{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:FZ4UE4LP7DO4HZPZCMWHDU6YCZ","short_pith_number":"pith:FZ4UE4LP","canonical_record":{"source":{"id":"1004.4093","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-04-23T10:44:50Z","cross_cats_sorted":[],"title_canon_sha256":"4a7e97fed95bd975401636c2b3f50989967b9891de39fc91cea84655339bcc30","abstract_canon_sha256":"8e8708f54c1f23227403305ef3f308ca042c89fb0f39ed2aeb9879ccf4316cb0"},"schema_version":"1.0"},"canonical_sha256":"2e7942716ff8ddc3e5f9132c71d3d8166c14fc785bd103c4c7dee55ecbe440a6","source":{"kind":"arxiv","id":"1004.4093","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.4093","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"arxiv_version","alias_value":"1004.4093v1","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.4093","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"pith_short_12","alias_value":"FZ4UE4LP7DO4","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FZ4UE4LP7DO4HZPZ","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FZ4UE4LP","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:FZ4UE4LP7DO4HZPZCMWHDU6YCZ","target":"record","payload":{"canonical_record":{"source":{"id":"1004.4093","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-04-23T10:44:50Z","cross_cats_sorted":[],"title_canon_sha256":"4a7e97fed95bd975401636c2b3f50989967b9891de39fc91cea84655339bcc30","abstract_canon_sha256":"8e8708f54c1f23227403305ef3f308ca042c89fb0f39ed2aeb9879ccf4316cb0"},"schema_version":"1.0"},"canonical_sha256":"2e7942716ff8ddc3e5f9132c71d3d8166c14fc785bd103c4c7dee55ecbe440a6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:02.209989Z","signature_b64":"c4Ul+1BMy7iH1+gqt57ZvspVF5ylUy7TRfZSq8xNet35uRdh0phK2vXszkIwZesF+1qp7NJHNBjb6ITeyHq+AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e7942716ff8ddc3e5f9132c71d3d8166c14fc785bd103c4c7dee55ecbe440a6","last_reissued_at":"2026-05-18T02:58:02.209403Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:02.209403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.4093","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":"2026-05-18T02:58:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LPM5cbZF2QJARXOe1ZTkZX/amqnGFGz+Cq9DKjRX8EMBRdk5QRnFLudS9xZvyTvnfUkRhz1/5sUuuCWYthfdDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:01:16.719529Z"},"content_sha256":"fa864f2d91d031c8d3b1fb765544983f09926690586eba6ff4ab8c84695c84f2","schema_version":"1.0","event_id":"sha256:fa864f2d91d031c8d3b1fb765544983f09926690586eba6ff4ab8c84695c84f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:FZ4UE4LP7DO4HZPZCMWHDU6YCZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytic and Nash equivalence relations of Nash maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Masahiro Shiota","submitted_at":"2010-04-23T10:44:50Z","abstract_excerpt":"Let $M$ and $N$ be Nash manifolds, and $f$ and $g$ Nash maps from $M$ to $N$. If $M$ and $N$ are compact and if $f$ and $g$ are analytically R-L equivalent, then they are Nash R-L equivalent. In the local case, $C^infty$ R-L equivalence of two Nash map germs implies Nash R-L equivalence. This shows a difference of Nash map germs and analytic map germs. Indeed, there are two analytic map germs from $(R^2,0)$ to $(R^4,0)$ which are $C^infty$ R-L equivalent but not analytically R-L equivalent."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.4093","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":"2026-05-18T02:58:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zo6LSX93sNzUtWELFGKZGV7ILvxPtxWATT513DjCJD+23Q/F9Jv9jM6DAUzV2V+13jCKoTSznxo+hm06IkNXAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:01:16.719879Z"},"content_sha256":"9ace863d286d24aa2c6b0bc29e071898fe754af21377d2c370ee7011c0a6b201","schema_version":"1.0","event_id":"sha256:9ace863d286d24aa2c6b0bc29e071898fe754af21377d2c370ee7011c0a6b201"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FZ4UE4LP7DO4HZPZCMWHDU6YCZ/bundle.json","state_url":"https://pith.science