{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:XZDKQ7FZXZUXEFQWN25IKK4HHB","short_pith_number":"pith:XZDKQ7FZ","canonical_record":{"source":{"id":"1407.7632","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-07-29T05:14:50Z","cross_cats_sorted":[],"title_canon_sha256":"b4fb7c9587432e8848d310de797d3b8bf4695b16ee6334acc0469ac60b7b919e","abstract_canon_sha256":"39d9a928bb6f57e7350d9a6011455ec26fae02e191d91e00a50178e7beb5b089"},"schema_version":"1.0"},"canonical_sha256":"be46a87cb9be697216166eba852b8738466b5535e2ccc4f7bcc2a46203a74c32","source":{"kind":"arxiv","id":"1407.7632","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.7632","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"arxiv_version","alias_value":"1407.7632v3","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.7632","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"pith_short_12","alias_value":"XZDKQ7FZXZUX","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XZDKQ7FZXZUXEFQW","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XZDKQ7FZ","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:XZDKQ7FZXZUXEFQWN25IKK4HHB","target":"record","payload":{"canonical_record":{"source":{"id":"1407.7632","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-07-29T05:14:50Z","cross_cats_sorted":[],"title_canon_sha256":"b4fb7c9587432e8848d310de797d3b8bf4695b16ee6334acc0469ac60b7b919e","abstract_canon_sha256":"39d9a928bb6f57e7350d9a6011455ec26fae02e191d91e00a50178e7beb5b089"},"schema_version":"1.0"},"canonical_sha256":"be46a87cb9be697216166eba852b8738466b5535e2ccc4f7bcc2a46203a74c32","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:57.050370Z","signature_b64":"xjpTYZBWHe+7xMRn6ME00HnrY6w36caerSJ+SrHUs4+Bcd0WO9buibbGQcWFBcygTvTZ9RCC7hgUE9O2M+jMCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be46a87cb9be697216166eba852b8738466b5535e2ccc4f7bcc2a46203a74c32","last_reissued_at":"2026-05-18T02:27:57.049689Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:57.049689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.7632","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:27:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yJlECACRQw5C7BfbnlIQZSYFVPo5131WU0LnzCgA4h8C6ik90W0m89aYG9XoznBj9vYN53JqMQdM1wgVdc90BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T11:04:59.107987Z"},"content_sha256":"1fc95869331a8a69d8e3b2ad749cb82177d50aa26b53cd923c368c7b6c1f8a60","schema_version":"1.0","event_id":"sha256:1fc95869331a8a69d8e3b2ad749cb82177d50aa26b53cd923c368c7b6c1f8a60"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:XZDKQ7FZXZUXEFQWN25IKK4HHB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A vanishing theorem on fake projective planes with enough automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"JongHae Keum","submitted_at":"2014-07-29T05:14:50Z","abstract_excerpt":"For every fake projective plane $X$ with automorphism group of order 21, we prove that $H^i(X, 2L)=0$ for all $i$ and for every ample line bundle $L$ with $L^2=1$. For every fake projective plane with automorphism group of order 9, we prove the same vanishing for every cubic root (and its twist by a 2-torsion) of the canonical bundle $K$. As an immediate consequence, there are exceptional sequences of length 3 on such fake projective planes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7632","kind":"arxiv","version":3},"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":"2026-05-18T02:27:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fNtHaD09qUbbxKzneh3Xq2RI0JjHU1HxeZJvfg1c2Q0BFoKafieCeKAEdk3CK3NvcfiSPSziy61vYymcxeK3CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T11:04:59.108329Z"},"content_sha256":"2971442dce3dd480e3cb1ad98062bc2d6e4d5f00b2c8a611811634216c392865","schema_version":"1.0","event_id":"sha256:2971442dce3dd480e3cb1ad98062bc2d6e4d5f00b2c8a611811634216c392865"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XZDKQ7FZXZUXEFQWN25IKK4HHB/bundle.json","state_url":"https://pith.science/pith/XZDKQ7FZXZUXEFQWN25IKK4HHB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XZDKQ7FZXZUXEFQWN25IKK4HHB/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":"2026-06-20T11:04:59Z","links":{"resolver":"https://pith.science/pith/XZDKQ7FZXZUXEFQWN25IKK4HHB","bundle":"https://pith.science/pith/XZDKQ7FZXZUXEFQWN25IKK4HHB/bundle.json","state":"https://pith.science/pith/XZDKQ7FZXZUXEFQWN25IKK4HHB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XZDKQ7FZXZUXEFQWN25IKK4HHB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XZDKQ7FZXZUXEFQWN25IKK4HHB","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":"39d9a928bb6f57e7350d9a6011455ec26fae02e191d91e00a50178e7beb5b089","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-07-29T05:14:50Z","title_canon_sha256":"b4fb7c9587432e8848d310de797d3b8bf4695b16ee6334acc0469ac60b7b919e"},"schema_version":"1.0","source":{"id":"1407.7632","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.7632","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"arxiv_version","alias_value":"1407.7632v3","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.7632","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"pith_short_12","alias_value":"XZDKQ7FZXZUX","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XZDKQ7FZXZUXEFQW","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XZDKQ7FZ","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:2971442dce3dd480e3cb1ad98062bc2d6e4d5f00b2c8a611811634216c392865","target":"graph","created_at":"2026-05-18T02:27:57Z","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":"For every fake projective plane $X$ with automorphism group of order 21, we prove that $H^i(X, 2L)=0$ for all $i$ and for every ample line bundle $L$ with $L^2=1$. For every fake projective plane with automorphism group of order 9, we prove the same vanishing for every cubic root (and its twist by a 2-torsion) of the canonical bundle $K$. As an immediate consequence, there are exceptional sequences of length 3 on such fake projective planes.","authors_text":"JongHae Keum","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-07-29T05:14:50Z","title":"A vanishing theorem on fake projective planes with enough automorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7632","kind":"arxiv","version":3},"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":"sha256:1fc95869331a8a69d8e3b2ad749cb82177d50aa26b53cd923c368c7b6c1f8a60","target":"record","created_at":"2026-05-18T02:27:57Z","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":"39d9a928bb6f57e7350d9a6011455ec26fae02e191d91e00a50178e7beb5b089","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-07-29T05:14:50Z","title_canon_sha256":"b4fb7c9587432e8848d310de797d3b8bf4695b16ee6334acc0469ac60b7b919e"},"schema_version":"1.0","source":{"id":"1407.7632","kind":"arxiv","version":3}},"canonical_sha256":"be46a87cb9be697216166eba852b8738466b5535e2ccc4f7bcc2a46203a74c32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be46a87cb9be697216166eba852b8738466b5535e2ccc4f7bcc2a46203a74c32","first_computed_at":"2026-05-18T02:27:57.049689Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:57.049689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xjpTYZBWHe+7xMRn6ME00HnrY6w36caerSJ+SrHUs4+Bcd0WO9buibbGQcWFBcygTvTZ9RCC7hgUE9O2M+jMCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:57.050370Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.7632","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1fc95869331a8a69d8e3b2ad749cb82177d50aa26b53cd923c368c7b6c1f8a60","sha256:2971442dce3dd480e3cb1ad98062bc2d6e4d5f00b2c8a611811634216c392865"],"state_sha256":"616e9d5868712f9245479b2d14a82713dff1cb2ac6aaf5b98166de41ea588b25"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9fEPlPDEY2czXN79KvmC9Vu0THt/UdE8ujtCclifIG7NQ6Z0poD84gQRUtkraS+oBAjfYGo5iU/2GnzCHqikBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T11:04:59.110150Z","bundle_sha256":"33e75ecd27991673fe253f3e068c96228b81ecdfba33616283584420a618f65c"}}