{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:RR27UPLDWD5N4SAQZRDK2AKRBU","short_pith_number":"pith:RR27UPLD","canonical_record":{"source":{"id":"1104.5159","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-27T14:57:43Z","cross_cats_sorted":[],"title_canon_sha256":"5aa5ecf6a76c0e1bc7dcc79d06777a909eec48e491f5828eb67f2bdc097535a3","abstract_canon_sha256":"753621d83e0e06823032ed58be3cc4e413c103ffca514df4d516d8f19ebbecf6"},"schema_version":"1.0"},"canonical_sha256":"8c75fa3d63b0fade4810cc46ad01510d133296a478cad0c8fd92aa4ad7188642","source":{"kind":"arxiv","id":"1104.5159","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.5159","created_at":"2026-05-18T04:23:22Z"},{"alias_kind":"arxiv_version","alias_value":"1104.5159v1","created_at":"2026-05-18T04:23:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.5159","created_at":"2026-05-18T04:23:22Z"},{"alias_kind":"pith_short_12","alias_value":"RR27UPLDWD5N","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RR27UPLDWD5N4SAQ","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RR27UPLD","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:RR27UPLDWD5N4SAQZRDK2AKRBU","target":"record","payload":{"canonical_record":{"source":{"id":"1104.5159","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-27T14:57:43Z","cross_cats_sorted":[],"title_canon_sha256":"5aa5ecf6a76c0e1bc7dcc79d06777a909eec48e491f5828eb67f2bdc097535a3","abstract_canon_sha256":"753621d83e0e06823032ed58be3cc4e413c103ffca514df4d516d8f19ebbecf6"},"schema_version":"1.0"},"canonical_sha256":"8c75fa3d63b0fade4810cc46ad01510d133296a478cad0c8fd92aa4ad7188642","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:22.500097Z","signature_b64":"DyWvzI/HLYm0UH7nlIzdLnsor3d15VLr77uUTnivEa2Uoa4ciFQv5tA5kiFF3yqJNwyuAy4ZHm/0r3o8YVm1AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8c75fa3d63b0fade4810cc46ad01510d133296a478cad0c8fd92aa4ad7188642","last_reissued_at":"2026-05-18T04:23:22.499523Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:22.499523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.5159","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":"2026-05-18T04:23:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6EDonpjXLVNQMq6Qu+jWmmfv31Kzf8mYGbnhU8BwfgmEDKatOveqF6n4mZHMW2WvwkrwWvA3r7FIDHcV5g4ECQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:11:15.688775Z"},"content_sha256":"be5b1bb2b4fff9b7de8f07ca3f2f3094715351ced4cbec8f11e3fedd2c418314","schema_version":"1.0","event_id":"sha256:be5b1bb2b4fff9b7de8f07ca3f2f3094715351ced4cbec8f11e3fedd2c418314"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:RR27UPLDWD5N4SAQZRDK2AKRBU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large 2-groups of automorphisms of curves with positive 2-rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Gabor Korchmaros, Massimo Giulietti","submitted_at":"2011-04-27T14:57:43Z","abstract_excerpt":"Let K be an algebraically closed field of characteristic 2, and let X be a curve over K of genus g>1 and 2-rank r>0. For 2-subgroups S of the K-automorphism group Aut(X) of X, the Nakajima bound is |S| < 4g-3. For every g=2^h+1>8, we construct a curve X attaining the Nakajima bound and determine its relevant properties: X is a bielliptic curve with r=g, and its K-automorphism group has a dihedral K-automorphism group of order 4(g-1) which fixes no point in X. Moreover, we provide a classification of 2-groups S of K-automorphisms not fixing a point of X and such that |S|> 2g-1."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5159","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":"2026-05-18T04:23:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GB9ZpIZpe7ZQEHtJEmCjfUXqY2a5N+52OTYIXTghVjb/VKzmkHcqJFm3NXpaZ2fhuEgn+MlY+pqPSA5I4njWAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:11:15.689118Z"},"content_sha256":"ce057f3452f7646a9eb09d9f7f1cc8966195b76ddf564d469b7126c1133374e6","schema_version":"1.0","event_id":"sha256:ce057f3452f7646a9eb09d9f7f1cc8966195b76ddf564d469b7126c1133374e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RR27UPLDWD5N4SAQZRDK2AKRBU/bundle.json","state_url":"https://pith.