{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:JOQ7PHESBIPKHZDSR6FHZQYXKD","short_pith_number":"pith:JOQ7PHES","canonical_record":{"source":{"id":"0801.1774","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2008-01-11T13:01:22Z","cross_cats_sorted":[],"title_canon_sha256":"98795c2c847bf9254b6dc303372a88e4e0fb1062fded3268f377e34489c496b9","abstract_canon_sha256":"fd80fb44f7a5f4538e545da6d5df62542d58d9f45dbe9043a8e198e78b89f914"},"schema_version":"1.0"},"canonical_sha256":"4ba1f79c920a1ea3e4728f8a7cc31750fbed950a1d2e95cd3914d30b21a3ba3f","source":{"kind":"arxiv","id":"0801.1774","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.1774","created_at":"2026-05-18T04:26:54Z"},{"alias_kind":"arxiv_version","alias_value":"0801.1774v2","created_at":"2026-05-18T04:26:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.1774","created_at":"2026-05-18T04:26:54Z"},{"alias_kind":"pith_short_12","alias_value":"JOQ7PHESBIPK","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"JOQ7PHESBIPKHZDS","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"JOQ7PHES","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:JOQ7PHESBIPKHZDSR6FHZQYXKD","target":"record","payload":{"canonical_record":{"source":{"id":"0801.1774","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2008-01-11T13:01:22Z","cross_cats_sorted":[],"title_canon_sha256":"98795c2c847bf9254b6dc303372a88e4e0fb1062fded3268f377e34489c496b9","abstract_canon_sha256":"fd80fb44f7a5f4538e545da6d5df62542d58d9f45dbe9043a8e198e78b89f914"},"schema_version":"1.0"},"canonical_sha256":"4ba1f79c920a1ea3e4728f8a7cc31750fbed950a1d2e95cd3914d30b21a3ba3f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:54.205981Z","signature_b64":"1q9OMP88cJjMAMAOcDIE31HpsQ7jNPQIElsYeLJIKV/miV9D5kzpKcbyE4UCT3UT2GoJuhAOysChrwQ1EDd4DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ba1f79c920a1ea3e4728f8a7cc31750fbed950a1d2e95cd3914d30b21a3ba3f","last_reissued_at":"2026-05-18T04:26:54.205448Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:54.205448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0801.1774","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":"2026-05-18T04:26:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XwZJGJEegc4SV37TjKjDQNVBrj4EwvOJNYZEsIjq6039lNs1NtZLGbKKQ3pCzAwWp90qwq5/meIPL1TTmbl/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T03:16:17.022610Z"},"content_sha256":"d258d5b76b10b3d3a801a62110b55bd08a89774b92d92a1c51996c46195089e8","schema_version":"1.0","event_id":"sha256:d258d5b76b10b3d3a801a62110b55bd08a89774b92d92a1c51996c46195089e8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:JOQ7PHESBIPKHZDSR6FHZQYXKD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence rates and source conditions for Tikhonov regularization with sparsity constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Dirk A. Lorenz","submitted_at":"2008-01-11T13:01:22Z","abstract_excerpt":"This paper addresses the regularization by sparsity constraints by means of weighted $\\ell^p$ penalties for $0\\leq p\\leq 2$. For $1\\leq p\\leq 2$ special attention is payed to convergence rates in norm and to source conditions. As main result it is proven that one gets a convergence rate in norm of $\\sqrt{\\delta}$ for $1\\leq p\\leq 2$ as soon as the unknown solution is sparse. The case $p=1$ needs a special technique where not only Bregman distances but also a so-called Bregman-Taylor distance has to be employed.\n  For $p<1$ only preliminary results are shown. These results indicate that, differ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.1774","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":"2026-05-18T04:26:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sQZMAmvBNYnz0qeQCZrS9V2v2h+8AgsCCG/yixUP7db8ALrHZbm2fJ3FCRlSJLZJ0OwjePqsvEPjKygbRKYcDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T03:16:17.023244Z"},"content_sha256":"0a70836ccd2c6a0804ca577dbdf7d2d342c6b7a3fbac9757e0c9191763cac9af","schema_version":"1.0","event_id":"sha256:0a70836ccd2c6a0804ca577dbdf7d2d342c6b7a3fbac9757e0c9191763cac9af"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JOQ7PHESBIPKHZDSR6FHZQYXKD/bundle.json","state_url":"https://pith.science/pith