{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ZYOGKUGZMBTIJWUVSCD4WM64OI","short_pith_number":"pith:ZYOGKUGZ","canonical_record":{"source":{"id":"2606.06632","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-06-04T18:31:11Z","cross_cats_sorted":["cs.NA","eess.IV","eess.SP","math.NA","stat.TH"],"title_canon_sha256":"32e4e4efdc204eb5ebc5eb227a5a7a6c0fd07f387ae7705fdda4b34fb5ea4d24","abstract_canon_sha256":"9e64073747038f151d293c6b14dd5ca192b733349ac4aa58d583c7057cf8e213"},"schema_version":"1.0"},"canonical_sha256":"ce1c6550d9606684da959087cb33dc722dea5252c21518403b169ec53d953749","source":{"kind":"arxiv","id":"2606.06632","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.06632","created_at":"2026-06-08T01:04:20Z"},{"alias_kind":"arxiv_version","alias_value":"2606.06632v1","created_at":"2026-06-08T01:04:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06632","created_at":"2026-06-08T01:04:20Z"},{"alias_kind":"pith_short_12","alias_value":"ZYOGKUGZMBTI","created_at":"2026-06-08T01:04:20Z"},{"alias_kind":"pith_short_16","alias_value":"ZYOGKUGZMBTIJWUV","created_at":"2026-06-08T01:04:20Z"},{"alias_kind":"pith_short_8","alias_value":"ZYOGKUGZ","created_at":"2026-06-08T01:04:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ZYOGKUGZMBTIJWUVSCD4WM64OI","target":"record","payload":{"canonical_record":{"source":{"id":"2606.06632","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-06-04T18:31:11Z","cross_cats_sorted":["cs.NA","eess.IV","eess.SP","math.NA","stat.TH"],"title_canon_sha256":"32e4e4efdc204eb5ebc5eb227a5a7a6c0fd07f387ae7705fdda4b34fb5ea4d24","abstract_canon_sha256":"9e64073747038f151d293c6b14dd5ca192b733349ac4aa58d583c7057cf8e213"},"schema_version":"1.0"},"canonical_sha256":"ce1c6550d9606684da959087cb33dc722dea5252c21518403b169ec53d953749","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-08T01:04:20.074670Z","signature_b64":"AeO21Ork2VQpJl9pqBXguKEvaNu9S9gPB6HjJkmF5Y1qSEaUOHtfyxFf1B3P94KaiuzwAAjgpSPbEQMz88NuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce1c6550d9606684da959087cb33dc722dea5252c21518403b169ec53d953749","last_reissued_at":"2026-06-08T01:04:20.073862Z","signature_status":"signed_v1","first_computed_at":"2026-06-08T01:04:20.073862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.06632","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-08T01:04:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OK5g26niELIL5oU3nV+5w3uBg7SU1MM/Qh+uPDtkvTrIeFRZFT6HNVn3yjjDWMfkjIfOFPmwVanfOW1iEqUUCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T10:31:45.853882Z"},"content_sha256":"75dc78788dec5470a48cd2d599776e69fcbe2651ad614be16157b8f27a403541","schema_version":"1.0","event_id":"sha256:75dc78788dec5470a48cd2d599776e69fcbe2651ad614be16157b8f27a403541"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ZYOGKUGZMBTIJWUVSCD4WM64OI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Smooth Hard-Thresholding for Singular Values with Stein's Unbiased Risk Estimate","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","eess.IV","eess.SP","math.NA","stat.TH"],"primary_cat":"math.ST","authors_text":"Guanzhong Yang","submitted_at":"2026-06-04T18:31:11Z","abstract_excerpt":"Low-rank matrix denoising is a central primitive in patch-based image restoration and many other inverse problems. Classical SVD-based image denoising methods often choose a truncation rank by matching residual singular-value energy with an estimated noise energy, but this rule is not a finite-sample risk principle because a fitted low-rank approximation inevitably absorbs part of the noise. This paper develops a mathematically rigorous alternative based on Stein's unbiased risk estimate (SURE). Since singular value hard thresholding is discontinuous and does not satisfy the hypotheses of Stei"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06632","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.06632/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-08T01:04:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"38IIN42t7RB2U2v+4eicspgkCUXQ0tau8e7DvOa/20gNXizgjiJOu6z7Bz9L9kR6Vw0kq0H3IikQZ/+Lu2/sBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T10:31:45.854274Z"},"content_sha256":"a34f70be7b395f246eff00279702ab27435b98a409a487fe096e63131b5af343","schema_version":"1.0","event_id":"sha256:a34f70be7b395f246eff00279702ab27435b98a409a487fe096e63131b5af343"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZYOGKUGZMBTIJWUVSCD4WM64OI/bundle.json","state_url":"https://pith.science