{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:KAEVHFU4DCEXCZK2JQ637Z6B62","short_pith_number":"pith:KAEVHFU4","canonical_record":{"source":{"id":"1608.07353","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-08-26T02:56:24Z","cross_cats_sorted":[],"title_canon_sha256":"97252bf5acfe07cc57c9d316aac33b42d9f672d1e975168149373ca722f6022c","abstract_canon_sha256":"3f7c8c18b20ced5b2097801fb15ff4cef43973890f27e10ca39cece793c6fb79"},"schema_version":"1.0"},"canonical_sha256":"500953969c188971655a4c3dbfe7c1f69a845cfce69688085e99cc0cb8863af8","source":{"kind":"arxiv","id":"1608.07353","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.07353","created_at":"2026-05-18T01:07:53Z"},{"alias_kind":"arxiv_version","alias_value":"1608.07353v1","created_at":"2026-05-18T01:07:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07353","created_at":"2026-05-18T01:07:53Z"},{"alias_kind":"pith_short_12","alias_value":"KAEVHFU4DCEX","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KAEVHFU4DCEXCZK2","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KAEVHFU4","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:KAEVHFU4DCEXCZK2JQ637Z6B62","target":"record","payload":{"canonical_record":{"source":{"id":"1608.07353","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-08-26T02:56:24Z","cross_cats_sorted":[],"title_canon_sha256":"97252bf5acfe07cc57c9d316aac33b42d9f672d1e975168149373ca722f6022c","abstract_canon_sha256":"3f7c8c18b20ced5b2097801fb15ff4cef43973890f27e10ca39cece793c6fb79"},"schema_version":"1.0"},"canonical_sha256":"500953969c188971655a4c3dbfe7c1f69a845cfce69688085e99cc0cb8863af8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:53.280681Z","signature_b64":"AD9f8gPysUYzSJFBMdjzjjCmxrHT0YPJuvQA6UtopX3nEAz5pPyjnGQfIG2kM/l3UmuALFNaZMO7HZsmNcfyDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"500953969c188971655a4c3dbfe7c1f69a845cfce69688085e99cc0cb8863af8","last_reissued_at":"2026-05-18T01:07:53.280130Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:53.280130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.07353","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":"2026-05-18T01:07:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L9PBjvDWYsXCwoFkzbN4K6osg7GLIK1EI1XzaXItnbJqtCCQwJomwvYWPZ9ejcHNV2vIuT1U1zIKQQkjqBtqAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T18:10:16.715189Z"},"content_sha256":"b004b5d4b366ad88e97f3ace66134e974dace125e69fcc90b04a812aee4dfc6f","schema_version":"1.0","event_id":"sha256:b004b5d4b366ad88e97f3ace66134e974dace125e69fcc90b04a812aee4dfc6f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:KAEVHFU4DCEXCZK2JQ637Z6B62","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Nash modification of a germ of complex analytic singularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Arturo Giles Flores","submitted_at":"2016-08-26T02:56:24Z","abstract_excerpt":"For a germ $(X,0) \\subset (\\mathbb{C}^n,0)$ of reduced, equidimensional complex analytic singularity its Nash modification can be constructed as an analytic subvariety $ Z \\subset \\mathbb{C}^n \\times G(k,n)$. We give a characterization of the subvarieties of $\\mathbb{C}^n \\times G(k,n)$ that are the Nash modification of its image under the projection to $\\mathbb{C}^n$. This result generalizes the characterization of conormal varieties as Legendrian subvarieties of $\\mathbb{C}^n \\times \\check{\\mathbb{P}}^{n-1}$ with its canonical contact structure. As a by-product we define the $d$-conormal spa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07353","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":"2026-05-18T01:07:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UIVUh3hn+CcHLfI82Wy0AfVifO/gFWUa3IF3ZCYBz26g/Ad8KVLZ5qn4mdiF5X8cuMqEaUgV1dmMQLIJKcISBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T18:10:16.715553Z"},"content_sha256":"e43ad443842c947cd714cb2a2ac67c38ecd578089693741a1e8ad1d1f82039fd","schema_version":"1.0","event_id":"sha256:e43ad443842c947cd714cb2a2ac67c38ecd578089693741a1e8ad1d1f82039fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KAEVHFU4DCEXCZK2JQ637Z6B62/bundle.json","state_url":"https://pith.science