{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:QCHPWLYICNVVAJJHBGYIYS4ZO2","short_pith_number":"pith:QCHPWLYI","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"},"canonical_sha256":"808efb2f08136b50252709b08c4b997692286f15c0fc0b1216f782269a267eff","source":{"kind":"arxiv","id":"1711.09031","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.09031","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"arxiv_version","alias_value":"1711.09031v1","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.09031","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"pith_short_12","alias_value":"QCHPWLYICNVV","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"QCHPWLYICNVVAJJH","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"QCHPWLYI","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:QCHPWLYICNVVAJJHBGYIYS4ZO2","target":"record","payload":{"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"},"canonical_sha256":"808efb2f08136b50252709b08c4b997692286f15c0fc0b1216f782269a267eff","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"},"source_kind":"arxiv","source_id":"1711.09031","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:56:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"juQsSuPZC9f2/HocllbOF64k5IwdmpizgAF7e1SAHeQhtr8L5FI51EduoPrbiHZD3U+ZOJHYVjH7IMVvbrZ1Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:44:09.944934Z"},"content_sha256":"88037274fc8cae8bcead1f4914dccf0e1d8f9b291210bf2aee1ee8aab48ba351","schema_version":"1.0","event_id":"sha256:88037274fc8cae8bcead1f4914dccf0e1d8f9b291210bf2aee1ee8aab48ba351"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:QCHPWLYICNVVAJJHBGYIYS4ZO2","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:56:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yhja0Cyyw0ShjUSo6ap7lSaBB6jeiuJ267U9zybRYzXjkUQzDAU5c/j2Ih/Kr1Bp8+/wSo5LxB5J5AiX5hhlDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:44:09.945637Z"},"content_sha256":"05e538fcc0333e1905676fbc9a47d2b56d9adc5870a40fd8b7dbd8ccd21653fc","schema_version":"1.0","event_id":"sha256:05e538fcc0333e1905676fbc9a47d2b56d9adc5870a40fd8b7dbd8ccd21653fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QCHPWLYICNVVAJJHBGYIYS4ZO2/bundle.json","state_url":"https://pith.science/pith/QCHPWLYICNVVAJJHBGYIYS4ZO2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QCHPWLYICNVVAJJHBGYIYS4ZO2/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T01:44:09Z","links":{"resolver":"https://pith.science/pith/QCHPWLYICNVVAJJHBGYIYS4ZO2","bundle":"https://pith.science/pith/QCHPWLYICNVVAJJHBGYIYS4ZO2/bundle.json","state":"https://pith.science/pith/QCHPWLYICNVVAJJHBGYIYS4ZO2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QCHPWLYICNVVAJJHBGYIYS4ZO2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QCHPWLYICNVVAJJHBGYIYS4ZO2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3558f989e7cb2f45e2a526cd021be7ec376a04a468baed26e2e2d1e8b9ff45d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-24T16:05:10Z","title_canon_sha256":"60007bcd2a3468908e67b862afe30063647a362374e2b8af85e43d0af8fc4e11"},"schema_version":"1.0","source":{"id":"1711.09031","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.09031","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"arxiv_version","alias_value":"1711.09031v1","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.09031","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"pith_short_12","alias_value":"QCHPWLYICNVV","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"QCHPWLYICNVVAJJH","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"QCHPWLYI","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:05e538fcc0333e1905676fbc9a47d2b56d9adc5870a40fd8b7dbd8ccd21653fc","target":"graph","created_at":"2026-05-17T23:56:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Adri\\'an V\\'azquez-\\'Avila, Christian Rubio-Montiel, Gabriela Araujo-Pardo, Gy\\\"orgy Kiss","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-24T16:05:10Z","title":"On chromatic indices of finite affine spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09031","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:88037274fc8cae8bcead1f4914dccf0e1d8f9b291210bf2aee1ee8aab48ba351","target":"record","created_at":"2026-05-17T23:56:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3558f989e7cb2f45e2a526cd021be7ec376a04a468baed26e2e2d1e8b9ff45d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-24T16:05:10Z","title_canon_sha256":"60007bcd2a3468908e67b862afe30063647a362374e2b8af85e43d0af8fc4e11"},"schema_version":"1.0","source":{"id":"1711.09031","kind":"arxiv","version":1}},"canonical_sha256":"808efb2f08136b50252709b08c4b997692286f15c0fc0b1216f782269a267eff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"808efb2f08136b50252709b08c4b997692286f15c0fc0b1216f782269a267eff","first_computed_at":"2026-05-17T23:56:30.137630Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:30.137630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hIHXZdRBidb2dhJBetejATScNtknujWPAud+wyUyqcdQVUCHOnh4kqtyQjJGaF4J3Imj+SmuTTdqFUIOMIeWCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:30.137986Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.09031","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88037274fc8cae8bcead1f4914dccf0e1d8f9b291210bf2aee1ee8aab48ba351","sha256:05e538fcc0333e1905676fbc9a47d2b56d9adc5870a40fd8b7dbd8ccd21653fc"],"state_sha256":"9001ba78ee8165f751af0656094ce6269cff2df48fa3fd2a2ed2d6404aa2a26c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rmWj2mLp4qEJOLaXzBXouaYGYII2bb4m/AYHuiWdLBydoaGTcH9nZ6/cRhUbyfMjoEEkBMbjoyTgkWa33/txAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T01:44:09.949671Z","bundle_sha256":"1152f26526491a5a2e96cc366d2e49eda55c8a12549756a00dbdbcd4d67e246e"}}