{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JLSTL4DYKH5EPXTQNAMHQ27JG5","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":"b0467775cdc4b8270d1c5c21c0f78da233bcf4498ce20a245a7c5fbb2778362d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-09-18T17:35:33Z","title_canon_sha256":"6aa2511ae083e1e04451f7de0f09b3f6b4bf3e1efce55e9a886ffb5f74ff3957"},"schema_version":"1.0","source":{"id":"1409.5385","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.5385","created_at":"2026-05-18T02:42:29Z"},{"alias_kind":"arxiv_version","alias_value":"1409.5385v1","created_at":"2026-05-18T02:42:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5385","created_at":"2026-05-18T02:42:29Z"},{"alias_kind":"pith_short_12","alias_value":"JLSTL4DYKH5E","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JLSTL4DYKH5EPXTQ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JLSTL4DY","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:66262a09d92b7dd6a0f28971328b13c262a1a3066c5e312796a0f76bd40f16b7","target":"graph","created_at":"2026-05-18T02:42:29Z","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 give some new methods for perfect reconstruction from frame and sampling erasures in finitely many steps. By bridging an erasure set we mean replacing the erased Fourier coefficients of a function with respect to a frame by appropriate linear combinations of the non-erased coefficients. We prove that if a minimal redundancy condition is satisfied bridging can always be done to make the reduced error operator nilpotent of index 2 using a bridge set of indices no larger than the cardinality of the erasure set. This results in perfect reconstruction of the erased coefficients in one final matr","authors_text":"David R. Larson, Sam L. Scholze","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-09-18T17:35:33Z","title":"Signal Reconstruction from Frame and Sampling Erasures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5385","kind":"arxiv","version":1},"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:de3d70bb0e5901bf460bf6bbcaa7707241bfba489ad00effceadf880ba8731da","target":"record","created_at":"2026-05-18T02:42:29Z","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":"b0467775cdc4b8270d1c5c21c0f78da233bcf4498ce20a245a7c5fbb2778362d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-09-18T17:35:33Z","title_canon_sha256":"6aa2511ae083e1e04451f7de0f09b3f6b4bf3e1efce55e9a886ffb5f74ff3957"},"schema_version":"1.0","source":{"id":"1409.5385","kind":"arxiv","version":1}},"canonical_sha256":"4ae535f07851fa47de706818786be93759b22f5c4ff0470ed321c7eb52d8ca9f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ae535f07851fa47de706818786be93759b22f5c4ff0470ed321c7eb52d8ca9f","first_computed_at":"2026-05-18T02:42:29.628270Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:29.628270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tGDNbiiYEoqvtLCqXQhIeKyw6PP7a7cd7eMcZQpBe+hBrZOJBhPBcclop7aiY9bbsyasYZqqwyoMfwTam5ltCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:29.629186Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.5385","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de3d70bb0e5901bf460bf6bbcaa7707241bfba489ad00effceadf880ba8731da","sha256:66262a09d92b7dd6a0f28971328b13c262a1a3066c5e312796a0f76bd40f16b7"],"state_sha256":"8a47ef576a218e57d458a20965f27ea885b3789a73b895b721c4db5f3af08f48"}