{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SDSM24P3T2OWQN2RFSRPMV35ZJ","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":"feeb3d9a7f6a67a09f4f21561c571fd17d2d4cba77ed01565a2a5dfbe703cc39","cross_cats_sorted":["cs.CV","math.NA","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-04-29T21:40:16Z","title_canon_sha256":"928e4a9138fb03ae219de98af2cce133644988bb4f5fc08ac7d9d6468279674e"},"schema_version":"1.0","source":{"id":"1605.00031","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00031","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00031v2","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00031","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"pith_short_12","alias_value":"SDSM24P3T2OW","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SDSM24P3T2OWQN2R","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SDSM24P3","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:56b5fdde8e73856f7797905a27d92c427c0cd9073de52538256f35b1cee987e6","target":"graph","created_at":"2026-05-18T00:23:57Z","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":"Wiatowski and B\\\"olcskei, 2015, proved that deformation stability and vertical translation invariance of deep convolutional neural network-based feature extractors are guaranteed by the network structure per se rather than the specific convolution kernels and non-linearities. While the translation invariance result applies to square-integrable functions, the deformation stability bound holds for band-limited functions only. Many signals of practical relevance (such as natural images) exhibit, however, sharp and curved discontinuities and are, hence, not band-limited. The main contribution of t","authors_text":"Helmut B\\\"olcskei, Philipp Grohs, Thomas Wiatowski","cross_cats":["cs.CV","math.NA","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-04-29T21:40:16Z","title":"Deep Convolutional Neural Networks on Cartoon Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00031","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:b72b5b8c920ef61987fc08d7c001cd59c129f13ece40189b3f4d5c57097f7fec","target":"record","created_at":"2026-05-18T00:23:57Z","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":"feeb3d9a7f6a67a09f4f21561c571fd17d2d4cba77ed01565a2a5dfbe703cc39","cross_cats_sorted":["cs.CV","math.NA","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-04-29T21:40:16Z","title_canon_sha256":"928e4a9138fb03ae219de98af2cce133644988bb4f5fc08ac7d9d6468279674e"},"schema_version":"1.0","source":{"id":"1605.00031","kind":"arxiv","version":2}},"canonical_sha256":"90e4cd71fb9e9d6837512ca2f6577dca7f6c8fc0ffb81925843bef91ae1b0b3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90e4cd71fb9e9d6837512ca2f6577dca7f6c8fc0ffb81925843bef91ae1b0b3d","first_computed_at":"2026-05-18T00:23:57.231443Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:57.231443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nfb0GM51DAv+kdNqGMxZ/k+CFq8Rzzl1fW4w3n+iu+BeUeB5/7YTi7hvrtdW3QWcX/zQS9nHxZrjRiYl7MPSDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:57.232088Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.00031","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b72b5b8c920ef61987fc08d7c001cd59c129f13ece40189b3f4d5c57097f7fec","sha256:56b5fdde8e73856f7797905a27d92c427c0cd9073de52538256f35b1cee987e6"],"state_sha256":"9fe9dbd35c6f82b7041571b39aca417f814545331fea22b10327f7e534472390"}