{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:BAGOBL3LJTIDHVXFNACUXZTQKX","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":"c4f35d12dc70de19a2ccadbaafa76d562a5965a35fe43911610c7f75b2b2276f","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2006-12-14T20:33:07Z","title_canon_sha256":"8b40eba080c9af2a3314d3e7452741e1403a34a5f3c0661b0a469e0d9d67f42c"},"schema_version":"1.0","source":{"id":"math/0612379","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0612379","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"arxiv_version","alias_value":"math/0612379v4","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612379","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"pith_short_12","alias_value":"BAGOBL3LJTID","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"BAGOBL3LJTIDHVXF","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"BAGOBL3L","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:1824c988126148e03850617ed6c15bbbcbd9830cbfc25bf32d1c354d2574bd0e","target":"graph","created_at":"2026-05-18T04:08:53Z","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":"The aim of this article is to present the category of bounded Frechet manifolds in respect to which we will review the geometry of Frechet manifolds with a stronger accent on its metric aspect. An inverse function theorem in the sense of Nash and Moser in this category is proved, and some applications to Riemannian geometry are given.","authors_text":"Olaf M\\\"uller","cross_cats":[],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2006-12-14T20:33:07Z","title":"A metric approach to Fr\\'echet geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612379","kind":"arxiv","version":4},"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":"sha256:52b448f0b76d7d69ef9caf69d6fb65ec21d047324087b2a1dc2d40ebcfc897e2","target":"record","created_at":"2026-05-18T04:08:53Z","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":"c4f35d12dc70de19a2ccadbaafa76d562a5965a35fe43911610c7f75b2b2276f","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2006-12-14T20:33:07Z","title_canon_sha256":"8b40eba080c9af2a3314d3e7452741e1403a34a5f3c0661b0a469e0d9d67f42c"},"schema_version":"1.0","source":{"id":"math/0612379","kind":"arxiv","version":4}},"canonical_sha256":"080ce0af6b4cd033d6e568054be67055c65260ea31aa27f503f3eb80a65ce0ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"080ce0af6b4cd033d6e568054be67055c65260ea31aa27f503f3eb80a65ce0ab","first_computed_at":"2026-05-18T04:08:53.059618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:53.059618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9l5TkZgqerIIgl9+2FoinW6C3uhiae92mfQt4t5Azh8k0GXNzJx4v6JfTPJTLovfcqDsjK/DESw308qK/caFDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:53.060443Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0612379","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52b448f0b76d7d69ef9caf69d6fb65ec21d047324087b2a1dc2d40ebcfc897e2","sha256:1824c988126148e03850617ed6c15bbbcbd9830cbfc25bf32d1c354d2574bd0e"],"state_sha256":"30684a149f14ced7633dfa1d79045d6e781b6f720074d755e5f3fc211c5ba149"}