{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:WS7KCPUDALZ2Q2EXC7EJ4HOO33","short_pith_number":"pith:WS7KCPUD","canonical_record":{"source":{"id":"2302.12298","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2023-02-18T13:20:28Z","cross_cats_sorted":[],"title_canon_sha256":"29205a4b1e4c0335dd2559d0e2d6dfc4f6b6a98063bc2c2c7844d299d0a329f1","abstract_canon_sha256":"92af5062a3f21d9b457f41d02f3149208673c0a778b4ea48de5dd2979b89a027"},"schema_version":"1.0"},"canonical_sha256":"b4bea13e8302f3a8689717c89e1dceded78a126655b9dbb45f99418aadd06db7","source":{"kind":"arxiv","id":"2302.12298","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.12298","created_at":"2026-07-05T05:45:07Z"},{"alias_kind":"arxiv_version","alias_value":"2302.12298v1","created_at":"2026-07-05T05:45:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.12298","created_at":"2026-07-05T05:45:07Z"},{"alias_kind":"pith_short_12","alias_value":"WS7KCPUDALZ2","created_at":"2026-07-05T05:45:07Z"},{"alias_kind":"pith_short_16","alias_value":"WS7KCPUDALZ2Q2EX","created_at":"2026-07-05T05:45:07Z"},{"alias_kind":"pith_short_8","alias_value":"WS7KCPUD","created_at":"2026-07-05T05:45:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:WS7KCPUDALZ2Q2EXC7EJ4HOO33","target":"record","payload":{"canonical_record":{"source":{"id":"2302.12298","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2023-02-18T13:20:28Z","cross_cats_sorted":[],"title_canon_sha256":"29205a4b1e4c0335dd2559d0e2d6dfc4f6b6a98063bc2c2c7844d299d0a329f1","abstract_canon_sha256":"92af5062a3f21d9b457f41d02f3149208673c0a778b4ea48de5dd2979b89a027"},"schema_version":"1.0"},"canonical_sha256":"b4bea13e8302f3a8689717c89e1dceded78a126655b9dbb45f99418aadd06db7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:45:07.967288Z","signature_b64":"YIXcxV2pDflgjUyp1eVu9leOjPkEwUOtRV+gtVR+U5vVg5RJHfsXJi4TDc/+1R3Nyo+KCVjM1Oov+2kDwfgLAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4bea13e8302f3a8689717c89e1dceded78a126655b9dbb45f99418aadd06db7","last_reissued_at":"2026-07-05T05:45:07.966796Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:45:07.966796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2302.12298","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":"2026-07-05T05:45:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vp1vGP1SsTMC7nm9hCEasCFPybDNPqV9OnDLStxzuIcbnSbsrEZA10EirMQHPMxgy1mTDrSInXFwVPBBt/MdDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-11T15:06:55.491682Z"},"content_sha256":"bca240106a2f10e4fdbe5066095f9103e97e8a8e9fb124471b2347e83fb34f41","schema_version":"1.0","event_id":"sha256:bca240106a2f10e4fdbe5066095f9103e97e8a8e9fb124471b2347e83fb34f41"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:WS7KCPUDALZ2Q2EXC7EJ4HOO33","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharpness of some Hardy-type inequalities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"George Tephnadze, Lars-Erik Persson, Natasha Samko","submitted_at":"2023-02-18T13:20:28Z","abstract_excerpt":"The current status concerning Hardy-type inequalities with sharp constants is presented and described in a unified convexity way. In particular, it is then natural to replace the Lebesgue measure $dx$ with the Haar measure $dx/x.$ There are also derived some new two-sided Hardy-type inequalities for monotone functions, where not only the two constants are sharp but also where the involved function spaces are (more) optimal. As applications, a number of both well-known and new Hardy-type inequalities are pointed out. And, in turn, these results are used to derive some new sharp information conc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.12298","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.12298/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:45:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UR3UHjTWG2NJrGZjWhOyGI5lc0hwgJ1urvlYsFhWejqCvF83KUEWrwnVZVu4SWyldi2bpBbM2avZ4z/zK8oDCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-11T15:06:55.492063Z"},"content_sha256":"57452cb30b8b4083ccf2e25a8347a560fa1ec1d72c0ed1a9831afffb0ce24beb","schema_version":"1.0","event_id":"sha256:57452cb30b8b4083ccf2e25a8347a560fa1ec1d72c0ed1a9831afffb0ce24beb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WS7KCPUDALZ2Q2EXC7EJ4HOO33/bundle.json","state_url":"https://pith.science