{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6SMOWPLALDZPAI4GY76I3DFUR4","short_pith_number":"pith:6SMOWPLA","canonical_record":{"source":{"id":"1510.03757","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-10-13T16:08:01Z","cross_cats_sorted":[],"title_canon_sha256":"9eb14f3e3d1ef309ea6e5cde5a5c28c6afd5291a1e02e95566dd3a04f55fa565","abstract_canon_sha256":"460da597bcd9c1d34926e416add02b54916a407df6154abd12b889a46c142667"},"schema_version":"1.0"},"canonical_sha256":"f498eb3d6058f2f02386c7fc8d8cb48f3366d6f9ac5db2f25ef6eecfabdc7e66","source":{"kind":"arxiv","id":"1510.03757","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03757","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03757v1","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03757","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"pith_short_12","alias_value":"6SMOWPLALDZP","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6SMOWPLALDZPAI4G","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6SMOWPLA","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6SMOWPLALDZPAI4GY76I3DFUR4","target":"record","payload":{"canonical_record":{"source":{"id":"1510.03757","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-10-13T16:08:01Z","cross_cats_sorted":[],"title_canon_sha256":"9eb14f3e3d1ef309ea6e5cde5a5c28c6afd5291a1e02e95566dd3a04f55fa565","abstract_canon_sha256":"460da597bcd9c1d34926e416add02b54916a407df6154abd12b889a46c142667"},"schema_version":"1.0"},"canonical_sha256":"f498eb3d6058f2f02386c7fc8d8cb48f3366d6f9ac5db2f25ef6eecfabdc7e66","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:16.249520Z","signature_b64":"JlEznuQcY5DlW1keIjoBX/0b4X2ayRhZYRQEEnLhDG7Ss3p6qPSHRHEnAt4KwnqgMs24lKXLNVqkbSOjcnrjDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f498eb3d6058f2f02386c7fc8d8cb48f3366d6f9ac5db2f25ef6eecfabdc7e66","last_reissued_at":"2026-05-18T01:30:16.248997Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:16.248997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.03757","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":"2026-05-18T01:30:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3zjLhayJCm3NX5L6tCGlZLk4qYy+0LKu/PvEoBUluW65uGUINgHpDwbGnf1GhucaPnITEmZCJS3RCxBalzsaDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:06:01.654455Z"},"content_sha256":"7f0d6e70818c5965d9fb59365248d3ed06350d391bdd8469fa0f6a2e669dec4e","schema_version":"1.0","event_id":"sha256:7f0d6e70818c5965d9fb59365248d3ed06350d391bdd8469fa0f6a2e669dec4e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6SMOWPLALDZPAI4GY76I3DFUR4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Isotopy of Morin singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Kentaro Saji","submitted_at":"2015-10-13T16:08:01Z","abstract_excerpt":"We define an equivalence relation called A-isotopy between finitely determined map-germs, which is a strengthened version of A-equivalence. We consider the number of A-isotopy classes of equidimensional Morin singularities, and some other well-known low-dimensional singularities. We also give an application to stable perturbations of simple equi-dimensional map-germs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03757","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":"2026-05-18T01:30:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dml1e7qm3BgK3tVa8tO0IXMSi3Cvb8TTqvJfLvYAkP641tlDuh2Bu23fPijfIx8WbdlXMiuqKLjpxkFhEmvoDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:06:01.655093Z"},"content_sha256":"6f9c656259c726aa7b08d549d234cb3877953c75a1aaf55fa0c6dc684b101807","schema_version":"1.0","event_id":"sha256:6f9c656259c726aa7b08d549d234cb3877953c75a1aaf55fa0c6dc684b101807"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6SMOWPLALDZPAI4GY76I3DFUR4/bundle.json","state_url":"https://pith.science/pith/6SMOWPLALDZPAI4GY76I3DFUR4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6SMOWPLALDZPAI4GY76I3DFUR4/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":"2026-05-26T16:06:01Z","links":{"resolver":"https://pith.science/pith/6SMOWPLALDZPAI4GY76I3DFUR4","bundle":"https://pith.science/pith/6SMOWPLALDZPAI4GY76I3DFUR4/bundle.json","state":"https://pith.science/pith/6SMOWPLALDZPAI4GY76I3DFUR4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6SMOWPLALDZPAI4GY76I3DFUR4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6SMOWPLALDZPAI4GY76I3DFUR4","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":"460da597bcd9c1d34926e416add02b54916a407df6154abd12b889a46c142667","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-10-13T16:08:01Z","title_canon_sha256":"9eb14f3e3d1ef309ea6e5cde5a5c28c6afd5291a1e02e95566dd3a04f55fa565"},"schema_version":"1.0","source":{"id":"1510.03757","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03757","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03757v1","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03757","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"pith_short_12","alias_value":"6SMOWPLALDZP","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6SMOWPLALDZPAI4G","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6SMOWPLA","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:6f9c656259c726aa7b08d549d234cb3877953c75a1aaf55fa0c6dc684b101807","target":"graph","created_at":"2026-05-18T01:30:16Z","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 define an equivalence relation called A-isotopy between finitely determined map-germs, which is a strengthened version of A-equivalence. We consider the number of A-isotopy classes of equidimensional Morin singularities, and some other well-known low-dimensional singularities. We also give an application to stable perturbations of simple equi-dimensional map-germs.","authors_text":"Kentaro Saji","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-10-13T16:08:01Z","title":"Isotopy of Morin singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03757","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":"sha256:7f0d6e70818c5965d9fb59365248d3ed06350d391bdd8469fa0f6a2e669dec4e","target":"record","created_at":"2026-05-18T01:30:16Z","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":"460da597bcd9c1d34926e416add02b54916a407df6154abd12b889a46c142667","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-10-13T16:08:01Z","title_canon_sha256":"9eb14f3e3d1ef309ea6e5cde5a5c28c6afd5291a1e02e95566dd3a04f55fa565"},"schema_version":"1.0","source":{"id":"1510.03757","kind":"arxiv","version":1}},"canonical_sha256":"f498eb3d6058f2f02386c7fc8d8cb48f3366d6f9ac5db2f25ef6eecfabdc7e66","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f498eb3d6058f2f02386c7fc8d8cb48f3366d6f9ac5db2f25ef6eecfabdc7e66","first_computed_at":"2026-05-18T01:30:16.248997Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:16.248997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JlEznuQcY5DlW1keIjoBX/0b4X2ayRhZYRQEEnLhDG7Ss3p6qPSHRHEnAt4KwnqgMs24lKXLNVqkbSOjcnrjDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:16.249520Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.03757","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f0d6e70818c5965d9fb59365248d3ed06350d391bdd8469fa0f6a2e669dec4e","sha256:6f9c656259c726aa7b08d549d234cb3877953c75a1aaf55fa0c6dc684b101807"],"state_sha256":"028abdeab895bf4e420da97833c079ca87d7fa2dc1603a6b792461d6e8852016"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I7VoFT8CJpVp4k3j2NXCe4U49M6KO1noy6LhVotTNaxn90Jjy9cCE6/ijpquCefUrFTr+IDsz7Txenh0pPTpCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T16:06:01.658475Z","bundle_sha256":"f631ddee996dc2e4e09b3e614711b001f22ba8548cadea565ed9666929769f00"}}