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Moreover, we prove that the achromatic index of $\\mathrm{AG}(n,q)$ is $q^{1.5n-1}$ for even $n,$ and we provi"},"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":"1711.09031","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-24T16:05:10Z","cross_cats_sorted":[],"title_canon_sha256":"60007bcd2a3468908e67b862afe30063647a362374e2b8af85e43d0af8fc4e11","abstract_canon_sha256":"3558f989e7cb2f45e2a526cd021be7ec376a04a468baed26e2e2d1e8b9ff45d7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:30.137986Z","signature_b64":"hIHXZdRBidb2dhJBetejATScNtknujWPAud+wyUyqcdQVUCHOnh4kqtyQjJGaF4J3Imj+SmuTTdqFUIOMIeWCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"808efb2f08136b50252709b08c4b997692286f15c0fc0b1216f782269a267eff","last_reissued_at":"2026-05-17T23:56:30.137630Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:30.137630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On chromatic indices of finite affine spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Adri\\'an V\\'azquez-\\'Avila, Christian Rubio-Montiel, Gabriela Araujo-Pardo, Gy\\\"orgy Kiss","submitted_at":"2017-11-24T16:05:10Z","abstract_excerpt":"The pseudoachromatic index of the finite affine space $\\mathrm{AG}(n,q),$ denoted by $\\psi'(\\mathrm{AG}(n,q)),$ is the the maximum number of colors in any complete line-coloring of $\\mathrm{AG}(n,q).$ When the coloring is also proper, the maximum number of colors is called the achromatic index of $\\mathrm{AG}(n,q).$ We prove that if $n$ is even then $\\psi'(\\mathrm{AG}(n,q))\\sim q^{1.5n-1}$; while when $n$ is odd the value is bounded by $q^{1.5(n-1)}<\\psi'(\\mathrm{AG}(n,q))<q^{1.5n-1}$. Moreover, we prove that the achromatic index of $\\mathrm{AG}(n,q)$ is $q^{1.5n-1}$ for even $n,$ and we provi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09031","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":"1711.09031","created_at":"2026-05-17T23:56:30.137688+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.09031v1","created_at":"2026-05-17T23:56:30.137688+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.09031","created_at":"2026-05-17T23:56:30.137688+00:00"},{"alias_kind":"pith_short_12","alias_value":"QCHPWLYICNVV","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"QCHPWLYICNVVAJJH","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"QCHPWLYI","created_at":"2026-05-18T12:31:37.085036+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/QCHPWLYICNVVAJJHBGYIYS4ZO2","json":"https://pith.science/pith/QCHPWLYICNVVAJJHBGYIYS4ZO2.json","graph_json":"https://pith.science/api/pith-number/QCHPWLYICNVVAJJHBGYIYS4ZO2/graph.json","events_json":"https://pith.science/api/pith-number/QCHPWLYICNVVAJJHBGYIYS4ZO2/events.json","paper":"https://pith.science/paper/QCHPWLYI"},"agent_actions":{"view_html":"https://pith.science/pith/QCHPWLYICNVVAJJHBGYIYS4ZO2","download_json":"https://pith.science/pith/QCHPWLYICNVVAJJHBGYIYS4ZO2.json","view_paper":"https://pith.science/paper/QCHPWLYI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.09031&json=true","fetch_graph":"https://pith.science/api/pith-number/QCHPWLYICNVVAJJHBGYIYS4ZO2/graph.json","fetch_events":"https://pith.science/api/pith-number/QCHPWLYICNVVAJJHBGYIYS4ZO2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QCHPWLYICNVVAJJHBGYIYS4ZO2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QCHPWLYICNVVAJJHBGYIYS4ZO2/action/storage_attestation","attest_author":"https://pith.science/pith/QCHPWLYICNVVAJJHBGYIYS4ZO2/action/author_attestation","sign_citation":"https://pith.science/pith/QCHPWLYICNVVAJJHBGYIYS4ZO2/action/citation_signature","submit_replication":"https://pith.science/pith/QCHPWLYICNVVAJJHBGYIYS4ZO2/action/replication_record"}},"created_at":"2026-05-17T23:56:30.137688+00:00","updated_at":"2026-05-17T23:56:30.137688+00:00"}