{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2646LBHKWBEOB7Q7IG3VIQUQE7","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":"6c0026e3c600a6a6fdc255d2fd23f68021716d63518997e5d90e3ecc2edac1f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-23T20:05:31Z","title_canon_sha256":"bc85ad42ee5468187e2ca90bf72f1c8c5fa3628fb72263af171a1956a283d952"},"schema_version":"1.0","source":{"id":"1710.08486","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.08486","created_at":"2026-05-17T23:49:44Z"},{"alias_kind":"arxiv_version","alias_value":"1710.08486v4","created_at":"2026-05-17T23:49:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.08486","created_at":"2026-05-17T23:49:44Z"},{"alias_kind":"pith_short_12","alias_value":"2646LBHKWBEO","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2646LBHKWBEOB7Q7","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2646LBHK","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:eaaf1fe2a00ec840e4798a05b168b44c72b8bca2b32ae4bf965e3d949d1c6d1a","target":"graph","created_at":"2026-05-17T23:49:44Z","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 prove the following 30-year old conjecture of Gy\\H{o}ri and Tuza: the edges of every $n$-vertex graph $G$ can be decomposed into complete graphs $C_1,\\ldots,C_\\ell$ of orders two and three such that $|C_1|+\\cdots+|C_\\ell|\\le (1/2+o(1))n^2$. This result implies the asymptotic version of the old result of Erd\\H{o}s, Goodman and P\\'osa that asserts the existence of such a decomposition with $\\ell\\le n^2/4$.","authors_text":"Bernard Lidick\\'y, Daniel Kr\\'al', Ta\\'isa L. Martins, Yanitsa Pehova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-23T20:05:31Z","title":"Decomposing graphs into edges and triangles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08486","kind":"arxiv","version":4},"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:bcddae0584188df1dd5529db828dc6aed873f1362e9535f451b1a567c76466b9","target":"record","created_at":"2026-05-17T23:49:44Z","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":"6c0026e3c600a6a6fdc255d2fd23f68021716d63518997e5d90e3ecc2edac1f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-23T20:05:31Z","title_canon_sha256":"bc85ad42ee5468187e2ca90bf72f1c8c5fa3628fb72263af171a1956a283d952"},"schema_version":"1.0","source":{"id":"1710.08486","kind":"arxiv","version":4}},"canonical_sha256":"d7b9e584eab048e0fe1f41b754429027d15ee010cfe9c13013986881707b7fcc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7b9e584eab048e0fe1f41b754429027d15ee010cfe9c13013986881707b7fcc","first_computed_at":"2026-05-17T23:49:44.223123Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:44.223123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rejzxSAMjggQImeJk+O0FDbjYYzUuUdLwdKAhKpEq4Q75W89wmv8fKkMirEd35/k0qwVZk7I2Bz7XS39hVhLDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:44.223716Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.08486","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bcddae0584188df1dd5529db828dc6aed873f1362e9535f451b1a567c76466b9","sha256:eaaf1fe2a00ec840e4798a05b168b44c72b8bca2b32ae4bf965e3d949d1c6d1a"],"state_sha256":"6fa5388bb0f0498b6bb1f88b4a9148088072570d0e4f9a0757d4bd64cd210468"}