{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:J4NLMCFICUCRM5NJT4FZTQP7UQ","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":"7d194dbc3757747f0880a51cb3ce82a25e19d23785b267ca7d83f3a74f1593c8","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2010-10-29T21:24:40Z","title_canon_sha256":"12685e704d80341f6fd39c99f104710f7ef4faa80ece3d6c98530375a0b41b74"},"schema_version":"1.0","source":{"id":"1011.0020","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.0020","created_at":"2026-05-18T04:37:30Z"},{"alias_kind":"arxiv_version","alias_value":"1011.0020v1","created_at":"2026-05-18T04:37:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.0020","created_at":"2026-05-18T04:37:30Z"},{"alias_kind":"pith_short_12","alias_value":"J4NLMCFICUCR","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"J4NLMCFICUCRM5NJ","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"J4NLMCFI","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:0e2e6109f9834ae5775c8b656d2fde1f6f6cae6c95001c8fdd98d08c285589dc","target":"graph","created_at":"2026-05-18T04:37:30Z","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":"A measure for the description of the chirality of triangles is introduced. The measure $X\\delta$ is zero for triangles with at least one mirror axe, i.e. equilateral or isosceles triangles, and positive or negative for scalane, i.e. left or right handed triangles, respectively.","authors_text":"Haifeng Ma, Thomas Greber","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2010-10-29T21:24:40Z","title":"A measure for the chirality of triangles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0020","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":"sha256:653e14c3aff1cf64a33379b8feab9a63a37dbefb596e26b3b2d425decc8cb9f4","target":"record","created_at":"2026-05-18T04:37:30Z","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":"7d194dbc3757747f0880a51cb3ce82a25e19d23785b267ca7d83f3a74f1593c8","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2010-10-29T21:24:40Z","title_canon_sha256":"12685e704d80341f6fd39c99f104710f7ef4faa80ece3d6c98530375a0b41b74"},"schema_version":"1.0","source":{"id":"1011.0020","kind":"arxiv","version":1}},"canonical_sha256":"4f1ab608a815051675a99f0b99c1ffa439a463136a9613a4915375d898201a19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f1ab608a815051675a99f0b99c1ffa439a463136a9613a4915375d898201a19","first_computed_at":"2026-05-18T04:37:30.738533Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:37:30.738533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zoVZhMdssPUBEnXXRbJdEaOe89eNqIifgub8HYI3a3ztrf1suCuJ8ppPlaaNVdV9ertE8aeS36S+MG6WZOtqBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:37:30.739271Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.0020","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:653e14c3aff1cf64a33379b8feab9a63a37dbefb596e26b3b2d425decc8cb9f4","sha256:0e2e6109f9834ae5775c8b656d2fde1f6f6cae6c95001c8fdd98d08c285589dc"],"state_sha256":"ea0eb3a78de20eb2ed7dc3c82040f36a804a704356ae3112073b49c90d7cb4b2"}