{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:TTSJUA6FUWJGRL4J6VIEU74KI7","short_pith_number":"pith:TTSJUA6F","canonical_record":{"source":{"id":"1212.5484","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-12-21T15:28:20Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"78e54ad6008c2faff35f3d86d205d524a2e7f8307dcce96bceb38d7223d727cd","abstract_canon_sha256":"1008ac25faf1c5b8724937a18443f3f7f91590fafd20ab1666e1853c33b59248"},"schema_version":"1.0"},"canonical_sha256":"9ce49a03c5a59268af89f5504a7f8a47f2f66fb6aa42bc4d45f48b5c1cc390fe","source":{"kind":"arxiv","id":"1212.5484","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5484","created_at":"2026-05-18T03:37:54Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5484v1","created_at":"2026-05-18T03:37:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5484","created_at":"2026-05-18T03:37:54Z"},{"alias_kind":"pith_short_12","alias_value":"TTSJUA6FUWJG","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TTSJUA6FUWJGRL4J","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TTSJUA6F","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:TTSJUA6FUWJGRL4J6VIEU74KI7","target":"record","payload":{"canonical_record":{"source":{"id":"1212.5484","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-12-21T15:28:20Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"78e54ad6008c2faff35f3d86d205d524a2e7f8307dcce96bceb38d7223d727cd","abstract_canon_sha256":"1008ac25faf1c5b8724937a18443f3f7f91590fafd20ab1666e1853c33b59248"},"schema_version":"1.0"},"canonical_sha256":"9ce49a03c5a59268af89f5504a7f8a47f2f66fb6aa42bc4d45f48b5c1cc390fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:54.262133Z","signature_b64":"R+9SURJLNQ7uu7NEa62Hx83lqA5JNJdSfwDGZyoKYqMnAV/D6+Xo5na0dIlTWHdwCNMGNYaDVI1LMPr935Y8DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ce49a03c5a59268af89f5504a7f8a47f2f66fb6aa42bc4d45f48b5c1cc390fe","last_reissued_at":"2026-05-18T03:37:54.261210Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:54.261210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.5484","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":"2026-05-18T03:37:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0MXbFk37Yx7Lx7/HfN8orsDRNMvN+3U8zOjyXFgnIYAgKj+wepbouZ2/LUezjXqDvAjJHCO70i1xChpkjTtsAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T23:02:07.596806Z"},"content_sha256":"67b71ae11cd404c4dc8d59b6b21fca24c96f9c4e5008540b111b381c7504b7e4","schema_version":"1.0","event_id":"sha256:67b71ae11cd404c4dc8d59b6b21fca24c96f9c4e5008540b111b381c7504b7e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:TTSJUA6FUWJGRL4J6VIEU74KI7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Brian\\c{c}on-Speder examples and the failure of weak Whitney regularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"David Trotman, Karim Bekka","submitted_at":"2012-12-21T15:28:20Z","abstract_excerpt":"It is easy to find real algebraic varieties with weakly Whitney regular stratifications which are not Whitney regular, and we give such an example in section 3 below. No examples are known among complex analytic varieties however, so that the natural question arises : do Whitney regularity and weak Whitney regularity coincide in the complex case ? As a test, in this paper we study the well-known Brian\\c{c}on-Speder examples.\n  We investigate systematically all of the (infinitely many) Brian\\c{c}on-Speder examples, and establish in particular that none of these examples are weakly Whitney regul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5484","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":"2026-05-18T03:37:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jzr344zC9P3IekWI+8aZa1tqa4F1j6ctOK6VH0iMtrWtwa16LnlZCK8+IYAk/BSsjbzz62OgruV6LxnSf/VbCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T23:02:07.597508Z"},"content_sha256":"97f2e856eb6120a9727a536ff38820e88c48129f1c2f6bb2a596f3ebee8e6f92","schema_version":"1.0","event_id":"sha256:97f2e856eb6120a9727a536ff38820e88c48129f1c2f6bb2a596f3ebee8e6f92"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TTSJUA6FUWJGRL4J6VIEU74KI7/bundle.json","state_url":"https://pith.