{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:VCZC63GI66NS2CJJBYBHMJPGUD","short_pith_number":"pith:VCZC63GI","canonical_record":{"source":{"id":"1312.2734","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-12-10T09:58:53Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"f08aeb796bf5aec9357251dfa4f72ef1a40951371039922b0f89d8a3e4d8c585","abstract_canon_sha256":"cd9bdb53814c087e4f7a6233a432f440fb0ff4af85ce204c9238b35a7651002f"},"schema_version":"1.0"},"canonical_sha256":"a8b22f6cc8f79b2d09290e027625e6a0d7b16ed21eb3b3f73fc563df9af622f8","source":{"kind":"arxiv","id":"1312.2734","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2734","created_at":"2026-05-18T02:43:24Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2734v2","created_at":"2026-05-18T02:43:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2734","created_at":"2026-05-18T02:43:24Z"},{"alias_kind":"pith_short_12","alias_value":"VCZC63GI66NS","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VCZC63GI66NS2CJJ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VCZC63GI","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:VCZC63GI66NS2CJJBYBHMJPGUD","target":"record","payload":{"canonical_record":{"source":{"id":"1312.2734","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-12-10T09:58:53Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"f08aeb796bf5aec9357251dfa4f72ef1a40951371039922b0f89d8a3e4d8c585","abstract_canon_sha256":"cd9bdb53814c087e4f7a6233a432f440fb0ff4af85ce204c9238b35a7651002f"},"schema_version":"1.0"},"canonical_sha256":"a8b22f6cc8f79b2d09290e027625e6a0d7b16ed21eb3b3f73fc563df9af622f8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:24.212184Z","signature_b64":"MmEYljBVg4noY301V+5B3MZiVJCX33WsFx+6UVd9oGHIymLRGIcBFw/ItTvkXq3nslD7f6d129+PS0wpCUSOAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8b22f6cc8f79b2d09290e027625e6a0d7b16ed21eb3b3f73fc563df9af622f8","last_reissued_at":"2026-05-18T02:43:24.211578Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:24.211578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.2734","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:43:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dMP4+ZcyaZh7GjmTf/dsg5gJ8glDOppHTAryZWrnNMaVo+v26KW1kObfWRBdVd0gu6kpXJM7pc5n/RftH+UJCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T13:03:44.002953Z"},"content_sha256":"bb3d4206284a5927c0dafe235ef4a8c793e78136fd7b2ece702041612731789d","schema_version":"1.0","event_id":"sha256:bb3d4206284a5927c0dafe235ef4a8c793e78136fd7b2ece702041612731789d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:VCZC63GI66NS2CJJBYBHMJPGUD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Besov regularity for operator equations on patchwise smooth manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.NA","authors_text":"Markus Weimar, Stephan Dahlke","submitted_at":"2013-12-10T09:58:53Z","abstract_excerpt":"We study regularity properties of solutions to operator equations on patchwise smooth manifolds $\\partial\\Omega$ such as, e.g., boundaries of polyhedral domains $\\Omega \\subset \\mathbb{R}^3$. Using suitable biorthogonal wavelet bases $\\Psi$, we introduce a new class of Besov-type spaces $B_{\\Psi,q}^\\alpha(L_p(\\partial \\Omega))$ of functions $u\\colon\\partial\\Omega\\rightarrow\\mathbb{C}$. Special attention is paid on the rate of convergence for best $n$-term wavelet approximation to functions in these scales since this determines the performance of adaptive numerical schemes. We show embeddings o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2734","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:43:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3bVH/nNyUGquIx+xcwnkU6rIpmLhJ8l0S78KkLqBdTKluN3TK1VftI/Tu+2Y/DWthalZmvLMRDiaLvgITrX/CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T13:03:44.003390Z"},"content_sha256":"6b541d3a6a76c4674954672b7638b259ae00b62049bae5c39806861492452b7a","schema_version":"1.0","event_id":"sha256:6b541d3a6a76c4674954672b7638b259ae00b62049bae5c39806861492452b7a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VCZC63GI66NS2CJJBYBHMJPGUD/bundle.json","state_url":"https://pith.science