{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GMEAV4EVS46Y3K6NHAAD2BUMQA","short_pith_number":"pith:GMEAV4EV","canonical_record":{"source":{"id":"1703.00293","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-01T13:38:49Z","cross_cats_sorted":[],"title_canon_sha256":"41cc6dc9fe0b8d395d3fd15d2964734e2c8132bf71e90b27670d33a8a6e3acce","abstract_canon_sha256":"13bc1913f0118088704910170062bf7afbff4a96a88718430e5cdacf874ecc4c"},"schema_version":"1.0"},"canonical_sha256":"33080af095973d8dabcd38003d068c801d87dae5e1feaaac1d62fab03db55c3b","source":{"kind":"arxiv","id":"1703.00293","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.00293","created_at":"2026-05-18T00:48:09Z"},{"alias_kind":"arxiv_version","alias_value":"1703.00293v2","created_at":"2026-05-18T00:48:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.00293","created_at":"2026-05-18T00:48:09Z"},{"alias_kind":"pith_short_12","alias_value":"GMEAV4EVS46Y","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GMEAV4EVS46Y3K6N","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GMEAV4EV","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GMEAV4EVS46Y3K6NHAAD2BUMQA","target":"record","payload":{"canonical_record":{"source":{"id":"1703.00293","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-01T13:38:49Z","cross_cats_sorted":[],"title_canon_sha256":"41cc6dc9fe0b8d395d3fd15d2964734e2c8132bf71e90b27670d33a8a6e3acce","abstract_canon_sha256":"13bc1913f0118088704910170062bf7afbff4a96a88718430e5cdacf874ecc4c"},"schema_version":"1.0"},"canonical_sha256":"33080af095973d8dabcd38003d068c801d87dae5e1feaaac1d62fab03db55c3b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:09.184871Z","signature_b64":"VfuMsMJT8KyFfEeQxWJGib9rVlEbJXf0SJr2WZeI9fjrZmVPKUHZCoyQN0odnyamGppKb2UPwxLJMLLRp1ncAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33080af095973d8dabcd38003d068c801d87dae5e1feaaac1d62fab03db55c3b","last_reissued_at":"2026-05-18T00:48:09.184279Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:09.184279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.00293","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZaOJRvoFd0bwsHWMWJ1c0eJ2fwdUjkafwHHCTwMDd2VodDz7j5KrG7ICPDA2Fq07bIGqF2sKH6n/764f7WihCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:40:45.091678Z"},"content_sha256":"ff4df452f95a39e4c38da67101fbecad050c9b1b38d968c5f409509deaa2760f","schema_version":"1.0","event_id":"sha256:ff4df452f95a39e4c38da67101fbecad050c9b1b38d968c5f409509deaa2760f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GMEAV4EVS46Y3K6NHAAD2BUMQA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Enriques' classification in characteristic $ p >0$ : the $P_{12}$-Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Binru Li (Universitaet Bayreuth), Fabrizio Catanese","submitted_at":"2017-03-01T13:38:49Z","abstract_excerpt":"The main goal of this paper is to show that Castelnuovo- Enriques' $P_{12}$-theorem also holds for algebraic surfaces $S$ defined over an algebraically closed field $k$ of positive characteristic ($char(k) = p > 0$). The $P_{12}$-theorem is a precise version of the rough classification of algebraic surfaces, in particular the conditions $P_{12} = 0$, $P_{12} = 1$,$P_{12} \\geq 2$ are respectively equivalent to : Kodaira dimension $-\\infty, 0 , \\geq 1$. The result relies on a main theorem describing the growth of the plurigenera for properly-elliptic or properly quasi-elliptic surfaces (surfaces"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00293","kind":"arxiv","version":2},"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":"2026-05-18T00:48:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gHk3WNxHpqVLnWbIyy8+kUPgO7C4FuJv1NdltAOVxbu2UmaTkd4nBryQ1yUZj+jY98s/fC89yZROLenpBM+yCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:40:45.092372Z"},"content_sha256":"f2dd6861b7b8742be5fac351533747e3bdc6ba57a41b8ac6d2bc07959c0b102a","schema_version":"1.0","event_id":"sha256:f2dd6861b7b8742be5fac351533747e3bdc6ba57a41b8ac6d2bc07959c0b102a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GMEAV4EVS46Y3K6NHAAD2BUMQA/bundle.json","state_url":"https://pith.science/pith/GMEAV4EVS46Y3K6NHAAD2BUMQA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GMEAV4EVS46Y3K6NHAAD2BUMQA/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":"2026-05-27T22:40:45Z","links":{"resolver":"https://pith.science/pith/GMEAV4EVS46Y3K6NHAAD2BUMQA","bundle":"https://pith.science/pith/GMEAV4EVS46Y3K6NHAAD2BUMQA/bundle.json","state":"https://pith.science/pith/GMEAV4EVS46Y3K6NHAAD2BUMQA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GMEAV4EVS46Y3K6NHAAD2BUMQA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GMEAV4EVS46Y3K6NHAAD2BUMQA","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":"13bc1913f0118088704910170062bf7afbff4a96a88718430e5cdacf874ecc4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-01T13:38:49Z","title_canon_sha256":"41cc6dc9fe0b8d395d3fd15d2964734e2c8132bf71e90b27670d33a8a6e3acce"},"schema_version":"1.0","source":{"id":"1703.00293","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.00293","created_at":"2026-05-18T00:48:09Z"},{"alias_kind":"arxiv_version","alias_value":"1703.00293v2","created_at":"2026-05-18T00:48:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.00293","created_at":"2026-05-18T00:48:09Z"},{"alias_kind":"pith_short_12","alias_value":"GMEAV4EVS46Y","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GMEAV4EVS46Y3K6N","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GMEAV4EV","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:f2dd6861b7b8742be5fac351533747e3bdc6ba57a41b8ac6d2bc07959c0b102a","target":"graph","created_at":"2026-05-18T00:48:09Z","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 main goal of this paper is to show that Castelnuovo- Enriques' $P_{12}$-theorem also holds for algebraic surfaces $S$ defined over an algebraically closed field $k$ of positive characteristic ($char(k) = p > 0$). The $P_{12}$-theorem is a precise version of the rough classification of algebraic surfaces, in particular the conditions $P_{12} = 0$, $P_{12} = 1$,$P_{12} \\geq 2$ are respectively equivalent to : Kodaira dimension $-\\infty, 0 , \\geq 1$. The result relies on a main theorem describing the growth of the plurigenera for properly-elliptic or properly quasi-elliptic surfaces (surfaces","authors_text":"Binru Li (Universitaet Bayreuth), Fabrizio Catanese","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-01T13:38:49Z","title":"Enriques' classification in characteristic $ p >0$ : the $P_{12}$-Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00293","kind":"arxiv","version":2},"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:ff4df452f95a39e4c38da67101fbecad050c9b1b38d968c5f409509deaa2760f","target":"record","created_at":"2026-05-18T00:48:09Z","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":"13bc1913f0118088704910170062bf7afbff4a96a88718430e5cdacf874ecc4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-01T13:38:49Z","title_canon_sha256":"41cc6dc9fe0b8d395d3fd15d2964734e2c8132bf71e90b27670d33a8a6e3acce"},"schema_version":"1.0","source":{"id":"1703.00293","kind":"arxiv","version":2}},"canonical_sha256":"33080af095973d8dabcd38003d068c801d87dae5e1feaaac1d62fab03db55c3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33080af095973d8dabcd38003d068c801d87dae5e1feaaac1d62fab03db55c3b","first_computed_at":"2026-05-18T00:48:09.184279Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:09.184279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VfuMsMJT8KyFfEeQxWJGib9rVlEbJXf0SJr2WZeI9fjrZmVPKUHZCoyQN0odnyamGppKb2UPwxLJMLLRp1ncAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:09.184871Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.00293","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff4df452f95a39e4c38da67101fbecad050c9b1b38d968c5f409509deaa2760f","sha256:f2dd6861b7b8742be5fac351533747e3bdc6ba57a41b8ac6d2bc07959c0b102a"],"state_sha256":"08f9438c6c54fd3e7d5b2b645acf47e36f4c4c18997b268ad898a6e4a5146201"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"af1KWrE6lfH+TABaFvYwBLexu/KbDwVlMQnW8KxOeWhyfN9I7OVc+RTU8SpVaetxFxHYDjTXbjW71H/2/lwJDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T22:40:45.096615Z","bundle_sha256":"77125b0a168c82bb85e59df9a229d524fe74d5d6135ef2dffbeb45112359ae29"}}