{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:JO2IIU652JXWBZAORNM7IOOTND","short_pith_number":"pith:JO2IIU65","canonical_record":{"source":{"id":"0809.3971","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-09-23T17:22:55Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"346079be4c5b4e93ca3b689df704b6b99aeee8e3431467f0b5fc7e43d34ea717","abstract_canon_sha256":"770bede1b799262e0261eff4846a25b61c791a4c09750147a846e12b89ce9cb1"},"schema_version":"1.0"},"canonical_sha256":"4bb48453ddd26f60e40e8b59f439d368cdcc48ece3e4397991b2e97d09bcaaad","source":{"kind":"arxiv","id":"0809.3971","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.3971","created_at":"2026-05-18T04:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"0809.3971v1","created_at":"2026-05-18T04:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.3971","created_at":"2026-05-18T04:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"JO2IIU652JXW","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"JO2IIU652JXWBZAO","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"JO2IIU65","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:JO2IIU652JXWBZAORNM7IOOTND","target":"record","payload":{"canonical_record":{"source":{"id":"0809.3971","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-09-23T17:22:55Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"346079be4c5b4e93ca3b689df704b6b99aeee8e3431467f0b5fc7e43d34ea717","abstract_canon_sha256":"770bede1b799262e0261eff4846a25b61c791a4c09750147a846e12b89ce9cb1"},"schema_version":"1.0"},"canonical_sha256":"4bb48453ddd26f60e40e8b59f439d368cdcc48ece3e4397991b2e97d09bcaaad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:25.385875Z","signature_b64":"HF4ZIXHCD6jR9NqrII3Ji+ClFQg2+CcUHAp413hezdU5foOYsCgTineDwTpKNtti2UUCIYnrMOdTv3oWb/gJBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bb48453ddd26f60e40e8b59f439d368cdcc48ece3e4397991b2e97d09bcaaad","last_reissued_at":"2026-05-18T04:41:25.385440Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:25.385440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0809.3971","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":"2026-05-18T04:41:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EhlEENhTVaaKrcdEunUUhmLNRCyCwgV1yLdNxOaifM4ZW0bsyLuXNWRpCGt8kEenJabtTrMVyuO6JG0JnHrDCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T23:33:23.968349Z"},"content_sha256":"2cdd0cbf904defbd54d994faab78b1ad800c077e9db5f30c421ffc0153e96d91","schema_version":"1.0","event_id":"sha256:2cdd0cbf904defbd54d994faab78b1ad800c077e9db5f30c421ffc0153e96d91"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:JO2IIU652JXWBZAORNM7IOOTND","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric idealizers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RA","authors_text":"Susan J. Sierra","submitted_at":"2008-09-23T17:22:55Z","abstract_excerpt":"Let X be a projective variety, $\\sigma$ an automorphism of X, L a $\\sigma$-ample invertible sheaf on X, and Z a closed subscheme of X. Inside the twisted homogeneous coordinate ring $B = B(X, L, \\sigma)$, let I be the right ideal of sections vanishing at Z. We study the subring R = k + I of B. Under mild conditions on Z and $\\sigma$, R is the idealizer of I in B: the maximal subring of B in which I is a two-sided ideal.\n  We give geometric conditions on Z and $\\sigma$ that determine the algebraic properties of R, and show that if Z and $\\sigma$ are sufficiently general, in a sense we make prec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.3971","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":"2026-05-18T04:41:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4yV7y7pj7tyaDlBxD8nqKFw9pYDcP2Da99TsMwauNAxnOSKUwL2iR/+HjJGI3gn5zJLhmnNzxEGlJCsKQG37Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T23:33:23.968826Z"},"content_sha256":"b0800234f899ff8d39f86793e62775437099e28971cdedd22416a1025d5e499b","schema_version":"1.0","event_id":"sha256:b0800234f899ff8d39f86793e62775437099e28971cdedd22416a1025d5e499b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JO2IIU652JXWBZAORNM7IOOTND/bundle.json","state_url":"https://pith.science