{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:KXX63WH6UGTQ6MOYCJJQ6TEAN2","short_pith_number":"pith:KXX63WH6","canonical_record":{"source":{"id":"1209.1378","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-06T19:33:12Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"5830dcce1752d540037c28a923ea0a982e06cfceff61cb033addda317ca97290","abstract_canon_sha256":"76aab6a37c87d3970264cd1f5e79daf44e44fc65d27f2cf321ccd76f169ac7df"},"schema_version":"1.0"},"canonical_sha256":"55efedd8fea1a70f31d812530f4c806e9dcba08f6dac6118fbf547255f1ad777","source":{"kind":"arxiv","id":"1209.1378","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1378","created_at":"2026-05-18T03:46:05Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1378v1","created_at":"2026-05-18T03:46:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1378","created_at":"2026-05-18T03:46:05Z"},{"alias_kind":"pith_short_12","alias_value":"KXX63WH6UGTQ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KXX63WH6UGTQ6MOY","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KXX63WH6","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:KXX63WH6UGTQ6MOYCJJQ6TEAN2","target":"record","payload":{"canonical_record":{"source":{"id":"1209.1378","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-06T19:33:12Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"5830dcce1752d540037c28a923ea0a982e06cfceff61cb033addda317ca97290","abstract_canon_sha256":"76aab6a37c87d3970264cd1f5e79daf44e44fc65d27f2cf321ccd76f169ac7df"},"schema_version":"1.0"},"canonical_sha256":"55efedd8fea1a70f31d812530f4c806e9dcba08f6dac6118fbf547255f1ad777","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:05.774111Z","signature_b64":"FQYF4QJWrIke/W3lcwGZAxtvLKiBDdfg84zMBjuw5oUcN6o6tpI0/RV4icdiMh3taHIjcHTnJGDYhvgQohqHBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55efedd8fea1a70f31d812530f4c806e9dcba08f6dac6118fbf547255f1ad777","last_reissued_at":"2026-05-18T03:46:05.773339Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:05.773339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.1378","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":"2026-05-18T03:46:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RE/BXq32xV39G1ZnCwii3cHsshk3ZwjWBLitkbFgSIZcA5GDMj1zq6lLwkJ0GB7G7rnn3XvYn2XLzS1V5d8+Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T02:25:21.448368Z"},"content_sha256":"15bd2c0633596b4f1b958014c33f32ed7940c42edc769a61f2c58e4642fd3ba2","schema_version":"1.0","event_id":"sha256:15bd2c0633596b4f1b958014c33f32ed7940c42edc769a61f2c58e4642fd3ba2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:KXX63WH6UGTQ6MOYCJJQ6TEAN2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Convergence of a Weak Greedy Algorithm for the Multivariate Haar Basis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Denka Kutzarova, S. Gogyan, S. J. Dilworth","submitted_at":"2012-09-06T19:33:12Z","abstract_excerpt":"We define a family of weak thresholding greedy algorithms for the multivariate Haar basis for $L_1[0,1]^d$ ($d \\ge 1$). We prove convergence and uniform boundedness of the weak greedy approximants for all $f \\in L_1[0,1]^d$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1378","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":"2026-05-18T03:46:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H29P3C7iP57ewUSjHSnoMw8PWMmEPfcGeQxshKayBH4mVA0qKKMhTlJmB3XAFQb9MC+ZQqquZx7nbec3+Zf9AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T02:25:21.448851Z"},"content_sha256":"50bdb4d5b4a71e1717bfbb0dd07bee8b67a1b107ad0affaba42932edf912a373","schema_version":"1.0","event_id":"sha256:50bdb4d5b4a71e1717bfbb0dd07bee8b67a1b107ad0affaba42932edf912a373"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KXX63WH6UGTQ6MOYCJJQ6TEAN2/bundle.json","state_url":"https://pith.science/pith/KXX63WH6UGTQ6MOYCJJQ6TEAN2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KXX63WH6UGTQ6MOYCJJQ6TEAN2/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":"2026-06-26T02:25:21Z","links":{"resolver":"https://pith.science/pith/KXX63WH6UGTQ6MOYCJJQ6TEAN2","bundle":"https://pith.science/pith/KXX63WH6UGTQ6MOYCJJQ6TEAN2/bundle.json","state":"https://pith.science/pith/KXX63WH6UGTQ6MOYCJJQ6TEAN2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KXX63WH6UGTQ6MOYCJJQ6TEAN2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KXX63WH6UGTQ6MOYCJJQ6TEAN2","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":"76aab6a37c87d3970264cd1f5e79daf44e44fc65d27f2cf321ccd76f169ac7df","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-06T19:33:12Z","title_canon_sha256":"5830dcce1752d540037c28a923ea0a982e06cfceff61cb033addda317ca97290"},"schema_version":"1.0","source":{"id":"1209.1378","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1378","created_at":"2026-05-18T03:46:05Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1378v1","created_at":"2026-05-18T03:46:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1378","created_at":"2026-05-18T03:46:05Z"},{"alias_kind":"pith_short_12","alias_value":"KXX63WH6UGTQ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KXX63WH6UGTQ6MOY","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KXX63WH6","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:50bdb4d5b4a71e1717bfbb0dd07bee8b67a1b107ad0affaba42932edf912a373","target":"graph","created_at":"2026-05-18T03:46:05Z","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 define a family of weak thresholding greedy algorithms for the multivariate Haar basis for $L_1[0,1]^d$ ($d \\ge 1$). We prove convergence and uniform boundedness of the weak greedy approximants for all $f \\in L_1[0,1]^d$.","authors_text":"Denka Kutzarova, S. Gogyan, S. J. Dilworth","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-06T19:33:12Z","title":"On the Convergence of a Weak Greedy Algorithm for the Multivariate Haar Basis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1378","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":"sha256:15bd2c0633596b4f1b958014c33f32ed7940c42edc769a61f2c58e4642fd3ba2","target":"record","created_at":"2026-05-18T03:46:05Z","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":"76aab6a37c87d3970264cd1f5e79daf44e44fc65d27f2cf321ccd76f169ac7df","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-06T19:33:12Z","title_canon_sha256":"5830dcce1752d540037c28a923ea0a982e06cfceff61cb033addda317ca97290"},"schema_version":"1.0","source":{"id":"1209.1378","kind":"arxiv","version":1}},"canonical_sha256":"55efedd8fea1a70f31d812530f4c806e9dcba08f6dac6118fbf547255f1ad777","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55efedd8fea1a70f31d812530f4c806e9dcba08f6dac6118fbf547255f1ad777","first_computed_at":"2026-05-18T03:46:05.773339Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:05.773339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FQYF4QJWrIke/W3lcwGZAxtvLKiBDdfg84zMBjuw5oUcN6o6tpI0/RV4icdiMh3taHIjcHTnJGDYhvgQohqHBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:05.774111Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.1378","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15bd2c0633596b4f1b958014c33f32ed7940c42edc769a61f2c58e4642fd3ba2","sha256:50bdb4d5b4a71e1717bfbb0dd07bee8b67a1b107ad0affaba42932edf912a373"],"state_sha256":"9e06835f42138a494698dad2bb5821c3bf5c488855a2ea36cf4914f834e3047b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IVx6oLh6Q0XFCbJpUUvMfeJ7Ceix6b4JRPtJjT/nBDztcSYjBoWSP1MPGxMICdKrtJgLcBAfNdOIxnO85KHpCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T02:25:21.451574Z","bundle_sha256":"8cd8680fd430231cbf1d4bb12e12cd8362be67b7802c7331ca3cab906b2ceef1"}}