{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:RXE62HOGQEUV7M22GYHNE5RWH6","short_pith_number":"pith:RXE62HOG","canonical_record":{"source":{"id":"1605.01251","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-04T12:44:52Z","cross_cats_sorted":[],"title_canon_sha256":"b6ca13c1e548a1cf307bf29bc2ac3dce0e09b20104a1421791040f0d36ff16dc","abstract_canon_sha256":"539c3f11ef3148590f9fac3ba8cf8480ce7b108ae7b597cf01218c11b41a9a51"},"schema_version":"1.0"},"canonical_sha256":"8dc9ed1dc681295fb35a360ed276363f968b7b4497f1b3c86cbf515345043ec7","source":{"kind":"arxiv","id":"1605.01251","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.01251","created_at":"2026-05-18T01:15:37Z"},{"alias_kind":"arxiv_version","alias_value":"1605.01251v1","created_at":"2026-05-18T01:15:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01251","created_at":"2026-05-18T01:15:37Z"},{"alias_kind":"pith_short_12","alias_value":"RXE62HOGQEUV","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RXE62HOGQEUV7M22","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RXE62HOG","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:RXE62HOGQEUV7M22GYHNE5RWH6","target":"record","payload":{"canonical_record":{"source":{"id":"1605.01251","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-04T12:44:52Z","cross_cats_sorted":[],"title_canon_sha256":"b6ca13c1e548a1cf307bf29bc2ac3dce0e09b20104a1421791040f0d36ff16dc","abstract_canon_sha256":"539c3f11ef3148590f9fac3ba8cf8480ce7b108ae7b597cf01218c11b41a9a51"},"schema_version":"1.0"},"canonical_sha256":"8dc9ed1dc681295fb35a360ed276363f968b7b4497f1b3c86cbf515345043ec7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:37.358934Z","signature_b64":"Ff3Fu7C4alGZaNZ+GWcsml5foQ6IKeiOwPVcmmTZ4qqENmvg+uDslH8poul5VTBU6Q6ICiw5wWUI76srOy/9Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8dc9ed1dc681295fb35a360ed276363f968b7b4497f1b3c86cbf515345043ec7","last_reissued_at":"2026-05-18T01:15:37.358165Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:37.358165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.01251","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":"2026-05-18T01:15:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ebK+maZPoFSZ8o5sOUneRwMQ+9Af0JrSB4NwCwSfOda1afeV45o0LdPWD4C0pRAgWHYW4vi44Mh2lH41BWzfAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T07:19:32.184435Z"},"content_sha256":"a739aeadf803902161a335279dc749ae80d4dc24469823a38d9307a53c415faa","schema_version":"1.0","event_id":"sha256:a739aeadf803902161a335279dc749ae80d4dc24469823a38d9307a53c415faa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:RXE62HOGQEUV7M22GYHNE5RWH6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Oscillation and variation for Riesz transform associated with Bessel operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dongyong Yang, Huoxiong Wu, Jing Zhang","submitted_at":"2016-05-04T12:44:52Z","abstract_excerpt":"Let $\\lambda>0$ and $\\triangle_\\lambda:=-\\frac{d^2}{dx^2}-\\frac{2\\lambda}{x} \\frac d{dx}$ be the Bessel operator on $\\mathbb R_+:=(0,\\infty)$. We show that the oscillation operator $\\mathcal{O}(R_{\\Delta_{\\lambda},\\ast})$ and variation operator $\\mathcal{V}_{\\rho}(R_{\\Delta_{\\lambda},\\ast})$ of the Riesz transform $R_{\\Delta_{\\lambda}}$ associated with\n  $\\Delta_\\lambda$ are both bounded on $L^p(\\mathbb R_+, dm_{\\lambda})$ for $p\\in(1,\\,\\infty)$, from $L^1(\\mathbb{R}_{+},dm_{\\lambda})$ to $L^{1,\\,\\infty}(\\mathbb{R}_{+},dm_{\\lambda})$, and from $L^{\\infty}(\\mathbb{R}_{+},dm_{\\lambda})$ to $BMO("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01251","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":"2026-05-18T01:15:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CvU2z1j0U276yVGrcJomSISg2pijQ6N7W26725C8ltqmhX66vp7EIrwKmVy6DjroUlaKYT7TCH0+kmz9Qzp5DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T07:19:32.184776Z"},"content_sha256":"7e873796e0df8846180a15537c15e99006d342b046e45e16baeedb98e3f50c51","schema_version":"1.0","event_id":"sha256:7e873796e0df8846180a15537c15e99006d342b046e45e16baeedb98e3f50c51"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RXE62HOGQEUV7M22GYHNE5RWH6/bundle.json","state_url":"https://