{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:2FOFAQVHOL7PR5IWOKVXJ2ZBOM","short_pith_number":"pith:2FOFAQVH","schema_version":"1.0","canonical_sha256":"d15c5042a772fef8f51672ab74eb217300db33a15bd5bde505f6ebed3477488b","source":{"kind":"arxiv","id":"1910.13623","version":2},"attestation_state":"computed","paper":{"title":"Remarks on the distribution of colors in Gallai colorings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Joseph Feffer, Jun Yan, Yaoying Fu","submitted_at":"2019-10-30T02:07:12Z","abstract_excerpt":"A Gallai coloring of a complete graph $K_n$ is an edge coloring without triangles colored with three different colors. A sequence $e_1\\ge \\dots \\ge e_k$ of positive integers is an $(n,k)$-sequence if $\\sum_{i=1}^k e_i=\\binom{n}{2}$. An $(n,k)$-sequence is a G-sequence if there is a Gallai coloring of $K_n$ with $k$ colors such that there are $e_i$ edges of color $i$ for all $i,1\\le i \\le k$. Gy\\'arf\\'as, P\\'alv\\\"olgyi, Patk\\'os and Wales proved that for any integer $k\\ge 3$ there exists an integer $g(k)$ such that every $(n,k)$-sequence is a G-sequence if and only if $n\\ge g(k)$. They showed t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1910.13623","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-10-30T02:07:12Z","cross_cats_sorted":[],"title_canon_sha256":"fe1e0ec0ac542e82b66563ad87403724418cb567d0cf3395b2c935bdb89bfbc8","abstract_canon_sha256":"243f7404f4892ba416e20ee6b96d42fa35a4c41bb822959f8d233566116f961f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:29:01.358596Z","signature_b64":"kIVrGdnrjMrGRpA5D3BVBG/8iTLC41ly7cFg9BBKZZ7sGGIFZa/kKNnkVh2Fvw5flqIVFIqUvSQXHtdtuLhhCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d15c5042a772fef8f51672ab74eb217300db33a15bd5bde505f6ebed3477488b","last_reissued_at":"2026-07-05T01:29:01.358037Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:29:01.358037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Remarks on the distribution of colors in Gallai colorings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Joseph Feffer, Jun Yan, Yaoying Fu","submitted_at":"2019-10-30T02:07:12Z","abstract_excerpt":"A Gallai coloring of a complete graph $K_n$ is an edge coloring without triangles colored with three different colors. A sequence $e_1\\ge \\dots \\ge e_k$ of positive integers is an $(n,k)$-sequence if $\\sum_{i=1}^k e_i=\\binom{n}{2}$. An $(n,k)$-sequence is a G-sequence if there is a Gallai coloring of $K_n$ with $k$ colors such that there are $e_i$ edges of color $i$ for all $i,1\\le i \\le k$. Gy\\'arf\\'as, P\\'alv\\\"olgyi, Patk\\'os and Wales proved that for any integer $k\\ge 3$ there exists an integer $g(k)$ such that every $(n,k)$-sequence is a G-sequence if and only if $n\\ge g(k)$. They showed t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.13623","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1910.13623/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1910.13623","created_at":"2026-07-05T01:29:01.358100+00:00"},{"alias_kind":"arxiv_version","alias_value":"1910.13623v2","created_at":"2026-07-05T01:29:01.358100+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.13623","created_at":"2026-07-05T01:29:01.358100+00:00"},{"alias_kind":"pith_short_12","alias_value":"2FOFAQVHOL7P","created_at":"2026-07-05T01:29:01.358100+00:00"},{"alias_kind":"pith_short_16","alias_value":"2FOFAQVHOL7PR5IW","created_at":"2026-07-05T01:29:01.358100+00:00"},{"alias_kind":"pith_short_8","alias_value":"2FOFAQVH","created_at":"2026-07-05T01:29:01.358100+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2FOFAQVHOL7PR5IWOKVXJ2ZBOM","json":"https://pith.science/pith/2FOFAQVHOL7PR5IWOKVXJ2ZBOM.json","graph_json":"https://pith.science/api/pith-number/2FOFAQVHOL7PR5IWOKVXJ2ZBOM/graph.json","events_json":"https://pith.science/api/pith-number/2FOFAQVHOL7PR5IWOKVXJ2ZBOM/events.json","paper":"https://pith.science/paper/2FOFAQVH"},"agent_actions":{"view_html":"https://pith.science/pith/2FOFAQVHOL7PR5IWOKVXJ2ZBOM","download_json":"https://pith.science/pith/2FOFAQVHOL7PR5IWOKVXJ2ZBOM.json","view_paper":"https://pith.science/paper/2FOFAQVH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1910.13623&json=true","fetch_graph":"https://pith.science/api/pith-number/2FOFAQVHOL7PR5IWOKVXJ2ZBOM/graph.json","fetch_events":"https://pith.science/api/pith-number/2FOFAQVHOL7PR5IWOKVXJ2ZBOM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2FOFAQVHOL7PR5IWOKVXJ2ZBOM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2FOFAQVHOL7PR5IWOKVXJ2ZBOM/action/storage_attestation","attest_author":"https://pith.science/pith/2FOFAQVHOL7PR5IWOKVXJ2ZBOM/action/author_attestation","sign_citation":"https://pith.science/pith/2FOFAQVHOL7PR5IWOKVXJ2ZBOM/action/citation_signature","submit_replication":"https://pith.science/pith/2FOFAQVHOL7PR5IWOKVXJ2ZBOM/action/replication_record"}},"created_at":"2026-07-05T01:29:01.358100+00:00","updated_at":"2026-07-05T01:29:01.358100+00:00"}