{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:UNNQWMEK35MEBDFQBJFLFCOAXY","short_pith_number":"pith:UNNQWMEK","canonical_record":{"source":{"id":"0906.5216","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-06-29T08:04:49Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"b848f65816af67c86cb4afbcf3a1ef4658abef971f371a90b4a9c49f19a5c1f0","abstract_canon_sha256":"5974acebe7280e339ba3e804e8e88665e66b31ea1a9c10b0185647c11957407d"},"schema_version":"1.0"},"canonical_sha256":"a35b0b308adf58408cb00a4ab289c0be082438273a481190d03f9777c2527576","source":{"kind":"arxiv","id":"0906.5216","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.5216","created_at":"2026-05-18T02:13:12Z"},{"alias_kind":"arxiv_version","alias_value":"0906.5216v1","created_at":"2026-05-18T02:13:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.5216","created_at":"2026-05-18T02:13:12Z"},{"alias_kind":"pith_short_12","alias_value":"UNNQWMEK35ME","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"UNNQWMEK35MEBDFQ","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"UNNQWMEK","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:UNNQWMEK35MEBDFQBJFLFCOAXY","target":"record","payload":{"canonical_record":{"source":{"id":"0906.5216","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-06-29T08:04:49Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"b848f65816af67c86cb4afbcf3a1ef4658abef971f371a90b4a9c49f19a5c1f0","abstract_canon_sha256":"5974acebe7280e339ba3e804e8e88665e66b31ea1a9c10b0185647c11957407d"},"schema_version":"1.0"},"canonical_sha256":"a35b0b308adf58408cb00a4ab289c0be082438273a481190d03f9777c2527576","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:13:12.088654Z","signature_b64":"6yUR0U2+m6HRElUgDeLxaE3F543dp0fv8dHqZ/k59ScOeXY0WIZxjPUm4lU88Zl//UipUlrFTZ7ROCVc6HGJCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a35b0b308adf58408cb00a4ab289c0be082438273a481190d03f9777c2527576","last_reissued_at":"2026-05-18T02:13:12.088267Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:13:12.088267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0906.5216","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":"2026-05-18T02:13:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hf19oAC62M9P261A0u8+E10YJVqb9TZ3t4039jEZ5i8riwoeRvZelWEdiYB+YsI0BJvorwBviJXGeDGnIzABDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:56:40.144507Z"},"content_sha256":"204d3547957dc6d53255df678659ad4c1c20e851cdc0a658a53af9dc90c6fb93","schema_version":"1.0","event_id":"sha256:204d3547957dc6d53255df678659ad4c1c20e851cdc0a658a53af9dc90c6fb93"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:UNNQWMEK35MEBDFQBJFLFCOAXY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the existence of dimension zero divisors in algebraic function fields defined over F_q","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Christophe Ritzenthaler, Robert Rolland, Stephane Ballet","submitted_at":"2009-06-29T08:04:49Z","abstract_excerpt":"Let F/F_q be an algebraic function field of genus g defined over a finite field F_q. We obtain new results on the existence, the number and the density of dimension zero divisors of degree g-k in F where k is a positive integer. In particular, for q=2,3 we prove that there always exists a dimension zero divisor of degree \\gamma-1 where \\gamma is the q-rank of F. We also give a necessary and sufficient condition for the existence of a dimension zero divisor of degree g-k for a hyperelliptic field F in terms of its Zeta function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.5216","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":"2026-05-18T02:13:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7tvSUHKJW+AphIn72XJCGKS2PIRwuPb5jKQ43YQ/yiUXbJATZv1pHumN9Xut/idd0IRGs0x1jkQBGQIzpmNeCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:56:40.144852Z"},"content_sha256":"baf3b75ca41e406eb6bd42424ca786e4eff6e88afdaed7efbf433c9534b72c8a","schema_version":"1.0","event_id":"sha256:baf3b75ca41e406eb6bd42424ca786e4eff6e88afdaed7efbf433c9534b72c8a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UNNQWMEK35MEBDFQBJFLFCOAXY/bundle.json","state_url":"https://pith.science