/pith/JO2IIU652JXWBZAORNM7IOOTND/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JO2IIU652JXWBZAORNM7IOOTND/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":"2026-06-28T23:33:23Z","links":{"resolver":"https://pith.science/pith/JO2IIU652JXWBZAORNM7IOOTND","bundle":"https://pith.science/pith/JO2IIU652JXWBZAORNM7IOOTND/bundle.json","state":"https://pith.science/pith/JO2IIU652JXWBZAORNM7IOOTND/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JO2IIU652JXWBZAORNM7IOOTND/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:JO2IIU652JXWBZAORNM7IOOTND","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":"770bede1b799262e0261eff4846a25b61c791a4c09750147a846e12b89ce9cb1","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-09-23T17:22:55Z","title_canon_sha256":"346079be4c5b4e93ca3b689df704b6b99aeee8e3431467f0b5fc7e43d34ea717"},"schema_version":"1.0","source":{"id":"0809.3971","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.3971","created_at":"2026-05-18T04:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"0809.3971v1","created_at":"2026-05-18T04:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.3971","created_at":"2026-05-18T04:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"JO2IIU652JXW","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"JO2IIU652JXWBZAO","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"JO2IIU65","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:b0800234f899ff8d39f86793e62775437099e28971cdedd22416a1025d5e499b","target":"graph","created_at":"2026-05-18T04:41:25Z","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":"Let X be a projective variety, $\\sigma$ an automorphism of X, L a $\\sigma$-ample invertible sheaf on X, and Z a closed subscheme of X. Inside the twisted homogeneous coordinate ring $B = B(X, L, \\sigma)$, let I be the right ideal of sections vanishing at Z. We study the subring R = k + I of B. Under mild conditions on Z and $\\sigma$, R is the idealizer of I in B: the maximal subring of B in which I is a two-sided ideal.\n  We give geometric conditions on Z and $\\sigma$ that determine the algebraic properties of R, and show that if Z and $\\sigma$ are sufficiently general, in a sense we make prec","authors_text":"Susan J. Sierra","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-09-23T17:22:55Z","title":"Geometric idealizers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.3971","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":"sha256:2cdd0cbf904defbd54d994faab78b1ad800c077e9db5f30c421ffc0153e96d91","target":"record","created_at":"2026-05-18T04:41:25Z","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":"770bede1b799262e0261eff4846a25b61c791a4c09750147a846e12b89ce9cb1","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-09-23T17:22:55Z","title_canon_sha256":"346079be4c5b4e93ca3b689df704b6b99aeee8e3431467f0b5fc7e43d34ea717"},"schema_version":"1.0","source":{"id":"0809.3971","kind":"arxiv","version":1}},"canonical_sha256":"4bb48453ddd26f60e40e8b59f439d368cdcc48ece3e4397991b2e97d09bcaaad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4bb48453ddd26f60e40e8b59f439d368cdcc48ece3e4397991b2e97d09bcaaad","first_computed_at":"2026-05-18T04:41:25.385440Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:25.385440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HF4ZIXHCD6jR9NqrII3Ji+ClFQg2+CcUHAp413hezdU5foOYsCgTineDwTpKNtti2UUCIYnrMOdTv3oWb/gJBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:25.385875Z","signed_message":"canonical_sha256_bytes"},"source_id":"0809.3971","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2cdd0cbf904defbd54d994faab78b1ad800c077e9db5f30c421ffc0153e96d91","sha256:b0800234f899ff8d39f86793e62775437099e28971cdedd22416a1025d5e499b"],"state_sha256":"8c5e4418bb8f7034c82a85e604cd4e960c50b575307b07f8cc53b98984625f96"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EopRz4xfgGn8kwreqTI4lBMwIefqzUY/MyS1bObzvYIXhso3nGVT6qJWq8fr5aQzmXIGAPrnNxvn1vX9/jvDBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T23:33:23.970700Z","bundle_sha256":"7597c906a9b8b6b6b76a32a25535c0a3b5ba4d1f0cc679e476072601761a82cd"}}