{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:63SZODWSHUJW5FJOLVJHDYJO37","short_pith_number":"pith:63SZODWS","canonical_record":{"source":{"id":"math/0306244","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.RA","submitted_at":"2003-06-16T19:33:28Z","cross_cats_sorted":["math.AG","math.QA"],"title_canon_sha256":"937e5fbf1f1c2795a63daddba3c391e9cfc36a725a0369d68b04e5cf9f0b2af7","abstract_canon_sha256":"97b2d9ed7866afc674a376104c97aa9440a207d8bd02e6416061213d92e8469c"},"schema_version":"1.0"},"canonical_sha256":"f6e5970ed23d136e952e5d5271e12edfe8e98d18bc5ad8c0dd491d3f1145682a","source":{"kind":"arxiv","id":"math/0306244","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0306244","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"arxiv_version","alias_value":"math/0306244v1","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0306244","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"pith_short_12","alias_value":"63SZODWSHUJW","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"63SZODWSHUJW5FJO","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"63SZODWS","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:63SZODWSHUJW5FJOLVJHDYJO37","target":"record","payload":{"canonical_record":{"source":{"id":"math/0306244","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.RA","submitted_at":"2003-06-16T19:33:28Z","cross_cats_sorted":["math.AG","math.QA"],"title_canon_sha256":"937e5fbf1f1c2795a63daddba3c391e9cfc36a725a0369d68b04e5cf9f0b2af7","abstract_canon_sha256":"97b2d9ed7866afc674a376104c97aa9440a207d8bd02e6416061213d92e8469c"},"schema_version":"1.0"},"canonical_sha256":"f6e5970ed23d136e952e5d5271e12edfe8e98d18bc5ad8c0dd491d3f1145682a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:28.809221Z","signature_b64":"MmZ8GwRWboPAIyiSRypPQk0MUlkc2VKGjXn7qNIN5tB7dal7G6INkWixsRQyBIO0eQg+xp0qSU+0LEPQnly9DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6e5970ed23d136e952e5d5271e12edfe8e98d18bc5ad8c0dd491d3f1145682a","last_reissued_at":"2026-05-18T01:05:28.808656Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:28.808656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0306244","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":"2026-05-18T01:05:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qNlNh8gaNFxlXD5nayzABV9AiHsKFgFqV3YcMtLj+jAmK0Yweptv9qBay5kvT0Ki1swEDiSkCJc8VazXnAHqAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:10:29.123861Z"},"content_sha256":"ecb150645e674b6aa4ac31f28b6f27657df47884f3f081d34499ef7dd175fe3f","schema_version":"1.0","event_id":"sha256:ecb150645e674b6aa4ac31f28b6f27657df47884f3f081d34499ef7dd175fe3f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:63SZODWSHUJW5FJOLVJHDYJO37","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Naive Noncommutative Blowing Up","license":"","headline":"","cross_cats":["math.AG","math.QA"],"primary_cat":"math.RA","authors_text":"D. Rogalski, D. S. Keeler, J. T. Stafford","submitted_at":"2003-06-16T19:33:28Z","abstract_excerpt":"Let B(X,L,s) be the twisted homogeneous coordinate ring of an irreducible variety X over an algebraically closed field k with dim X > 1. Assume that c in X and s in Aut(X) are in sufficiently general position. We show that if one follows the commutative prescription for blowing up X at c, but in this noncommutative setting, one obtains a noncommutative ring R=R(X,c,L,s) with surprising properties. In particular:\n (1) R is always noetherian but never strongly noetherian.\n (2) If R is generated in degree one then the images of the R-point modules in qgr(R) are naturally in (1-1) correspondence w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0306244","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":"2026-05-18T01:05:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6JIJqjVE1zwkfijuGRJHWUFrTCTLAtCcUahEx56xtiqnDd0L6DC6w1ulbtkqsheDJhlqS2w8ZUL30xZPqoksAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:10:29.124449Z"},"content_sha256":"9b1318acd4f610fa474c236619fad392f51f7570e0388fc0f585ccfb660c00ad","schema_version":"1.0","event_id":"sha256:9b1318acd4f610fa474c236619fad392f51f7570e0388fc0f585ccfb660c00ad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/63SZODWSHUJW5FJOLVJHDYJO37/bundle.json","state_url":"https://pith.science/pith/63SZODWSHUJW5FJOLVJHDYJO37/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/63SZODWSHUJW5FJOLVJHDYJO37/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":"2026-05-26T22:10:29Z","links":{"resolver":"https://pith.science/pith/63SZODWSHUJW5FJOLVJHDYJO37","bundle":"https://pith.science/pith/63SZODWSHUJW5FJOLVJHDYJO37/bundle.json","state":"https://pith.science/pith/63SZODWSHUJW5FJOLVJHDYJO37/state.json","well_known_bundle":"https://pith.science/.well-known/pith/63SZODWSHUJW5FJOLVJHDYJO37/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:63SZODWSHUJW5FJOLVJHDYJO37","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":"97b2d9ed7866afc674a376104c97aa9440a207d8bd02e6416061213d92e8469c","cross_cats_sorted":["math.AG","math.QA"],"license":"","primary_cat":"math.RA","submitted_at":"2003-06-16T19:33:28Z","title_canon_sha256":"937e5fbf1f1c2795a63daddba3c391e9cfc36a725a0369d68b04e5cf9f0b2af7"},"schema_version":"1.0","source":{"id":"math/0306244","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0306244","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"arxiv_version","alias_value":"math/0306244v1","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0306244","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"pith_short_12","alias_value":"63SZODWSHUJW","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"63SZODWSHUJW5FJO","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"63SZODWS","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:9b1318acd4f610fa474c236619fad392f51f7570e0388fc0f585ccfb660c00ad","target":"graph","created_at":"2026-05-18T01:05:28Z","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":"Let B(X,L,s) be the twisted homogeneous coordinate ring of an irreducible variety X over an algebraically closed field k with dim X > 1. Assume that c in X and s in Aut(X) are in sufficiently general position. We show that if one follows the commutative prescription for blowing up X at c, but in this noncommutative setting, one obtains a noncommutative ring R=R(X,c,L,s) with surprising properties. In particular:\n (1) R is always noetherian but never strongly noetherian.\n (2) If R is generated in degree one then the images of the R-point modules in qgr(R) are naturally in (1-1) correspondence w","authors_text":"D. Rogalski, D. S. Keeler, J. T. Stafford","cross_cats":["math.AG","math.QA"],"headline":"","license":"","primary_cat":"math.RA","submitted_at":"2003-06-16T19:33:28Z","title":"Naive Noncommutative Blowing Up"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0306244","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:ecb150645e674b6aa4ac31f28b6f27657df47884f3f081d34499ef7dd175fe3f","target":"record","created_at":"2026-05-18T01:05:28Z","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":"97b2d9ed7866afc674a376104c97aa9440a207d8bd02e6416061213d92e8469c","cross_cats_sorted":["math.AG","math.QA"],"license":"","primary_cat":"math.RA","submitted_at":"2003-06-16T19:33:28Z","title_canon_sha256":"937e5fbf1f1c2795a63daddba3c391e9cfc36a725a0369d68b04e5cf9f0b2af7"},"schema_version":"1.0","source":{"id":"math/0306244","kind":"arxiv","version":1}},"canonical_sha256":"f6e5970ed23d136e952e5d5271e12edfe8e98d18bc5ad8c0dd491d3f1145682a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6e5970ed23d136e952e5d5271e12edfe8e98d18bc5ad8c0dd491d3f1145682a","first_computed_at":"2026-05-18T01:05:28.808656Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:28.808656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MmZ8GwRWboPAIyiSRypPQk0MUlkc2VKGjXn7qNIN5tB7dal7G6INkWixsRQyBIO0eQg+xp0qSU+0LEPQnly9DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:28.809221Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0306244","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ecb150645e674b6aa4ac31f28b6f27657df47884f3f081d34499ef7dd175fe3f","sha256:9b1318acd4f610fa474c236619fad392f51f7570e0388fc0f585ccfb660c00ad"],"state_sha256":"f8ee8710a81643246d2d24c2693a10a2c448f52f20348305b041f84dc5fe90b5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Za7f3Y3E8Ws5wJcNOEpTAG/WXSPG1gy1L63q2MuDq4HP+FIEpHQ+bmleyJVPpUGObmzxB3sP0IAE/DwdtGKJBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T22:10:29.127446Z","bundle_sha256":"cfa2cf842a8b3aeadeef67040e760564f7a13ff41f4dacdd32700bac60e9ed2c"}}