{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WGOROANOF55AVX7646LFQVHQKS","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":"00ed82f592f48e3b2cc876e870c116f4095f4a092c68a46704c7f117b33cc919","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-04T15:43:26Z","title_canon_sha256":"1c91854db7b2047c1caffb7ac88789bfc30c0a2901a89de864fcf6c456f3e0db"},"schema_version":"1.0","source":{"id":"1312.1213","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1213","created_at":"2026-05-18T03:05:34Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1213v1","created_at":"2026-05-18T03:05:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1213","created_at":"2026-05-18T03:05:34Z"},{"alias_kind":"pith_short_12","alias_value":"WGOROANOF55A","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WGOROANOF55AVX76","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WGOROANO","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:c5541d1560eefab849c9d03dc7916721349bd4c716889e1cae09d5e7968b9489","target":"graph","created_at":"2026-05-18T03:05:34Z","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":"One of the most basic results in graph theory states that every graph with at least two vertices has two vertices with the same degree. Since there are graphs without $3$ vertices of the same degree, it is natural to ask if for any fixed $k$, every graph $G$ is ``close'' to a graph $G'$ with $k$ vertices of the same degree. Our main result in this paper is that this is indeed the case. Specifically, we show that for any positive integer $k$, there is a constant $C=C(k)$, so that given any graph $G$, one can remove from $G$ at most $C$ vertices and thus obtain a new graph $G'$ that contains at ","authors_text":"Asaf Shapira, Raphael Yuster, Yair Caro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-04T15:43:26Z","title":"Forcing $k$-repetitions in degree sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1213","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:b2bfcd98dab1a88de9bb9e077a3a5e23b2f9acd4e519e7f21b8c347df6688f9b","target":"record","created_at":"2026-05-18T03:05:34Z","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":"00ed82f592f48e3b2cc876e870c116f4095f4a092c68a46704c7f117b33cc919","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-04T15:43:26Z","title_canon_sha256":"1c91854db7b2047c1caffb7ac88789bfc30c0a2901a89de864fcf6c456f3e0db"},"schema_version":"1.0","source":{"id":"1312.1213","kind":"arxiv","version":1}},"canonical_sha256":"b19d1701ae2f7a0adffee7965854f054b7f845a2966d99df19c34abc154be761","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b19d1701ae2f7a0adffee7965854f054b7f845a2966d99df19c34abc154be761","first_computed_at":"2026-05-18T03:05:34.653838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:34.653838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aqKyLiTnTPgNd385/NaEo94n+PsmsimZe25kfaoSBDZaC0iD5p9QQrNUsEtYZyxlPmNn7OMdcgSrNy3Dkt5vDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:34.654499Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1213","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2bfcd98dab1a88de9bb9e077a3a5e23b2f9acd4e519e7f21b8c347df6688f9b","sha256:c5541d1560eefab849c9d03dc7916721349bd4c716889e1cae09d5e7968b9489"],"state_sha256":"31d501ef9e61adacd1cea465011feb36bf8431c364474ee8e72f4e1238449d01"}