{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GGDLQ77G67YWQSMDMDNKE5RNPE","short_pith_number":"pith:GGDLQ77G","canonical_record":{"source":{"id":"1711.11134","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-11-29T22:23:34Z","cross_cats_sorted":[],"title_canon_sha256":"a81820481a277aa71882a82874652d6e40908e1c24c41a3a5e3c9137e71652b1","abstract_canon_sha256":"d231e1f97127743fa63a07bb590032fc0cd1b3f0531392035e36f9965889f0aa"},"schema_version":"1.0"},"canonical_sha256":"3186b87fe6f7f168498360daa2762d793ac96c0371d55ffe03518872304d5cbe","source":{"kind":"arxiv","id":"1711.11134","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.11134","created_at":"2026-05-17T23:46:04Z"},{"alias_kind":"arxiv_version","alias_value":"1711.11134v2","created_at":"2026-05-17T23:46:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.11134","created_at":"2026-05-17T23:46:04Z"},{"alias_kind":"pith_short_12","alias_value":"GGDLQ77G67YW","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"GGDLQ77G67YWQSMD","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"GGDLQ77G","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GGDLQ77G67YWQSMDMDNKE5RNPE","target":"record","payload":{"canonical_record":{"source":{"id":"1711.11134","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-11-29T22:23:34Z","cross_cats_sorted":[],"title_canon_sha256":"a81820481a277aa71882a82874652d6e40908e1c24c41a3a5e3c9137e71652b1","abstract_canon_sha256":"d231e1f97127743fa63a07bb590032fc0cd1b3f0531392035e36f9965889f0aa"},"schema_version":"1.0"},"canonical_sha256":"3186b87fe6f7f168498360daa2762d793ac96c0371d55ffe03518872304d5cbe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:04.389174Z","signature_b64":"ZoypQijvLlO94+35ke2QDAn1SJjYpfoICFiBSWXHNX3fYfNSg5MT+hjHOdGzkhtYm1AyXlPmo4PMtc42NFokCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3186b87fe6f7f168498360daa2762d793ac96c0371d55ffe03518872304d5cbe","last_reissued_at":"2026-05-17T23:46:04.388433Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:04.388433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.11134","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":"2026-05-17T23:46:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7PotdNVuCYLeZyAMY9SIc9iKSFYTWt+ODV9AkHVfniboEpcwXnqowl47h5zTA9av8hxVItghxmIvqg7V0JHpBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T05:40:57.880331Z"},"content_sha256":"f12c94dc0c6fab50f6316239f039fd4989b4509c06ddbf22e43e1b5dd3563522","schema_version":"1.0","event_id":"sha256:f12c94dc0c6fab50f6316239f039fd4989b4509c06ddbf22e43e1b5dd3563522"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GGDLQ77G67YWQSMDMDNKE5RNPE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Deformation Formulas for Parameterized Hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Brian Hepler","submitted_at":"2017-11-29T22:23:34Z","abstract_excerpt":"We investigate one-parameter deformations of functions on affine space which define parameterizable hypersurfaces. With the assumption of isolated polar activity at the origin, we are able to completely express the L\\^{e} numbers of the special fiber in terms of the L\\^{e} numbers of the generic fiber and the characteristic polar multiplicities of the comparison, a perverse sheaf naturally associated to any reduced complex analytic space on which the constant sheaf $\\Q_X^\\bullet[\\dim X]$ is perverse. This generalizes the classical formula for the Milnor number of a plane curve in terms of doub"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11134","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":"2026-05-17T23:46:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sGcqXcpOGAzry5s9Hurm6H7DvMilUVFtoK78L48AfNcm+lOnpjphNLqI4wttALPAoAJcBYXUASnM6fabEssKBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T05:40:57.880677Z"},"content_sha256":"1d0675300eb14aa59457de8ede6c9bbc1009d4759d49c77324fe34c01f0b433f","schema_version":"1.0","event_id":"sha256:1d0675300eb14aa59457de8ede6c9bbc1009d4759d49c77324fe34c01f0b433f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GGDLQ77G67YWQSMDMDNKE5RNPE/bundle.json","state_url":"https://pith.