{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IG5QGISRYPKVDGNPK3QTIQKFL2","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":"32e902a90d05e46c1164e9b7a49c81202810ecf63cf1e2eb5b34901e1b0781d3","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-01T21:10:12Z","title_canon_sha256":"87a4a8a0f02d72347addd0417906fe03d0f7d2e0208fe04c442f1bf7fce5f011"},"schema_version":"1.0","source":{"id":"1002.0337","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.0337","created_at":"2026-05-18T02:09:21Z"},{"alias_kind":"arxiv_version","alias_value":"1002.0337v1","created_at":"2026-05-18T02:09:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.0337","created_at":"2026-05-18T02:09:21Z"},{"alias_kind":"pith_short_12","alias_value":"IG5QGISRYPKV","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IG5QGISRYPKVDGNP","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IG5QGISR","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:e51d29b9e003c26ac575534b97929e5a9de2fe65f029ac4d30b2eb6ef56e0bf4","target":"graph","created_at":"2026-05-18T02:09:21Z","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 show how the description of a shear-free ray congruence in Minkowski space as an evolving family of semi-conformal mappings can naturally be formulated on a finite graph. For this, we introduce the notion of holomorphic function on a graph. On a regular coloured graph of degree three, we recover the space-time picture. In the spirit of twistor theory, where a light ray is the more fundamental object from which space-time points should be derived, the line graph, whose points are the edges of the original graph, should be considered as the basic object. The Penrose twistor correspondence is ","authors_text":"Mohammad Wehbe, Paul Baird","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-01T21:10:12Z","title":"Twistor theory on a finite graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0337","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":"sha256:7c42e10383b18ab90d8b020f8b2a7a4fd35312de92dd4bb8c6d51218d36b18d4","target":"record","created_at":"2026-05-18T02:09:21Z","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":"32e902a90d05e46c1164e9b7a49c81202810ecf63cf1e2eb5b34901e1b0781d3","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-01T21:10:12Z","title_canon_sha256":"87a4a8a0f02d72347addd0417906fe03d0f7d2e0208fe04c442f1bf7fce5f011"},"schema_version":"1.0","source":{"id":"1002.0337","kind":"arxiv","version":1}},"canonical_sha256":"41bb032251c3d55199af56e13441455e9344e5a2043e87b40f581941c46816de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41bb032251c3d55199af56e13441455e9344e5a2043e87b40f581941c46816de","first_computed_at":"2026-05-18T02:09:21.320124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:09:21.320124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/y+XwnCVWGg0eSnyOkeHfkOSUus7ITxWXo5klv0MQcQ/EgosPH+0VsUJYMH4dlLdQF2IkMm20B5E/w6/u3SMBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:09:21.320848Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.0337","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c42e10383b18ab90d8b020f8b2a7a4fd35312de92dd4bb8c6d51218d36b18d4","sha256:e51d29b9e003c26ac575534b97929e5a9de2fe65f029ac4d30b2eb6ef56e0bf4"],"state_sha256":"19075f76b5d2bdf19acb1efebee80767ecff62a72aadc0a6e8aaa6900af05e08"}