{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:4DASXJMHKQ6PAELKTO2AHNE754","short_pith_number":"pith:4DASXJMH","canonical_record":{"source":{"id":"1107.2713","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-14T02:26:50Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"2c0ea29714f6d16bd41caebc94aa4c82dacdacb862e0a739fd5cd02892ee90e8","abstract_canon_sha256":"96ed355b9615fb904915ff97d28b3edf18cbed7efcccff6640738dae65c77723"},"schema_version":"1.0"},"canonical_sha256":"e0c12ba587543cf0116a9bb403b49fef36feb8504e99512a616a2be846b4d5dc","source":{"kind":"arxiv","id":"1107.2713","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2713","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2713v2","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2713","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"pith_short_12","alias_value":"4DASXJMHKQ6P","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4DASXJMHKQ6PAELK","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4DASXJMH","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:4DASXJMHKQ6PAELKTO2AHNE754","target":"record","payload":{"canonical_record":{"source":{"id":"1107.2713","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-14T02:26:50Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"2c0ea29714f6d16bd41caebc94aa4c82dacdacb862e0a739fd5cd02892ee90e8","abstract_canon_sha256":"96ed355b9615fb904915ff97d28b3edf18cbed7efcccff6640738dae65c77723"},"schema_version":"1.0"},"canonical_sha256":"e0c12ba587543cf0116a9bb403b49fef36feb8504e99512a616a2be846b4d5dc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:31.704501Z","signature_b64":"MYEPy6USrOyhfA3ZVlQq2Rku+wkKazFw7n1eciM3IyOUEP5FL4/4FUInjg7Jry3ItCxpZXpwy1acC9JwYzzpBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0c12ba587543cf0116a9bb403b49fef36feb8504e99512a616a2be846b4d5dc","last_reissued_at":"2026-05-18T02:46:31.704092Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:31.704092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.2713","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:46:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nNPy38/tjEmCVRN+zNgTqnSwcnRZ5wL8oz6js7o9PmGfGT+eNpdNrD+kWZ8V7N3sjxGijOYSDOmtCHbHUd6aAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T10:19:09.358524Z"},"content_sha256":"6d577d2b0300d84b3ae444a6a5857ae525073457eb395131af8a7238815b35d8","schema_version":"1.0","event_id":"sha256:6d577d2b0300d84b3ae444a6a5857ae525073457eb395131af8a7238815b35d8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:4DASXJMHKQ6PAELKTO2AHNE754","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On toric schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Fred Rohrer","submitted_at":"2011-07-14T02:26:50Z","abstract_excerpt":"Studying toric varieties from a scheme-theoretical point of view leads to toric schemes, i.e. \"toric varieties over arbitrary base rings\". It is shown how the base ring affects the geometry of a toric scheme. Moreover, generalisations of results by Cox and Mustata allow to describe quasicoherent sheaves on toric schemes in terms of graded modules. Finally, a toric version of the Serre-Grothendieck correspondence relates cohomology of quasicoherent sheaves on toric schemes to local cohomology of graded modules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2713","kind":"arxiv","version":2},"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":"2026-05-18T02:46:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WykfDJCCJtIP1/k0wJao1V4Bs0w10U7I8u/xaB1VmmlHpHhAwN47UNeseUL2vuossFFKMig+uy41F5Sbcwl3Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T10:19:09.358863Z"},"content_sha256":"d64731fbd1209de5047e9f03b1df4a096718b5854eb3e98c198dda9c094ea4e5","schema_version":"1.0","event_id":"sha256:d64731fbd1209de5047e9f03b1df4a096718b5854eb3e98c198dda9c094ea4e5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4DASXJMHKQ6PAELKTO2AHNE754/bundle.json","state_url":"https://pith.science/pith/4DASXJMHKQ6PAELKTO2AHNE754/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4DASXJMHKQ6PAELKTO2AHNE754/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":"2026-06-05T10:19:09Z","links":{"resolver":"https://pith.science/pith/4DASXJMHKQ6PAELKTO2AHNE754","bundle":"https://pith.science/pith/4DASXJMHKQ6PAELKTO2AHNE754/bundle.json","state":"https://pith.science/pith/4DASXJMHKQ6PAELKTO2AHNE754/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4DASXJMHKQ6PAELKTO2AHNE754/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4DASXJMHKQ6PAELKTO2AHNE754","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":"96ed355b9615fb904915ff97d28b3edf18cbed7efcccff6640738dae65c77723","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-14T02:26:50Z","title_canon_sha256":"2c0ea29714f6d16bd41caebc94aa4c82dacdacb862e0a739fd5cd02892ee90e8"},"schema_version":"1.0","source":{"id":"1107.2713","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2713","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2713v2","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2713","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"pith_short_12","alias_value":"4DASXJMHKQ6P","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4DASXJMHKQ6PAELK","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4DASXJMH","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:d64731fbd1209de5047e9f03b1df4a096718b5854eb3e98c198dda9c094ea4e5","target":"graph","created_at":"2026-05-18T02:46:31Z","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":"Studying toric varieties from a scheme-theoretical point of view leads to toric schemes, i.e. \"toric varieties over arbitrary base rings\". It is shown how the base ring affects the geometry of a toric scheme. Moreover, generalisations of results by Cox and Mustata allow to describe quasicoherent sheaves on toric schemes in terms of graded modules. Finally, a toric version of the Serre-Grothendieck correspondence relates cohomology of quasicoherent sheaves on toric schemes to local cohomology of graded modules.","authors_text":"Fred Rohrer","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-14T02:26:50Z","title":"On toric schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2713","kind":"arxiv","version":2},"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":"sha256:6d577d2b0300d84b3ae444a6a5857ae525073457eb395131af8a7238815b35d8","target":"record","created_at":"2026-05-18T02:46:31Z","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":"96ed355b9615fb904915ff97d28b3edf18cbed7efcccff6640738dae65c77723","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-14T02:26:50Z","title_canon_sha256":"2c0ea29714f6d16bd41caebc94aa4c82dacdacb862e0a739fd5cd02892ee90e8"},"schema_version":"1.0","source":{"id":"1107.2713","kind":"arxiv","version":2}},"canonical_sha256":"e0c12ba587543cf0116a9bb403b49fef36feb8504e99512a616a2be846b4d5dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0c12ba587543cf0116a9bb403b49fef36feb8504e99512a616a2be846b4d5dc","first_computed_at":"2026-05-18T02:46:31.704092Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:31.704092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MYEPy6USrOyhfA3ZVlQq2Rku+wkKazFw7n1eciM3IyOUEP5FL4/4FUInjg7Jry3ItCxpZXpwy1acC9JwYzzpBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:31.704501Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.2713","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d577d2b0300d84b3ae444a6a5857ae525073457eb395131af8a7238815b35d8","sha256:d64731fbd1209de5047e9f03b1df4a096718b5854eb3e98c198dda9c094ea4e5"],"state_sha256":"3f10c4e11af00a5f8778e056f6afcb42de91ccb28cf938e733e285699cfba8c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DjJczK1Gr6XQw92b9Oi1YMfMsCADppnCso/G2/JP11b61eGF4AmQVaBBUSfEYmcS9WagpCbGffzOx1TxYoEjAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T10:19:09.360781Z","bundle_sha256":"b26273d9ed428eabd3bd71a6dda0ec8899ea29d9696fbaf72b05184397db4e0f"}}