pith.science/pith/RXE62HOGQEUV7M22GYHNE5RWH6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RXE62HOGQEUV7M22GYHNE5RWH6/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":"2026-06-25T07:19:32Z","links":{"resolver":"https://pith.science/pith/RXE62HOGQEUV7M22GYHNE5RWH6","bundle":"https://pith.science/pith/RXE62HOGQEUV7M22GYHNE5RWH6/bundle.json","state":"https://pith.science/pith/RXE62HOGQEUV7M22GYHNE5RWH6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RXE62HOGQEUV7M22GYHNE5RWH6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RXE62HOGQEUV7M22GYHNE5RWH6","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":"539c3f11ef3148590f9fac3ba8cf8480ce7b108ae7b597cf01218c11b41a9a51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-04T12:44:52Z","title_canon_sha256":"b6ca13c1e548a1cf307bf29bc2ac3dce0e09b20104a1421791040f0d36ff16dc"},"schema_version":"1.0","source":{"id":"1605.01251","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.01251","created_at":"2026-05-18T01:15:37Z"},{"alias_kind":"arxiv_version","alias_value":"1605.01251v1","created_at":"2026-05-18T01:15:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01251","created_at":"2026-05-18T01:15:37Z"},{"alias_kind":"pith_short_12","alias_value":"RXE62HOGQEUV","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RXE62HOGQEUV7M22","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RXE62HOG","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:7e873796e0df8846180a15537c15e99006d342b046e45e16baeedb98e3f50c51","target":"graph","created_at":"2026-05-18T01:15:37Z","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":"Let $\\lambda>0$ and $\\triangle_\\lambda:=-\\frac{d^2}{dx^2}-\\frac{2\\lambda}{x} \\frac d{dx}$ be the Bessel operator on $\\mathbb R_+:=(0,\\infty)$. We show that the oscillation operator $\\mathcal{O}(R_{\\Delta_{\\lambda},\\ast})$ and variation operator $\\mathcal{V}_{\\rho}(R_{\\Delta_{\\lambda},\\ast})$ of the Riesz transform $R_{\\Delta_{\\lambda}}$ associated with\n  $\\Delta_\\lambda$ are both bounded on $L^p(\\mathbb R_+, dm_{\\lambda})$ for $p\\in(1,\\,\\infty)$, from $L^1(\\mathbb{R}_{+},dm_{\\lambda})$ to $L^{1,\\,\\infty}(\\mathbb{R}_{+},dm_{\\lambda})$, and from $L^{\\infty}(\\mathbb{R}_{+},dm_{\\lambda})$ to $BMO(","authors_text":"Dongyong Yang, Huoxiong Wu, Jing Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-04T12:44:52Z","title":"Oscillation and variation for Riesz transform associated with Bessel operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01251","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:a739aeadf803902161a335279dc749ae80d4dc24469823a38d9307a53c415faa","target":"record","created_at":"2026-05-18T01:15:37Z","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":"539c3f11ef3148590f9fac3ba8cf8480ce7b108ae7b597cf01218c11b41a9a51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-04T12:44:52Z","title_canon_sha256":"b6ca13c1e548a1cf307bf29bc2ac3dce0e09b20104a1421791040f0d36ff16dc"},"schema_version":"1.0","source":{"id":"1605.01251","kind":"arxiv","version":1}},"canonical_sha256":"8dc9ed1dc681295fb35a360ed276363f968b7b4497f1b3c86cbf515345043ec7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8dc9ed1dc681295fb35a360ed276363f968b7b4497f1b3c86cbf515345043ec7","first_computed_at":"2026-05-18T01:15:37.358165Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:37.358165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ff3Fu7C4alGZaNZ+GWcsml5foQ6IKeiOwPVcmmTZ4qqENmvg+uDslH8poul5VTBU6Q6ICiw5wWUI76srOy/9Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:37.358934Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.01251","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a739aeadf803902161a335279dc749ae80d4dc24469823a38d9307a53c415faa","sha256:7e873796e0df8846180a15537c15e99006d342b046e45e16baeedb98e3f50c51"],"state_sha256":"08d393d3067bdfa2af89f12397900d5b42b378daf064672aef925bc6e7b69f40"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S4iLGmpwq7Ed/i6PylAFUNtMe/XJVs+dpcOgSJY2NjtQNzXcC+O/zsnu/AHfM49o0NCRxCJFR0qTbj9y+Dj/AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T07:19:32.186616Z","bundle_sha256":"588cc06d95e2c348bb7fffb97ffa3228614c106dcb3db278ec342fc544c6b553"}}