{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JVVB72NOM6VHSFKROVODGSPNIR","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":"d96a039056de6aa2b78cd014ac44e16696e1f2a4be26722dfeddd5d9d6744364","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-02-16T22:31:53Z","title_canon_sha256":"e487021e40fdcd5a2b80dd4a379c8d587062354165f0a027d010ef81ea29b991"},"schema_version":"1.0","source":{"id":"1602.05233","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05233","created_at":"2026-05-18T01:20:28Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05233v1","created_at":"2026-05-18T01:20:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05233","created_at":"2026-05-18T01:20:28Z"},{"alias_kind":"pith_short_12","alias_value":"JVVB72NOM6VH","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JVVB72NOM6VHSFKR","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JVVB72NO","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:f53def0c60d97fd4d8536c9d13b212be6c1331220e00f9d63422765a36bc0333","target":"graph","created_at":"2026-05-18T01:20:28Z","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":"Given a graded monoid A with 1, one can construct a projective monoid scheme MProj(A) analogous to Proj(R) of a graded ring R. This paper is concerned with the study of quasicoherent sheaves (of pointed sets) on MProj(A), and we prove several basic results regarding these. We show that:\n  1.) Every quasicoherent sheaf F on MProj(A) can be constructed from a graded A--set in analogy with the construction of quasicoherent sheaves on Proj(R) from graded R--modules.\n  2.) High enough twists of coherent sheaves are generated by finitely many global sections, hence that every coherent sheaf is a quo","authors_text":"Matt Szczesny, Oliver Lorscheid","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-02-16T22:31:53Z","title":"Quasicoherent sheaves on projective schemes over F_1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05233","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:d9216e9eb51ceb1e4daed27fe12552986dd7e2f88cc0e93d48ed7830c2ee4642","target":"record","created_at":"2026-05-18T01:20:28Z","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":"d96a039056de6aa2b78cd014ac44e16696e1f2a4be26722dfeddd5d9d6744364","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-02-16T22:31:53Z","title_canon_sha256":"e487021e40fdcd5a2b80dd4a379c8d587062354165f0a027d010ef81ea29b991"},"schema_version":"1.0","source":{"id":"1602.05233","kind":"arxiv","version":1}},"canonical_sha256":"4d6a1fe9ae67aa791551755c3349ed4445c621c29ad8cbba9f5b966011705454","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d6a1fe9ae67aa791551755c3349ed4445c621c29ad8cbba9f5b966011705454","first_computed_at":"2026-05-18T01:20:28.816797Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:28.816797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/G3Nh9N3K8v52EiYD2ss0EYM4+9UlOZuMq+370Vf1rjI9TyTJQIiEExPLTCZUqoctN5sB5wEPhmZbguXaAjICA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:28.817290Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.05233","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9216e9eb51ceb1e4daed27fe12552986dd7e2f88cc0e93d48ed7830c2ee4642","sha256:f53def0c60d97fd4d8536c9d13b212be6c1331220e00f9d63422765a36bc0333"],"state_sha256":"e333ba0ade1c719fb09dcf1dd0aa8deb7ed03e41d9547348bfbe56f7ceab55dd"}