{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NHGSDIKUEVFEXIPRF3G3UCIPZ3","short_pith_number":"pith:NHGSDIKU","canonical_record":{"source":{"id":"1806.04909","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-06-13T09:17:48Z","cross_cats_sorted":[],"title_canon_sha256":"7d525c90e33dc619a9673773e373a8d69ffd66916fb3a4fdf917fcf8d7108e71","abstract_canon_sha256":"97ff8b7c30d404425c93ef78686030b21b95328b2a8fec276839daf92331dce0"},"schema_version":"1.0"},"canonical_sha256":"69cd21a154254a4ba1f12ecdba090fcec176f28a023f26edfa78e007a4efd29b","source":{"kind":"arxiv","id":"1806.04909","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.04909","created_at":"2026-05-17T23:47:07Z"},{"alias_kind":"arxiv_version","alias_value":"1806.04909v2","created_at":"2026-05-17T23:47:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.04909","created_at":"2026-05-17T23:47:07Z"},{"alias_kind":"pith_short_12","alias_value":"NHGSDIKUEVFE","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NHGSDIKUEVFEXIPR","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NHGSDIKU","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NHGSDIKUEVFEXIPRF3G3UCIPZ3","target":"record","payload":{"canonical_record":{"source":{"id":"1806.04909","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-06-13T09:17:48Z","cross_cats_sorted":[],"title_canon_sha256":"7d525c90e33dc619a9673773e373a8d69ffd66916fb3a4fdf917fcf8d7108e71","abstract_canon_sha256":"97ff8b7c30d404425c93ef78686030b21b95328b2a8fec276839daf92331dce0"},"schema_version":"1.0"},"canonical_sha256":"69cd21a154254a4ba1f12ecdba090fcec176f28a023f26edfa78e007a4efd29b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:07.401461Z","signature_b64":"/4Ubq4yS84n6Z9PgYgGVygcHNfR20MMlfMMJww3PE6JMIptBO7my3EwVzHJFtupbi0eN2Ou+LiumBz5Oi/TtAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69cd21a154254a4ba1f12ecdba090fcec176f28a023f26edfa78e007a4efd29b","last_reissued_at":"2026-05-17T23:47:07.400839Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:07.400839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.04909","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":"2026-05-17T23:47:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jnr9CG7jDxZNp6mjGM9XVBYnWMpG+ca3o7nzH76eUFzBRLoiUrPZyeBjUTXIWYH3IdhsknmaATKuDXQN5ZUGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:46:23.591850Z"},"content_sha256":"f3560ea3dee3f3d4b5d138f1706b506a568c91f0b2667c013ef65512aa796624","schema_version":"1.0","event_id":"sha256:f3560ea3dee3f3d4b5d138f1706b506a568c91f0b2667c013ef65512aa796624"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NHGSDIKUEVFEXIPRF3G3UCIPZ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weighted inequalities for iterated Copson integral operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Lubo\\v{s} Pick, Martin K\\v{r}epela","submitted_at":"2018-06-13T09:17:48Z","abstract_excerpt":"We solve a long-standing open problem in theory of weighted inequalities concerning iterated Copson operators. We use a constructive approximation method based on a new discretization principle that is developed here. In result, we characterize all weight functions $w,v,u$ on $(0,\\infty)$ for which there exists a constant $C$ such that the inequality $$ \\left(\\int_0^{\\infty}\\left(\\int_t^\\infty \\left(\\int_s^{\\infty}h(y)\\,\\text{d}y\\right)^mu(s) \\,\\text{d}s\\right)^{\\frac{q}{m}}w(t)\\,\\text{d}t\\right)^{\\frac{1}{q}} \\le C \\left(\\int_0^{\\infty}h(t)^pv(t)\\,\\text{d}t\\right)^{\\frac{1}{p}} $$ holds for e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.04909","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":"2026-05-17T23:47:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jOZcSHDPvsTpNuijZ/AE1oDgpQ22oF9WI/Vtuu00w/tEg5WnIeaY78VKe9flLEwv4xmVIxgdG+D1JDWFnHMoCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:46:23.592192Z"},"content_sha256":"03b8d3a961febd5c34cf902db6370af92f96a4599fec753daddb6abb88c404c1","schema_version":"1.0","event_id":"sha256:03b8d3a961febd5c34cf902db6370af92f96a4599fec753daddb6abb88c404c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NHGSDIKUEVFEXIPRF3G3UCIPZ3/bundle.json","state_url":"https://pith.science/pith/NHGSDIKUEVFEXIPRF3G3UCIPZ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NHGSDIKUEVFEXIPRF3G3UCIPZ3/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":"2026-06-05T12:46:23Z","links":{"resolver":"https://pith.science/pith/NHGSDIKUEVFEXIPRF3G3UCIPZ3","bundle":"https://pith.science/pith/NHGSDIKUEVFEXIPRF3G3UCIPZ3/bundle.json","state":"https://pith.science/pith/NHGSDIKUEVFEXIPRF3G3UCIPZ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NHGSDIKUEVFEXIPRF3G3UCIPZ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NHGSDIKUEVFEXIPRF3G3UCIPZ3","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":"97ff8b7c30d404425c93ef78686030b21b95328b2a8fec276839daf92331dce0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-06-13T09:17:48Z","title_canon_sha256":"7d525c90e33dc619a9673773e373a8d69ffd66916fb3a4fdf917fcf8d7108e71"},"schema_version":"1.0","source":{"id":"1806.04909","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.04909","created_at":"2026-05-17T23:47:07Z"},{"alias_kind":"arxiv_version","alias_value":"1806.04909v2","created_at":"2026-05-17T23:47:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.04909","created_at":"2026-05-17T23:47:07Z"},{"alias_kind":"pith_short_12","alias_value":"NHGSDIKUEVFE","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NHGSDIKUEVFEXIPR","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NHGSDIKU","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:03b8d3a961febd5c34cf902db6370af92f96a4599fec753daddb6abb88c404c1","target":"graph","created_at":"2026-05-17T23:47:07Z","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"},"paper":{"abstract_excerpt":"We solve a long-standing open problem in theory of weighted inequalities concerning iterated Copson operators. We use a constructive approximation method based on a new discretization principle that is developed here. In result, we characterize all weight functions $w,v,u$ on $(0,\\infty)$ for which there exists a constant $C$ such that the inequality $$ \\left(\\int_0^{\\infty}\\left(\\int_t^\\infty \\left(\\int_s^{\\infty}h(y)\\,\\text{d}y\\right)^mu(s) \\,\\text{d}s\\right)^{\\frac{q}{m}}w(t)\\,\\text{d}t\\right)^{\\frac{1}{q}} \\le C \\left(\\int_0^{\\infty}h(t)^pv(t)\\,\\text{d}t\\right)^{\\frac{1}{p}} $$ holds for e","authors_text":"Lubo\\v{s} Pick, Martin K\\v{r}epela","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-06-13T09:17:48Z","title":"Weighted inequalities for iterated Copson integral operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.04909","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:f3560ea3dee3f3d4b5d138f1706b506a568c91f0b2667c013ef65512aa796624","target":"record","created_at":"2026-05-17T23:47:07Z","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":"97ff8b7c30d404425c93ef78686030b21b95328b2a8fec276839daf92331dce0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-06-13T09:17:48Z","title_canon_sha256":"7d525c90e33dc619a9673773e373a8d69ffd66916fb3a4fdf917fcf8d7108e71"},"schema_version":"1.0","source":{"id":"1806.04909","kind":"arxiv","version":2}},"canonical_sha256":"69cd21a154254a4ba1f12ecdba090fcec176f28a023f26edfa78e007a4efd29b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69cd21a154254a4ba1f12ecdba090fcec176f28a023f26edfa78e007a4efd29b","first_computed_at":"2026-05-17T23:47:07.400839Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:07.400839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/4Ubq4yS84n6Z9PgYgGVygcHNfR20MMlfMMJww3PE6JMIptBO7my3EwVzHJFtupbi0eN2Ou+LiumBz5Oi/TtAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:07.401461Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.04909","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3560ea3dee3f3d4b5d138f1706b506a568c91f0b2667c013ef65512aa796624","sha256:03b8d3a961febd5c34cf902db6370af92f96a4599fec753daddb6abb88c404c1"],"state_sha256":"01c8f8837dd94662d450dc37fc0fbd400a891377917e8fecd02fc723f36447de"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/mposfO+2FIZMlJhGfyPEIl9n18KqEOnzIiHjht02lzeenQ0iBPWB/+xqaCq0hk/barh0kU+OZn3iBZP4vW7Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T12:46:23.594269Z","bundle_sha256":"0ac8099c9cfa6b0dae741a1313e020ebd922002bc01fec3df6b0f8d83e5c0fde"}}