{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:UQYPVFFDYK7HNE4SSTEULOOAWJ","short_pith_number":"pith:UQYPVFFD","canonical_record":{"source":{"id":"2501.08719","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-01-15T10:59:22Z","cross_cats_sorted":[],"title_canon_sha256":"98a58f57eae1dfcbf702ec09e34c9ca4530e93c0327bacb055d0b1797cdbc0ad","abstract_canon_sha256":"bfa9a23dbd1dce956d720815f7abf54168f120421a4611e922e3a0b16051cf00"},"schema_version":"1.0"},"canonical_sha256":"a430fa94a3c2be76939294c945b9c0b25275ec47b85bcedcd80c067099ec7644","source":{"kind":"arxiv","id":"2501.08719","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.08719","created_at":"2026-07-05T10:01:25Z"},{"alias_kind":"arxiv_version","alias_value":"2501.08719v1","created_at":"2026-07-05T10:01:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.08719","created_at":"2026-07-05T10:01:25Z"},{"alias_kind":"pith_short_12","alias_value":"UQYPVFFDYK7H","created_at":"2026-07-05T10:01:25Z"},{"alias_kind":"pith_short_16","alias_value":"UQYPVFFDYK7HNE4S","created_at":"2026-07-05T10:01:25Z"},{"alias_kind":"pith_short_8","alias_value":"UQYPVFFD","created_at":"2026-07-05T10:01:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:UQYPVFFDYK7HNE4SSTEULOOAWJ","target":"record","payload":{"canonical_record":{"source":{"id":"2501.08719","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-01-15T10:59:22Z","cross_cats_sorted":[],"title_canon_sha256":"98a58f57eae1dfcbf702ec09e34c9ca4530e93c0327bacb055d0b1797cdbc0ad","abstract_canon_sha256":"bfa9a23dbd1dce956d720815f7abf54168f120421a4611e922e3a0b16051cf00"},"schema_version":"1.0"},"canonical_sha256":"a430fa94a3c2be76939294c945b9c0b25275ec47b85bcedcd80c067099ec7644","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:01:25.033209Z","signature_b64":"Nv6wjrwWLLCeX57GMuDBgA4OHYn68w77Itkbu2jx5I7Tgf3cUQFyJnECHq0QgWfy1aQ/2bPcuclPcJtFt3tMAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a430fa94a3c2be76939294c945b9c0b25275ec47b85bcedcd80c067099ec7644","last_reissued_at":"2026-07-05T10:01:25.032804Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:01:25.032804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.08719","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":"2026-07-05T10:01:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kYC9KHiRPTqclNitSYuAlGEkSqHpUo290T+sAjSe0RffM1TvbI9/I60O0SnvKRUIUm+Ik87uuQZjSL51Ba/nAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T01:53:34.236078Z"},"content_sha256":"6f7cb268831e0c4f3a7d75a62269b4ea68a97dbeb88ad44b0dd7a235e76c6b08","schema_version":"1.0","event_id":"sha256:6f7cb268831e0c4f3a7d75a62269b4ea68a97dbeb88ad44b0dd7a235e76c6b08"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:UQYPVFFDYK7HNE4SSTEULOOAWJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extrapolated Hard Thresholding Algorithms with Finite Length for Composite $\\ell_0$ Penalized Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Fan Wu, Jiazhen Wei, Wei Bian","submitted_at":"2025-01-15T10:59:22Z","abstract_excerpt":"For a class of sparse optimization problems with the penalty function of $\\|(\\cdot)_+\\|_0$, we first characterize its local minimizers and then propose an extrapolated hard thresholding algorithm to solve such problems. We show that the iterates generated by the proposed algorithm with $\\epsilon>0$ (where $\\epsilon$ is the dry friction coefficient) have finite length, without relying on the Kurdyka-{\\L}ojasiewicz inequality. Furthermore, we demonstrate that the algorithm converges to an $\\epsilon$-local minimizer of this problem. For the special case that $\\epsilon=0$, we establish that any ac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.08719","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/2501.08719/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":"2026-07-05T10:01:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ckv1CBE7XwOsThcJNDGp7+WDc8xqCauaXehMIzQ4PSmna2c9jYWCpNiuyqOp59Z52jWDN95vwdvj5bjavFcwCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T01:53:34.236573Z"},"content_sha256":"3f3846070d89f8ab3adba6b10850c9be01a72943d379c8f52e0bd69d33fd35ba","schema_version":"1.0","event_id":"sha256:3f3846070d89f8ab3adba6b10850c9be01a72943d379c8f52e0bd69d33fd35ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UQYPVFFDYK7HNE4SSTEULOOAWJ/bundle.json","state_url":"https://pith