{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:2RZMEFYTUQ46JKEJJWMOZLLRVX","short_pith_number":"pith:2RZMEFYT","canonical_record":{"source":{"id":"0801.3423","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2008-01-22T17:27:12Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"3c3e231971c0d59c0d5916d82363218af1d1752abf1ed7501d20df4749518494","abstract_canon_sha256":"6139de0d88008abc9434ad96ff10bf4a4ec1ec27480c87fb8f17d7a224552811"},"schema_version":"1.0"},"canonical_sha256":"d472c21713a439e4a8894d98ecad71add819a84507c405d28cf86f04cbb66656","source":{"kind":"arxiv","id":"0801.3423","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.3423","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"arxiv_version","alias_value":"0801.3423v1","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.3423","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"pith_short_12","alias_value":"2RZMEFYTUQ46","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"2RZMEFYTUQ46JKEJ","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"2RZMEFYT","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:2RZMEFYTUQ46JKEJJWMOZLLRVX","target":"record","payload":{"canonical_record":{"source":{"id":"0801.3423","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2008-01-22T17:27:12Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"3c3e231971c0d59c0d5916d82363218af1d1752abf1ed7501d20df4749518494","abstract_canon_sha256":"6139de0d88008abc9434ad96ff10bf4a4ec1ec27480c87fb8f17d7a224552811"},"schema_version":"1.0"},"canonical_sha256":"d472c21713a439e4a8894d98ecad71add819a84507c405d28cf86f04cbb66656","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:11.888358Z","signature_b64":"O1L2PLad/U/fLk0e7Nuv1sckMDvuKDG/+lZJnu1KgToX+l7eWMJSxcHK48cyKaYPsKgu3KswE45o+IrzkhcODQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d472c21713a439e4a8894d98ecad71add819a84507c405d28cf86f04cbb66656","last_reissued_at":"2026-05-18T02:58:11.887750Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:11.887750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0801.3423","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":"2026-05-18T02:58:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8aljRUCdxZ2L5IiUb+sYorjCOn3lD8DLQiJUEgyW1RjNCYj5johpW+cjW6beZEhSyFR4GQwc0a4vlFlDEkDDBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:43:34.975271Z"},"content_sha256":"1f2455c7fc3562bd7dc4f0fc6c1d9532fa953cfbb716cd40826f9706f3a42f9b","schema_version":"1.0","event_id":"sha256:1f2455c7fc3562bd7dc4f0fc6c1d9532fa953cfbb716cd40826f9706f3a42f9b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:2RZMEFYTUQ46JKEJJWMOZLLRVX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Automorphism groups of algebraic curves with p-rank zero","license":"","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"Gabor Korchmaros, Massimo Giulietti","submitted_at":"2008-01-22T17:27:12Z","abstract_excerpt":"In positive characteristic, algebraic curves can have many more automorphisms than expected from the classical Hurwitz's bound. There even exist algebraic curves of arbitrary high genus g with more than 16g^4 automorphisms. It has been observed on many occasions that the most anomalous examples invariably have zero p-rank. In this paper, the K-automorphism group Aut(X) of a zero 2-rank algebraic curve X defined over an algebraically closed field K of characteristic 2 is investigated. The main result is that if the curve has genus g greater than or equal to 2, and |Aut(X)|>24g^2, then Aut(X) ha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.3423","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":"2026-05-18T02:58:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VzhF2U4AQO4Sp8W0+sQ2K/v4T3tTZpiON6RnoDpQeCNtz8bBqj2yYcZ55gQFruLnYkc2p8As54ifZzX5a5E5Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:43:34.975905Z"},"content_sha256":"654adc1a0f380ce8df59958c2cf98421fa0607bad0ad2b220cff8ec8e56d7e8a","schema_version":"1.0","event_id":"sha256:654adc1a0f380ce8df59958c2cf98421fa0607bad0ad2b220cff8ec8e56d7e8a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2RZMEFYTUQ46JKEJJWMOZLLRVX/bundle.json","state_url":"https://pith.science/pith/2RZMEFYTUQ46JKEJJWMOZLLRVX