{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:QCS75DQZAAOHGLYWB3NGDNYFF6","short_pith_number":"pith:QCS75DQZ","canonical_record":{"source":{"id":"1111.7263","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-11-30T18:22:10Z","cross_cats_sorted":["math.AG","math.CO","math.RT"],"title_canon_sha256":"c4ee05aeeee5f66853036da150c9d50dba5fdacd9a29569bc503c78bb5e5645a","abstract_canon_sha256":"564b8c8a9ebb250e33074558d89482d29bd83627c923b56099b6ea935c1c3104"},"schema_version":"1.0"},"canonical_sha256":"80a5fe8e19001c732f160eda61b7052f80a04dd3c20fd4c196f323429ed54e08","source":{"kind":"arxiv","id":"1111.7263","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.7263","created_at":"2026-05-18T03:25:59Z"},{"alias_kind":"arxiv_version","alias_value":"1111.7263v3","created_at":"2026-05-18T03:25:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.7263","created_at":"2026-05-18T03:25:59Z"},{"alias_kind":"pith_short_12","alias_value":"QCS75DQZAAOH","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QCS75DQZAAOHGLYW","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QCS75DQZ","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:QCS75DQZAAOHGLYWB3NGDNYFF6","target":"record","payload":{"canonical_record":{"source":{"id":"1111.7263","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-11-30T18:22:10Z","cross_cats_sorted":["math.AG","math.CO","math.RT"],"title_canon_sha256":"c4ee05aeeee5f66853036da150c9d50dba5fdacd9a29569bc503c78bb5e5645a","abstract_canon_sha256":"564b8c8a9ebb250e33074558d89482d29bd83627c923b56099b6ea935c1c3104"},"schema_version":"1.0"},"canonical_sha256":"80a5fe8e19001c732f160eda61b7052f80a04dd3c20fd4c196f323429ed54e08","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:59.664555Z","signature_b64":"unIbOv1g8U1ju6Am+DomdvJj+rLQy6WudniIpDniDRSo+ldsrge3M6FfGRA29MfGCfaH/+qBPTwetfvOJjulCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80a5fe8e19001c732f160eda61b7052f80a04dd3c20fd4c196f323429ed54e08","last_reissued_at":"2026-05-18T03:25:59.664009Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:59.664009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.7263","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:25:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x78MKbbWngwUrgaH0L8kQYTTCeRzTHCbTRKYYPSmsoVqqqrMEKR03HVbetbUu/g7QSJipm5lQqngh+9/5XXEAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:23:05.299570Z"},"content_sha256":"8a23a7feaa4a6bf9761bc5c742be405d40db36a8ec1698799c9ebbc878e9ed52","schema_version":"1.0","event_id":"sha256:8a23a7feaa4a6bf9761bc5c742be405d40db36a8ec1698799c9ebbc878e9ed52"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:QCS75DQZAAOHGLYWB3NGDNYFF6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relations between the minors of a generic matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CO","math.RT"],"primary_cat":"math.AC","authors_text":"Aldo Conca, Matteo Varbaro, Winfried Bruns","submitted_at":"2011-11-30T18:22:10Z","abstract_excerpt":"It is well-known that the Pl\\\"ucker relations generate the ideal of relations of the maximal minors of a generic matrix. In this paper we discuss the relations between minors of a (non-maximal) fixed size. We will exhibit minimal relations in degrees 2 (non-Pl\\\"ucker in general) and 3, and give some evidence for our conjecture that we have found the generating system of the ideal of relations. The approach is through the representation theory of the general linear group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.7263","kind":"arxiv","version":3},"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":"2026-05-18T03:25:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IPJ0zJ0AUDU7gJkODU0TulPYx9JFhZcV9A01/qhY2YmaH81zUAKOtu0Fq4uJQ1NooGOR/tKD50blxgHJDmLlBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:23:05.299981Z"},"content_sha256":"dc61a978d1849396fb9b4c8da478d8871efa7b7e6ecea965da0876b03394ef79","schema_version":"1.0","event_id":"sha256:dc61a978d1849396fb9b4c8da478d8871efa7b7e6ecea965da0876b03394ef79"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QCS75DQZAAOHGLYWB3NGDNYFF6/bundle.json","state_url":"https://pith.science/pith/QCS75DQZAAOHGLYWB3NGDNYFF6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QCS75DQZAAOHGLYWB3NGDNYFF6/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":"2026-05-27T00:23:05Z","links":{"resolver":"https://pith.science/pith/QCS75DQZAAOHGLYWB3NGDNYFF6","bundle":"https://pith.science/pith/QCS75DQZAAOHGLYWB3NGDNYFF6/bundle.json","state":"https://pith.science/pith/QCS75DQZAAOHGLYWB3NGDNYFF6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QCS75DQZAAOHGLYWB3NGDNYFF6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QCS75DQZAAOHGLYWB3NGDNYFF6","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":"564b8c8a9ebb250e33074558d89482d29bd83627c923b56099b6ea935c1c3104","cross_cats_sorted":["math.AG","math.CO","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-11-30T18:22:10Z","title_canon_sha256":"c4ee05aeeee5f66853036da150c9d50dba5fdacd9a29569bc503c78bb5e5645a"},"schema_version":"1.0","source":{"id":"1111.7263","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.7263","created_at":"2026-05-18T03:25:59Z"},{"alias_kind":"arxiv_version","alias_value":"1111.7263v3","created_at":"2026-05-18T03:25:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.7263","created_at":"2026-05-18T03:25:59Z"},{"alias_kind":"pith_short_12","alias_value":"QCS75DQZAAOH","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QCS75DQZAAOHGLYW","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QCS75DQZ","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:dc61a978d1849396fb9b4c8da478d8871efa7b7e6ecea965da0876b03394ef79","target":"graph","created_at":"2026-05-18T03:25:59Z","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":"It is well-known that the Pl\\\"ucker relations generate the ideal of relations of the maximal minors of a generic matrix. In this paper we discuss the relations between minors of a (non-maximal) fixed size. We will exhibit minimal relations in degrees 2 (non-Pl\\\"ucker in general) and 3, and give some evidence for our conjecture that we have found the generating system of the ideal of relations. The approach is through the representation theory of the general linear group.","authors_text":"Aldo Conca, Matteo Varbaro, Winfried Bruns","cross_cats":["math.AG","math.CO","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-11-30T18:22:10Z","title":"Relations between the minors of a generic matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.7263","kind":"arxiv","version":3},"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":"sha256:8a23a7feaa4a6bf9761bc5c742be405d40db36a8ec1698799c9ebbc878e9ed52","target":"record","created_at":"2026-05-18T03:25:59Z","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":"564b8c8a9ebb250e33074558d89482d29bd83627c923b56099b6ea935c1c3104","cross_cats_sorted":["math.AG","math.CO","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-11-30T18:22:10Z","title_canon_sha256":"c4ee05aeeee5f66853036da150c9d50dba5fdacd9a29569bc503c78bb5e5645a"},"schema_version":"1.0","source":{"id":"1111.7263","kind":"arxiv","version":3}},"canonical_sha256":"80a5fe8e19001c732f160eda61b7052f80a04dd3c20fd4c196f323429ed54e08","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80a5fe8e19001c732f160eda61b7052f80a04dd3c20fd4c196f323429ed54e08","first_computed_at":"2026-05-18T03:25:59.664009Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:59.664009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"unIbOv1g8U1ju6Am+DomdvJj+rLQy6WudniIpDniDRSo+ldsrge3M6FfGRA29MfGCfaH/+qBPTwetfvOJjulCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:59.664555Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.7263","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a23a7feaa4a6bf9761bc5c742be405d40db36a8ec1698799c9ebbc878e9ed52","sha256:dc61a978d1849396fb9b4c8da478d8871efa7b7e6ecea965da0876b03394ef79"],"state_sha256":"69085b996f714e7a38d3bccab2a8e8dd557f5c472df826f62d38989c65c18480"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3kNJfvzkY56WKcGJeA4Ic6hp+7vrl9D3VVVtI2lyWDEkWitNKdv5YCdXBTJm8hKoiSYDUnmPu8l04v2IO+glDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T00:23:05.303212Z","bundle_sha256":"c96dcd0309bc092f38859ae38390457d729d263f9c44f1babcde5c064ef5b2cf"}}