/pith/KAEVHFU4DCEXCZK2JQ637Z6B62/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KAEVHFU4DCEXCZK2JQ637Z6B62/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":"2026-06-21T18:10:16Z","links":{"resolver":"https://pith.science/pith/KAEVHFU4DCEXCZK2JQ637Z6B62","bundle":"https://pith.science/pith/KAEVHFU4DCEXCZK2JQ637Z6B62/bundle.json","state":"https://pith.science/pith/KAEVHFU4DCEXCZK2JQ637Z6B62/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KAEVHFU4DCEXCZK2JQ637Z6B62/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KAEVHFU4DCEXCZK2JQ637Z6B62","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":"3f7c8c18b20ced5b2097801fb15ff4cef43973890f27e10ca39cece793c6fb79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-08-26T02:56:24Z","title_canon_sha256":"97252bf5acfe07cc57c9d316aac33b42d9f672d1e975168149373ca722f6022c"},"schema_version":"1.0","source":{"id":"1608.07353","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.07353","created_at":"2026-05-18T01:07:53Z"},{"alias_kind":"arxiv_version","alias_value":"1608.07353v1","created_at":"2026-05-18T01:07:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07353","created_at":"2026-05-18T01:07:53Z"},{"alias_kind":"pith_short_12","alias_value":"KAEVHFU4DCEX","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KAEVHFU4DCEXCZK2","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KAEVHFU4","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:e43ad443842c947cd714cb2a2ac67c38ecd578089693741a1e8ad1d1f82039fd","target":"graph","created_at":"2026-05-18T01:07:53Z","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 a germ $(X,0) \\subset (\\mathbb{C}^n,0)$ of reduced, equidimensional complex analytic singularity its Nash modification can be constructed as an analytic subvariety $ Z \\subset \\mathbb{C}^n \\times G(k,n)$. We give a characterization of the subvarieties of $\\mathbb{C}^n \\times G(k,n)$ that are the Nash modification of its image under the projection to $\\mathbb{C}^n$. This result generalizes the characterization of conormal varieties as Legendrian subvarieties of $\\mathbb{C}^n \\times \\check{\\mathbb{P}}^{n-1}$ with its canonical contact structure. As a by-product we define the $d$-conormal spa","authors_text":"Arturo Giles Flores","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-08-26T02:56:24Z","title":"On the Nash modification of a germ of complex analytic singularity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07353","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:b004b5d4b366ad88e97f3ace66134e974dace125e69fcc90b04a812aee4dfc6f","target":"record","created_at":"2026-05-18T01:07:53Z","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":"3f7c8c18b20ced5b2097801fb15ff4cef43973890f27e10ca39cece793c6fb79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-08-26T02:56:24Z","title_canon_sha256":"97252bf5acfe07cc57c9d316aac33b42d9f672d1e975168149373ca722f6022c"},"schema_version":"1.0","source":{"id":"1608.07353","kind":"arxiv","version":1}},"canonical_sha256":"500953969c188971655a4c3dbfe7c1f69a845cfce69688085e99cc0cb8863af8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"500953969c188971655a4c3dbfe7c1f69a845cfce69688085e99cc0cb8863af8","first_computed_at":"2026-05-18T01:07:53.280130Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:53.280130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AD9f8gPysUYzSJFBMdjzjjCmxrHT0YPJuvQA6UtopX3nEAz5pPyjnGQfIG2kM/l3UmuALFNaZMO7HZsmNcfyDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:53.280681Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.07353","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b004b5d4b366ad88e97f3ace66134e974dace125e69fcc90b04a812aee4dfc6f","sha256:e43ad443842c947cd714cb2a2ac67c38ecd578089693741a1e8ad1d1f82039fd"],"state_sha256":"bd0cb4e28036ce26f89652d2c37ee8549ac5326d8759ba771ec7f2cc5da8e24a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8BTdfC++EuRsbJx2hw28ffHDJy0NBErEoCHNgV2bHqRLCxapVc5FBjrw8bC61Bqnz2jXZKYEem8lIZ1HeQ7/Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T18:10:16.717541Z","bundle_sha256":"32aeda3a6bbd494de0772db10e959c45ccc603d29e036d7ff3e037022bacff6a"}}