{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:3WFZKV7MK6A72RCZDKQFF6NREK","short_pith_number":"pith:3WFZKV7M","canonical_record":{"source":{"id":"0905.3036","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-05-19T07:29:41Z","cross_cats_sorted":[],"title_canon_sha256":"b422bb5706761981beb32032075553811a3df684cde57d08829670557683fe11","abstract_canon_sha256":"da39af1d764d41f1f2f3e0a22ff6a2cfa57e9688f29835e8e0414ddf11901869"},"schema_version":"1.0"},"canonical_sha256":"dd8b9557ec5781fd44591aa052f9b12292d4d72b98d6d09bab5b611d04d41a9a","source":{"kind":"arxiv","id":"0905.3036","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.3036","created_at":"2026-05-18T02:13:38Z"},{"alias_kind":"arxiv_version","alias_value":"0905.3036v1","created_at":"2026-05-18T02:13:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.3036","created_at":"2026-05-18T02:13:38Z"},{"alias_kind":"pith_short_12","alias_value":"3WFZKV7MK6A7","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"3WFZKV7MK6A72RCZ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"3WFZKV7M","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:3WFZKV7MK6A72RCZDKQFF6NREK","target":"record","payload":{"canonical_record":{"source":{"id":"0905.3036","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-05-19T07:29:41Z","cross_cats_sorted":[],"title_canon_sha256":"b422bb5706761981beb32032075553811a3df684cde57d08829670557683fe11","abstract_canon_sha256":"da39af1d764d41f1f2f3e0a22ff6a2cfa57e9688f29835e8e0414ddf11901869"},"schema_version":"1.0"},"canonical_sha256":"dd8b9557ec5781fd44591aa052f9b12292d4d72b98d6d09bab5b611d04d41a9a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:13:38.740743Z","signature_b64":"+mnqCIl4nfaPxLEjlDw/b/+bkHo5KID7c9OhMLB3vkEytfqdWu4+YBS1FMGK5bZubMVt9DSi3yD5tfIAT4mwAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd8b9557ec5781fd44591aa052f9b12292d4d72b98d6d09bab5b611d04d41a9a","last_reissued_at":"2026-05-18T02:13:38.740116Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:13:38.740116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0905.3036","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":"2026-05-18T02:13:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ej+treJNUNxRFkm1NCPpXhub/O9GaaCionNl4VlYzgwbn6H0oNVX0B4P0HqCHarhQgls1+uHUXERqK9rnsa4CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:10:16.583885Z"},"content_sha256":"9e54578e84d2879f17a7849245dbc78b7ab926971191db72fba6626de1e77dec","schema_version":"1.0","event_id":"sha256:9e54578e84d2879f17a7849245dbc78b7ab926971191db72fba6626de1e77dec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:3WFZKV7MK6A72RCZDKQFF6NREK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the convergence of greedy algorithms for initial segments of the Haar basis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. Zsak, E. Odell, S.J. Dilworth, Th. Schlumprecht","submitted_at":"2009-05-19T07:29:41Z","abstract_excerpt":"We consider the $X$-Greedy Algorithm and the Dual Greedy Algorithm in a finite-dimensional Banach space with a strictly monotone basis as the dictionary. We show that when the dictionary is an initial segment of the Haar basis in $L_p[0,1]$ ($1 < p < \\infty$) then the algorithms terminate after finitely many iterations and that the number of iterations is bounded by a function of the length of the initial segment. We also prove a more general result for a class of strictly monotone bases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.3036","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":""},"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":"2026-05-18T02:13:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NqL3FTwZx38RP6XRvxNExVndvWU+ztH9yMuHf7l4ZQ1uEE7mOs5OaeoNMl1MZM5fgYfAXUDttbVDwMJwtexFAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:10:16.584234Z"},"content_sha256":"0750abdb3d8ebf8bc441730b34dd55adcbd797eea786522e138302b6bca0fda4","schema_version":"1.0","event_id":"sha256:0750abdb3d8ebf8bc441730b34dd55adcbd797eea786522e138302b6bca0fda4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3WFZKV7MK6A72RCZDKQFF6NREK/bundle.json","state