{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:6MG4GQ3JHFBEPIPQXHXDQS5XBQ","short_pith_number":"pith:6MG4GQ3J","canonical_record":{"source":{"id":"1706.02032","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-07T02:41:11Z","cross_cats_sorted":[],"title_canon_sha256":"d68fbe78c7174c0648f0d29ea17bfae4d7a532f69e6d7c8247040a04cf97ac13","abstract_canon_sha256":"844c75d15244a2823b930a2c0b91e52663cf0607c0698142b4fce13426b9e2d7"},"schema_version":"1.0"},"canonical_sha256":"f30dc34369394247a1f0b9ee384bb70c156329dcf4e5a28a955c3d11ec024c3d","source":{"kind":"arxiv","id":"1706.02032","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02032","created_at":"2026-05-18T00:31:55Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02032v1","created_at":"2026-05-18T00:31:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02032","created_at":"2026-05-18T00:31:55Z"},{"alias_kind":"pith_short_12","alias_value":"6MG4GQ3JHFBE","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6MG4GQ3JHFBEPIPQ","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6MG4GQ3J","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:6MG4GQ3JHFBEPIPQXHXDQS5XBQ","target":"record","payload":{"canonical_record":{"source":{"id":"1706.02032","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-07T02:41:11Z","cross_cats_sorted":[],"title_canon_sha256":"d68fbe78c7174c0648f0d29ea17bfae4d7a532f69e6d7c8247040a04cf97ac13","abstract_canon_sha256":"844c75d15244a2823b930a2c0b91e52663cf0607c0698142b4fce13426b9e2d7"},"schema_version":"1.0"},"canonical_sha256":"f30dc34369394247a1f0b9ee384bb70c156329dcf4e5a28a955c3d11ec024c3d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:55.825986Z","signature_b64":"L32vKLImUURxJ2kK7moMYv6ktPiAPfq6CWhg5r6BvwSE38KrdSnThRBNaQwTvyIPXF+9bPqSEJlcv9HknUpRCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f30dc34369394247a1f0b9ee384bb70c156329dcf4e5a28a955c3d11ec024c3d","last_reissued_at":"2026-05-18T00:31:55.825495Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:55.825495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.02032","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":"2026-05-18T00:31:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lc7wNbOdxatO9TTSSWOB8ray8sQaoKxTmvW3Eo4fGxviSFL4V60SI39YdJzV8ug6zxuXH3EowAbbxiBrQSqsCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T04:03:13.096606Z"},"content_sha256":"856b77a8cf38c91110de673765c3359053e452efa304a4e9d6c6b9ef09c8ec9d","schema_version":"1.0","event_id":"sha256:856b77a8cf38c91110de673765c3359053e452efa304a4e9d6c6b9ef09c8ec9d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:6MG4GQ3JHFBEPIPQXHXDQS5XBQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local Euler Obstruction and Chern-Mather classes of Determinantal Varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Xiping Zhang","submitted_at":"2017-06-07T02:41:11Z","abstract_excerpt":"For $m\\geq n$, Let $K$ be an algebraic closed base field, and define $\\tau_{m,n,k}$ to be the set of $m\\times n$ matrices over $K$ with kernel dimension $\\geq k$. This is a projective subvariety of $\\mathbb{P}^{mn-1}$, and is usually called determinantal variety. In most cases $\\tau_{m,n,k}$ is singular with singular locus $\\tau_{m,n,k+1}$. In this paper we compute the local Euler obstruction of $\\tau_{m,n,k}$, and we prove that the characteristic cycle of the intersection cohomology complex of $\\tau_{m,n,k}$ is irreducible. We also give an explicit formula for the Chern-Mather class of $\\tau_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02032","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":"2026-05-18T00:31:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hKHmXb8efMu6sVxAmCgXnpMCgNEAzxw1DqAN3c+Dlv3+uibGl2SGn9fq1cbAPhoCd1PWIknVDLv2zWl8xy0TDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T04:03:13.097182Z"},"content_sha256":"6693920a5b72b353456c95c0f4f81d5dae9c1020b6e399aa8271c8e447ffc993","schema_version":"1.0","event_id":"sha256:6693920a5b72b353456c95c0f4f81d5dae9c1020b6e399aa8271c8e447ffc993"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6MG4GQ3JHFBEPIPQXHXDQS5XBQ/bundle.json","state_url":"https://pith