science/pith/TTSJUA6FUWJGRL4J6VIEU74KI7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TTSJUA6FUWJGRL4J6VIEU74KI7/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":"2026-06-05T23:02:07Z","links":{"resolver":"https://pith.science/pith/TTSJUA6FUWJGRL4J6VIEU74KI7","bundle":"https://pith.science/pith/TTSJUA6FUWJGRL4J6VIEU74KI7/bundle.json","state":"https://pith.science/pith/TTSJUA6FUWJGRL4J6VIEU74KI7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TTSJUA6FUWJGRL4J6VIEU74KI7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TTSJUA6FUWJGRL4J6VIEU74KI7","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":"1008ac25faf1c5b8724937a18443f3f7f91590fafd20ab1666e1853c33b59248","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-12-21T15:28:20Z","title_canon_sha256":"78e54ad6008c2faff35f3d86d205d524a2e7f8307dcce96bceb38d7223d727cd"},"schema_version":"1.0","source":{"id":"1212.5484","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5484","created_at":"2026-05-18T03:37:54Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5484v1","created_at":"2026-05-18T03:37:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5484","created_at":"2026-05-18T03:37:54Z"},{"alias_kind":"pith_short_12","alias_value":"TTSJUA6FUWJG","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TTSJUA6FUWJGRL4J","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TTSJUA6F","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:97f2e856eb6120a9727a536ff38820e88c48129f1c2f6bb2a596f3ebee8e6f92","target":"graph","created_at":"2026-05-18T03:37:54Z","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 easy to find real algebraic varieties with weakly Whitney regular stratifications which are not Whitney regular, and we give such an example in section 3 below. No examples are known among complex analytic varieties however, so that the natural question arises : do Whitney regularity and weak Whitney regularity coincide in the complex case ? As a test, in this paper we study the well-known Brian\\c{c}on-Speder examples.\n  We investigate systematically all of the (infinitely many) Brian\\c{c}on-Speder examples, and establish in particular that none of these examples are weakly Whitney regul","authors_text":"David Trotman, Karim Bekka","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-12-21T15:28:20Z","title":"Brian\\c{c}on-Speder examples and the failure of weak Whitney regularity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5484","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":"sha256:67b71ae11cd404c4dc8d59b6b21fca24c96f9c4e5008540b111b381c7504b7e4","target":"record","created_at":"2026-05-18T03:37:54Z","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":"1008ac25faf1c5b8724937a18443f3f7f91590fafd20ab1666e1853c33b59248","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-12-21T15:28:20Z","title_canon_sha256":"78e54ad6008c2faff35f3d86d205d524a2e7f8307dcce96bceb38d7223d727cd"},"schema_version":"1.0","source":{"id":"1212.5484","kind":"arxiv","version":1}},"canonical_sha256":"9ce49a03c5a59268af89f5504a7f8a47f2f66fb6aa42bc4d45f48b5c1cc390fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ce49a03c5a59268af89f5504a7f8a47f2f66fb6aa42bc4d45f48b5c1cc390fe","first_computed_at":"2026-05-18T03:37:54.261210Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:54.261210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R+9SURJLNQ7uu7NEa62Hx83lqA5JNJdSfwDGZyoKYqMnAV/D6+Xo5na0dIlTWHdwCNMGNYaDVI1LMPr935Y8DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:54.262133Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.5484","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67b71ae11cd404c4dc8d59b6b21fca24c96f9c4e5008540b111b381c7504b7e4","sha256:97f2e856eb6120a9727a536ff38820e88c48129f1c2f6bb2a596f3ebee8e6f92"],"state_sha256":"f4d1826fa803b9638e5c21e6c20c99822d28783cb868d6a765e8cce5a411817e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sMPiyPYhRX7vZ0rcUdcaLBOxq/uIfauHGsFur76sNTDrHskbWLfaLsCpduRtCCQ64aOcKedW/kZqzWpzwDSaCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T23:02:07.602260Z","bundle_sha256":"874bbbe0caf28db1c1bf431a653719592ed7d1c93c779f0c77fa237c846fc729"}}