{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:B37J3JBIDE3MM4DOZ7RSKGRZ72","short_pith_number":"pith:B37J3JBI","schema_version":"1.0","canonical_sha256":"0efe9da4281936c6706ecfe3251a39fe92ff9e89acee681caee83cdc16a23a2b","source":{"kind":"arxiv","id":"1502.04955","version":2},"attestation_state":"computed","paper":{"title":"Decompositions of edge-colored infinite complete graphs into monochromatic paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"D. T. Soukup, L. Soukup, M. Elekes, Z. Szentmikl\\'ossy","submitted_at":"2015-02-17T16:49:05Z","abstract_excerpt":"An $r$-edge coloring of a graph or hypergraph $G=(V,E)$ is a map $c:E\\to \\{0, \\dots, r-1\\}$. Extending results of Rado and answering questions of Rado, Gy\\'arf\\'as and S\\'ark\\\"ozy we prove that\n  (1.) the vertex set of every $r$-edge colored countably infinite complete $k$-uniform hypergraph can be partitioned into $r$ monochromatic tight paths with distinct colors (a tight path in a $k$-uniform hypergraph is a sequence of distinct vertices such that every set of $k$ consecutive vertices forms an edge),\n  (2.) for all natural numbers $r$ and $k$ there is a natural number $M$ such that the vert"},"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":"1502.04955","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-02-17T16:49:05Z","cross_cats_sorted":[],"title_canon_sha256":"59811ecf316df9e5ab1abae08558fd6322fff1b502278385ea95b699d56b8ee2","abstract_canon_sha256":"8106447abf42970f7dafa03c86ed5877fa7980c51cbb4cc7629d135a3e187875"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:18.994039Z","signature_b64":"c7FkdSnixkh13pHxs2z0KCG8h1kvZWdSZ3TrZR57tl0fPTlDnrJNog72atm+oNFbkMoQzFqmViEUbX3tep7mBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0efe9da4281936c6706ecfe3251a39fe92ff9e89acee681caee83cdc16a23a2b","last_reissued_at":"2026-05-18T01:23:18.993381Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:18.993381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Decompositions of edge-colored infinite complete graphs into monochromatic paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"D. T. Soukup, L. Soukup, M. Elekes, Z. Szentmikl\\'ossy","submitted_at":"2015-02-17T16:49:05Z","abstract_excerpt":"An $r$-edge coloring of a graph or hypergraph $G=(V,E)$ is a map $c:E\\to \\{0, \\dots, r-1\\}$. Extending results of Rado and answering questions of Rado, Gy\\'arf\\'as and S\\'ark\\\"ozy we prove that\n  (1.) the vertex set of every $r$-edge colored countably infinite complete $k$-uniform hypergraph can be partitioned into $r$ monochromatic tight paths with distinct colors (a tight path in a $k$-uniform hypergraph is a sequence of distinct vertices such that every set of $k$ consecutive vertices forms an edge),\n  (2.) for all natural numbers $r$ and $k$ there is a natural number $M$ such that the vert"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04955","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":""},"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":"1502.04955","created_at":"2026-05-18T01:23:18.993486+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.04955v2","created_at":"2026-05-18T01:23:18.993486+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04955","created_at":"2026-05-18T01:23:18.993486+00:00"},{"alias_kind":"pith_short_12","alias_value":"B37J3JBIDE3M","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"B37J3JBIDE3MM4DO","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"B37J3JBI","created_at":"2026-05-18T12:29:14.074870+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/B37J3JBIDE3MM4DOZ7RSKGRZ72","json":"https://pith.science/pith/B37J3JBIDE3MM4DOZ7RSKGRZ72.json","graph_json":"https://pith.science/api/pith-number/B37J3JBIDE3MM4DOZ7RSKGRZ72/graph.json","events_json":"https://pith.science/api/pith-number/B37J3JBIDE3MM4DOZ7RSKGRZ72/events.json","paper":"https://pith.science/paper/B37J3JBI"},"agent_actions":{"view_html":"https://pith.science/pith/B37J3JBIDE3MM4DOZ7RSKGRZ72","download_json":"https://pith.science/pith/B37J3JBIDE3MM4DOZ7RSKGRZ72.json","view_paper":"https://pith.science/paper/B37J3JBI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.04955&json=true","fetch_graph":"https://pith.science/api/pith-number/B37J3JBIDE3MM4DOZ7RSKGRZ72/graph.json","fetch_events":"https://pith.science/api/pith-number/B37J3JBIDE3MM4DOZ7RSKGRZ72/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B37J3JBIDE3MM4DOZ7RSKGRZ72/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B37J3JBIDE3MM4DOZ7RSKGRZ72/action/storage_attestation","attest_author":"https://pith.science/pith/B37J3JBIDE3MM4DOZ7RSKGRZ72/action/author_attestation","sign_citation":"https://pith.science/pith/B37J3JBIDE3MM4DOZ7RSKGRZ72/action/citation_signature","submit_replication":"https://pith.science/pith/B37J3JBIDE3MM4DOZ7RSKGRZ72/action/replication_record"}},"created_at":"2026-05-18T01:23:18.993486+00:00","updated_at":"2026-05-18T01:23:18.993486+00:00"}