{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:6SVZXGHG4KDNHTI6RYQR24BGYV","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":"4ebeba6bf4b433a19903b99344beff660766d4687e0c1414f94a6a31ab17b055","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-22T07:18:47Z","title_canon_sha256":"8b1d24f803b598267c31f74ee380b310b997409ba973a616ab354e4b170bfd2b"},"schema_version":"1.0","source":{"id":"1908.08232","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.08232","created_at":"2026-07-04T23:59:10Z"},{"alias_kind":"arxiv_version","alias_value":"1908.08232v1","created_at":"2026-07-04T23:59:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08232","created_at":"2026-07-04T23:59:10Z"},{"alias_kind":"pith_short_12","alias_value":"6SVZXGHG4KDN","created_at":"2026-07-04T23:59:10Z"},{"alias_kind":"pith_short_16","alias_value":"6SVZXGHG4KDNHTI6","created_at":"2026-07-04T23:59:10Z"},{"alias_kind":"pith_short_8","alias_value":"6SVZXGHG","created_at":"2026-07-04T23:59:10Z"}],"graph_snapshots":[{"event_id":"sha256:e56fcd4577fc15c4bdd7a06d85a9feba822a85318e12eedb780622986e2a2d34","target":"graph","created_at":"2026-07-04T23:59:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.08232/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider equivalence relations among smooth map germs with respect to geometry of G-structures on the target space germ. These equivalence relations are natural generalization of right-left equivalence (i.e., A-equivalence) in the sense of Thom-Mather depending on geometric structures on the target space germ. Unfortunately, these equivalence relations are not necessarily geometric subgroups in the sense of Damon (1984). However, we have interesting applications of these equivalence relations.","authors_text":"Hiroshi Teramoto, Masatomo Takahashi, Shyuichi Izumiya","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-22T07:18:47Z","title":"Geometric equivalence among smooth map germs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08232","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:a278cd2829c0d659cee0dd3e75945d81d90a56805f258a3d98483304595de036","target":"record","created_at":"2026-07-04T23:59:10Z","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":"4ebeba6bf4b433a19903b99344beff660766d4687e0c1414f94a6a31ab17b055","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-22T07:18:47Z","title_canon_sha256":"8b1d24f803b598267c31f74ee380b310b997409ba973a616ab354e4b170bfd2b"},"schema_version":"1.0","source":{"id":"1908.08232","kind":"arxiv","version":1}},"canonical_sha256":"f4ab9b98e6e286d3cd1e8e211d7026c55d339d3ed9f44180c9ca3805815c68ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4ab9b98e6e286d3cd1e8e211d7026c55d339d3ed9f44180c9ca3805815c68ae","first_computed_at":"2026-07-04T23:59:10.806022Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:59:10.806022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rkl/SsZd4agydm7FWfztz+aCHt6C1pCEylFOjHJdS0jryltw1SJZJgFYZ0t7g9Re7bjBHX75JIV/YMjuCJdeAg==","signature_status":"signed_v1","signed_at":"2026-07-04T23:59:10.806504Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.08232","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a278cd2829c0d659cee0dd3e75945d81d90a56805f258a3d98483304595de036","sha256:e56fcd4577fc15c4bdd7a06d85a9feba822a85318e12eedb780622986e2a2d34"],"state_sha256":"59cfd1c3e46346c506c8e8ac99510aced13f3326e94ca4bfb9ee52b86d74804b"}