{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:LTYZQH7DOYN4I2IEP6O3FAHEFQ","short_pith_number":"pith:LTYZQH7D","schema_version":"1.0","canonical_sha256":"5cf1981fe3761bc469047f9db280e42c28ad8ec4eb757218017e91f082eeb842","source":{"kind":"arxiv","id":"1510.06932","version":1},"attestation_state":"computed","paper":{"title":"A Note on Altermatic Number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hossein Hajiabolhassan, Meysam Alishahi","submitted_at":"2015-10-23T13:46:53Z","abstract_excerpt":"In view of Tucker's lemma (an equivalent combinatorial version of the Borsuk- Ulam theorem), the present authors (2013) introduced the kth altermatic number of a graph G as a tight lower bound for the chromatic number of G. In this note, we present a purely combinatorial proof for this result."},"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":"1510.06932","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-23T13:46:53Z","cross_cats_sorted":[],"title_canon_sha256":"c53fccf5d096b5aa81451ffc354f09b70ee29f1836e32b6a084c3a9e1c23b97d","abstract_canon_sha256":"2ee5f9b16855d48cff3bf39347e32ef7c2eb55a90cea755315fa11fa5b637ba3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:22.683037Z","signature_b64":"gy1/ki7ueOPT4VJprE9kXAhakeRrxyoKQq9suTFevFV69RiVd5MjImBDpyhjULc/71MqBRqShK1yZYqIXPoNBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cf1981fe3761bc469047f9db280e42c28ad8ec4eb757218017e91f082eeb842","last_reissued_at":"2026-05-18T01:29:22.682342Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:22.682342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Note on Altermatic Number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hossein Hajiabolhassan, Meysam Alishahi","submitted_at":"2015-10-23T13:46:53Z","abstract_excerpt":"In view of Tucker's lemma (an equivalent combinatorial version of the Borsuk- Ulam theorem), the present authors (2013) introduced the kth altermatic number of a graph G as a tight lower bound for the chromatic number of G. In this note, we present a purely combinatorial proof for this result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06932","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":"1510.06932","created_at":"2026-05-18T01:29:22.682464+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.06932v1","created_at":"2026-05-18T01:29:22.682464+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.06932","created_at":"2026-05-18T01:29:22.682464+00:00"},{"alias_kind":"pith_short_12","alias_value":"LTYZQH7DOYN4","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"LTYZQH7DOYN4I2IE","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"LTYZQH7D","created_at":"2026-05-18T12:29:29.992203+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/LTYZQH7DOYN4I2IEP6O3FAHEFQ","json":"https://pith.science/pith/LTYZQH7DOYN4I2IEP6O3FAHEFQ.json","graph_json":"https://pith.science/api/pith-number/LTYZQH7DOYN4I2IEP6O3FAHEFQ/graph.json","events_json":"https://pith.science/api/pith-number/LTYZQH7DOYN4I2IEP6O3FAHEFQ/events.json","paper":"https://pith.science/paper/LTYZQH7D"},"agent_actions":{"view_html":"https://pith.science/pith/LTYZQH7DOYN4I2IEP6O3FAHEFQ","download_json":"https://pith.science/pith/LTYZQH7DOYN4I2IEP6O3FAHEFQ.json","view_paper":"https://pith.science/paper/LTYZQH7D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.06932&json=true","fetch_graph":"https://pith.science/api/pith-number/LTYZQH7DOYN4I2IEP6O3FAHEFQ/graph.json","fetch_events":"https://pith.science/api/pith-number/LTYZQH7DOYN4I2IEP6O3FAHEFQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LTYZQH7DOYN4I2IEP6O3FAHEFQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LTYZQH7DOYN4I2IEP6O3FAHEFQ/action/storage_attestation","attest_author":"https://pith.science/pith/LTYZQH7DOYN4I2IEP6O3FAHEFQ/action/author_attestation","sign_citation":"https://pith.science/pith/LTYZQH7DOYN4I2IEP6O3FAHEFQ/action/citation_signature","submit_replication":"https://pith.science/pith/LTYZQH7DOYN4I2IEP6O3FAHEFQ/action/replication_record"}},"created_at":"2026-05-18T01:29:22.682464+00:00","updated_at":"2026-05-18T01:29:22.682464+00:00"}