{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JVVB72NOM6VHSFKROVODGSPNIR","short_pith_number":"pith:JVVB72NO","canonical_record":{"source":{"id":"1602.05233","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-02-16T22:31:53Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"e487021e40fdcd5a2b80dd4a379c8d587062354165f0a027d010ef81ea29b991","abstract_canon_sha256":"d96a039056de6aa2b78cd014ac44e16696e1f2a4be26722dfeddd5d9d6744364"},"schema_version":"1.0"},"canonical_sha256":"4d6a1fe9ae67aa791551755c3349ed4445c621c29ad8cbba9f5b966011705454","source":{"kind":"arxiv","id":"1602.05233","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JVVB72NOM6VHSFKROVODGSPNIR","target":"record","payload":{"canonical_record":{"source":{"id":"1602.05233","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-02-16T22:31:53Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"e487021e40fdcd5a2b80dd4a379c8d587062354165f0a027d010ef81ea29b991","abstract_canon_sha256":"d96a039056de6aa2b78cd014ac44e16696e1f2a4be26722dfeddd5d9d6744364"},"schema_version":"1.0"},"canonical_sha256":"4d6a1fe9ae67aa791551755c3349ed4445c621c29ad8cbba9f5b966011705454","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:28.817290Z","signature_b64":"/G3Nh9N3K8v52EiYD2ss0EYM4+9UlOZuMq+370Vf1rjI9TyTJQIiEExPLTCZUqoctN5sB5wEPhmZbguXaAjICA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d6a1fe9ae67aa791551755c3349ed4445c621c29ad8cbba9f5b966011705454","last_reissued_at":"2026-05-18T01:20:28.816797Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:28.816797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.05233","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":"2026-05-18T01:20:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZmZ+UrENieNTkrBCtxzCEzRAZhkMaogCdLvl1VKnBBSQ5FPQjGgZ8paSScZ/ofkm57fk+oDEf1PtAeapyC5CDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T23:37:00.129526Z"},"content_sha256":"d9216e9eb51ceb1e4daed27fe12552986dd7e2f88cc0e93d48ed7830c2ee4642","schema_version":"1.0","event_id":"sha256:d9216e9eb51ceb1e4daed27fe12552986dd7e2f88cc0e93d48ed7830c2ee4642"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JVVB72NOM6VHSFKROVODGSPNIR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quasicoherent sheaves on projective schemes over F_1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Matt Szczesny, Oliver Lorscheid","submitted_at":"2016-02-16T22:31:53Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05233","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":"2026-05-18T01:20:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w75GOTPiQ/lJTwhtEQa4qaH7tgTUYmGdFvw6V0YHXlIyLqpr4/Sz4DHo/u881jlXGsHP3QovvsXG1rrTsnPyCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T23:37:00.129992Z"},"content_sha256":"f53def0c60d97fd4d8536c9d13b212be6c1331220e00f9d63422765a36bc0333","schema_version":"1.0","event_id":"sha256:f53def0c60d97fd4d8536c9d13b212be6c1331220e00f9d63422765a36bc0333"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JVVB72NOM6VHSFKROVODGSPNIR/bundle.json","state_url":"https://pith.science/pith/JVVB72NOM6VHSFKROVODGSPNIR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JVVB72NOM6VHSFKROVODGSPNIR/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":"2026-06-24T23:37:00Z","links":{"resolver":"https://pith.science/pith/JVVB72NOM6VHSFKROVODGSPNIR","bundle":"https://pith.science/pith/JVVB72NOM6VHSFKROVODGSPNIR/bundle.json","state":"https://pith.science/pith/JVVB72NOM6VHSFKROVODGSPNIR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JVVB72NOM6VHSFKROVODGSPNIR/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"29+XZ07JTa2odQr2h7nNiGsa1BQqVhee+j/8sKm33nNtR9i3EnQv+3XFz6FlMF4Cst8H78LYJysE7SOBmsR0Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T23:37:00.132548Z","bundle_sha256":"284942610480f8647e04825099fab341338c1931cdba005e2f418446fbe50504"}}