/pith/WS7KCPUDALZ2Q2EXC7EJ4HOO33/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WS7KCPUDALZ2Q2EXC7EJ4HOO33/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":"2026-07-11T15:06:55Z","links":{"resolver":"https://pith.science/pith/WS7KCPUDALZ2Q2EXC7EJ4HOO33","bundle":"https://pith.science/pith/WS7KCPUDALZ2Q2EXC7EJ4HOO33/bundle.json","state":"https://pith.science/pith/WS7KCPUDALZ2Q2EXC7EJ4HOO33/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WS7KCPUDALZ2Q2EXC7EJ4HOO33/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:WS7KCPUDALZ2Q2EXC7EJ4HOO33","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":"92af5062a3f21d9b457f41d02f3149208673c0a778b4ea48de5dd2979b89a027","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2023-02-18T13:20:28Z","title_canon_sha256":"29205a4b1e4c0335dd2559d0e2d6dfc4f6b6a98063bc2c2c7844d299d0a329f1"},"schema_version":"1.0","source":{"id":"2302.12298","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.12298","created_at":"2026-07-05T05:45:07Z"},{"alias_kind":"arxiv_version","alias_value":"2302.12298v1","created_at":"2026-07-05T05:45:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.12298","created_at":"2026-07-05T05:45:07Z"},{"alias_kind":"pith_short_12","alias_value":"WS7KCPUDALZ2","created_at":"2026-07-05T05:45:07Z"},{"alias_kind":"pith_short_16","alias_value":"WS7KCPUDALZ2Q2EX","created_at":"2026-07-05T05:45:07Z"},{"alias_kind":"pith_short_8","alias_value":"WS7KCPUD","created_at":"2026-07-05T05:45:07Z"}],"graph_snapshots":[{"event_id":"sha256:57452cb30b8b4083ccf2e25a8347a560fa1ec1d72c0ed1a9831afffb0ce24beb","target":"graph","created_at":"2026-07-05T05:45:07Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2302.12298/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The current status concerning Hardy-type inequalities with sharp constants is presented and described in a unified convexity way. In particular, it is then natural to replace the Lebesgue measure $dx$ with the Haar measure $dx/x.$ There are also derived some new two-sided Hardy-type inequalities for monotone functions, where not only the two constants are sharp but also where the involved function spaces are (more) optimal. As applications, a number of both well-known and new Hardy-type inequalities are pointed out. And, in turn, these results are used to derive some new sharp information conc","authors_text":"George Tephnadze, Lars-Erik Persson, Natasha Samko","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2023-02-18T13:20:28Z","title":"Sharpness of some Hardy-type inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.12298","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:bca240106a2f10e4fdbe5066095f9103e97e8a8e9fb124471b2347e83fb34f41","target":"record","created_at":"2026-07-05T05:45:07Z","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":"92af5062a3f21d9b457f41d02f3149208673c0a778b4ea48de5dd2979b89a027","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2023-02-18T13:20:28Z","title_canon_sha256":"29205a4b1e4c0335dd2559d0e2d6dfc4f6b6a98063bc2c2c7844d299d0a329f1"},"schema_version":"1.0","source":{"id":"2302.12298","kind":"arxiv","version":1}},"canonical_sha256":"b4bea13e8302f3a8689717c89e1dceded78a126655b9dbb45f99418aadd06db7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4bea13e8302f3a8689717c89e1dceded78a126655b9dbb45f99418aadd06db7","first_computed_at":"2026-07-05T05:45:07.966796Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:45:07.966796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YIXcxV2pDflgjUyp1eVu9leOjPkEwUOtRV+gtVR+U5vVg5RJHfsXJi4TDc/+1R3Nyo+KCVjM1Oov+2kDwfgLAw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:45:07.967288Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.12298","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bca240106a2f10e4fdbe5066095f9103e97e8a8e9fb124471b2347e83fb34f41","sha256:57452cb30b8b4083ccf2e25a8347a560fa1ec1d72c0ed1a9831afffb0ce24beb"],"state_sha256":"773891637551d8958d1d963437e239a82d8ea8f44c80a648cf7ea9a033ce3da0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vmFKiBqxweOtxdG7f4S6/S/9AFmdSgVlHYUqd2lrQrAO5GquugbH9QbsjkI8VxAgvq7F73tkzBE+BqmwftPpBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-11T15:06:55.494250Z","bundle_sha256":"316daa577835383dd156c701ca6d4b7f969ae464c5a16a41360f5268a27110cc"}}