{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:PLJ243SOPPHXLT4F2G6DP2ABUW","short_pith_number":"pith:PLJ243SO","canonical_record":{"source":{"id":"1610.04145","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-10-13T15:57:03Z","cross_cats_sorted":[],"title_canon_sha256":"2274a2c55cd612670e059583654984f636cc6e1fcd90a4fd8a56cb1c5eb6d4a1","abstract_canon_sha256":"6d25dc0a9dcb5aa29caa92fbfe4787b3874fa0251707f010bd5333a874828ef4"},"schema_version":"1.0"},"canonical_sha256":"7ad3ae6e4e7bcf75cf85d1bc37e801a5a9a07e25447a5725d6f4cf491d9de2e5","source":{"kind":"arxiv","id":"1610.04145","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.04145","created_at":"2026-05-18T00:49:51Z"},{"alias_kind":"arxiv_version","alias_value":"1610.04145v2","created_at":"2026-05-18T00:49:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04145","created_at":"2026-05-18T00:49:51Z"},{"alias_kind":"pith_short_12","alias_value":"PLJ243SOPPHX","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PLJ243SOPPHXLT4F","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PLJ243SO","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:PLJ243SOPPHXLT4F2G6DP2ABUW","target":"record","payload":{"canonical_record":{"source":{"id":"1610.04145","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-10-13T15:57:03Z","cross_cats_sorted":[],"title_canon_sha256":"2274a2c55cd612670e059583654984f636cc6e1fcd90a4fd8a56cb1c5eb6d4a1","abstract_canon_sha256":"6d25dc0a9dcb5aa29caa92fbfe4787b3874fa0251707f010bd5333a874828ef4"},"schema_version":"1.0"},"canonical_sha256":"7ad3ae6e4e7bcf75cf85d1bc37e801a5a9a07e25447a5725d6f4cf491d9de2e5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:51.498946Z","signature_b64":"W+zBcbhHajVf9tLwYHwuBZgX+qE9Hdq5lP+Rs0TehlnLfns3SLTJH8BtwC5LCRwyU+xJFhN162FASXNeMlIgBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ad3ae6e4e7bcf75cf85d1bc37e801a5a9a07e25447a5725d6f4cf491d9de2e5","last_reissued_at":"2026-05-18T00:49:51.498609Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:51.498609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.04145","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":"2026-05-18T00:49:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"33W0cdpzZQQ89WDOCaT/x5+rVPxxtrFxoDqtF+xM/WChI8T1jbl3nT+fYLaCqlNB/p1EWBF+JewThiIgxMJOBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T01:00:52.269074Z"},"content_sha256":"bbc5c399cbdf24bc64f9f6632bd85cfad9965f338909dd2a23f7de26f9ad2cb0","schema_version":"1.0","event_id":"sha256:bbc5c399cbdf24bc64f9f6632bd85cfad9965f338909dd2a23f7de26f9ad2cb0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:PLJ243SOPPHXLT4F2G6DP2ABUW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On uniform boundedness of dyadic averaging operators in spaces of Hardy-Sobolev type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Andreas Seeger, Gustavo Garrig\\'os, Tino Ullrich","submitted_at":"2016-10-13T15:57:03Z","abstract_excerpt":"We give an alternative proof of recent results by the authors on uniform boundedness of dyadic averaging operators in (quasi-)Banach spaces of Hardy-Sobolev and Triebel-Lizorkin type. This result served as the main tool to establish Schauder basis properties of suitable enumerations of the univariate Haar system in the mentioned spaces. The rather elementary proof here is based on characterizations of the respective spaces in terms of orthogonal compactly supported Daubechies wavelets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04145","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":"2026-05-18T00:49:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jTcplbznbaXaUAX/TAk9T2zPqm1BrriP6xSrDYt1mdldcLj4HsayCE2KCvJKEMjOO67RZ7P8qMBfBCQegFwvBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T01:00:52.269441Z"},"content_sha256":"05633a049641d6118331ab6a48691ceae188134e324f3301a051d0cc64b51a4a","schema_version":"1.0","event_id":"sha256:05633a049641d6118331ab6a48691ceae188134e324f3301a051d0cc64b51a4a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PLJ243SOPPHXLT4F2G6DP2ABUW/bundle.json","state_url":"https://pith