{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:XH2GEZ3YQMJHKQG5UYSS7LF35V","short_pith_number":"pith:XH2GEZ3Y","schema_version":"1.0","canonical_sha256":"b9f462677883127540dda6252facbbed4b17cfd405454a466b9139eee080ecda","source":{"kind":"arxiv","id":"1607.01605","version":1},"attestation_state":"computed","paper":{"title":"The chromatic number of the square of the 8-cube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Janne I. Kokkala, Patric R. J. \\\"Osterg{\\aa}rd","submitted_at":"2016-07-06T13:11:13Z","abstract_excerpt":"A cube-like graph is a Cayley graph for the elementary abelian group of order $2^n$. In studies of the chromatic number of cube-like graphs, the $k$th power of the $n$-dimensional hypercube, $Q_n^k$, is frequently considered. This coloring problem can be considered in the framework of coding theory, as the graph $Q_n^k$ can be constructed with one vertex for each binary word of length $n$ and edges between vertices exactly when the Hamming distance between the corresponding words is at most $k$. Consequently, a proper coloring of $Q_n^k$ corresponds to a partition of the $n$-dimensional binary"},"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":"1607.01605","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-07-06T13:11:13Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"3d76975d31536f39cd758c398de30b594000aa4e4f98f5e5e628e02dd0c05a01","abstract_canon_sha256":"e20f1bb1625255b9cd87cf80aa60eac1e5c2e3fa55e56a3af82ca93ce2dc562c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:25.835404Z","signature_b64":"CsBlTlOKMPzUlXsfKKWaoP1eiM9H3qRaBI52B7EITB4Dk5URnrzC4lkerowaxjLKKxxGuHcAWhVR3AaD/oykAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9f462677883127540dda6252facbbed4b17cfd405454a466b9139eee080ecda","last_reissued_at":"2026-05-18T01:11:25.834943Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:25.834943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The chromatic number of the square of the 8-cube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Janne I. Kokkala, Patric R. J. \\\"Osterg{\\aa}rd","submitted_at":"2016-07-06T13:11:13Z","abstract_excerpt":"A cube-like graph is a Cayley graph for the elementary abelian group of order $2^n$. In studies of the chromatic number of cube-like graphs, the $k$th power of the $n$-dimensional hypercube, $Q_n^k$, is frequently considered. This coloring problem can be considered in the framework of coding theory, as the graph $Q_n^k$ can be constructed with one vertex for each binary word of length $n$ and edges between vertices exactly when the Hamming distance between the corresponding words is at most $k$. Consequently, a proper coloring of $Q_n^k$ corresponds to a partition of the $n$-dimensional binary"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01605","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1607.01605","created_at":"2026-05-18T01:11:25.835028+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.01605v1","created_at":"2026-05-18T01:11:25.835028+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01605","created_at":"2026-05-18T01:11:25.835028+00:00"},{"alias_kind":"pith_short_12","alias_value":"XH2GEZ3YQMJH","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"XH2GEZ3YQMJHKQG5","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"XH2GEZ3Y","created_at":"2026-05-18T12:30:51.357362+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/XH2GEZ3YQMJHKQG5UYSS7LF35V","json":"https://pith.science/pith/XH2GEZ3YQMJHKQG5UYSS7LF35V.json","graph_json":"https://pith.science/api/pith-number/XH2GEZ3YQMJHKQG5UYSS7LF35V/graph.json","events_json":"https://pith.science/api/pith-number/XH2GEZ3YQMJHKQG5UYSS7LF35V/events.json","paper":"https://pith.science/paper/XH2GEZ3Y"},"agent_actions":{"view_html":"https://pith.science/pith/XH2GEZ3YQMJHKQG5UYSS7LF35V","download_json":"https://pith.science/pith/XH2GEZ3YQMJHKQG5UYSS7LF35V.json","view_paper":"https://pith.science/paper/XH2GEZ3Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.01605&json=true","fetch_graph":"https://pith.science/api/pith-number/XH2GEZ3YQMJHKQG5UYSS7LF35V/graph.json","fetch_events":"https://pith.science/api/pith-number/XH2GEZ3YQMJHKQG5UYSS7LF35V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XH2GEZ3YQMJHKQG5UYSS7LF35V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XH2GEZ3YQMJHKQG5UYSS7LF35V/action/storage_attestation","attest_author":"https://pith.science/pith/XH2GEZ3YQMJHKQG5UYSS7LF35V/action/author_attestation","sign_citation":"https://pith.science/pith/XH2GEZ3YQMJHKQG5UYSS7LF35V/action/citation_signature","submit_replication":"https://pith.science/pith/XH2GEZ3YQMJHKQG5UYSS7LF35V/action/replication_record"}},"created_at":"2026-05-18T01:11:25.835028+00:00","updated_at":"2026-05-18T01:11:25.835028+00:00"}