{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:CKTT5FSD6DW2YNHNSH44RN6NOE","short_pith_number":"pith:CKTT5FSD","canonical_record":{"source":{"id":"1106.0742","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-06-05T00:44:55Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"31ac157bea478baa3b074fe9dd5c87e9eaa44fb4f634495908d37333008d3151","abstract_canon_sha256":"93fb40a766e7c598821a3bf214973322eff38c6a25025c7390b0bdaf20272452"},"schema_version":"1.0"},"canonical_sha256":"12a73e9643f0edac34ed91f9c8b7cd713a6706c47713075121591c28f6dc902f","source":{"kind":"arxiv","id":"1106.0742","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.0742","created_at":"2026-05-18T04:12:32Z"},{"alias_kind":"arxiv_version","alias_value":"1106.0742v2","created_at":"2026-05-18T04:12:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0742","created_at":"2026-05-18T04:12:32Z"},{"alias_kind":"pith_short_12","alias_value":"CKTT5FSD6DW2","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CKTT5FSD6DW2YNHN","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CKTT5FSD","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:CKTT5FSD6DW2YNHNSH44RN6NOE","target":"record","payload":{"canonical_record":{"source":{"id":"1106.0742","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-06-05T00:44:55Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"31ac157bea478baa3b074fe9dd5c87e9eaa44fb4f634495908d37333008d3151","abstract_canon_sha256":"93fb40a766e7c598821a3bf214973322eff38c6a25025c7390b0bdaf20272452"},"schema_version":"1.0"},"canonical_sha256":"12a73e9643f0edac34ed91f9c8b7cd713a6706c47713075121591c28f6dc902f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:32.129819Z","signature_b64":"WsXwA4BCez2CVI12lhr7FF/Sp9UjPq4Vhbp2a5m6dQZW2Up8ryD3nQMbVP1E5VF5jM1hvwi9tzG5X8nUFJNKAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12a73e9643f0edac34ed91f9c8b7cd713a6706c47713075121591c28f6dc902f","last_reissued_at":"2026-05-18T04:12:32.129234Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:32.129234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.0742","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":"2026-05-18T04:12:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1/TnVDusmbEp2XUIN4uKr0Gg/UlZdULvM/x6x58gLaP+1RMGvOhk5kN9tseDnwv32lLuybs+3Tev/oFMcXBSCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T00:57:55.437549Z"},"content_sha256":"f816b2dcaba3c4f8868730a316d6aceb6cebb1eddcde60b73b35e66006bcb596","schema_version":"1.0","event_id":"sha256:f816b2dcaba3c4f8868730a316d6aceb6cebb1eddcde60b73b35e66006bcb596"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:CKTT5FSD6DW2YNHNSH44RN6NOE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rees Algebras of Diagonal Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Kuei-Nuan Lin","submitted_at":"2011-06-05T00:44:55Z","abstract_excerpt":"There is a natural epimorphism from the symmetric algebra to the Rees algebra of an ideal. When this epimorphism is an isomorphism, we say that the ideal is of linear type. Given two determinantal rings over a field, we consider the diagonal ideal, the kernel of the multiplication map. We prove that the diagonal ideal is of linear type and recover the defining ideal of the Rees algebra in some special cases. The special fiber ring of the diagonal ideal is the homogeneous coordinate ring of the join variety."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0742","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":"2026-05-18T04:12:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qpuhg2yfKz1F98kSv7Lx9NzJmE5Xh1auuo5HP6PU/Mbir1Za8jqLEFT2mlhiNvp94tfYyMHx1wodW3QUnMDtAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T00:57:55.437890Z"},"content_sha256":"d7fb7a0c82de4d5652346926711a465e9873c007a50d72273ed247ed33e88b19","schema_version":"1.0","event_id":"sha256:d7fb7a0c82de4d5652346926711a465e9873c007a50d72273ed247ed33e88b19"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CKTT5FSD6DW2YNHNSH44RN6NOE/bundle.json","state_url":"https://pith