{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:R5GRUOA7OQBVEHJUYDRBOXOZMD","short_pith_number":"pith:R5GRUOA7","canonical_record":{"source":{"id":"1405.7776","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-05-30T05:01:45Z","cross_cats_sorted":[],"title_canon_sha256":"afd145276cc1ba8d95b6f6b5f4e502215c29b116953c6db8a9c43e513b2b123c","abstract_canon_sha256":"4bd4b1cacad69f66f9c38658a2a635a9c9d2a334d308d599b73a670fbe3da8ad"},"schema_version":"1.0"},"canonical_sha256":"8f4d1a381f7403521d34c0e2175dd960ffc27a842f48f33613e055275b7a3a65","source":{"kind":"arxiv","id":"1405.7776","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.7776","created_at":"2026-05-18T02:50:49Z"},{"alias_kind":"arxiv_version","alias_value":"1405.7776v1","created_at":"2026-05-18T02:50:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.7776","created_at":"2026-05-18T02:50:49Z"},{"alias_kind":"pith_short_12","alias_value":"R5GRUOA7OQBV","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"R5GRUOA7OQBVEHJU","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"R5GRUOA7","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:R5GRUOA7OQBVEHJUYDRBOXOZMD","target":"record","payload":{"canonical_record":{"source":{"id":"1405.7776","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-05-30T05:01:45Z","cross_cats_sorted":[],"title_canon_sha256":"afd145276cc1ba8d95b6f6b5f4e502215c29b116953c6db8a9c43e513b2b123c","abstract_canon_sha256":"4bd4b1cacad69f66f9c38658a2a635a9c9d2a334d308d599b73a670fbe3da8ad"},"schema_version":"1.0"},"canonical_sha256":"8f4d1a381f7403521d34c0e2175dd960ffc27a842f48f33613e055275b7a3a65","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:49.869897Z","signature_b64":"2Ol3kRD3XqBMScAiX/14I3kVNT8U6IJ0utvZ/MVIkNfX4sji/3ymgpKIvL4mOaPHGSqTZCHOdkgN5DLBbKYnDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f4d1a381f7403521d34c0e2175dd960ffc27a842f48f33613e055275b7a3a65","last_reissued_at":"2026-05-18T02:50:49.869192Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:49.869192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.7776","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":"2026-05-18T02:50:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RbRkoAd4nDw7KV72/OMNl1XZI5JDHbR5yopnSulV8zNiG+Fm82JmulCJxnsVJjuQq1Fl2sBluDtDPhNb4yQMCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T18:22:25.522888Z"},"content_sha256":"fc995679e35733d91f851ce751839477265c968b91ffe74d6814d38ee4ad6824","schema_version":"1.0","event_id":"sha256:fc995679e35733d91f851ce751839477265c968b91ffe74d6814d38ee4ad6824"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:R5GRUOA7OQBVEHJUYDRBOXOZMD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Euler sequence for complete smooth k*-surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Antonio Laface, Manuel Melo","submitted_at":"2014-05-30T05:01:45Z","abstract_excerpt":"In this note we introduce exact sequences of sheaves on a complete smooth k*-surface without elliptic points. These sequences are an attempt to generalize the Euler sequence for a toric variety to complexity one surfaces. As an application we show that such a surface is rigid if and only if it is Fano."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7776","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":"2026-05-18T02:50:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cP9LDdaK/49+Ae3IssqeTukUInIl4fMyqIZ7r5ARTveAs0QvyfLQBt9vLSC4lTd+sOz4mCovBTbzxhNUIB5eCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T18:22:25.523477Z"},"content_sha256":"949fe22c231271208571d35cd5ba6e4600e5b1645a88de5cda47f16a3636891e","schema_version":"1.0","event_id":"sha256:949fe22c231271208571d35cd5ba6e4600e5b1645a88de5cda47f16a3636891e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R5GRUOA7OQBVEHJUYDRBOXOZMD/bundle.json","state_url":"https://