.science/pith/UQYPVFFDYK7HNE4SSTEULOOAWJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UQYPVFFDYK7HNE4SSTEULOOAWJ/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":"2026-08-06T01:53:34Z","links":{"resolver":"https://pith.science/pith/UQYPVFFDYK7HNE4SSTEULOOAWJ","bundle":"https://pith.science/pith/UQYPVFFDYK7HNE4SSTEULOOAWJ/bundle.json","state":"https://pith.science/pith/UQYPVFFDYK7HNE4SSTEULOOAWJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UQYPVFFDYK7HNE4SSTEULOOAWJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:UQYPVFFDYK7HNE4SSTEULOOAWJ","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":"bfa9a23dbd1dce956d720815f7abf54168f120421a4611e922e3a0b16051cf00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-01-15T10:59:22Z","title_canon_sha256":"98a58f57eae1dfcbf702ec09e34c9ca4530e93c0327bacb055d0b1797cdbc0ad"},"schema_version":"1.0","source":{"id":"2501.08719","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.08719","created_at":"2026-07-05T10:01:25Z"},{"alias_kind":"arxiv_version","alias_value":"2501.08719v1","created_at":"2026-07-05T10:01:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.08719","created_at":"2026-07-05T10:01:25Z"},{"alias_kind":"pith_short_12","alias_value":"UQYPVFFDYK7H","created_at":"2026-07-05T10:01:25Z"},{"alias_kind":"pith_short_16","alias_value":"UQYPVFFDYK7HNE4S","created_at":"2026-07-05T10:01:25Z"},{"alias_kind":"pith_short_8","alias_value":"UQYPVFFD","created_at":"2026-07-05T10:01:25Z"}],"graph_snapshots":[{"event_id":"sha256:3f3846070d89f8ab3adba6b10850c9be01a72943d379c8f52e0bd69d33fd35ba","target":"graph","created_at":"2026-07-05T10:01:25Z","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/2501.08719/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a class of sparse optimization problems with the penalty function of $\\|(\\cdot)_+\\|_0$, we first characterize its local minimizers and then propose an extrapolated hard thresholding algorithm to solve such problems. We show that the iterates generated by the proposed algorithm with $\\epsilon>0$ (where $\\epsilon$ is the dry friction coefficient) have finite length, without relying on the Kurdyka-{\\L}ojasiewicz inequality. Furthermore, we demonstrate that the algorithm converges to an $\\epsilon$-local minimizer of this problem. For the special case that $\\epsilon=0$, we establish that any ac","authors_text":"Fan Wu, Jiazhen Wei, Wei Bian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-01-15T10:59:22Z","title":"Extrapolated Hard Thresholding Algorithms with Finite Length for Composite $\\ell_0$ Penalized Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.08719","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":"sha256:6f7cb268831e0c4f3a7d75a62269b4ea68a97dbeb88ad44b0dd7a235e76c6b08","target":"record","created_at":"2026-07-05T10:01:25Z","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":"bfa9a23dbd1dce956d720815f7abf54168f120421a4611e922e3a0b16051cf00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-01-15T10:59:22Z","title_canon_sha256":"98a58f57eae1dfcbf702ec09e34c9ca4530e93c0327bacb055d0b1797cdbc0ad"},"schema_version":"1.0","source":{"id":"2501.08719","kind":"arxiv","version":1}},"canonical_sha256":"a430fa94a3c2be76939294c945b9c0b25275ec47b85bcedcd80c067099ec7644","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a430fa94a3c2be76939294c945b9c0b25275ec47b85bcedcd80c067099ec7644","first_computed_at":"2026-07-05T10:01:25.032804Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:01:25.032804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nv6wjrwWLLCeX57GMuDBgA4OHYn68w77Itkbu2jx5I7Tgf3cUQFyJnECHq0QgWfy1aQ/2bPcuclPcJtFt3tMAA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:01:25.033209Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.08719","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f7cb268831e0c4f3a7d75a62269b4ea68a97dbeb88ad44b0dd7a235e76c6b08","sha256:3f3846070d89f8ab3adba6b10850c9be01a72943d379c8f52e0bd69d33fd35ba"],"state_sha256":"7e32c87c4632722aeee0cdeb0f4adfde9645510ef9834ccb1c46b6684cf287a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PYbGATRbDCtxJsDjrP7wXdmog3T+++Vwb6fEu2JP0zcQdk29GRpxMIaHWzMCwmZHiry2d08wGadVBnjomHtiCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T01:53:34.240428Z","bundle_sha256":"e7f4b80ca15c197a4e955664ec047ce67a260b723ed31a6300d813bd87821ba1"}}