science/pith/RR27UPLDWD5N4SAQZRDK2AKRBU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RR27UPLDWD5N4SAQZRDK2AKRBU/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":"2026-05-30T05:11:15Z","links":{"resolver":"https://pith.science/pith/RR27UPLDWD5N4SAQZRDK2AKRBU","bundle":"https://pith.science/pith/RR27UPLDWD5N4SAQZRDK2AKRBU/bundle.json","state":"https://pith.science/pith/RR27UPLDWD5N4SAQZRDK2AKRBU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RR27UPLDWD5N4SAQZRDK2AKRBU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RR27UPLDWD5N4SAQZRDK2AKRBU","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":"753621d83e0e06823032ed58be3cc4e413c103ffca514df4d516d8f19ebbecf6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-27T14:57:43Z","title_canon_sha256":"5aa5ecf6a76c0e1bc7dcc79d06777a909eec48e491f5828eb67f2bdc097535a3"},"schema_version":"1.0","source":{"id":"1104.5159","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.5159","created_at":"2026-05-18T04:23:22Z"},{"alias_kind":"arxiv_version","alias_value":"1104.5159v1","created_at":"2026-05-18T04:23:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.5159","created_at":"2026-05-18T04:23:22Z"},{"alias_kind":"pith_short_12","alias_value":"RR27UPLDWD5N","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RR27UPLDWD5N4SAQ","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RR27UPLD","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:ce057f3452f7646a9eb09d9f7f1cc8966195b76ddf564d469b7126c1133374e6","target":"graph","created_at":"2026-05-18T04:23:22Z","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 K be an algebraically closed field of characteristic 2, and let X be a curve over K of genus g>1 and 2-rank r>0. For 2-subgroups S of the K-automorphism group Aut(X) of X, the Nakajima bound is |S| < 4g-3. For every g=2^h+1>8, we construct a curve X attaining the Nakajima bound and determine its relevant properties: X is a bielliptic curve with r=g, and its K-automorphism group has a dihedral K-automorphism group of order 4(g-1) which fixes no point in X. Moreover, we provide a classification of 2-groups S of K-automorphisms not fixing a point of X and such that |S|> 2g-1.","authors_text":"Gabor Korchmaros, Massimo Giulietti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-27T14:57:43Z","title":"Large 2-groups of automorphisms of curves with positive 2-rank"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5159","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:be5b1bb2b4fff9b7de8f07ca3f2f3094715351ced4cbec8f11e3fedd2c418314","target":"record","created_at":"2026-05-18T04:23:22Z","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":"753621d83e0e06823032ed58be3cc4e413c103ffca514df4d516d8f19ebbecf6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-27T14:57:43Z","title_canon_sha256":"5aa5ecf6a76c0e1bc7dcc79d06777a909eec48e491f5828eb67f2bdc097535a3"},"schema_version":"1.0","source":{"id":"1104.5159","kind":"arxiv","version":1}},"canonical_sha256":"8c75fa3d63b0fade4810cc46ad01510d133296a478cad0c8fd92aa4ad7188642","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c75fa3d63b0fade4810cc46ad01510d133296a478cad0c8fd92aa4ad7188642","first_computed_at":"2026-05-18T04:23:22.499523Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:22.499523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DyWvzI/HLYm0UH7nlIzdLnsor3d15VLr77uUTnivEa2Uoa4ciFQv5tA5kiFF3yqJNwyuAy4ZHm/0r3o8YVm1AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:22.500097Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.5159","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be5b1bb2b4fff9b7de8f07ca3f2f3094715351ced4cbec8f11e3fedd2c418314","sha256:ce057f3452f7646a9eb09d9f7f1cc8966195b76ddf564d469b7126c1133374e6"],"state_sha256":"b2796f53fd3893d9ed4ea27885ee83cf76fe1112c9a96be271a2f995ec6a5c29"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3C5XvrsOTs9CjWea7KWcx0J69KmtHNqJrxKf5buBT/adx0MjtP9EDb1CGchKpTKrY3LNu/SLOTI7Uo/7HjRWDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T05:11:15.691139Z","bundle_sha256":"c0d2495bcbeb65e49edb333a5523f15232e687f07095555f4e832f7a6f41495c"}}