science/pith/GGDLQ77G67YWQSMDMDNKE5RNPE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GGDLQ77G67YWQSMDMDNKE5RNPE/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":"2026-06-25T05:40:57Z","links":{"resolver":"https://pith.science/pith/GGDLQ77G67YWQSMDMDNKE5RNPE","bundle":"https://pith.science/pith/GGDLQ77G67YWQSMDMDNKE5RNPE/bundle.json","state":"https://pith.science/pith/GGDLQ77G67YWQSMDMDNKE5RNPE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GGDLQ77G67YWQSMDMDNKE5RNPE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GGDLQ77G67YWQSMDMDNKE5RNPE","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":"d231e1f97127743fa63a07bb590032fc0cd1b3f0531392035e36f9965889f0aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-11-29T22:23:34Z","title_canon_sha256":"a81820481a277aa71882a82874652d6e40908e1c24c41a3a5e3c9137e71652b1"},"schema_version":"1.0","source":{"id":"1711.11134","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.11134","created_at":"2026-05-17T23:46:04Z"},{"alias_kind":"arxiv_version","alias_value":"1711.11134v2","created_at":"2026-05-17T23:46:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.11134","created_at":"2026-05-17T23:46:04Z"},{"alias_kind":"pith_short_12","alias_value":"GGDLQ77G67YW","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"GGDLQ77G67YWQSMD","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"GGDLQ77G","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:1d0675300eb14aa59457de8ede6c9bbc1009d4759d49c77324fe34c01f0b433f","target":"graph","created_at":"2026-05-17T23:46:04Z","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 investigate one-parameter deformations of functions on affine space which define parameterizable hypersurfaces. With the assumption of isolated polar activity at the origin, we are able to completely express the L\\^{e} numbers of the special fiber in terms of the L\\^{e} numbers of the generic fiber and the characteristic polar multiplicities of the comparison, a perverse sheaf naturally associated to any reduced complex analytic space on which the constant sheaf $\\Q_X^\\bullet[\\dim X]$ is perverse. This generalizes the classical formula for the Milnor number of a plane curve in terms of doub","authors_text":"Brian Hepler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-11-29T22:23:34Z","title":"Deformation Formulas for Parameterized Hypersurfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11134","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:f12c94dc0c6fab50f6316239f039fd4989b4509c06ddbf22e43e1b5dd3563522","target":"record","created_at":"2026-05-17T23:46:04Z","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":"d231e1f97127743fa63a07bb590032fc0cd1b3f0531392035e36f9965889f0aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-11-29T22:23:34Z","title_canon_sha256":"a81820481a277aa71882a82874652d6e40908e1c24c41a3a5e3c9137e71652b1"},"schema_version":"1.0","source":{"id":"1711.11134","kind":"arxiv","version":2}},"canonical_sha256":"3186b87fe6f7f168498360daa2762d793ac96c0371d55ffe03518872304d5cbe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3186b87fe6f7f168498360daa2762d793ac96c0371d55ffe03518872304d5cbe","first_computed_at":"2026-05-17T23:46:04.388433Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:04.388433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZoypQijvLlO94+35ke2QDAn1SJjYpfoICFiBSWXHNX3fYfNSg5MT+hjHOdGzkhtYm1AyXlPmo4PMtc42NFokCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:04.389174Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.11134","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f12c94dc0c6fab50f6316239f039fd4989b4509c06ddbf22e43e1b5dd3563522","sha256:1d0675300eb14aa59457de8ede6c9bbc1009d4759d49c77324fe34c01f0b433f"],"state_sha256":"212c08f96913e21eb3879295e14d6f1afb33f39423b4fe1f2771dff796c8b6b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H1t0M6tAi3hfeqHqH6OAf+QsTHR9cf1d25U/P66zXpqWkB0La0uFHGO6r0+c+26vd4DQog6/ujBy8b45WI/HAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T05:40:57.882638Z","bundle_sha256":"d335ca0b11b3ad306bc0b6a97a3739353288046355df19175d5ed93a8af55893"}}