{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:F6KPEVXARKDJ6GFU5EDORA65YL","short_pith_number":"pith:F6KPEVXA","canonical_record":{"source":{"id":"1801.00151","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-12-30T16:48:44Z","cross_cats_sorted":[],"title_canon_sha256":"fd4854e515c6498efc550186b07c8c0c1631d8da07031a915b10ec7f123394fd","abstract_canon_sha256":"a5a7009363d68b2d1403aadd0107f92ed72bf0cde2c4b35f3978daaefc9b7231"},"schema_version":"1.0"},"canonical_sha256":"2f94f256e08a869f18b4e906e883ddc2c2a5ab0c4e371d418bbe26ef3cf6b7b7","source":{"kind":"arxiv","id":"1801.00151","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00151","created_at":"2026-05-18T00:13:10Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00151v1","created_at":"2026-05-18T00:13:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00151","created_at":"2026-05-18T00:13:10Z"},{"alias_kind":"pith_short_12","alias_value":"F6KPEVXARKDJ","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"F6KPEVXARKDJ6GFU","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"F6KPEVXA","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:F6KPEVXARKDJ6GFU5EDORA65YL","target":"record","payload":{"canonical_record":{"source":{"id":"1801.00151","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-12-30T16:48:44Z","cross_cats_sorted":[],"title_canon_sha256":"fd4854e515c6498efc550186b07c8c0c1631d8da07031a915b10ec7f123394fd","abstract_canon_sha256":"a5a7009363d68b2d1403aadd0107f92ed72bf0cde2c4b35f3978daaefc9b7231"},"schema_version":"1.0"},"canonical_sha256":"2f94f256e08a869f18b4e906e883ddc2c2a5ab0c4e371d418bbe26ef3cf6b7b7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:10.599173Z","signature_b64":"d3yNWD9Wu6xfQf2JlCA+QDmX++CCA66J1CPMsHEEevX2xIOzyzAvphg1kt6X2lM3gmw1wzQGeI94zY9d/ud8Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f94f256e08a869f18b4e906e883ddc2c2a5ab0c4e371d418bbe26ef3cf6b7b7","last_reissued_at":"2026-05-18T00:13:10.598436Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:10.598436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.00151","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":"2026-05-18T00:13:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yn8blfnK6RIZrh8L/YTF3Jad/kXUXVLyPRRb5RrlIvTKnO3w1azPbT0AxsDXUsdfUExBftKks/RZJG8UTKBiBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T13:02:41.085546Z"},"content_sha256":"43ee666fc879307fe574325dc749cbd68d0ab222255733347750e093cfdc29b9","schema_version":"1.0","event_id":"sha256:43ee666fc879307fe574325dc749cbd68d0ab222255733347750e093cfdc29b9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:F6KPEVXARKDJ6GFU5EDORA65YL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monads on projective varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Helena Soares, Pedro Macias Marques, Simone Marchesi","submitted_at":"2017-12-30T16:48:44Z","abstract_excerpt":"We generalise Fl\\o{}ystad's theorem on the existence of monads on the projective space to a larger set of projective varieties. We consider a variety $X$, a line bundle $L$ on $X$, and a base-point-free linear system of sections of $L$ giving a morphism to the projective space whose image is either arithmetically Cohen-Macaulay (ACM), or linearly normal and not contained in a quadric. We give necessary and sufficient conditions on integers $a$, $b$, and $c$ for a monad of type \\[ 0\\to(L^\\vee)^a\\to\\mathcal{O}_{X}^{\\,b}\\to L^c\\to0 \\] to exist. We show that under certain conditions there exists a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00151","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":"2026-05-18T00:13:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KjLb5R4JCY18zgQosQ3WQnexzI4jLmc50cvzBMwwm5QVucyEnCi2OkPGY+YTb9WRSU7v4wkmqtiU9NDzoBv/DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T13:02:41.085898Z"},"content_sha256":"b57f110931ed48dfd00ab48d7e8704f824544f84219bb00ff386eff8601487a3","schema_version":"1.0","event_id":"sha256:b57f110931ed48dfd00ab48d7e8704f824544f84219bb00ff386eff8601487a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F6KPEVXARKDJ6GFU5EDORA65YL/bundle.json","state_url":"https://pith.science/