1212.5417","created_at":"2026-05-18T02:53:27.220777+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.5417v1","created_at":"2026-05-18T02:53:27.220777+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5417","created_at":"2026-05-18T02:53:27.220777+00:00"},{"alias_kind":"pith_short_12","alias_value":"4MTIR7INT77Y","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"4MTIR7INT77YTWQE","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"4MTIR7IN","created_at":"2026-05-18T12:26:53.410803+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/4MTIR7INT77YTWQEYSQN5BGDNC","json":"https://pith.science/pith/4MTIR7INT77YTWQEYSQN5BGDNC.json","graph_json":"https://pith.science/api/pith-number/4MTIR7INT77YTWQEYSQN5BGDNC/graph.json","events_json":"https://pith.science/api/pith-number/4MTIR7INT77YTWQEYSQN5BGDNC/events.json","paper":"https://pith.science/paper/4MTIR7IN"},"agent_actions":{"view_html":"https://pith.science/pith/4MTIR7INT77YTWQEYSQN5BGDNC","download_json":"https://pith.science/pith/4MTIR7INT77YTWQEYSQN5BGDNC.json","view_paper":"https://pith.science/paper/4MTIR7IN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.5417&json=true","fetch_graph":"https://pith.science/api/pith-number/4MTIR7INT77YTWQEYSQN5BGDNC/graph.json","fetch_events":"https://pith.science/api/pith-number/4MTIR7INT77YTWQEYSQN5BGDNC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4MTIR7INT77YTWQEYSQN5BGDNC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4MTIR7INT77YTWQEYSQN5BGDNC/action/storage_attestation","attest_author":"https://pith.science/pith/4MTIR7INT77YTWQEYSQN5BGDNC/action/author_attestation","sign_citation":"https://pith.science/pith/4MTIR7INT77YTWQEYSQN5BGDNC/action/citation_signature","submit_replication":"https://pith.science/pith/4MTIR7INT77YTWQEYSQN5BGDNC/action/replication_record"}},"created_at":"2026-05-18T02:53:27.220777+00:00","updated_at":"2026-05-18T02:53:27.220777+00:00"}