/pith/FZ4UE4LP7DO4HZPZCMWHDU6YCZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FZ4UE4LP7DO4HZPZCMWHDU6YCZ/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":"2026-06-05T08:01:16Z","links":{"resolver":"https://pith.science/pith/FZ4UE4LP7DO4HZPZCMWHDU6YCZ","bundle":"https://pith.science/pith/FZ4UE4LP7DO4HZPZCMWHDU6YCZ/bundle.json","state":"https://pith.science/pith/FZ4UE4LP7DO4HZPZCMWHDU6YCZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FZ4UE4LP7DO4HZPZCMWHDU6YCZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:FZ4UE4LP7DO4HZPZCMWHDU6YCZ","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":"8e8708f54c1f23227403305ef3f308ca042c89fb0f39ed2aeb9879ccf4316cb0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-04-23T10:44:50Z","title_canon_sha256":"4a7e97fed95bd975401636c2b3f50989967b9891de39fc91cea84655339bcc30"},"schema_version":"1.0","source":{"id":"1004.4093","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.4093","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"arxiv_version","alias_value":"1004.4093v1","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.4093","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"pith_short_12","alias_value":"FZ4UE4LP7DO4","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FZ4UE4LP7DO4HZPZ","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FZ4UE4LP","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:9ace863d286d24aa2c6b0bc29e071898fe754af21377d2c370ee7011c0a6b201","target":"graph","created_at":"2026-05-18T02:58:02Z","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":"Let $M$ and $N$ be Nash manifolds, and $f$ and $g$ Nash maps from $M$ to $N$. If $M$ and $N$ are compact and if $f$ and $g$ are analytically R-L equivalent, then they are Nash R-L equivalent. In the local case, $C^infty$ R-L equivalence of two Nash map germs implies Nash R-L equivalence. This shows a difference of Nash map germs and analytic map germs. Indeed, there are two analytic map germs from $(R^2,0)$ to $(R^4,0)$ which are $C^infty$ R-L equivalent but not analytically R-L equivalent.","authors_text":"Masahiro Shiota","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-04-23T10:44:50Z","title":"Analytic and Nash equivalence relations of Nash maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.4093","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:fa864f2d91d031c8d3b1fb765544983f09926690586eba6ff4ab8c84695c84f2","target":"record","created_at":"2026-05-18T02:58:02Z","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":"8e8708f54c1f23227403305ef3f308ca042c89fb0f39ed2aeb9879ccf4316cb0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-04-23T10:44:50Z","title_canon_sha256":"4a7e97fed95bd975401636c2b3f50989967b9891de39fc91cea84655339bcc30"},"schema_version":"1.0","source":{"id":"1004.4093","kind":"arxiv","version":1}},"canonical_sha256":"2e7942716ff8ddc3e5f9132c71d3d8166c14fc785bd103c4c7dee55ecbe440a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e7942716ff8ddc3e5f9132c71d3d8166c14fc785bd103c4c7dee55ecbe440a6","first_computed_at":"2026-05-18T02:58:02.209403Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:02.209403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c4Ul+1BMy7iH1+gqt57ZvspVF5ylUy7TRfZSq8xNet35uRdh0phK2vXszkIwZesF+1qp7NJHNBjb6ITeyHq+AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:02.209989Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.4093","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa864f2d91d031c8d3b1fb765544983f09926690586eba6ff4ab8c84695c84f2","sha256:9ace863d286d24aa2c6b0bc29e071898fe754af21377d2c370ee7011c0a6b201"],"state_sha256":"82ec744cf6bd6b444a3533317df78f92fd6ea32b2c6a12b23ccfd9e071f7eef6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CYDWSUxdht1RuqwLM3t/S06S1uVS2THp+SKSOFNRZO+LVDrYJ82x1vCbE6Hi7ZpAC3mXIe8O7YIhevWLY0gyBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T08:01:16.721860Z","bundle_sha256":"91869a1fa41ce79cf1824e770a205e07cb387f2c8ca271764365610a64584904"}}