pith.science/pith/R5GRUOA7OQBVEHJUYDRBOXOZMD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R5GRUOA7OQBVEHJUYDRBOXOZMD/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":"2026-05-29T18:22:25Z","links":{"resolver":"https://pith.science/pith/R5GRUOA7OQBVEHJUYDRBOXOZMD","bundle":"https://pith.science/pith/R5GRUOA7OQBVEHJUYDRBOXOZMD/bundle.json","state":"https://pith.science/pith/R5GRUOA7OQBVEHJUYDRBOXOZMD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R5GRUOA7OQBVEHJUYDRBOXOZMD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:R5GRUOA7OQBVEHJUYDRBOXOZMD","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":"4bd4b1cacad69f66f9c38658a2a635a9c9d2a334d308d599b73a670fbe3da8ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-05-30T05:01:45Z","title_canon_sha256":"afd145276cc1ba8d95b6f6b5f4e502215c29b116953c6db8a9c43e513b2b123c"},"schema_version":"1.0","source":{"id":"1405.7776","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.7776","created_at":"2026-05-18T02:50:49Z"},{"alias_kind":"arxiv_version","alias_value":"1405.7776v1","created_at":"2026-05-18T02:50:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.7776","created_at":"2026-05-18T02:50:49Z"},{"alias_kind":"pith_short_12","alias_value":"R5GRUOA7OQBV","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"R5GRUOA7OQBVEHJU","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"R5GRUOA7","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:949fe22c231271208571d35cd5ba6e4600e5b1645a88de5cda47f16a3636891e","target":"graph","created_at":"2026-05-18T02:50:49Z","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 this note we introduce exact sequences of sheaves on a complete smooth k*-surface without elliptic points. These sequences are an attempt to generalize the Euler sequence for a toric variety to complexity one surfaces. As an application we show that such a surface is rigid if and only if it is Fano.","authors_text":"Antonio Laface, Manuel Melo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-05-30T05:01:45Z","title":"Euler sequence for complete smooth k*-surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7776","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:fc995679e35733d91f851ce751839477265c968b91ffe74d6814d38ee4ad6824","target":"record","created_at":"2026-05-18T02:50:49Z","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":"4bd4b1cacad69f66f9c38658a2a635a9c9d2a334d308d599b73a670fbe3da8ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-05-30T05:01:45Z","title_canon_sha256":"afd145276cc1ba8d95b6f6b5f4e502215c29b116953c6db8a9c43e513b2b123c"},"schema_version":"1.0","source":{"id":"1405.7776","kind":"arxiv","version":1}},"canonical_sha256":"8f4d1a381f7403521d34c0e2175dd960ffc27a842f48f33613e055275b7a3a65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f4d1a381f7403521d34c0e2175dd960ffc27a842f48f33613e055275b7a3a65","first_computed_at":"2026-05-18T02:50:49.869192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:49.869192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2Ol3kRD3XqBMScAiX/14I3kVNT8U6IJ0utvZ/MVIkNfX4sji/3ymgpKIvL4mOaPHGSqTZCHOdkgN5DLBbKYnDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:49.869897Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.7776","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc995679e35733d91f851ce751839477265c968b91ffe74d6814d38ee4ad6824","sha256:949fe22c231271208571d35cd5ba6e4600e5b1645a88de5cda47f16a3636891e"],"state_sha256":"b9150cb9ebd7622ff72a81eef29ada496096e105300148ca0d8769750b36f9c6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D3KoimdIEdE2ftZcRzZbBM9L5+3gtuS80Ndk17XuyILKjN5XqcE3U9iZp8bPkgkMFpDosYOy677i7aJHbz1PBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T18:22:25.526857Z","bundle_sha256":"ac250008a20b9ef2f4252e32d5a8b60dc04ec573ea5ef8a775aac4d0ff21bb77"}}