{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:C6X5GU564WHOQAOX4S5XRQWIU6","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":"aa8924a124b30defb9dcf393db8fe34f9c3a2c44cd0ed41ac3258ade238bb1f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-01-29T12:22:44Z","title_canon_sha256":"1da292e101985daad114fededdcf35f09aaa757f6b4e6fbb52f1b49ee1e55abb"},"schema_version":"1.0","source":{"id":"1601.08077","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.08077","created_at":"2026-05-18T00:43:18Z"},{"alias_kind":"arxiv_version","alias_value":"1601.08077v3","created_at":"2026-05-18T00:43:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.08077","created_at":"2026-05-18T00:43:18Z"},{"alias_kind":"pith_short_12","alias_value":"C6X5GU564WHO","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C6X5GU564WHOQAOX","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C6X5GU56","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:224dca0b97069305f399aa8fcd0cd2a0a5d096bcb204f9a050e1d369882ccd5e","target":"graph","created_at":"2026-05-18T00:43:18Z","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 k-Dirac operator is a differential operator which is natural to geometric structure of a parabolic type. We will give a set of initial conditions for this operator. In the proof of the claim we will need to adapt some parts from the theory of exterior differential systems to the setting of weighted differential operators.","authors_text":"Tomas Salac","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-01-29T12:22:44Z","title":"k-Dirac operator and the Cartan-Kahler theorem for weighted differential operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.08077","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:d361691dabee772e0bb06236687ae5f5f0bd4a4df20fd3e6986272266650003c","target":"record","created_at":"2026-05-18T00:43:18Z","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":"aa8924a124b30defb9dcf393db8fe34f9c3a2c44cd0ed41ac3258ade238bb1f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-01-29T12:22:44Z","title_canon_sha256":"1da292e101985daad114fededdcf35f09aaa757f6b4e6fbb52f1b49ee1e55abb"},"schema_version":"1.0","source":{"id":"1601.08077","kind":"arxiv","version":3}},"canonical_sha256":"17afd353bee58ee801d7e4bb78c2c8a7a8dfcdf2b12aeecc9e2303c222423411","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17afd353bee58ee801d7e4bb78c2c8a7a8dfcdf2b12aeecc9e2303c222423411","first_computed_at":"2026-05-18T00:43:18.675304Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:18.675304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nqr4EimH8ezY/HE771MGeCP3ukpOtmstPEoLQ8GAum+9h67fbbrvyI0In0SzwQKNvB2jh+osJ1zFPGYYv5nGBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:18.676045Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.08077","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d361691dabee772e0bb06236687ae5f5f0bd4a4df20fd3e6986272266650003c","sha256:224dca0b97069305f399aa8fcd0cd2a0a5d096bcb204f9a050e1d369882ccd5e"],"state_sha256":"8f50fc09dc157def46d456e34b15f1310ca85c51e6c8159eeb30b94444613ded"}