/JOQ7PHESBIPKHZDSR6FHZQYXKD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JOQ7PHESBIPKHZDSR6FHZQYXKD/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":"2026-06-08T03:16:17Z","links":{"resolver":"https://pith.science/pith/JOQ7PHESBIPKHZDSR6FHZQYXKD","bundle":"https://pith.science/pith/JOQ7PHESBIPKHZDSR6FHZQYXKD/bundle.json","state":"https://pith.science/pith/JOQ7PHESBIPKHZDSR6FHZQYXKD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JOQ7PHESBIPKHZDSR6FHZQYXKD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:JOQ7PHESBIPKHZDSR6FHZQYXKD","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":"fd80fb44f7a5f4538e545da6d5df62542d58d9f45dbe9043a8e198e78b89f914","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2008-01-11T13:01:22Z","title_canon_sha256":"98795c2c847bf9254b6dc303372a88e4e0fb1062fded3268f377e34489c496b9"},"schema_version":"1.0","source":{"id":"0801.1774","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.1774","created_at":"2026-05-18T04:26:54Z"},{"alias_kind":"arxiv_version","alias_value":"0801.1774v2","created_at":"2026-05-18T04:26:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.1774","created_at":"2026-05-18T04:26:54Z"},{"alias_kind":"pith_short_12","alias_value":"JOQ7PHESBIPK","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"JOQ7PHESBIPKHZDS","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"JOQ7PHES","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:0a70836ccd2c6a0804ca577dbdf7d2d342c6b7a3fbac9757e0c9191763cac9af","target":"graph","created_at":"2026-05-18T04:26:54Z","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":"This paper addresses the regularization by sparsity constraints by means of weighted $\\ell^p$ penalties for $0\\leq p\\leq 2$. For $1\\leq p\\leq 2$ special attention is payed to convergence rates in norm and to source conditions. As main result it is proven that one gets a convergence rate in norm of $\\sqrt{\\delta}$ for $1\\leq p\\leq 2$ as soon as the unknown solution is sparse. The case $p=1$ needs a special technique where not only Bregman distances but also a so-called Bregman-Taylor distance has to be employed.\n  For $p<1$ only preliminary results are shown. These results indicate that, differ","authors_text":"Dirk A. Lorenz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2008-01-11T13:01:22Z","title":"Convergence rates and source conditions for Tikhonov regularization with sparsity constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.1774","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:d258d5b76b10b3d3a801a62110b55bd08a89774b92d92a1c51996c46195089e8","target":"record","created_at":"2026-05-18T04:26:54Z","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":"fd80fb44f7a5f4538e545da6d5df62542d58d9f45dbe9043a8e198e78b89f914","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2008-01-11T13:01:22Z","title_canon_sha256":"98795c2c847bf9254b6dc303372a88e4e0fb1062fded3268f377e34489c496b9"},"schema_version":"1.0","source":{"id":"0801.1774","kind":"arxiv","version":2}},"canonical_sha256":"4ba1f79c920a1ea3e4728f8a7cc31750fbed950a1d2e95cd3914d30b21a3ba3f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ba1f79c920a1ea3e4728f8a7cc31750fbed950a1d2e95cd3914d30b21a3ba3f","first_computed_at":"2026-05-18T04:26:54.205448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:54.205448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1q9OMP88cJjMAMAOcDIE31HpsQ7jNPQIElsYeLJIKV/miV9D5kzpKcbyE4UCT3UT2GoJuhAOysChrwQ1EDd4DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:54.205981Z","signed_message":"canonical_sha256_bytes"},"source_id":"0801.1774","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d258d5b76b10b3d3a801a62110b55bd08a89774b92d92a1c51996c46195089e8","sha256:0a70836ccd2c6a0804ca577dbdf7d2d342c6b7a3fbac9757e0c9191763cac9af"],"state_sha256":"c1cbb6c3b76ecb30d2c2ee242465867fdd8ccc9049f860c94d1d0b5ab3e879eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5g6TfS56FOon2Q6DMAD3KdQ/tBqXotFlSuW4COrCG+IiUX+bskwcYi9ZEu+nOHHByIIDj29QI6XJLj15yuNmAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T03:16:17.026936Z","bundle_sha256":"260e385c19e255f2c1bb468bce23eb03348af5a8b8717e6cc27551e3f495d2aa"}}