{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:WJIU3V5SPR7GXH2OYJ2H56VKYS","short_pith_number":"pith:WJIU3V5S","canonical_record":{"source":{"id":"1308.6045","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-28T03:27:03Z","cross_cats_sorted":[],"title_canon_sha256":"73ca1deedb0ca15a77481b570065770b529bd4a959c03c500d3bb16e2daea159","abstract_canon_sha256":"f5862394513fb76bec910119ec56c4e55601a856cade6e34f37df4548f64946b"},"schema_version":"1.0"},"canonical_sha256":"b2514dd7b27c7e6b9f4ec2747efaaac4ad86f6f02c08da69d11deb7f68f597d0","source":{"kind":"arxiv","id":"1308.6045","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.6045","created_at":"2026-05-18T00:43:23Z"},{"alias_kind":"arxiv_version","alias_value":"1308.6045v2","created_at":"2026-05-18T00:43:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6045","created_at":"2026-05-18T00:43:23Z"},{"alias_kind":"pith_short_12","alias_value":"WJIU3V5SPR7G","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WJIU3V5SPR7GXH2O","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WJIU3V5S","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:WJIU3V5SPR7GXH2OYJ2H56VKYS","target":"record","payload":{"canonical_record":{"source":{"id":"1308.6045","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-28T03:27:03Z","cross_cats_sorted":[],"title_canon_sha256":"73ca1deedb0ca15a77481b570065770b529bd4a959c03c500d3bb16e2daea159","abstract_canon_sha256":"f5862394513fb76bec910119ec56c4e55601a856cade6e34f37df4548f64946b"},"schema_version":"1.0"},"canonical_sha256":"b2514dd7b27c7e6b9f4ec2747efaaac4ad86f6f02c08da69d11deb7f68f597d0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:23.486829Z","signature_b64":"Pl5YeWNhQYIPCAHIyd+hyYEo8zrRo9C+tN1lJO9MFJx+nin0i+9HM7SvIhyAgGowLeJek9mU9R/9yojMcTCfCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2514dd7b27c7e6b9f4ec2747efaaac4ad86f6f02c08da69d11deb7f68f597d0","last_reissued_at":"2026-05-18T00:43:23.486218Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:23.486218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.6045","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":"2026-05-18T00:43:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IRzcW8oR56W9Zm1Ypb8TG4KFROSCxuZMCIH9JDzaND6ip1l8JWyNwLQN6RpEAiTQP5zaQ1u0b3UIyn8U2mGXAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:10:44.933419Z"},"content_sha256":"1e8bbfecf9c696ad5891dad2dac3b4ecaa24834bf4b7ee64269ab844ff73c121","schema_version":"1.0","event_id":"sha256:1e8bbfecf9c696ad5891dad2dac3b4ecaa24834bf4b7ee64269ab844ff73c121"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:WJIU3V5SPR7GXH2OYJ2H56VKYS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Discriminant of the ordinary transversal singularity type. The global equivalence class","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andr\\'as N\\'emethi, Dmitry Kerner, Maxim Kazarian","submitted_at":"2013-08-28T03:27:03Z","abstract_excerpt":"Consider a space X with the singular locus of positive dimension, Z=Sing(X). Suppose both Z and X are locally complete intersections at each point. The transversal type of X along Z is generically constant but at some points of Z it degenerates. In the previous work we have introduced (locally) the discriminant of the transversal type, a subscheme of Z, that reflects these degenerations whenever the generic transversal type is \"ordinary\". We have established the basic local properties of the discriminant.\n  In the current paper we consider the global case. We compute the equivalence class of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6045","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":"2026-05-18T00:43:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kSjdGAR7twECfV0W3o5tToB2s8xPP49xN8Bif7VCQHoQfJLDy2dp0FBJ6d+24oJ7tuScc1PdkO+iTgehAG9IDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:10:44.933771Z"},"content_sha256":"09f4dac2da3a602ebde41a782d636db6bc645413228802c1c6fb08271aab13af","schema_version":"1.0","event_id":"sha256:09f4dac2da3a602ebde41a782d636db6bc645413228802c1c6fb08271aab13af"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WJIU3V5SPR7GXH2OYJ2H56VKYS/bundle.json","state_url":"https://pith.science