.science/pith/CKTT5FSD6DW2YNHNSH44RN6NOE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CKTT5FSD6DW2YNHNSH44RN6NOE/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":"2026-06-02T00:57:55Z","links":{"resolver":"https://pith.science/pith/CKTT5FSD6DW2YNHNSH44RN6NOE","bundle":"https://pith.science/pith/CKTT5FSD6DW2YNHNSH44RN6NOE/bundle.json","state":"https://pith.science/pith/CKTT5FSD6DW2YNHNSH44RN6NOE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CKTT5FSD6DW2YNHNSH44RN6NOE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CKTT5FSD6DW2YNHNSH44RN6NOE","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":"93fb40a766e7c598821a3bf214973322eff38c6a25025c7390b0bdaf20272452","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-06-05T00:44:55Z","title_canon_sha256":"31ac157bea478baa3b074fe9dd5c87e9eaa44fb4f634495908d37333008d3151"},"schema_version":"1.0","source":{"id":"1106.0742","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.0742","created_at":"2026-05-18T04:12:32Z"},{"alias_kind":"arxiv_version","alias_value":"1106.0742v2","created_at":"2026-05-18T04:12:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0742","created_at":"2026-05-18T04:12:32Z"},{"alias_kind":"pith_short_12","alias_value":"CKTT5FSD6DW2","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CKTT5FSD6DW2YNHN","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CKTT5FSD","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:d7fb7a0c82de4d5652346926711a465e9873c007a50d72273ed247ed33e88b19","target":"graph","created_at":"2026-05-18T04:12:32Z","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":"There is a natural epimorphism from the symmetric algebra to the Rees algebra of an ideal. When this epimorphism is an isomorphism, we say that the ideal is of linear type. Given two determinantal rings over a field, we consider the diagonal ideal, the kernel of the multiplication map. We prove that the diagonal ideal is of linear type and recover the defining ideal of the Rees algebra in some special cases. The special fiber ring of the diagonal ideal is the homogeneous coordinate ring of the join variety.","authors_text":"Kuei-Nuan Lin","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-06-05T00:44:55Z","title":"Rees Algebras of Diagonal Ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0742","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:f816b2dcaba3c4f8868730a316d6aceb6cebb1eddcde60b73b35e66006bcb596","target":"record","created_at":"2026-05-18T04:12:32Z","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":"93fb40a766e7c598821a3bf214973322eff38c6a25025c7390b0bdaf20272452","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-06-05T00:44:55Z","title_canon_sha256":"31ac157bea478baa3b074fe9dd5c87e9eaa44fb4f634495908d37333008d3151"},"schema_version":"1.0","source":{"id":"1106.0742","kind":"arxiv","version":2}},"canonical_sha256":"12a73e9643f0edac34ed91f9c8b7cd713a6706c47713075121591c28f6dc902f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12a73e9643f0edac34ed91f9c8b7cd713a6706c47713075121591c28f6dc902f","first_computed_at":"2026-05-18T04:12:32.129234Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:32.129234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WsXwA4BCez2CVI12lhr7FF/Sp9UjPq4Vhbp2a5m6dQZW2Up8ryD3nQMbVP1E5VF5jM1hvwi9tzG5X8nUFJNKAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:32.129819Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.0742","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f816b2dcaba3c4f8868730a316d6aceb6cebb1eddcde60b73b35e66006bcb596","sha256:d7fb7a0c82de4d5652346926711a465e9873c007a50d72273ed247ed33e88b19"],"state_sha256":"e653a228ab58b435799c5c58643007e9c49742f7076d4ee031dcde00ab67a132"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xqEcDhSNwzdI9wv+ntZsYibpsL85cZkNbdGjbrpvGzqzQrlPeM7IZgt/Jk5gZPC+AoxeX27U9gwU7P+zoRnYDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T00:57:55.439795Z","bundle_sha256":"b89fa2e0f7394108a8f1234bed3d4ff2f1d5b4d727ed3cf24dd71093f2711c9e"}}