{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:WVB7AURNZTZGXHSQ2RLMFPJVYJ","short_pith_number":"pith:WVB7AURN","canonical_record":{"source":{"id":"1306.3390","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-06-14T13:23:48Z","cross_cats_sorted":["cs.SC"],"title_canon_sha256":"a0d33d67d1c4d43e7bdb732a81f7cccae07fc302d62a7cfaeb95ced62859f5f9","abstract_canon_sha256":"18225c9f7886956bce66b39728b9d6eef5d4b108caed680bec977c1726c9b74f"},"schema_version":"1.0"},"canonical_sha256":"b543f0522dccf26b9e50d456c2bd35c2499c362af7183d379a92d43df9b256d2","source":{"kind":"arxiv","id":"1306.3390","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3390","created_at":"2026-05-18T03:04:37Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3390v2","created_at":"2026-05-18T03:04:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3390","created_at":"2026-05-18T03:04:37Z"},{"alias_kind":"pith_short_12","alias_value":"WVB7AURNZTZG","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WVB7AURNZTZGXHSQ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WVB7AURN","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:WVB7AURNZTZGXHSQ2RLMFPJVYJ","target":"record","payload":{"canonical_record":{"source":{"id":"1306.3390","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-06-14T13:23:48Z","cross_cats_sorted":["cs.SC"],"title_canon_sha256":"a0d33d67d1c4d43e7bdb732a81f7cccae07fc302d62a7cfaeb95ced62859f5f9","abstract_canon_sha256":"18225c9f7886956bce66b39728b9d6eef5d4b108caed680bec977c1726c9b74f"},"schema_version":"1.0"},"canonical_sha256":"b543f0522dccf26b9e50d456c2bd35c2499c362af7183d379a92d43df9b256d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:37.704380Z","signature_b64":"OscdBbTucxQSVO9lP8tdLOaHCFBhgXiRUMYbHXhG7wPqBbaLcRC0T0LMZUyeaCE20da60L2E03ZVT+8Iz1VQDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b543f0522dccf26b9e50d456c2bd35c2499c362af7183d379a92d43df9b256d2","last_reissued_at":"2026-05-18T03:04:37.703612Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:37.703612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.3390","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":"2026-05-18T03:04:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kmvQa5Lx82kMzIYzOT510IWpt8WQf5jtmWOJgWmrNYcAJFoplaPAwqmiAcbd0MsdpnpE1mB5za1qvjQh4k1BCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T02:56:50.278828Z"},"content_sha256":"6d2daf2c7ea7b58528cda794d4a6d3be1c926426a859170c371088e05f0a1c06","schema_version":"1.0","event_id":"sha256:6d2daf2c7ea7b58528cda794d4a6d3be1c926426a859170c371088e05f0a1c06"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:WVB7AURNZTZGXHSQ2RLMFPJVYJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Degeneracy loci and polynomial equation solving","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"math.AG","authors_text":"Bernd Bank, Gr\\'egoire Lecerf, Guillermo Matera, Joos Heintz, Marc Giusti, Pablo Solern\\'o","submitted_at":"2013-06-14T13:23:48Z","abstract_excerpt":"Let V be a smooth equidimensional quasi-affine variety of dimension r over the complex numbers $C$ and let $F$ be a $(p\\times s)$-matrix of coordinate functions of $C[V]$, where $s\\ge p+r$. The pair $(V,F)$ determines a vector bundle $E$ of rank $s-p$ over $W:=\\{x\\in V:\\mathrm{rk} F(x)=p\\}$. We associate with $(V,F)$ a descending chain of degeneracy loci of E (the generic polar varieties of $V$ represent a typical example of this situation).\n  The maximal degree of these degeneracy loci constitutes the essential ingredient for the uniform, bounded error probabilistic pseudo-polynomial time alg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3390","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":"2026-05-18T03:04:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o42VIrXtn8Ar1M0d/u6LquS99DsCTK0DYJCaFkCcj4tSK5E0iyh6GmwFVP7BUDQ0jVgCGWergkbfXd97M9hoAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T02:56:50.279165Z"},"content_sha256":"1d8964c9314cfb0a4091b538d2b4414f263eb87cdf9bda5e6ff0c0bf8508f7af","schema_version":"1.0","event_id":"sha256:1d8964c9314cfb0a4091b538d2b4414f263eb87cdf9bda5e6ff0c0bf8508f7af"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WVB7AURNZTZGXHSQ2RLMFPJVYJ/bundle.json","state_url":"https://pith.science/pith/WVB7AURNZTZGXHSQ2RLMFPJVYJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WVB7AURNZTZGXHSQ2RLMFPJVYJ/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":"2026-06-24T02:56:50Z","links":{"resolver":"https://pith.science/pith/WVB7AURNZTZGXHSQ2RLMFPJVYJ","bundle":"https://pith.science/pith/WVB7AURNZTZGXHSQ2RLMFPJVYJ/bundle.json","state":"https://pith.science/pith/WVB7AURNZTZGXHSQ2RLMFPJVYJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WVB7AURNZTZGXHSQ2RLMFPJVYJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WVB7AURNZTZGXHSQ2RLMFPJVYJ","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":"18225c9f7886956bce66b39728b9d6eef5d4b108caed680bec977c1726c9b74f","cross_cats_sorted":["cs.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-06-14T13:23:48Z","title_canon_sha256":"a0d33d67d1c4d43e7bdb732a81f7cccae07fc302d62a7cfaeb95ced62859f5f9"},"schema_version":"1.0","source":{"id":"1306.3390","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3390","created_at":"2026-05-18T03:04:37Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3390v2","created_at":"2026-05-18T03:04:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3390","created_at":"2026-05-18T03:04:37Z"},{"alias_kind":"pith_short_12","alias_value":"WVB7AURNZTZG","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WVB7AURNZTZGXHSQ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WVB7AURN","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:1d8964c9314cfb0a4091b538d2b4414f263eb87cdf9bda5e6ff0c0bf8508f7af","target":"graph","created_at":"2026-05-18T03:04:37Z","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 V be a smooth equidimensional quasi-affine variety of dimension r over the complex numbers $C$ and let $F$ be a $(p\\times s)$-matrix of coordinate functions of $C[V]$, where $s\\ge p+r$. The pair $(V,F)$ determines a vector bundle $E$ of rank $s-p$ over $W:=\\{x\\in V:\\mathrm{rk} F(x)=p\\}$. We associate with $(V,F)$ a descending chain of degeneracy loci of E (the generic polar varieties of $V$ represent a typical example of this situation).\n  The maximal degree of these degeneracy loci constitutes the essential ingredient for the uniform, bounded error probabilistic pseudo-polynomial time alg","authors_text":"Bernd Bank, Gr\\'egoire Lecerf, Guillermo Matera, Joos Heintz, Marc Giusti, Pablo Solern\\'o","cross_cats":["cs.SC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-06-14T13:23:48Z","title":"Degeneracy loci and polynomial equation solving"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3390","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":"sha256:6d2daf2c7ea7b58528cda794d4a6d3be1c926426a859170c371088e05f0a1c06","target":"record","created_at":"2026-05-18T03:04:37Z","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":"18225c9f7886956bce66b39728b9d6eef5d4b108caed680bec977c1726c9b74f","cross_cats_sorted":["cs.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-06-14T13:23:48Z","title_canon_sha256":"a0d33d67d1c4d43e7bdb732a81f7cccae07fc302d62a7cfaeb95ced62859f5f9"},"schema_version":"1.0","source":{"id":"1306.3390","kind":"arxiv","version":2}},"canonical_sha256":"b543f0522dccf26b9e50d456c2bd35c2499c362af7183d379a92d43df9b256d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b543f0522dccf26b9e50d456c2bd35c2499c362af7183d379a92d43df9b256d2","first_computed_at":"2026-05-18T03:04:37.703612Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:37.703612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OscdBbTucxQSVO9lP8tdLOaHCFBhgXiRUMYbHXhG7wPqBbaLcRC0T0LMZUyeaCE20da60L2E03ZVT+8Iz1VQDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:37.704380Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.3390","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d2daf2c7ea7b58528cda794d4a6d3be1c926426a859170c371088e05f0a1c06","sha256:1d8964c9314cfb0a4091b538d2b4414f263eb87cdf9bda5e6ff0c0bf8508f7af"],"state_sha256":"e66a4edf6e24ad6c88fac24a3f2de08f95916239382aa51cda8feb060a9e104f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HSm4vqu4e0XzUg/lCvErxssHMu8+gXmPvOmparT+hOCrhAL+3hQiDNC0bnv4+xcsiBLj60ihYjXZ//4DeNGwDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T02:56:50.281122Z","bundle_sha256":"ce126ef89a113126c6653d993e254eab5719a07b10274a6d9eda76e4abfadf12"}}