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2RZMEFYTUQ46JKEJJWMOZLLRVX/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":"2026-05-31T07:43:34Z","links":{"resolver":"https://pith.science/pith/2RZMEFYTUQ46JKEJJWMOZLLRVX","bundle":"https://pith.science/pith/2RZMEFYTUQ46JKEJJWMOZLLRVX/bundle.json","state":"https://pith.science/pith/2RZMEFYTUQ46JKEJJWMOZLLRVX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2RZMEFYTUQ46JKEJJWMOZLLRVX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:2RZMEFYTUQ46JKEJJWMOZLLRVX","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":"6139de0d88008abc9434ad96ff10bf4a4ec1ec27480c87fb8f17d7a224552811","cross_cats_sorted":["math.GR"],"license":"","primary_cat":"math.AG","submitted_at":"2008-01-22T17:27:12Z","title_canon_sha256":"3c3e231971c0d59c0d5916d82363218af1d1752abf1ed7501d20df4749518494"},"schema_version":"1.0","source":{"id":"0801.3423","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.3423","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"arxiv_version","alias_value":"0801.3423v1","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.3423","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"pith_short_12","alias_value":"2RZMEFYTUQ46","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"2RZMEFYTUQ46JKEJ","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"2RZMEFYT","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:654adc1a0f380ce8df59958c2cf98421fa0607bad0ad2b220cff8ec8e56d7e8a","target":"graph","created_at":"2026-05-18T02:58:11Z","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":"In positive characteristic, algebraic curves can have many more automorphisms than expected from the classical Hurwitz's bound. There even exist algebraic curves of arbitrary high genus g with more than 16g^4 automorphisms. It has been observed on many occasions that the most anomalous examples invariably have zero p-rank. In this paper, the K-automorphism group Aut(X) of a zero 2-rank algebraic curve X defined over an algebraically closed field K of characteristic 2 is investigated. The main result is that if the curve has genus g greater than or equal to 2, and |Aut(X)|>24g^2, then Aut(X) ha","authors_text":"Gabor Korchmaros, Massimo Giulietti","cross_cats":["math.GR"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2008-01-22T17:27:12Z","title":"Automorphism groups of algebraic curves with p-rank zero"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.3423","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":"sha256:1f2455c7fc3562bd7dc4f0fc6c1d9532fa953cfbb716cd40826f9706f3a42f9b","target":"record","created_at":"2026-05-18T02:58:11Z","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":"6139de0d88008abc9434ad96ff10bf4a4ec1ec27480c87fb8f17d7a224552811","cross_cats_sorted":["math.GR"],"license":"","primary_cat":"math.AG","submitted_at":"2008-01-22T17:27:12Z","title_canon_sha256":"3c3e231971c0d59c0d5916d82363218af1d1752abf1ed7501d20df4749518494"},"schema_version":"1.0","source":{"id":"0801.3423","kind":"arxiv","version":1}},"canonical_sha256":"d472c21713a439e4a8894d98ecad71add819a84507c405d28cf86f04cbb66656","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d472c21713a439e4a8894d98ecad71add819a84507c405d28cf86f04cbb66656","first_computed_at":"2026-05-18T02:58:11.887750Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:11.887750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O1L2PLad/U/fLk0e7Nuv1sckMDvuKDG/+lZJnu1KgToX+l7eWMJSxcHK48cyKaYPsKgu3KswE45o+IrzkhcODQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:11.888358Z","signed_message":"canonical_sha256_bytes"},"source_id":"0801.3423","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f2455c7fc3562bd7dc4f0fc6c1d9532fa953cfbb716cd40826f9706f3a42f9b","sha256:654adc1a0f380ce8df59958c2cf98421fa0607bad0ad2b220cff8ec8e56d7e8a"],"state_sha256":"bd2024cf57b5695748d53ed985c1ceff92f2e046498cb95f5b1d0d5ca89b7b5c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L8npcS+cczWO+c4UE8d7Yk5PeQ9OF8bBlCep4LwK8yCSIRuB6JboeYV7O8EuZ9iNnPnP3apOj7m5AxgAnVNODA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T07:43:34.979011Z","bundle_sha256":"f04d03d3db878945a40431637caf440fbb2b70f8d2e806fb31da9f513700f047"}}