{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:5VD23DRND6POEVHPLE66TQEHSX","short_pith_number":"pith:5VD23DRN","canonical_record":{"source":{"id":"1308.6139","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-28T12:04:52Z","cross_cats_sorted":[],"title_canon_sha256":"7f576b70f78138dd3512d36d020f7afc70473dbff6e797b3508ce63e4e231d14","abstract_canon_sha256":"92c05aff4ecb9722277f43fd4b4ee4013fc1ddf03676c92461d309a1a65ff987"},"schema_version":"1.0"},"canonical_sha256":"ed47ad8e2d1f9ee254ef593de9c08795d4f7b0e6818feaab4a280e0d0430b16d","source":{"kind":"arxiv","id":"1308.6139","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.6139","created_at":"2026-05-18T03:14:48Z"},{"alias_kind":"arxiv_version","alias_value":"1308.6139v1","created_at":"2026-05-18T03:14:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6139","created_at":"2026-05-18T03:14:48Z"},{"alias_kind":"pith_short_12","alias_value":"5VD23DRND6PO","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5VD23DRND6POEVHP","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5VD23DRN","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:5VD23DRND6POEVHPLE66TQEHSX","target":"record","payload":{"canonical_record":{"source":{"id":"1308.6139","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-28T12:04:52Z","cross_cats_sorted":[],"title_canon_sha256":"7f576b70f78138dd3512d36d020f7afc70473dbff6e797b3508ce63e4e231d14","abstract_canon_sha256":"92c05aff4ecb9722277f43fd4b4ee4013fc1ddf03676c92461d309a1a65ff987"},"schema_version":"1.0"},"canonical_sha256":"ed47ad8e2d1f9ee254ef593de9c08795d4f7b0e6818feaab4a280e0d0430b16d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:48.985766Z","signature_b64":"PjGN1pVc+ALDJBJ0t6uqjWJD5ccLTrWBYjop72hIxB8txhMJ3UXtKa070gGdz7c0Os2nnaR6l6yzxjjyO1CiCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed47ad8e2d1f9ee254ef593de9c08795d4f7b0e6818feaab4a280e0d0430b16d","last_reissued_at":"2026-05-18T03:14:48.984925Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:48.984925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.6139","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":"2026-05-18T03:14:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D00CNlC3+xo4GpCPYP4a5oYK5mwL7jMHRvcYWkS4B3hNDItA2SB1YkZsr8FhNHrn3UCOz1e8/fhYgilEiU2eDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T23:15:00.889434Z"},"content_sha256":"1f05c73d239f634f880da26a10a4177f26872d7bfb15e8522d882c3ce68ef097","schema_version":"1.0","event_id":"sha256:1f05c73d239f634f880da26a10a4177f26872d7bfb15e8522d882c3ce68ef097"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:5VD23DRND6POEVHPLE66TQEHSX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the structure of self-complementary graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Nicolas Trotignon","submitted_at":"2013-08-28T12:04:52Z","abstract_excerpt":"A \\emph{self-complementary} graph is a graph isomorphic to its complement. An isomorphism between $G$ and its complement, viewed as a permutation of $V(G)$, is then called an \\emph{antimorphism}. A \\emph{skew partition} of $G$ is a partition of $V(G)$ into 4 sets $A,B,C,D$ such that there is no edge between $A,B$ and every possible edge between $C,D$. A \\emph{symmetric partition} of $G$ is a partition of $V(G)$ into 4 sets $A,B,C,D$ such that there is no edge between $A, D$, no edge between $B, C$, every possible edge between $A,B$ and every possible edge between $C,D$.\n  We give a new proof o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6139","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":"2026-05-18T03:14:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J0KeNpZ1WWI4Dp4ROIlV5/CHDY8mrOfrPs/xV+rjLcp/sBdCfaXOXeLzd5ICwje3UpCvuBCdtZasxXOXOJaXDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T23:15:00.889854Z"},"content_sha256":"ce3697b2566f6b5dc7aba4578b29d12d6fa1505f8acde4fb34aa5354b1f9c54f","schema_version":"1.0","event_id":"sha256:ce3697b2566f6b5dc7aba4578b29d12d6fa1505f8acde4fb34aa5354b1f9c54f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5VD23DRND6POEVHPLE66TQEHSX/bundle.json","state_url":"https://pith.science