.science/pith/PLJ243SOPPHXLT4F2G6DP2ABUW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PLJ243SOPPHXLT4F2G6DP2ABUW/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":"2026-05-20T01:00:52Z","links":{"resolver":"https://pith.science/pith/PLJ243SOPPHXLT4F2G6DP2ABUW","bundle":"https://pith.science/pith/PLJ243SOPPHXLT4F2G6DP2ABUW/bundle.json","state":"https://pith.science/pith/PLJ243SOPPHXLT4F2G6DP2ABUW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PLJ243SOPPHXLT4F2G6DP2ABUW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PLJ243SOPPHXLT4F2G6DP2ABUW","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":"6d25dc0a9dcb5aa29caa92fbfe4787b3874fa0251707f010bd5333a874828ef4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-10-13T15:57:03Z","title_canon_sha256":"2274a2c55cd612670e059583654984f636cc6e1fcd90a4fd8a56cb1c5eb6d4a1"},"schema_version":"1.0","source":{"id":"1610.04145","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.04145","created_at":"2026-05-18T00:49:51Z"},{"alias_kind":"arxiv_version","alias_value":"1610.04145v2","created_at":"2026-05-18T00:49:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04145","created_at":"2026-05-18T00:49:51Z"},{"alias_kind":"pith_short_12","alias_value":"PLJ243SOPPHX","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PLJ243SOPPHXLT4F","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PLJ243SO","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:05633a049641d6118331ab6a48691ceae188134e324f3301a051d0cc64b51a4a","target":"graph","created_at":"2026-05-18T00:49:51Z","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 give an alternative proof of recent results by the authors on uniform boundedness of dyadic averaging operators in (quasi-)Banach spaces of Hardy-Sobolev and Triebel-Lizorkin type. This result served as the main tool to establish Schauder basis properties of suitable enumerations of the univariate Haar system in the mentioned spaces. The rather elementary proof here is based on characterizations of the respective spaces in terms of orthogonal compactly supported Daubechies wavelets.","authors_text":"Andreas Seeger, Gustavo Garrig\\'os, Tino Ullrich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-10-13T15:57:03Z","title":"On uniform boundedness of dyadic averaging operators in spaces of Hardy-Sobolev type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04145","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:bbc5c399cbdf24bc64f9f6632bd85cfad9965f338909dd2a23f7de26f9ad2cb0","target":"record","created_at":"2026-05-18T00:49:51Z","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":"6d25dc0a9dcb5aa29caa92fbfe4787b3874fa0251707f010bd5333a874828ef4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-10-13T15:57:03Z","title_canon_sha256":"2274a2c55cd612670e059583654984f636cc6e1fcd90a4fd8a56cb1c5eb6d4a1"},"schema_version":"1.0","source":{"id":"1610.04145","kind":"arxiv","version":2}},"canonical_sha256":"7ad3ae6e4e7bcf75cf85d1bc37e801a5a9a07e25447a5725d6f4cf491d9de2e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ad3ae6e4e7bcf75cf85d1bc37e801a5a9a07e25447a5725d6f4cf491d9de2e5","first_computed_at":"2026-05-18T00:49:51.498609Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:51.498609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W+zBcbhHajVf9tLwYHwuBZgX+qE9Hdq5lP+Rs0TehlnLfns3SLTJH8BtwC5LCRwyU+xJFhN162FASXNeMlIgBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:51.498946Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.04145","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bbc5c399cbdf24bc64f9f6632bd85cfad9965f338909dd2a23f7de26f9ad2cb0","sha256:05633a049641d6118331ab6a48691ceae188134e324f3301a051d0cc64b51a4a"],"state_sha256":"97605403180ce1444d711957fd82ed30a6988fa97eb5a5eec2bc8d0a80856452"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Z7uA2z6ucC9t8FnbK+3iSnPPIqMfDrYjnk4sq00W8eGG9xfVKABU2d3RZuHNkVLqVj4k6bdBf9mg07t1l0pDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T01:00:52.271719Z","bundle_sha256":"133ef65862966198aa86c437b7b2a43d2bb72df473050a9c550e70221a050f22"}}