{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:ECXAGJDHHSX7OZ3Y5WRNF6D4CE","short_pith_number":"pith:ECXAGJDH","canonical_record":{"source":{"id":"math/9805075","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"1998-05-18T09:09:40Z","cross_cats_sorted":[],"title_canon_sha256":"307233736e83c3579d1eccf359f77e2f1ca679dc52414782d3bdfce9b12f3924","abstract_canon_sha256":"5c98e4ca46e465d78b3d474386d5a4da41c32f503c2a2da5c68be3fd417fc02e"},"schema_version":"1.0"},"canonical_sha256":"20ae0324673caff76778eda2d2f87c111f15c6a020df125f25b9abc3d40a0c9a","source":{"kind":"arxiv","id":"math/9805075","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9805075","created_at":"2026-05-18T00:29:34Z"},{"alias_kind":"arxiv_version","alias_value":"math/9805075v2","created_at":"2026-05-18T00:29:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9805075","created_at":"2026-05-18T00:29:34Z"},{"alias_kind":"pith_short_12","alias_value":"ECXAGJDHHSX7","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"ECXAGJDHHSX7OZ3Y","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"ECXAGJDH","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:ECXAGJDHHSX7OZ3Y5WRNF6D4CE","target":"record","payload":{"canonical_record":{"source":{"id":"math/9805075","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"1998-05-18T09:09:40Z","cross_cats_sorted":[],"title_canon_sha256":"307233736e83c3579d1eccf359f77e2f1ca679dc52414782d3bdfce9b12f3924","abstract_canon_sha256":"5c98e4ca46e465d78b3d474386d5a4da41c32f503c2a2da5c68be3fd417fc02e"},"schema_version":"1.0"},"canonical_sha256":"20ae0324673caff76778eda2d2f87c111f15c6a020df125f25b9abc3d40a0c9a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:34.231277Z","signature_b64":"g9gB5qrrJKYZQS5M7Ajp0y0FMSB7kX/B63iuecv8CBJb4rpj3yN280aue2E4lQTrWEa0LgXCusE/D247OqYtAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20ae0324673caff76778eda2d2f87c111f15c6a020df125f25b9abc3d40a0c9a","last_reissued_at":"2026-05-18T00:29:34.230716Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:34.230716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9805075","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":"2026-05-18T00:29:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VapteYIJirqArdiDOVACvmP0zs7VLVnRij9TTShS+YeCfAihihfw1NKv844B8I9QR9h76/eQoINhPlJnwIiBAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:14:10.973643Z"},"content_sha256":"28a3ee534379cdc988893b885e366fe85467d8ef9abe03b150fb07d4a5f52557","schema_version":"1.0","event_id":"sha256:28a3ee534379cdc988893b885e366fe85467d8ef9abe03b150fb07d4a5f52557"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:ECXAGJDHHSX7OZ3Y5WRNF6D4CE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic equisingularity and topology of complex hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Mihai Tibar","submitted_at":"1998-05-18T09:09:40Z","abstract_excerpt":"We consider an equisingularity problem for polynomial families of affine hypersurfaces $X_\\tau \\subset \\mathbb C^n$ with (at worst) isolated singularities. We show that the constancy of the global polar invariants $\\gamma^* (X_\\tau)$ is equivalent to the $t$-equisingularity at infinity, an asymptotic-type equisingularity that we introduce. We prove that $\\gamma^*$-constancy implies C$^\\infty$-triviality in the neighbourhood of infinity. We show how the invariants $\\gamma^*$ enter in the description of a CW-complex model of a hypersurface $X_\\tau$ and therefore provide in particular new invaria"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9805075","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":"2026-05-18T00:29:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JSshqT6qP12D5g2A0hX9iIISJVwdQOfX7XtahV7XsVVYVLFvYYjSN180tbNcjSrJesiGVN3uT+K4r7B2+2ghBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:14:10.974418Z"},"content_sha256":"b5317632d0e477e2cf2cbe9ef8b5c76a306985bdb5260b7021271f183101398b","schema_version":"1.0","event_id":"sha256:b5317632d0e477e2cf2cbe9ef8b5c76a306985bdb5260b7021271f183101398b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ECXAGJDHHSX7OZ3Y5WRNF6D4CE/bundle.json","state_url":"https://pith.science/pith/ECXAGJDHHSX7OZ3Y5WRNF6D4CE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ECXAGJDHHSX7OZ3Y5WRNF6D4CE/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":"2026-05-30T23:14:10Z","links":{"resolver":"https://pith.science/pith/ECXAGJDHHSX7OZ3Y5WRNF6D4CE","bundle":"https://pith.science/pith/ECXAGJDHHSX7OZ3Y5WRNF6D4CE/bundle.json","state":"https://pith.science/pith/ECXAGJDHHSX7OZ3Y5WRNF6D4CE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ECXAGJDHHSX7OZ3Y5WRNF6D4CE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:ECXAGJDHHSX7OZ3Y5WRNF6D4CE","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":"5c98e4ca46e465d78b3d474386d5a4da41c32f503c2a2da5c68be3fd417fc02e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"1998-05-18T09:09:40Z","title_canon_sha256":"307233736e83c3579d1eccf359f77e2f1ca679dc52414782d3bdfce9b12f3924"},"schema_version":"1.0","source":{"id":"math/9805075","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9805075","created_at":"2026-05-18T00:29:34Z"},{"alias_kind":"arxiv_version","alias_value":"math/9805075v2","created_at":"2026-05-18T00:29:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9805075","created_at":"2026-05-18T00:29:34Z"},{"alias_kind":"pith_short_12","alias_value":"ECXAGJDHHSX7","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"ECXAGJDHHSX7OZ3Y","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"ECXAGJDH","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:b5317632d0e477e2cf2cbe9ef8b5c76a306985bdb5260b7021271f183101398b","target":"graph","created_at":"2026-05-18T00:29:34Z","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":"We consider an equisingularity problem for polynomial families of affine hypersurfaces $X_\\tau \\subset \\mathbb C^n$ with (at worst) isolated singularities. We show that the constancy of the global polar invariants $\\gamma^* (X_\\tau)$ is equivalent to the $t$-equisingularity at infinity, an asymptotic-type equisingularity that we introduce. We prove that $\\gamma^*$-constancy implies C$^\\infty$-triviality in the neighbourhood of infinity. We show how the invariants $\\gamma^*$ enter in the description of a CW-complex model of a hypersurface $X_\\tau$ and therefore provide in particular new invaria","authors_text":"Mihai Tibar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"1998-05-18T09:09:40Z","title":"Asymptotic equisingularity and topology of complex hypersurfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9805075","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":"sha256:28a3ee534379cdc988893b885e366fe85467d8ef9abe03b150fb07d4a5f52557","target":"record","created_at":"2026-05-18T00:29:34Z","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":"5c98e4ca46e465d78b3d474386d5a4da41c32f503c2a2da5c68be3fd417fc02e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"1998-05-18T09:09:40Z","title_canon_sha256":"307233736e83c3579d1eccf359f77e2f1ca679dc52414782d3bdfce9b12f3924"},"schema_version":"1.0","source":{"id":"math/9805075","kind":"arxiv","version":2}},"canonical_sha256":"20ae0324673caff76778eda2d2f87c111f15c6a020df125f25b9abc3d40a0c9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20ae0324673caff76778eda2d2f87c111f15c6a020df125f25b9abc3d40a0c9a","first_computed_at":"2026-05-18T00:29:34.230716Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:34.230716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g9gB5qrrJKYZQS5M7Ajp0y0FMSB7kX/B63iuecv8CBJb4rpj3yN280aue2E4lQTrWEa0LgXCusE/D247OqYtAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:34.231277Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9805075","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28a3ee534379cdc988893b885e366fe85467d8ef9abe03b150fb07d4a5f52557","sha256:b5317632d0e477e2cf2cbe9ef8b5c76a306985bdb5260b7021271f183101398b"],"state_sha256":"97f60192209d3ec504044037e69f90b9fba5f1cdde10fd5d1f34c4da9feaadb7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1mztLvvTEr1Kqbl+50ZxSrfvkxK5Kn8xhAoUBgrIKt9qHY8y2T/s4nJh2UJS3cFpFUe1j8wHh4x58+UdcLBFCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:14:10.978819Z","bundle_sha256":"2162ff6c095461a41d6544c6673c3e74bb5f2aef793a85ddc65348e4ffbab6e2"}}