.science/pith/6MG4GQ3JHFBEPIPQXHXDQS5XBQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6MG4GQ3JHFBEPIPQXHXDQS5XBQ/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":"2026-08-20T04:03:13Z","links":{"resolver":"https://pith.science/pith/6MG4GQ3JHFBEPIPQXHXDQS5XBQ","bundle":"https://pith.science/pith/6MG4GQ3JHFBEPIPQXHXDQS5XBQ/bundle.json","state":"https://pith.science/pith/6MG4GQ3JHFBEPIPQXHXDQS5XBQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6MG4GQ3JHFBEPIPQXHXDQS5XBQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6MG4GQ3JHFBEPIPQXHXDQS5XBQ","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":"844c75d15244a2823b930a2c0b91e52663cf0607c0698142b4fce13426b9e2d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-07T02:41:11Z","title_canon_sha256":"d68fbe78c7174c0648f0d29ea17bfae4d7a532f69e6d7c8247040a04cf97ac13"},"schema_version":"1.0","source":{"id":"1706.02032","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02032","created_at":"2026-05-18T00:31:55Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02032v1","created_at":"2026-05-18T00:31:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02032","created_at":"2026-05-18T00:31:55Z"},{"alias_kind":"pith_short_12","alias_value":"6MG4GQ3JHFBE","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6MG4GQ3JHFBEPIPQ","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6MG4GQ3J","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:6693920a5b72b353456c95c0f4f81d5dae9c1020b6e399aa8271c8e447ffc993","target":"graph","created_at":"2026-05-18T00:31:55Z","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":"For $m\\geq n$, Let $K$ be an algebraic closed base field, and define $\\tau_{m,n,k}$ to be the set of $m\\times n$ matrices over $K$ with kernel dimension $\\geq k$. This is a projective subvariety of $\\mathbb{P}^{mn-1}$, and is usually called determinantal variety. In most cases $\\tau_{m,n,k}$ is singular with singular locus $\\tau_{m,n,k+1}$. In this paper we compute the local Euler obstruction of $\\tau_{m,n,k}$, and we prove that the characteristic cycle of the intersection cohomology complex of $\\tau_{m,n,k}$ is irreducible. We also give an explicit formula for the Chern-Mather class of $\\tau_","authors_text":"Xiping Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-07T02:41:11Z","title":"Local Euler Obstruction and Chern-Mather classes of Determinantal Varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02032","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":"sha256:856b77a8cf38c91110de673765c3359053e452efa304a4e9d6c6b9ef09c8ec9d","target":"record","created_at":"2026-05-18T00:31:55Z","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":"844c75d15244a2823b930a2c0b91e52663cf0607c0698142b4fce13426b9e2d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-07T02:41:11Z","title_canon_sha256":"d68fbe78c7174c0648f0d29ea17bfae4d7a532f69e6d7c8247040a04cf97ac13"},"schema_version":"1.0","source":{"id":"1706.02032","kind":"arxiv","version":1}},"canonical_sha256":"f30dc34369394247a1f0b9ee384bb70c156329dcf4e5a28a955c3d11ec024c3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f30dc34369394247a1f0b9ee384bb70c156329dcf4e5a28a955c3d11ec024c3d","first_computed_at":"2026-05-18T00:31:55.825495Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:55.825495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L32vKLImUURxJ2kK7moMYv6ktPiAPfq6CWhg5r6BvwSE38KrdSnThRBNaQwTvyIPXF+9bPqSEJlcv9HknUpRCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:55.825986Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.02032","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:856b77a8cf38c91110de673765c3359053e452efa304a4e9d6c6b9ef09c8ec9d","sha256:6693920a5b72b353456c95c0f4f81d5dae9c1020b6e399aa8271c8e447ffc993"],"state_sha256":"4b130a0b3138af599d526ab7acc8eefb49b160a8efaa844a8891ff1ccde12d97"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DmThOe5c1zSAkVZ76TrEO0tJlUFZCJaJqM2JNTm1ewBMrkL5pt1ZwLjUO0sl3KN17odST3Ra22UvuLeHUVP+Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T04:03:13.101804Z","bundle_sha256":"e5d45fe12809345d71903db0e1745085a418c9e8580a540ddfff4d5c2d9cdb09"}}