{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:T6B23Y7436OB4FJ7LCOPHYDWAC","short_pith_number":"pith:T6B23Y74","canonical_record":{"source":{"id":"1005.3585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-05-20T04:05:55Z","cross_cats_sorted":[],"title_canon_sha256":"8011507fdbfa83502339895d046fc737b3823cf2ed2299ddb9357675d3fef40c","abstract_canon_sha256":"9b3d1c7fa13d3fa1656f534c4a36c6345e83d529dce02f7754e1b821683e1111"},"schema_version":"1.0"},"canonical_sha256":"9f83ade3fcdf9c1e153f589cf3e076008f168b47e7884d98b5368e62b72904df","source":{"kind":"arxiv","id":"1005.3585","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.3585","created_at":"2026-05-18T04:20:14Z"},{"alias_kind":"arxiv_version","alias_value":"1005.3585v1","created_at":"2026-05-18T04:20:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.3585","created_at":"2026-05-18T04:20:14Z"},{"alias_kind":"pith_short_12","alias_value":"T6B23Y7436OB","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"T6B23Y7436OB4FJ7","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"T6B23Y74","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:T6B23Y7436OB4FJ7LCOPHYDWAC","target":"record","payload":{"canonical_record":{"source":{"id":"1005.3585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-05-20T04:05:55Z","cross_cats_sorted":[],"title_canon_sha256":"8011507fdbfa83502339895d046fc737b3823cf2ed2299ddb9357675d3fef40c","abstract_canon_sha256":"9b3d1c7fa13d3fa1656f534c4a36c6345e83d529dce02f7754e1b821683e1111"},"schema_version":"1.0"},"canonical_sha256":"9f83ade3fcdf9c1e153f589cf3e076008f168b47e7884d98b5368e62b72904df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:14.756035Z","signature_b64":"l116noAsbUm9NAt70gvfhJmal7Fc7dl16f29FmSEA/kf4eKFChbz+w0iP01okkOZozAq3v6++IDk+EBdyNwgCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f83ade3fcdf9c1e153f589cf3e076008f168b47e7884d98b5368e62b72904df","last_reissued_at":"2026-05-18T04:20:14.755603Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:14.755603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.3585","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":"2026-05-18T04:20:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w7CY2QsESS/JBiycCjM+sqy5knQ/53HmqhAV/02j/y427RFbD2De1hGHfMpKAjVil/wB9lieuML3KjVaHOegBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:56:19.282658Z"},"content_sha256":"25b32f47461b9d4bb077e9a23da97413c4ec31c190cbdeea003e45c2a1fd41f5","schema_version":"1.0","event_id":"sha256:25b32f47461b9d4bb077e9a23da97413c4ec31c190cbdeea003e45c2a1fd41f5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:T6B23Y7436OB4FJ7LCOPHYDWAC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equality of symmetrized tensors and the coordinate ring of the flag variety","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrew Berget","submitted_at":"2010-05-20T04:05:55Z","abstract_excerpt":"In this note we give a transparent proof of a result of da Cruz and Dias da Silva on the equality of symmetrized decomposable tensors. This will be done by explaining that their result follows from the fact that the coordinate ring of a flag variety is a unique factorization domain."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.3585","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":"2026-05-18T04:20:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JNvwQS12ghgR9O9mwJNhNq5JifFarmBWdz6DkVWchcL9vTsnWUkiWNdJfyZV1XQODpDf9eQVu1BZDP29TImsCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:56:19.283350Z"},"content_sha256":"d9c508342a5a0ebde71a99a2930d9ff719cfad94e3a1912403deb7398ddac3dd","schema_version":"1.0","event_id":"sha256:d9c508342a5a0ebde71a99a2930d9ff719cfad94e3a1912403deb7398ddac3dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T6B23Y7436OB4FJ7LCOPHYDWAC/bundle.json","state_url":"https://pith.science/pith/T6B23Y7436OB4FJ7LCOPHYDWAC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T6B23Y7436OB4FJ7LCOPHYDWAC/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":"2026-05-26T01:56:19Z","links":{"resolver":"https://pith.science/pith/T6B23Y7436OB4FJ7LCOPHYDWAC","bundle":"https://pith.science/pith/T6B23Y7436OB4FJ7LCOPHYDWAC/bundle.json","state":"https://pith.science/pith/T6B23Y7436OB4FJ7LCOPHYDWAC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T6B23Y7436OB4FJ7LCOPHYDWAC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:T6B23Y7436OB4FJ7LCOPHYDWAC","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":"9b3d1c7fa13d3fa1656f534c4a36c6345e83d529dce02f7754e1b821683e1111","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-05-20T04:05:55Z","title_canon_sha256":"8011507fdbfa83502339895d046fc737b3823cf2ed2299ddb9357675d3fef40c"},"schema_version":"1.0","source":{"id":"1005.3585","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.3585","created_at":"2026-05-18T04:20:14Z"},{"alias_kind":"arxiv_version","alias_value":"1005.3585v1","created_at":"2026-05-18T04:20:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.3585","created_at":"2026-05-18T04:20:14Z"},{"alias_kind":"pith_short_12","alias_value":"T6B23Y7436OB","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"T6B23Y7436OB4FJ7","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"T6B23Y74","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:d9c508342a5a0ebde71a99a2930d9ff719cfad94e3a1912403deb7398ddac3dd","target":"graph","created_at":"2026-05-18T04:20:14Z","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":"In this note we give a transparent proof of a result of da Cruz and Dias da Silva on the equality of symmetrized decomposable tensors. This will be done by explaining that their result follows from the fact that the coordinate ring of a flag variety is a unique factorization domain.","authors_text":"Andrew Berget","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-05-20T04:05:55Z","title":"Equality of symmetrized tensors and the coordinate ring of the flag variety"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.3585","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":"sha256:25b32f47461b9d4bb077e9a23da97413c4ec31c190cbdeea003e45c2a1fd41f5","target":"record","created_at":"2026-05-18T04:20:14Z","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":"9b3d1c7fa13d3fa1656f534c4a36c6345e83d529dce02f7754e1b821683e1111","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-05-20T04:05:55Z","title_canon_sha256":"8011507fdbfa83502339895d046fc737b3823cf2ed2299ddb9357675d3fef40c"},"schema_version":"1.0","source":{"id":"1005.3585","kind":"arxiv","version":1}},"canonical_sha256":"9f83ade3fcdf9c1e153f589cf3e076008f168b47e7884d98b5368e62b72904df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f83ade3fcdf9c1e153f589cf3e076008f168b47e7884d98b5368e62b72904df","first_computed_at":"2026-05-18T04:20:14.755603Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:14.755603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l116noAsbUm9NAt70gvfhJmal7Fc7dl16f29FmSEA/kf4eKFChbz+w0iP01okkOZozAq3v6++IDk+EBdyNwgCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:14.756035Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.3585","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25b32f47461b9d4bb077e9a23da97413c4ec31c190cbdeea003e45c2a1fd41f5","sha256:d9c508342a5a0ebde71a99a2930d9ff719cfad94e3a1912403deb7398ddac3dd"],"state_sha256":"ec364f44cbb8bfe451464b953ba9067374921c31e3e10fab9a6b785caeb2ea4d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uEZDCB6sJ9PnZ2ZQu0IRydc+Q55mcu0nktZNsQu6ZvQrKQQjL58NRRr1a+Vqj0VeMK1DMyjAzcyjA8y7Fd3aBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T01:56:19.286777Z","bundle_sha256":"3fff50c8cae0d75f05fe52d19478109d220362e52396c44ffc74dc83a16eff49"}}