pith/F6KPEVXARKDJ6GFU5EDORA65YL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F6KPEVXARKDJ6GFU5EDORA65YL/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":"2026-06-22T13:02:41Z","links":{"resolver":"https://pith.science/pith/F6KPEVXARKDJ6GFU5EDORA65YL","bundle":"https://pith.science/pith/F6KPEVXARKDJ6GFU5EDORA65YL/bundle.json","state":"https://pith.science/pith/F6KPEVXARKDJ6GFU5EDORA65YL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F6KPEVXARKDJ6GFU5EDORA65YL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:F6KPEVXARKDJ6GFU5EDORA65YL","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":"a5a7009363d68b2d1403aadd0107f92ed72bf0cde2c4b35f3978daaefc9b7231","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-12-30T16:48:44Z","title_canon_sha256":"fd4854e515c6498efc550186b07c8c0c1631d8da07031a915b10ec7f123394fd"},"schema_version":"1.0","source":{"id":"1801.00151","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00151","created_at":"2026-05-18T00:13:10Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00151v1","created_at":"2026-05-18T00:13:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00151","created_at":"2026-05-18T00:13:10Z"},{"alias_kind":"pith_short_12","alias_value":"F6KPEVXARKDJ","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"F6KPEVXARKDJ6GFU","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"F6KPEVXA","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:b57f110931ed48dfd00ab48d7e8704f824544f84219bb00ff386eff8601487a3","target":"graph","created_at":"2026-05-18T00:13:10Z","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":"We generalise Fl\\o{}ystad's theorem on the existence of monads on the projective space to a larger set of projective varieties. We consider a variety $X$, a line bundle $L$ on $X$, and a base-point-free linear system of sections of $L$ giving a morphism to the projective space whose image is either arithmetically Cohen-Macaulay (ACM), or linearly normal and not contained in a quadric. We give necessary and sufficient conditions on integers $a$, $b$, and $c$ for a monad of type \\[ 0\\to(L^\\vee)^a\\to\\mathcal{O}_{X}^{\\,b}\\to L^c\\to0 \\] to exist. We show that under certain conditions there exists a","authors_text":"Helena Soares, Pedro Macias Marques, Simone Marchesi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-12-30T16:48:44Z","title":"Monads on projective varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00151","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":"sha256:43ee666fc879307fe574325dc749cbd68d0ab222255733347750e093cfdc29b9","target":"record","created_at":"2026-05-18T00:13:10Z","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":"a5a7009363d68b2d1403aadd0107f92ed72bf0cde2c4b35f3978daaefc9b7231","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-12-30T16:48:44Z","title_canon_sha256":"fd4854e515c6498efc550186b07c8c0c1631d8da07031a915b10ec7f123394fd"},"schema_version":"1.0","source":{"id":"1801.00151","kind":"arxiv","version":1}},"canonical_sha256":"2f94f256e08a869f18b4e906e883ddc2c2a5ab0c4e371d418bbe26ef3cf6b7b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f94f256e08a869f18b4e906e883ddc2c2a5ab0c4e371d418bbe26ef3cf6b7b7","first_computed_at":"2026-05-18T00:13:10.598436Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:10.598436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d3yNWD9Wu6xfQf2JlCA+QDmX++CCA66J1CPMsHEEevX2xIOzyzAvphg1kt6X2lM3gmw1wzQGeI94zY9d/ud8Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:10.599173Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.00151","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43ee666fc879307fe574325dc749cbd68d0ab222255733347750e093cfdc29b9","sha256:b57f110931ed48dfd00ab48d7e8704f824544f84219bb00ff386eff8601487a3"],"state_sha256":"002163a5dacafd5f26dfad4913d0f16c2f4eb98c4a09e720af3cdea5db48ff6f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dR5bsne9g0NZPpaxjhFnPbuVGN4KOcSms7GbjliQxjiCEA8DTIQYpRhntmaZBI+Aw1zv9FioGSvUnXLl3IyWBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T13:02:41.087855Z","bundle_sha256":"b9b3f2975aff612db500a9e3a77446eedd955556b73f73e58c40c503fab43d96"}}