/pith/ZYOGKUGZMBTIJWUVSCD4WM64OI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZYOGKUGZMBTIJWUVSCD4WM64OI/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":"2026-06-11T10:31:45Z","links":{"resolver":"https://pith.science/pith/ZYOGKUGZMBTIJWUVSCD4WM64OI","bundle":"https://pith.science/pith/ZYOGKUGZMBTIJWUVSCD4WM64OI/bundle.json","state":"https://pith.science/pith/ZYOGKUGZMBTIJWUVSCD4WM64OI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZYOGKUGZMBTIJWUVSCD4WM64OI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZYOGKUGZMBTIJWUVSCD4WM64OI","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":"9e64073747038f151d293c6b14dd5ca192b733349ac4aa58d583c7057cf8e213","cross_cats_sorted":["cs.NA","eess.IV","eess.SP","math.NA","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-06-04T18:31:11Z","title_canon_sha256":"32e4e4efdc204eb5ebc5eb227a5a7a6c0fd07f387ae7705fdda4b34fb5ea4d24"},"schema_version":"1.0","source":{"id":"2606.06632","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.06632","created_at":"2026-06-08T01:04:20Z"},{"alias_kind":"arxiv_version","alias_value":"2606.06632v1","created_at":"2026-06-08T01:04:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06632","created_at":"2026-06-08T01:04:20Z"},{"alias_kind":"pith_short_12","alias_value":"ZYOGKUGZMBTI","created_at":"2026-06-08T01:04:20Z"},{"alias_kind":"pith_short_16","alias_value":"ZYOGKUGZMBTIJWUV","created_at":"2026-06-08T01:04:20Z"},{"alias_kind":"pith_short_8","alias_value":"ZYOGKUGZ","created_at":"2026-06-08T01:04:20Z"}],"graph_snapshots":[{"event_id":"sha256:a34f70be7b395f246eff00279702ab27435b98a409a487fe096e63131b5af343","target":"graph","created_at":"2026-06-08T01:04:20Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.06632/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Low-rank matrix denoising is a central primitive in patch-based image restoration and many other inverse problems. Classical SVD-based image denoising methods often choose a truncation rank by matching residual singular-value energy with an estimated noise energy, but this rule is not a finite-sample risk principle because a fitted low-rank approximation inevitably absorbs part of the noise. This paper develops a mathematically rigorous alternative based on Stein's unbiased risk estimate (SURE). Since singular value hard thresholding is discontinuous and does not satisfy the hypotheses of Stei","authors_text":"Guanzhong Yang","cross_cats":["cs.NA","eess.IV","eess.SP","math.NA","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-06-04T18:31:11Z","title":"Smooth Hard-Thresholding for Singular Values with Stein's Unbiased Risk Estimate"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06632","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":"sha256:75dc78788dec5470a48cd2d599776e69fcbe2651ad614be16157b8f27a403541","target":"record","created_at":"2026-06-08T01:04:20Z","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":"9e64073747038f151d293c6b14dd5ca192b733349ac4aa58d583c7057cf8e213","cross_cats_sorted":["cs.NA","eess.IV","eess.SP","math.NA","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-06-04T18:31:11Z","title_canon_sha256":"32e4e4efdc204eb5ebc5eb227a5a7a6c0fd07f387ae7705fdda4b34fb5ea4d24"},"schema_version":"1.0","source":{"id":"2606.06632","kind":"arxiv","version":1}},"canonical_sha256":"ce1c6550d9606684da959087cb33dc722dea5252c21518403b169ec53d953749","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce1c6550d9606684da959087cb33dc722dea5252c21518403b169ec53d953749","first_computed_at":"2026-06-08T01:04:20.073862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-08T01:04:20.073862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AeO21Ork2VQpJl9pqBXguKEvaNu9S9gPB6HjJkmF5Y1qSEaUOHtfyxFf1B3P94KaiuzwAAjgpSPbEQMz88NuCw==","signature_status":"signed_v1","signed_at":"2026-06-08T01:04:20.074670Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.06632","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75dc78788dec5470a48cd2d599776e69fcbe2651ad614be16157b8f27a403541","sha256:a34f70be7b395f246eff00279702ab27435b98a409a487fe096e63131b5af343"],"state_sha256":"3253f93f5883f097208b28c5104410a9aa51763adc57466e53d4badce3be8f84"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DEy8lFAy3vQMVDhMAdpJeEeeN88wMTXbc2uO4Ku6r9OZwTOjk7iZTIXnHbB7tkn1AV7m0F3KP7SutbjKNELMBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T10:31:45.856431Z","bundle_sha256":"3f663810fdd4d312bdfa450f5f7d9a77d9316467843a07091bbe9de12ba1bf6b"}}