/pith/5VD23DRND6POEVHPLE66TQEHSX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5VD23DRND6POEVHPLE66TQEHSX/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":"2026-07-04T23:15:00Z","links":{"resolver":"https://pith.science/pith/5VD23DRND6POEVHPLE66TQEHSX","bundle":"https://pith.science/pith/5VD23DRND6POEVHPLE66TQEHSX/bundle.json","state":"https://pith.science/pith/5VD23DRND6POEVHPLE66TQEHSX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5VD23DRND6POEVHPLE66TQEHSX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5VD23DRND6POEVHPLE66TQEHSX","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":"92c05aff4ecb9722277f43fd4b4ee4013fc1ddf03676c92461d309a1a65ff987","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-28T12:04:52Z","title_canon_sha256":"7f576b70f78138dd3512d36d020f7afc70473dbff6e797b3508ce63e4e231d14"},"schema_version":"1.0","source":{"id":"1308.6139","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.6139","created_at":"2026-05-18T03:14:48Z"},{"alias_kind":"arxiv_version","alias_value":"1308.6139v1","created_at":"2026-05-18T03:14:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6139","created_at":"2026-05-18T03:14:48Z"},{"alias_kind":"pith_short_12","alias_value":"5VD23DRND6PO","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5VD23DRND6POEVHP","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5VD23DRN","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:ce3697b2566f6b5dc7aba4578b29d12d6fa1505f8acde4fb34aa5354b1f9c54f","target":"graph","created_at":"2026-05-18T03:14:48Z","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 \\emph{self-complementary} graph is a graph isomorphic to its complement. An isomorphism between $G$ and its complement, viewed as a permutation of $V(G)$, is then called an \\emph{antimorphism}. A \\emph{skew partition} of $G$ is a partition of $V(G)$ into 4 sets $A,B,C,D$ such that there is no edge between $A,B$ and every possible edge between $C,D$. A \\emph{symmetric partition} of $G$ is a partition of $V(G)$ into 4 sets $A,B,C,D$ such that there is no edge between $A, D$, no edge between $B, C$, every possible edge between $A,B$ and every possible edge between $C,D$.\n  We give a new proof o","authors_text":"Nicolas Trotignon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-28T12:04:52Z","title":"On the structure of self-complementary graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6139","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":"sha256:1f05c73d239f634f880da26a10a4177f26872d7bfb15e8522d882c3ce68ef097","target":"record","created_at":"2026-05-18T03:14:48Z","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":"92c05aff4ecb9722277f43fd4b4ee4013fc1ddf03676c92461d309a1a65ff987","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-28T12:04:52Z","title_canon_sha256":"7f576b70f78138dd3512d36d020f7afc70473dbff6e797b3508ce63e4e231d14"},"schema_version":"1.0","source":{"id":"1308.6139","kind":"arxiv","version":1}},"canonical_sha256":"ed47ad8e2d1f9ee254ef593de9c08795d4f7b0e6818feaab4a280e0d0430b16d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed47ad8e2d1f9ee254ef593de9c08795d4f7b0e6818feaab4a280e0d0430b16d","first_computed_at":"2026-05-18T03:14:48.984925Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:48.984925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PjGN1pVc+ALDJBJ0t6uqjWJD5ccLTrWBYjop72hIxB8txhMJ3UXtKa070gGdz7c0Os2nnaR6l6yzxjjyO1CiCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:48.985766Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.6139","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f05c73d239f634f880da26a10a4177f26872d7bfb15e8522d882c3ce68ef097","sha256:ce3697b2566f6b5dc7aba4578b29d12d6fa1505f8acde4fb34aa5354b1f9c54f"],"state_sha256":"0719ef327bcd18e69e5a63008580ee8cc0a2e678695bc916547dd4b8dbbbad87"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zPmcMvbqg6kEzxNDqL9eBr0CiuC+qymkIXU9ziqIEpWNkXYfwuVwy4L3Cl+COSeqG+A5Bt0Tz4Zt26hTbMSlDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T23:15:00.891959Z","bundle_sha256":"7f45e7ee6f8fa166ff204f6c29f66554b1093cb97efe1bd8941cb3c870ebeb1c"}}