{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:QKEK2FFSUJZFNAP54YQKFC2Z43","short_pith_number":"pith:QKEK2FFS","canonical_record":{"source":{"id":"1008.1947","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-08-11T15:59:34Z","cross_cats_sorted":[],"title_canon_sha256":"fe7350c51e559c1d40fd53b10d8c4fd4393b00ed87b145fa07f7086e0da19d6e","abstract_canon_sha256":"6cdcb54f3fe2f63376eed88505aac96e81165521e7e9bccbe3ca249e1d6f2bcf"},"schema_version":"1.0"},"canonical_sha256":"8288ad14b2a2725681fde620a28b59e6d0a6e90e2c5cee835ac9bce9ab58691b","source":{"kind":"arxiv","id":"1008.1947","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.1947","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"arxiv_version","alias_value":"1008.1947v1","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1947","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"pith_short_12","alias_value":"QKEK2FFSUJZF","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"QKEK2FFSUJZFNAP5","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"QKEK2FFS","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:QKEK2FFSUJZFNAP54YQKFC2Z43","target":"record","payload":{"canonical_record":{"source":{"id":"1008.1947","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-08-11T15:59:34Z","cross_cats_sorted":[],"title_canon_sha256":"fe7350c51e559c1d40fd53b10d8c4fd4393b00ed87b145fa07f7086e0da19d6e","abstract_canon_sha256":"6cdcb54f3fe2f63376eed88505aac96e81165521e7e9bccbe3ca249e1d6f2bcf"},"schema_version":"1.0"},"canonical_sha256":"8288ad14b2a2725681fde620a28b59e6d0a6e90e2c5cee835ac9bce9ab58691b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:01.950561Z","signature_b64":"gn/Xn5hvEPHp1jbIJu6B36d7sL2EVLn9OuOooq9RbagVjNhrhldyf1FupzgOfPmhwQGBSTSY8PwcfccrYkOqCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8288ad14b2a2725681fde620a28b59e6d0a6e90e2c5cee835ac9bce9ab58691b","last_reissued_at":"2026-05-18T02:58:01.949940Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:01.949940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.1947","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":"2026-05-18T02:58:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BWQn9NmQmH4Pl4dKig3bltBO6SebCpRwGRUSFAA0ArZ9HsIMzPHM0NbaUkvsuGcBuaRzpr/p8szyw72F6UMPBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:25:50.772597Z"},"content_sha256":"306c03a057da30648e7f8bb8c77989932fa3fb9f2eea4b64ccf7fa3ba1d045b6","schema_version":"1.0","event_id":"sha256:306c03a057da30648e7f8bb8c77989932fa3fb9f2eea4b64ccf7fa3ba1d045b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:QKEK2FFSUJZFNAP54YQKFC2Z43","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constructing projective varieties in weighted flag varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Balazs Szendroi, Muhammad Imran Qureshi","submitted_at":"2010-08-11T15:59:34Z","abstract_excerpt":"We compute the Hilbert series of general weighted flag varieties and discuss a computer-aided method to determine their defining equations. We apply our results to weighted flag varieties coming from the Lie groups of type G_2 and GL(6), to construct some families of polarised projective varieties in codimensions 8 and 6, respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1947","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":"2026-05-18T02:58:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZcFk6l26Cob3dhUjp+pavmgiJDc+mBOstTdxu3suJ6ND8aEbcn6TftUJDTd6FijVSSidgD8I4MfpohznoDvIBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:25:50.773221Z"},"content_sha256":"5a27975d03012b072413a7471105b66726bb9479ed3ff0da719abbc5f711f09c","schema_version":"1.0","event_id":"sha256:5a27975d03012b072413a7471105b66726bb9479ed3ff0da719abbc5f711f09c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QKEK2FFSUJZFNAP54YQKFC2Z43/bundle.json","state_url":"https://pith.science/pith/QKEK2FFSUJZFNAP54YQKFC2Z43/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QKEK2FFSUJZFNAP54YQKFC2Z43/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":"2026-05-30T02:25:50Z","links":{"resolver":"https://pith.science/pith/QKEK2FFSUJZFNAP54YQKFC2Z43","bundle":"https://pith.science/pith/QKEK2FFSUJZFNAP54YQKFC2Z43/bundle.json","state":"https://pith.science/pith/QKEK2FFSUJZFNAP54YQKFC2Z43/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QKEK2FFSUJZFNAP54YQKFC2Z43/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:QKEK2FFSUJZFNAP54YQKFC2Z43","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":"6cdcb54f3fe2f63376eed88505aac96e81165521e7e9bccbe3ca249e1d6f2bcf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-08-11T15:59:34Z","title_canon_sha256":"fe7350c51e559c1d40fd53b10d8c4fd4393b00ed87b145fa07f7086e0da19d6e"},"schema_version":"1.0","source":{"id":"1008.1947","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.1947","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"arxiv_version","alias_value":"1008.1947v1","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1947","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"pith_short_12","alias_value":"QKEK2FFSUJZF","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"QKEK2FFSUJZFNAP5","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"QKEK2FFS","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:5a27975d03012b072413a7471105b66726bb9479ed3ff0da719abbc5f711f09c","target":"graph","created_at":"2026-05-18T02:58:01Z","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":"We compute the Hilbert series of general weighted flag varieties and discuss a computer-aided method to determine their defining equations. We apply our results to weighted flag varieties coming from the Lie groups of type G_2 and GL(6), to construct some families of polarised projective varieties in codimensions 8 and 6, respectively.","authors_text":"Balazs Szendroi, Muhammad Imran Qureshi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-08-11T15:59:34Z","title":"Constructing projective varieties in weighted flag varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1947","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":"sha256:306c03a057da30648e7f8bb8c77989932fa3fb9f2eea4b64ccf7fa3ba1d045b6","target":"record","created_at":"2026-05-18T02:58:01Z","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":"6cdcb54f3fe2f63376eed88505aac96e81165521e7e9bccbe3ca249e1d6f2bcf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-08-11T15:59:34Z","title_canon_sha256":"fe7350c51e559c1d40fd53b10d8c4fd4393b00ed87b145fa07f7086e0da19d6e"},"schema_version":"1.0","source":{"id":"1008.1947","kind":"arxiv","version":1}},"canonical_sha256":"8288ad14b2a2725681fde620a28b59e6d0a6e90e2c5cee835ac9bce9ab58691b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8288ad14b2a2725681fde620a28b59e6d0a6e90e2c5cee835ac9bce9ab58691b","first_computed_at":"2026-05-18T02:58:01.949940Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:01.949940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gn/Xn5hvEPHp1jbIJu6B36d7sL2EVLn9OuOooq9RbagVjNhrhldyf1FupzgOfPmhwQGBSTSY8PwcfccrYkOqCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:01.950561Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.1947","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:306c03a057da30648e7f8bb8c77989932fa3fb9f2eea4b64ccf7fa3ba1d045b6","sha256:5a27975d03012b072413a7471105b66726bb9479ed3ff0da719abbc5f711f09c"],"state_sha256":"747fdf21e4f95e9eca0624ea38c1216e84c7d4fa26a53b1dc08e0932e5129bae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TBZairpYp9fEszsnzMMiELyq6xEzYH3ezt0o1joQfnwHCI1LxoKWgxAyEyW/9LIDWhjZ1yy7yK2ubErkkqTNBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T02:25:50.776204Z","bundle_sha256":"0116bc355aa9520bc3fda749b7eda4da989956c900847e209348c4d781b95471"}}