{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:XU4VRTQE4DWDTCUJB2EY7LLHCV","short_pith_number":"pith:XU4VRTQE","schema_version":"1.0","canonical_sha256":"bd3958ce04e0ec398a890e898fad6715683d08a7f0e58012e87136ab21b003f4","source":{"kind":"arxiv","id":"0811.4569","version":2},"attestation_state":"computed","paper":{"title":"Analytic equivalence of normal crossing functions on a real analytic manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Goulwen Fichou (IRMAR), Masahiro Shiota","submitted_at":"2008-11-27T15:48:48Z","abstract_excerpt":"By Hironaka Desingularization Theorem, any real analytic function has only normal crossing singularities after a suitable modification. We focus on the analytic equivalence of such functions with only normal crossing singularities. We prove that for such functions $C^{\\infty}$ right equivalence implies analytic equivalence. We prove moreover that the cardinality of the set of equivalence classes is zero or countable."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0811.4569","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-11-27T15:48:48Z","cross_cats_sorted":[],"title_canon_sha256":"8b574fa3192fb4ff9ad82f8c5caa223b30af4daa526fc5afdb2ff7f5c6db6703","abstract_canon_sha256":"125714150e7cf2edc2e2df1c10f010a07c5dc4df5cd4ac45f371bad101a6f0b9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:10.906408Z","signature_b64":"pn1prDg1DZgCEiMQHiJkTnG5tfz2KHFnD/UBFlcykvwuYfYiGxckRA4zB0V1bN2wQ6MOnqDMh0SoPn6ejGL3DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd3958ce04e0ec398a890e898fad6715683d08a7f0e58012e87136ab21b003f4","last_reissued_at":"2026-05-18T02:58:10.905847Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:10.905847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analytic equivalence of normal crossing functions on a real analytic manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Goulwen Fichou (IRMAR), Masahiro Shiota","submitted_at":"2008-11-27T15:48:48Z","abstract_excerpt":"By Hironaka Desingularization Theorem, any real analytic function has only normal crossing singularities after a suitable modification. We focus on the analytic equivalence of such functions with only normal crossing singularities. We prove that for such functions $C^{\\infty}$ right equivalence implies analytic equivalence. We prove moreover that the cardinality of the set of equivalence classes is zero or countable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.4569","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0811.4569","created_at":"2026-05-18T02:58:10.905940+00:00"},{"alias_kind":"arxiv_version","alias_value":"0811.4569v2","created_at":"2026-05-18T02:58:10.905940+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.4569","created_at":"2026-05-18T02:58:10.905940+00:00"},{"alias_kind":"pith_short_12","alias_value":"XU4VRTQE4DWD","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"XU4VRTQE4DWDTCUJ","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"XU4VRTQE","created_at":"2026-05-18T12:25:58.018023+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XU4VRTQE4DWDTCUJB2EY7LLHCV","json":"https://pith.science/pith/XU4VRTQE4DWDTCUJB2EY7LLHCV.json","graph_json":"https://pith.science/api/pith-number/XU4VRTQE4DWDTCUJB2EY7LLHCV/graph.json","events_json":"https://pith.science/api/pith-number/XU4VRTQE4DWDTCUJB2EY7LLHCV/events.json","paper":"https://pith.science/paper/XU4VRTQE"},"agent_actions":{"view_html":"https://pith.science/pith/XU4VRTQE4DWDTCUJB2EY7LLHCV","download_json":"https://pith.science/pith/XU4VRTQE4DWDTCUJB2EY7LLHCV.json","view_paper":"https://pith.science/paper/XU4VRTQE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0811.4569&json=true","fetch_graph":"https://pith.science/api/pith-number/XU4VRTQE4DWDTCUJB2EY7LLHCV/graph.json","fetch_events":"https://pith.science/api/pith-number/XU4VRTQE4DWDTCUJB2EY7LLHCV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XU4VRTQE4DWDTCUJB2EY7LLHCV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XU4VRTQE4DWDTCUJB2EY7LLHCV/action/storage_attestation","attest_author":"https://pith.science/pith/XU4VRTQE4DWDTCUJB2EY7LLHCV/action/author_attestation","sign_citation":"https://pith.science/pith/XU4VRTQE4DWDTCUJB2EY7LLHCV/action/citation_signature","submit_replication":"https://pith.science/pith/XU4VRTQE4DWDTCUJB2EY7LLHCV/action/replication_record"}},"created_at":"2026-05-18T02:58:10.905940+00:00","updated_at":"2026-05-18T02:58:10.905940+00:00"}