{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ULRBCTTQWX7U6YYO4MLTOM6ZS3","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":"166e597600e8ac353cac15cb60a6cfc0ddb0215a0c19dcd6c5ffc6f4f3ec97c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-30T08:51:27Z","title_canon_sha256":"7eca16368f6d2511ba55a22d051a9e866096894f095ae18b005200724eab9ded"},"schema_version":"1.0","source":{"id":"1307.0186","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.0186","created_at":"2026-05-18T02:17:34Z"},{"alias_kind":"arxiv_version","alias_value":"1307.0186v1","created_at":"2026-05-18T02:17:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0186","created_at":"2026-05-18T02:17:34Z"},{"alias_kind":"pith_short_12","alias_value":"ULRBCTTQWX7U","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"ULRBCTTQWX7U6YYO","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"ULRBCTTQ","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:57c138793389f97f6cd5216de76ef6d2b0058824886b0283bb3f559c01eb1ef9","target":"graph","created_at":"2026-05-18T02:17:34Z","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":"We present a formula for the regular part of a sectorial form that represents a general linear second-order differential expression that may include lower-order terms. The formula is given in terms of the original coefficients. It shows that the regular part is again a differential sectorial form and allows to characterise when also the singular part is sectorial. While this generalises earlier results on pure second-order differential expressions, it also shows that lower-order terms truly introduce new behaviour.","authors_text":"A.F.M. ter Elst, Manfred Sauter","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-30T08:51:27Z","title":"The regular part of second-order differential sectorial forms with lower-order terms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0186","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":"sha256:885d62d339bf6d6e029cfe613915d65da3122f315f04d29f7535c04525b0c73e","target":"record","created_at":"2026-05-18T02:17:34Z","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":"166e597600e8ac353cac15cb60a6cfc0ddb0215a0c19dcd6c5ffc6f4f3ec97c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-30T08:51:27Z","title_canon_sha256":"7eca16368f6d2511ba55a22d051a9e866096894f095ae18b005200724eab9ded"},"schema_version":"1.0","source":{"id":"1307.0186","kind":"arxiv","version":1}},"canonical_sha256":"a2e2114e70b5ff4f630ee3173733d996c654acf8f8aeb34828c7a3316139ee77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2e2114e70b5ff4f630ee3173733d996c654acf8f8aeb34828c7a3316139ee77","first_computed_at":"2026-05-18T02:17:34.016779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:34.016779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tkRxa0xRByFzqS7HRmfqmMnnchn2FMsf91+XBGQfVo/1bJy0hdGRNOZ08fJrE+NjnJP0aL7SrqR62jtKJ9SIBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:34.017400Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.0186","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:885d62d339bf6d6e029cfe613915d65da3122f315f04d29f7535c04525b0c73e","sha256:57c138793389f97f6cd5216de76ef6d2b0058824886b0283bb3f559c01eb1ef9"],"state_sha256":"fc625d98ca81934ca826f7b3f4e3f30c108a3e6e819ecf108519984e871fe294"}