{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:QXL5PA2JRA3YY5RTDDOHHXOGKK","short_pith_number":"pith:QXL5PA2J","canonical_record":{"source":{"id":"1402.0949","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-05T06:54:01Z","cross_cats_sorted":[],"title_canon_sha256":"6ac25bee6395c37fbf90c1f9c21daa778704a6eec6723aa7309461c6b21d08c8","abstract_canon_sha256":"13d62d54402100c6b5decfcc1b85b7ee1fff7f31a0eed8e1ae65af2f8656a42d"},"schema_version":"1.0"},"canonical_sha256":"85d7d7834988378c763318dc73ddc65289442a5bfee068940d5b26d69d64077c","source":{"kind":"arxiv","id":"1402.0949","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0949","created_at":"2026-05-18T03:00:02Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0949v1","created_at":"2026-05-18T03:00:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0949","created_at":"2026-05-18T03:00:02Z"},{"alias_kind":"pith_short_12","alias_value":"QXL5PA2JRA3Y","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QXL5PA2JRA3YY5RT","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QXL5PA2J","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:QXL5PA2JRA3YY5RTDDOHHXOGKK","target":"record","payload":{"canonical_record":{"source":{"id":"1402.0949","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-05T06:54:01Z","cross_cats_sorted":[],"title_canon_sha256":"6ac25bee6395c37fbf90c1f9c21daa778704a6eec6723aa7309461c6b21d08c8","abstract_canon_sha256":"13d62d54402100c6b5decfcc1b85b7ee1fff7f31a0eed8e1ae65af2f8656a42d"},"schema_version":"1.0"},"canonical_sha256":"85d7d7834988378c763318dc73ddc65289442a5bfee068940d5b26d69d64077c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:02.214573Z","signature_b64":"GY+G6xFAxCAuPMBpaZ5x6dnv3Tghux1I+hUaRyPBirG57d/EL58ttBRyFlOG/LrUUve2CJddNVxko0yfN08zDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85d7d7834988378c763318dc73ddc65289442a5bfee068940d5b26d69d64077c","last_reissued_at":"2026-05-18T03:00:02.214023Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:02.214023Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.0949","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":"2026-05-18T03:00:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JUDuKZqB+iuNXCbnwC0c3Bblqb0orlZLcOBMaSPquY2Tx5r4rUf0Mw+1EfswP8/KcGhQA0+S8pDQ7/6XWykUAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:28:58.044185Z"},"content_sha256":"51694e6d72f1bc8c0353dd80e4fdc45960a39bce4cda9ba7d75ff1154647a635","schema_version":"1.0","event_id":"sha256:51694e6d72f1bc8c0353dd80e4fdc45960a39bce4cda9ba7d75ff1154647a635"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:QXL5PA2JRA3YY5RTDDOHHXOGKK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A short proof of Kotzig's theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gleb Nenashev","submitted_at":"2014-02-05T06:54:01Z","abstract_excerpt":"A new shortest proof of Kotzig's Theorem about graphs with unique perfect matching is presented in this paper. It is well known that Kotzig's theorem is a consequence of Yeo's Theorem about edge-colored graph without alternating cycle. We present a proof of Yeo's Theorem based on the same ideas as our proof of Kotzig's theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0949","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":"2026-05-18T03:00:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PDC26rYAP+Gqnz2US5tU+W2Z4n6l0xlOejABHRy74Zk1Ae7X4mliebi3Ld2pjuyJnvSe8BglD9Ux2fiQ9PJrAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:28:58.044861Z"},"content_sha256":"1f0765f1224154dd2083d141814f3f1b1788fcc0f2c4612957d5dac610976e1e","schema_version":"1.0","event_id":"sha256:1f0765f1224154dd2083d141814f3f1b1788fcc0f2c4612957d5dac610976e1e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QXL5PA2JRA3YY5RTDDOHHXOGKK/bundle.json","state_url":"https://pith.science/pith/QXL5PA2JRA3YY5RTDDOHHXOGKK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QXL5PA2JRA3YY5RTDDOHHXOGKK/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":"2026-05-27T07:28:58Z","links":{"resolver":"https://pith.science/pith/QXL5PA2JRA3YY5RTDDOHHXOGKK","bundle":"https://pith.science/pith/QXL5PA2JRA3YY5RTDDOHHXOGKK/bundle.json","state":"https://pith.science/pith/QXL5PA2JRA3YY5RTDDOHHXOGKK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QXL5PA2JRA3YY5RTDDOHHXOGKK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QXL5PA2JRA3YY5RTDDOHHXOGKK","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":"13d62d54402100c6b5decfcc1b85b7ee1fff7f31a0eed8e1ae65af2f8656a42d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-05T06:54:01Z","title_canon_sha256":"6ac25bee6395c37fbf90c1f9c21daa778704a6eec6723aa7309461c6b21d08c8"},"schema_version":"1.0","source":{"id":"1402.0949","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0949","created_at":"2026-05-18T03:00:02Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0949v1","created_at":"2026-05-18T03:00:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0949","created_at":"2026-05-18T03:00:02Z"},{"alias_kind":"pith_short_12","alias_value":"QXL5PA2JRA3Y","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QXL5PA2JRA3YY5RT","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QXL5PA2J","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:1f0765f1224154dd2083d141814f3f1b1788fcc0f2c4612957d5dac610976e1e","target":"graph","created_at":"2026-05-18T03:00:02Z","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 new shortest proof of Kotzig's Theorem about graphs with unique perfect matching is presented in this paper. It is well known that Kotzig's theorem is a consequence of Yeo's Theorem about edge-colored graph without alternating cycle. We present a proof of Yeo's Theorem based on the same ideas as our proof of Kotzig's theorem.","authors_text":"Gleb Nenashev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-05T06:54:01Z","title":"A short proof of Kotzig's theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0949","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":"sha256:51694e6d72f1bc8c0353dd80e4fdc45960a39bce4cda9ba7d75ff1154647a635","target":"record","created_at":"2026-05-18T03:00:02Z","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":"13d62d54402100c6b5decfcc1b85b7ee1fff7f31a0eed8e1ae65af2f8656a42d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-05T06:54:01Z","title_canon_sha256":"6ac25bee6395c37fbf90c1f9c21daa778704a6eec6723aa7309461c6b21d08c8"},"schema_version":"1.0","source":{"id":"1402.0949","kind":"arxiv","version":1}},"canonical_sha256":"85d7d7834988378c763318dc73ddc65289442a5bfee068940d5b26d69d64077c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85d7d7834988378c763318dc73ddc65289442a5bfee068940d5b26d69d64077c","first_computed_at":"2026-05-18T03:00:02.214023Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:02.214023Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GY+G6xFAxCAuPMBpaZ5x6dnv3Tghux1I+hUaRyPBirG57d/EL58ttBRyFlOG/LrUUve2CJddNVxko0yfN08zDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:02.214573Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.0949","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51694e6d72f1bc8c0353dd80e4fdc45960a39bce4cda9ba7d75ff1154647a635","sha256:1f0765f1224154dd2083d141814f3f1b1788fcc0f2c4612957d5dac610976e1e"],"state_sha256":"eecb737b5334bdabe55715c39fca68cdc2cf144f5f5cbf4f66166d1b5433b993"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+ygcd1c/57jpMUPXaD9pei7FnAArWz9Xbe0zYRUC4GXuZwqf3EZn7Vtzwgq1u0SEp6xK2PQQCUkWX+DGSrefBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T07:28:58.048255Z","bundle_sha256":"08f6d62f6cd04638945d85306f6311d5298e5a49ef49769106d8ff433805d940"}}