_url":"https://pith.science/pith/3WFZKV7MK6A72RCZDKQFF6NREK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3WFZKV7MK6A72RCZDKQFF6NREK/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":"2026-06-02T05:10:16Z","links":{"resolver":"https://pith.science/pith/3WFZKV7MK6A72RCZDKQFF6NREK","bundle":"https://pith.science/pith/3WFZKV7MK6A72RCZDKQFF6NREK/bundle.json","state":"https://pith.science/pith/3WFZKV7MK6A72RCZDKQFF6NREK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3WFZKV7MK6A72RCZDKQFF6NREK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:3WFZKV7MK6A72RCZDKQFF6NREK","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":"da39af1d764d41f1f2f3e0a22ff6a2cfa57e9688f29835e8e0414ddf11901869","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-05-19T07:29:41Z","title_canon_sha256":"b422bb5706761981beb32032075553811a3df684cde57d08829670557683fe11"},"schema_version":"1.0","source":{"id":"0905.3036","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.3036","created_at":"2026-05-18T02:13:38Z"},{"alias_kind":"arxiv_version","alias_value":"0905.3036v1","created_at":"2026-05-18T02:13:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.3036","created_at":"2026-05-18T02:13:38Z"},{"alias_kind":"pith_short_12","alias_value":"3WFZKV7MK6A7","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"3WFZKV7MK6A72RCZ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"3WFZKV7M","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:0750abdb3d8ebf8bc441730b34dd55adcbd797eea786522e138302b6bca0fda4","target":"graph","created_at":"2026-05-18T02:13:38Z","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 consider the $X$-Greedy Algorithm and the Dual Greedy Algorithm in a finite-dimensional Banach space with a strictly monotone basis as the dictionary. We show that when the dictionary is an initial segment of the Haar basis in $L_p[0,1]$ ($1 < p < \\infty$) then the algorithms terminate after finitely many iterations and that the number of iterations is bounded by a function of the length of the initial segment. We also prove a more general result for a class of strictly monotone bases.","authors_text":"A. Zsak, E. Odell, S.J. Dilworth, Th. Schlumprecht","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-05-19T07:29:41Z","title":"On the convergence of greedy algorithms for initial segments of the Haar basis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.3036","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":"sha256:9e54578e84d2879f17a7849245dbc78b7ab926971191db72fba6626de1e77dec","target":"record","created_at":"2026-05-18T02:13:38Z","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":"da39af1d764d41f1f2f3e0a22ff6a2cfa57e9688f29835e8e0414ddf11901869","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-05-19T07:29:41Z","title_canon_sha256":"b422bb5706761981beb32032075553811a3df684cde57d08829670557683fe11"},"schema_version":"1.0","source":{"id":"0905.3036","kind":"arxiv","version":1}},"canonical_sha256":"dd8b9557ec5781fd44591aa052f9b12292d4d72b98d6d09bab5b611d04d41a9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd8b9557ec5781fd44591aa052f9b12292d4d72b98d6d09bab5b611d04d41a9a","first_computed_at":"2026-05-18T02:13:38.740116Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:13:38.740116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+mnqCIl4nfaPxLEjlDw/b/+bkHo5KID7c9OhMLB3vkEytfqdWu4+YBS1FMGK5bZubMVt9DSi3yD5tfIAT4mwAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:13:38.740743Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.3036","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e54578e84d2879f17a7849245dbc78b7ab926971191db72fba6626de1e77dec","sha256:0750abdb3d8ebf8bc441730b34dd55adcbd797eea786522e138302b6bca0fda4"],"state_sha256":"0da34eeee8d1258896186e9065c6d7a47abe1f66cc90d659c90e16360dff6932"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nVJnJDuQa4a+qsA6liw1xU0QFCijzid9NsAShHLFHXiQ6aQymKPPSjEVD2OeuFYbYPHRGIfg+IkJuZu/DyCWDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T05:10:16.586180Z","bundle_sha256":"4fe16f6334630547febbc930c78f4c8c05ad8574f539c96e14ecee0a2ab026e8"}}