/pith/WJIU3V5SPR7GXH2OYJ2H56VKYS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WJIU3V5SPR7GXH2OYJ2H56VKYS/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":"2026-06-01T18:10:44Z","links":{"resolver":"https://pith.science/pith/WJIU3V5SPR7GXH2OYJ2H56VKYS","bundle":"https://pith.science/pith/WJIU3V5SPR7GXH2OYJ2H56VKYS/bundle.json","state":"https://pith.science/pith/WJIU3V5SPR7GXH2OYJ2H56VKYS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WJIU3V5SPR7GXH2OYJ2H56VKYS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WJIU3V5SPR7GXH2OYJ2H56VKYS","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":"f5862394513fb76bec910119ec56c4e55601a856cade6e34f37df4548f64946b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-28T03:27:03Z","title_canon_sha256":"73ca1deedb0ca15a77481b570065770b529bd4a959c03c500d3bb16e2daea159"},"schema_version":"1.0","source":{"id":"1308.6045","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.6045","created_at":"2026-05-18T00:43:23Z"},{"alias_kind":"arxiv_version","alias_value":"1308.6045v2","created_at":"2026-05-18T00:43:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6045","created_at":"2026-05-18T00:43:23Z"},{"alias_kind":"pith_short_12","alias_value":"WJIU3V5SPR7G","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WJIU3V5SPR7GXH2O","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WJIU3V5S","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:09f4dac2da3a602ebde41a782d636db6bc645413228802c1c6fb08271aab13af","target":"graph","created_at":"2026-05-18T00:43:23Z","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":"Consider a space X with the singular locus of positive dimension, Z=Sing(X). Suppose both Z and X are locally complete intersections at each point. The transversal type of X along Z is generically constant but at some points of Z it degenerates. In the previous work we have introduced (locally) the discriminant of the transversal type, a subscheme of Z, that reflects these degenerations whenever the generic transversal type is \"ordinary\". We have established the basic local properties of the discriminant.\n  In the current paper we consider the global case. We compute the equivalence class of t","authors_text":"Andr\\'as N\\'emethi, Dmitry Kerner, Maxim Kazarian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-28T03:27:03Z","title":"Discriminant of the ordinary transversal singularity type. The global equivalence class"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6045","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":"sha256:1e8bbfecf9c696ad5891dad2dac3b4ecaa24834bf4b7ee64269ab844ff73c121","target":"record","created_at":"2026-05-18T00:43:23Z","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":"f5862394513fb76bec910119ec56c4e55601a856cade6e34f37df4548f64946b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-28T03:27:03Z","title_canon_sha256":"73ca1deedb0ca15a77481b570065770b529bd4a959c03c500d3bb16e2daea159"},"schema_version":"1.0","source":{"id":"1308.6045","kind":"arxiv","version":2}},"canonical_sha256":"b2514dd7b27c7e6b9f4ec2747efaaac4ad86f6f02c08da69d11deb7f68f597d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2514dd7b27c7e6b9f4ec2747efaaac4ad86f6f02c08da69d11deb7f68f597d0","first_computed_at":"2026-05-18T00:43:23.486218Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:23.486218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pl5YeWNhQYIPCAHIyd+hyYEo8zrRo9C+tN1lJO9MFJx+nin0i+9HM7SvIhyAgGowLeJek9mU9R/9yojMcTCfCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:23.486829Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.6045","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e8bbfecf9c696ad5891dad2dac3b4ecaa24834bf4b7ee64269ab844ff73c121","sha256:09f4dac2da3a602ebde41a782d636db6bc645413228802c1c6fb08271aab13af"],"state_sha256":"2db0570f9535f806877f28c011f9f7b3995f4b662a2b5274f42cc798a63dbbf4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lpZJ18LL5sL9dISuV0BLEqFfDEK0HcGtQNahbcQgNVi7VnYygPRZrTPYvOyrOo6uG5SvD0D6Sk63x+ny6FoUAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T18:10:44.935764Z","bundle_sha256":"b0bf9d9860f29658bc26810fad666420c4cbc49f57381c1c2c2ceaf8d1cd49c4"}}