/pith/VCZC63GI66NS2CJJBYBHMJPGUD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VCZC63GI66NS2CJJBYBHMJPGUD/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":"2026-06-06T13:03:44Z","links":{"resolver":"https://pith.science/pith/VCZC63GI66NS2CJJBYBHMJPGUD","bundle":"https://pith.science/pith/VCZC63GI66NS2CJJBYBHMJPGUD/bundle.json","state":"https://pith.science/pith/VCZC63GI66NS2CJJBYBHMJPGUD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VCZC63GI66NS2CJJBYBHMJPGUD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VCZC63GI66NS2CJJBYBHMJPGUD","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":"cd9bdb53814c087e4f7a6233a432f440fb0ff4af85ce204c9238b35a7651002f","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-12-10T09:58:53Z","title_canon_sha256":"f08aeb796bf5aec9357251dfa4f72ef1a40951371039922b0f89d8a3e4d8c585"},"schema_version":"1.0","source":{"id":"1312.2734","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2734","created_at":"2026-05-18T02:43:24Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2734v2","created_at":"2026-05-18T02:43:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2734","created_at":"2026-05-18T02:43:24Z"},{"alias_kind":"pith_short_12","alias_value":"VCZC63GI66NS","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VCZC63GI66NS2CJJ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VCZC63GI","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:6b541d3a6a76c4674954672b7638b259ae00b62049bae5c39806861492452b7a","target":"graph","created_at":"2026-05-18T02:43:24Z","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":"We study regularity properties of solutions to operator equations on patchwise smooth manifolds $\\partial\\Omega$ such as, e.g., boundaries of polyhedral domains $\\Omega \\subset \\mathbb{R}^3$. Using suitable biorthogonal wavelet bases $\\Psi$, we introduce a new class of Besov-type spaces $B_{\\Psi,q}^\\alpha(L_p(\\partial \\Omega))$ of functions $u\\colon\\partial\\Omega\\rightarrow\\mathbb{C}$. Special attention is paid on the rate of convergence for best $n$-term wavelet approximation to functions in these scales since this determines the performance of adaptive numerical schemes. We show embeddings o","authors_text":"Markus Weimar, Stephan Dahlke","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-12-10T09:58:53Z","title":"Besov regularity for operator equations on patchwise smooth manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2734","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:bb3d4206284a5927c0dafe235ef4a8c793e78136fd7b2ece702041612731789d","target":"record","created_at":"2026-05-18T02:43:24Z","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":"cd9bdb53814c087e4f7a6233a432f440fb0ff4af85ce204c9238b35a7651002f","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-12-10T09:58:53Z","title_canon_sha256":"f08aeb796bf5aec9357251dfa4f72ef1a40951371039922b0f89d8a3e4d8c585"},"schema_version":"1.0","source":{"id":"1312.2734","kind":"arxiv","version":2}},"canonical_sha256":"a8b22f6cc8f79b2d09290e027625e6a0d7b16ed21eb3b3f73fc563df9af622f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8b22f6cc8f79b2d09290e027625e6a0d7b16ed21eb3b3f73fc563df9af622f8","first_computed_at":"2026-05-18T02:43:24.211578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:24.211578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MmEYljBVg4noY301V+5B3MZiVJCX33WsFx+6UVd9oGHIymLRGIcBFw/ItTvkXq3nslD7f6d129+PS0wpCUSOAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:24.212184Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.2734","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb3d4206284a5927c0dafe235ef4a8c793e78136fd7b2ece702041612731789d","sha256:6b541d3a6a76c4674954672b7638b259ae00b62049bae5c39806861492452b7a"],"state_sha256":"c2052823204436807d5fcdc9420a6e97bc51053caef9c1e09419320e3668f31a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P1orjdyJ3KkkyLPsNm/SQPmG2EGyf1s8DOE0cGh1A+J+dZlfpWtaNoBYZs8sQPY/2CtNTgR2v2Tpz10w2RpwAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T13:03:44.006406Z","bundle_sha256":"c9189d6879ffbcedc06a76be6560d6ecc350caf1f735f2816d0679c146ffe120"}}