/pith/UNNQWMEK35MEBDFQBJFLFCOAXY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UNNQWMEK35MEBDFQBJFLFCOAXY/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":"2026-05-28T21:56:40Z","links":{"resolver":"https://pith.science/pith/UNNQWMEK35MEBDFQBJFLFCOAXY","bundle":"https://pith.science/pith/UNNQWMEK35MEBDFQBJFLFCOAXY/bundle.json","state":"https://pith.science/pith/UNNQWMEK35MEBDFQBJFLFCOAXY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UNNQWMEK35MEBDFQBJFLFCOAXY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:UNNQWMEK35MEBDFQBJFLFCOAXY","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":"5974acebe7280e339ba3e804e8e88665e66b31ea1a9c10b0185647c11957407d","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-06-29T08:04:49Z","title_canon_sha256":"b848f65816af67c86cb4afbcf3a1ef4658abef971f371a90b4a9c49f19a5c1f0"},"schema_version":"1.0","source":{"id":"0906.5216","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.5216","created_at":"2026-05-18T02:13:12Z"},{"alias_kind":"arxiv_version","alias_value":"0906.5216v1","created_at":"2026-05-18T02:13:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.5216","created_at":"2026-05-18T02:13:12Z"},{"alias_kind":"pith_short_12","alias_value":"UNNQWMEK35ME","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"UNNQWMEK35MEBDFQ","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"UNNQWMEK","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:baf3b75ca41e406eb6bd42424ca786e4eff6e88afdaed7efbf433c9534b72c8a","target":"graph","created_at":"2026-05-18T02:13:12Z","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":"Let F/F_q be an algebraic function field of genus g defined over a finite field F_q. We obtain new results on the existence, the number and the density of dimension zero divisors of degree g-k in F where k is a positive integer. In particular, for q=2,3 we prove that there always exists a dimension zero divisor of degree \\gamma-1 where \\gamma is the q-rank of F. We also give a necessary and sufficient condition for the existence of a dimension zero divisor of degree g-k for a hyperelliptic field F in terms of its Zeta function.","authors_text":"Christophe Ritzenthaler, Robert Rolland, Stephane Ballet","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-06-29T08:04:49Z","title":"On the existence of dimension zero divisors in algebraic function fields defined over F_q"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.5216","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":"sha256:204d3547957dc6d53255df678659ad4c1c20e851cdc0a658a53af9dc90c6fb93","target":"record","created_at":"2026-05-18T02:13:12Z","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":"5974acebe7280e339ba3e804e8e88665e66b31ea1a9c10b0185647c11957407d","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-06-29T08:04:49Z","title_canon_sha256":"b848f65816af67c86cb4afbcf3a1ef4658abef971f371a90b4a9c49f19a5c1f0"},"schema_version":"1.0","source":{"id":"0906.5216","kind":"arxiv","version":1}},"canonical_sha256":"a35b0b308adf58408cb00a4ab289c0be082438273a481190d03f9777c2527576","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a35b0b308adf58408cb00a4ab289c0be082438273a481190d03f9777c2527576","first_computed_at":"2026-05-18T02:13:12.088267Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:13:12.088267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6yUR0U2+m6HRElUgDeLxaE3F543dp0fv8dHqZ/k59ScOeXY0WIZxjPUm4lU88Zl//UipUlrFTZ7ROCVc6HGJCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:13:12.088654Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.5216","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:204d3547957dc6d53255df678659ad4c1c20e851cdc0a658a53af9dc90c6fb93","sha256:baf3b75ca41e406eb6bd42424ca786e4eff6e88afdaed7efbf433c9534b72c8a"],"state_sha256":"fb877037e72bf39e3811e83436c3ff7933b3968839fdbedfa02c3dec04d1ffed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gxauusjI1Xj7Bj4uQhIv79iEa0mFUKLc4Eph6bVyjKNwYOZJkcMeIs1NyMeR0Grew6DVRFKS3xlLLvRxFeDoBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T21:56:40.147151Z","bundle_sha256":"122d09e94596da2eb824055be69fa61db75445a560bf5d36dd0b9b5d1b50907e"}}