{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:J4NLMCFICUCRM5NJT4FZTQP7UQ","short_pith_number":"pith:J4NLMCFI","canonical_record":{"source":{"id":"1011.0020","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2010-10-29T21:24:40Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"12685e704d80341f6fd39c99f104710f7ef4faa80ece3d6c98530375a0b41b74","abstract_canon_sha256":"7d194dbc3757747f0880a51cb3ce82a25e19d23785b267ca7d83f3a74f1593c8"},"schema_version":"1.0"},"canonical_sha256":"4f1ab608a815051675a99f0b99c1ffa439a463136a9613a4915375d898201a19","source":{"kind":"arxiv","id":"1011.0020","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:J4NLMCFICUCRM5NJT4FZTQP7UQ","target":"record","payload":{"canonical_record":{"source":{"id":"1011.0020","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2010-10-29T21:24:40Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"12685e704d80341f6fd39c99f104710f7ef4faa80ece3d6c98530375a0b41b74","abstract_canon_sha256":"7d194dbc3757747f0880a51cb3ce82a25e19d23785b267ca7d83f3a74f1593c8"},"schema_version":"1.0"},"canonical_sha256":"4f1ab608a815051675a99f0b99c1ffa439a463136a9613a4915375d898201a19","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:37:30.739271Z","signature_b64":"zoVZhMdssPUBEnXXRbJdEaOe89eNqIifgub8HYI3a3ztrf1suCuJ8ppPlaaNVdV9ertE8aeS36S+MG6WZOtqBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f1ab608a815051675a99f0b99c1ffa439a463136a9613a4915375d898201a19","last_reissued_at":"2026-05-18T04:37:30.738533Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:37:30.738533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.0020","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:37:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6o990km6FXYkfrHcx3gVYC8xM/wyfUxmcv+fn0tt6lh0fwM8vSgFscdYiWjAzKbKdi9+BWZfqAXxfZUqpbv0DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:35:56.792070Z"},"content_sha256":"653e14c3aff1cf64a33379b8feab9a63a37dbefb596e26b3b2d425decc8cb9f4","schema_version":"1.0","event_id":"sha256:653e14c3aff1cf64a33379b8feab9a63a37dbefb596e26b3b2d425decc8cb9f4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:J4NLMCFICUCRM5NJT4FZTQP7UQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A measure for the chirality of triangles","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Haifeng Ma, Thomas Greber","submitted_at":"2010-10-29T21:24:40Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0020","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:37:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yYIIbMQLOeisjhW4RVov9AI07gUipTxRnmzgxqi/+i7cUSFl5mLSERHPfi3xfDZp4IdcqyPxh+G4PWS7HzDcAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:35:56.792811Z"},"content_sha256":"0e2e6109f9834ae5775c8b656d2fde1f6f6cae6c95001c8fdd98d08c285589dc","schema_version":"1.0","event_id":"sha256:0e2e6109f9834ae5775c8b656d2fde1f6f6cae6c95001c8fdd98d08c285589dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J4NLMCFICUCRM5NJT4FZTQP7UQ/bundle.json","state_url":"https://pith.science/pith/J4NLMCFICUCRM5NJT4FZTQP7UQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J4NLMCFICUCRM5NJT4FZTQP7UQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T22:35:56Z","links":{"resolver":"https://pith.science/pith/J4NLMCFICUCRM5NJT4FZTQP7UQ","bundle":"https://pith.science/pith/J4NLMCFICUCRM5NJT4FZTQP7UQ/bundle.json","state":"https://pith.science/pith/J4NLMCFICUCRM5NJT4FZTQP7UQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J4NLMCFICUCRM5NJT4FZTQP7UQ/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GrU7leIAT5KXSFfOYf0hLGA4Ai7CiLSAePdXAmjgizMdL6ewsEC5kw7aihtDP/9Dv4Y6THkxtm1lELbkfiCCBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:35:56.797031Z","bundle_sha256":"0fb949384e85de290d58c2bef7353c74e9e482c1cfa9a369f176d9854caa0021"}}