{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:56RGGHCXOU6M4OCM3CHRIBC77Q","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":"f0fee31480003fa1a7ac49195add5f74b0ee194d52821a64181c8986e573f070","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-03T19:13:41Z","title_canon_sha256":"e37b98d182089cd36c48552bbc7d1491177248b4ad1d0a7bb3fe26a8c53916d3"},"schema_version":"1.0","source":{"id":"1107.0488","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0488","created_at":"2026-05-18T04:03:06Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0488v2","created_at":"2026-05-18T04:03:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0488","created_at":"2026-05-18T04:03:06Z"},{"alias_kind":"pith_short_12","alias_value":"56RGGHCXOU6M","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"56RGGHCXOU6M4OCM","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"56RGGHCX","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:8c00aa9fcfa1990d95fecd83253bda9799cdfca25e282b73a588df2f275ad8a3","target":"graph","created_at":"2026-05-18T04:03:06Z","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":"For $M$ being a closed manifold or the Euclidean space we present a detailed proof of regularity properties of the composition of $H^s$-regular diffeomorphisms of $M$ for $s > 1/2\\dim M + 1$.","authors_text":"Hasan Inci, Peter Topalov, Thomas Kappeler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-03T19:13:41Z","title":"On the regularity of the composition of diffeomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0488","kind":"arxiv","version":2},"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":"sha256:5655a6b3519b848272d11b3c2da5621486e48af50dc5094ecdb7f2bd70ff5590","target":"record","created_at":"2026-05-18T04:03:06Z","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":"f0fee31480003fa1a7ac49195add5f74b0ee194d52821a64181c8986e573f070","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-03T19:13:41Z","title_canon_sha256":"e37b98d182089cd36c48552bbc7d1491177248b4ad1d0a7bb3fe26a8c53916d3"},"schema_version":"1.0","source":{"id":"1107.0488","kind":"arxiv","version":2}},"canonical_sha256":"efa2631c57753cce384cd88f14045ffc0ca8b912b46a920c269f417f4d02e4d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"efa2631c57753cce384cd88f14045ffc0ca8b912b46a920c269f417f4d02e4d0","first_computed_at":"2026-05-18T04:03:06.878330Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:06.878330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+dJpVXIz/5nFwyQj+J/HukD7NggKHx3e5nZU+Wgi/DR3eMtO/6Q8LjPHaQH+t0pyu4FswLt6qbBRP19isUUoBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:06.879143Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0488","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5655a6b3519b848272d11b3c2da5621486e48af50dc5094ecdb7f2bd70ff5590","sha256:8c00aa9fcfa1990d95fecd83253bda9799cdfca25e282b73a588df2f275ad8a3"],"state_sha256":"4b47c08ef1a7fb99377fbeaa16c9eeffd47b5c020e5b8b57dddead291bff9669"}