{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MJTMMSUD36H742OL5FHJJTRPKG","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":"d85d135023a13e563b847c4dec3829aeb772e6722224709a1e7fce1169c6ae55","cross_cats_sorted":["math.AP","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-17T15:31:54Z","title_canon_sha256":"c78d5686e5042b56f53814f94b7923d2193f1790869ce24be5c4fbe7d0b01a0b"},"schema_version":"1.0","source":{"id":"1504.04538","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04538","created_at":"2026-05-18T01:31:18Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04538v2","created_at":"2026-05-18T01:31:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04538","created_at":"2026-05-18T01:31:18Z"},{"alias_kind":"pith_short_12","alias_value":"MJTMMSUD36H7","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MJTMMSUD36H742OL","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MJTMMSUD","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:765849733526893921e902522ccb3994e404222ea1d4ad9590d01ba12299f177","target":"graph","created_at":"2026-05-18T01:31:18Z","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":"In this paper, we establish compactness for various geometric curvature energies including integral Menger curvature, and tangent-point repulsive potentials, defined a priori on the class of compact, embedded $m$-dimensional Lipschitz submanifolds in ${\\mathbb{R}}^n$. It turns out that due to a smoothing effect any sequence of submanifolds with uniformly bounded energy contains a subsequence converging in $C^1$ to a limit submanifold.\n  This result has two applications. The first one is an isotopy finiteness theorem: there are only finitely many isotopy types of such submanifolds below a given","authors_text":"Heiko von der Mosel, Pawe{\\l} Strzelecki, S{\\l}awomir Kolasi\\'nski","cross_cats":["math.AP","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-17T15:31:54Z","title":"Compactness and isotopy finiteness for submanifolds with uniformly bounded geometric curvature energies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04538","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:c61cf4e58b861baa52339f07710e07e747ff5d4a000566bec0e399ac3fc5f775","target":"record","created_at":"2026-05-18T01:31:18Z","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":"d85d135023a13e563b847c4dec3829aeb772e6722224709a1e7fce1169c6ae55","cross_cats_sorted":["math.AP","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-17T15:31:54Z","title_canon_sha256":"c78d5686e5042b56f53814f94b7923d2193f1790869ce24be5c4fbe7d0b01a0b"},"schema_version":"1.0","source":{"id":"1504.04538","kind":"arxiv","version":2}},"canonical_sha256":"6266c64a83df8ffe69cbe94e94ce2f51b6d65d5b107a2cfe2f0223d18f4e3f67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6266c64a83df8ffe69cbe94e94ce2f51b6d65d5b107a2cfe2f0223d18f4e3f67","first_computed_at":"2026-05-18T01:31:18.736767Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:18.736767Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4VXlHR/Cpm2+4znP8HlU9KUpaL3UjbgDXd6LoHz4PZBF77egK5YgpRXg1vFttSVPPX0uxc8aZz10GBZqM1brDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:18.737351Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.04538","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c61cf4e58b861baa52339f07710e07e747ff5d4a000566bec0e399ac3fc5f775","sha256:765849733526893921e902522ccb3994e404222ea1d4ad9590d01ba12299f177"],"state_sha256":"627f11d1ca8053f7262fbaeb4b581250ac9ccdf1c17f1653da81eab89f7fb09d"}