{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:QTJY5OUHSNIZ7EI24RBGX6GXTC","short_pith_number":"pith:QTJY5OUH","schema_version":"1.0","canonical_sha256":"84d38eba8793519f911ae4426bf8d7989f8cb625d8cb44ba3f382f8e6aa4b048","source":{"kind":"arxiv","id":"1710.05290","version":2},"attestation_state":"computed","paper":{"title":"Z2-indices and Hedetniemi's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"Takahiro Matsushita","submitted_at":"2017-10-15T06:59:55Z","abstract_excerpt":"The $\\mathbb{Z}_2$-index ${\\rm ind}(X)$ of a $\\mathbb{Z}_2$-CW-complex $X$ is the smallest number $n$ such that there is a $\\mathbb{Z}_2$-map from $X$ to $S^n$. Here we consider $S^n$ as a $\\mathbb{Z}_2$-space by the antipodal map. Hedetniemi's conjecture is a long standing conjecture in graph theory concerning the graph coloring problem of tensor products of finite graphs. We show that if Hedetniemi's conjecture is true, then ${\\rm ind}(X \\times Y) = \\min \\{ {\\rm ind}(X) , {\\rm ind}(Y)\\}$ for every pair $X$ and $Y$ of finite $\\mathbb{Z}_2$-complexes."},"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":"1710.05290","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-10-15T06:59:55Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"1b51fbdf32501399a6a3c891432dc4043a9d34b09b42840b2669b79a46f2c956","abstract_canon_sha256":"672579944ccfb92909bd62104721422c8e79e05dba9cfa3dc2c0667176e0858f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:53.130710Z","signature_b64":"STinZHWzhEE+JLxnnqo+rf8M2tTJjk/82Dzr8o7ruPZeUjMhbj4aYwJCGXtYVu6q8e6Vy52B2yOv7DKOqaSpDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84d38eba8793519f911ae4426bf8d7989f8cb625d8cb44ba3f382f8e6aa4b048","last_reissued_at":"2026-05-17T23:49:53.130279Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:53.130279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Z2-indices and Hedetniemi's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"Takahiro Matsushita","submitted_at":"2017-10-15T06:59:55Z","abstract_excerpt":"The $\\mathbb{Z}_2$-index ${\\rm ind}(X)$ of a $\\mathbb{Z}_2$-CW-complex $X$ is the smallest number $n$ such that there is a $\\mathbb{Z}_2$-map from $X$ to $S^n$. Here we consider $S^n$ as a $\\mathbb{Z}_2$-space by the antipodal map. Hedetniemi's conjecture is a long standing conjecture in graph theory concerning the graph coloring problem of tensor products of finite graphs. We show that if Hedetniemi's conjecture is true, then ${\\rm ind}(X \\times Y) = \\min \\{ {\\rm ind}(X) , {\\rm ind}(Y)\\}$ for every pair $X$ and $Y$ of finite $\\mathbb{Z}_2$-complexes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05290","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":"1710.05290","created_at":"2026-05-17T23:49:53.130357+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.05290v2","created_at":"2026-05-17T23:49:53.130357+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05290","created_at":"2026-05-17T23:49:53.130357+00:00"},{"alias_kind":"pith_short_12","alias_value":"QTJY5OUHSNIZ","created_at":"2026-05-18T12:31:39.905425+00:00"},{"alias_kind":"pith_short_16","alias_value":"QTJY5OUHSNIZ7EI2","created_at":"2026-05-18T12:31:39.905425+00:00"},{"alias_kind":"pith_short_8","alias_value":"QTJY5OUH","created_at":"2026-05-18T12:31:39.905425+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/QTJY5OUHSNIZ7EI24RBGX6GXTC","json":"https://pith.science/pith/QTJY5OUHSNIZ7EI24RBGX6GXTC.json","graph_json":"https://pith.science/api/pith-number/QTJY5OUHSNIZ7EI24RBGX6GXTC/graph.json","events_json":"https://pith.science/api/pith-number/QTJY5OUHSNIZ7EI24RBGX6GXTC/events.json","paper":"https://pith.science/paper/QTJY5OUH"},"agent_actions":{"view_html":"https://pith.science/pith/QTJY5OUHSNIZ7EI24RBGX6GXTC","download_json":"https://pith.science/pith/QTJY5OUHSNIZ7EI24RBGX6GXTC.json","view_paper":"https://pith.science/paper/QTJY5OUH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.05290&json=true","fetch_graph":"https://pith.science/api/pith-number/QTJY5OUHSNIZ7EI24RBGX6GXTC/graph.json","fetch_events":"https://pith.science/api/pith-number/QTJY5OUHSNIZ7EI24RBGX6GXTC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QTJY5OUHSNIZ7EI24RBGX6GXTC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QTJY5OUHSNIZ7EI24RBGX6GXTC/action/storage_attestation","attest_author":"https://pith.science/pith/QTJY5OUHSNIZ7EI24RBGX6GXTC/action/author_attestation","sign_citation":"https://pith.science/pith/QTJY5OUHSNIZ7EI24RBGX6GXTC/action/citation_signature","submit_replication":"https://pith.science/pith/QTJY5OUHSNIZ7EI24RBGX6GXTC/action/replication_record"}},"created_at":"2026-05-17T23:49:53.130357+00:00","updated_at":"2026-05-17T23:49:53.130357+00:00"}