{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:GE7FDF6CT236GNMMQYMD2FBRV5","short_pith_number":"pith:GE7FDF6C","canonical_record":{"source":{"id":"1404.2690","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-04-10T04:33:40Z","cross_cats_sorted":[],"title_canon_sha256":"18b2d63dbb73902b273828bcda9a0d9dbd7241b4c95cb74efe598bc626741eda","abstract_canon_sha256":"0b46e61800c48531b6262408797a117ba97d32c6be0b37beab9a72765ca1dc40"},"schema_version":"1.0"},"canonical_sha256":"313e5197c29eb7e3358c86183d1431af568072a433d5899b4e97e7909048ee83","source":{"kind":"arxiv","id":"1404.2690","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.2690","created_at":"2026-05-18T02:54:29Z"},{"alias_kind":"arxiv_version","alias_value":"1404.2690v1","created_at":"2026-05-18T02:54:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2690","created_at":"2026-05-18T02:54:29Z"},{"alias_kind":"pith_short_12","alias_value":"GE7FDF6CT236","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GE7FDF6CT236GNMM","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GE7FDF6C","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:GE7FDF6CT236GNMMQYMD2FBRV5","target":"record","payload":{"canonical_record":{"source":{"id":"1404.2690","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-04-10T04:33:40Z","cross_cats_sorted":[],"title_canon_sha256":"18b2d63dbb73902b273828bcda9a0d9dbd7241b4c95cb74efe598bc626741eda","abstract_canon_sha256":"0b46e61800c48531b6262408797a117ba97d32c6be0b37beab9a72765ca1dc40"},"schema_version":"1.0"},"canonical_sha256":"313e5197c29eb7e3358c86183d1431af568072a433d5899b4e97e7909048ee83","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:29.781521Z","signature_b64":"rOzjNcukxP6ma913w6nHJL0k//d2xJanf+0OdyDpmHn8TUzW8NsqOFSsBq0yToSoSnYF+vwll4HPJxy9ho3UBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"313e5197c29eb7e3358c86183d1431af568072a433d5899b4e97e7909048ee83","last_reissued_at":"2026-05-18T02:54:29.780915Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:29.780915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.2690","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":"2026-05-18T02:54:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fr3OF80IACECV4XCfpiO8Vix31uGn1n0rzhDohc+8eYebcSDDRQJXYLo+HBOrd2X7C+jBtUOn4BIVhtbYYJqBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T01:34:16.213864Z"},"content_sha256":"77bd830113e558c35a3de51a0ad6979f62a2210fbd5fce2c5044ce0f7e6beeb7","schema_version":"1.0","event_id":"sha256:77bd830113e558c35a3de51a0ad6979f62a2210fbd5fce2c5044ce0f7e6beeb7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:GE7FDF6CT236GNMMQYMD2FBRV5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Kakeya maximal operator on the variable Lebesgue spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Hiroki Saito, Hitoshi Tanaka","submitted_at":"2014-04-10T04:33:40Z","abstract_excerpt":"We shall verify the Kakeya (Nikodym) maximal operator $K_{N}$, $N\\gg 1$, is bounded on the variable Lebesgue space $L^{p(\\cdot)}(\\mathbb{R}^2)$ when the exponent function $p(\\cdot)$ is $N$-modified locally log-H\\\"{o}lder continuous and log-H\\\"{o}lder continuous at infinity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2690","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":"2026-05-18T02:54:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p0uZTvo4KyiKkiemmI2LmU05rA4ZRO/BVkNrMh3ood2UZNKwBw3K05yDQCZJF2BDmuFuKCp6SnbgC6OjNYA7AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T01:34:16.214448Z"},"content_sha256":"f691822d54b397ed8437eeae35965c6eb5eb5a9e491108f717b30298a44f63ce","schema_version":"1.0","event_id":"sha256:f691822d54b397ed8437eeae35965c6eb5eb5a9e491108f717b30298a44f63ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GE7FDF6CT236GNMMQYMD2FBRV5/bundle.json","state_url":"https://pith.science/pith/GE7FDF6CT236GNMMQYMD2FBRV5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GE7FDF6CT236GNMMQYMD2FBRV5/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":"2026-06-08T01:34:16Z","links":{"resolver":"https://pith.science/pith/GE7FDF6CT236GNMMQYMD2FBRV5","bundle":"https://pith.science/pith/GE7FDF6CT236GNMMQYMD2FBRV5/bundle.json","state":"https://pith.science/pith/GE7FDF6CT236GNMMQYMD2FBRV5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GE7FDF6CT236GNMMQYMD2FBRV5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GE7FDF6CT236GNMMQYMD2FBRV5","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":"0b46e61800c48531b6262408797a117ba97d32c6be0b37beab9a72765ca1dc40","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-04-10T04:33:40Z","title_canon_sha256":"18b2d63dbb73902b273828bcda9a0d9dbd7241b4c95cb74efe598bc626741eda"},"schema_version":"1.0","source":{"id":"1404.2690","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.2690","created_at":"2026-05-18T02:54:29Z"},{"alias_kind":"arxiv_version","alias_value":"1404.2690v1","created_at":"2026-05-18T02:54:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2690","created_at":"2026-05-18T02:54:29Z"},{"alias_kind":"pith_short_12","alias_value":"GE7FDF6CT236","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GE7FDF6CT236GNMM","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GE7FDF6C","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:f691822d54b397ed8437eeae35965c6eb5eb5a9e491108f717b30298a44f63ce","target":"graph","created_at":"2026-05-18T02:54:29Z","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 shall verify the Kakeya (Nikodym) maximal operator $K_{N}$, $N\\gg 1$, is bounded on the variable Lebesgue space $L^{p(\\cdot)}(\\mathbb{R}^2)$ when the exponent function $p(\\cdot)$ is $N$-modified locally log-H\\\"{o}lder continuous and log-H\\\"{o}lder continuous at infinity.","authors_text":"Hiroki Saito, Hitoshi Tanaka","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-04-10T04:33:40Z","title":"The Kakeya maximal operator on the variable Lebesgue spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2690","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":"sha256:77bd830113e558c35a3de51a0ad6979f62a2210fbd5fce2c5044ce0f7e6beeb7","target":"record","created_at":"2026-05-18T02:54:29Z","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":"0b46e61800c48531b6262408797a117ba97d32c6be0b37beab9a72765ca1dc40","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-04-10T04:33:40Z","title_canon_sha256":"18b2d63dbb73902b273828bcda9a0d9dbd7241b4c95cb74efe598bc626741eda"},"schema_version":"1.0","source":{"id":"1404.2690","kind":"arxiv","version":1}},"canonical_sha256":"313e5197c29eb7e3358c86183d1431af568072a433d5899b4e97e7909048ee83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"313e5197c29eb7e3358c86183d1431af568072a433d5899b4e97e7909048ee83","first_computed_at":"2026-05-18T02:54:29.780915Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:29.780915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rOzjNcukxP6ma913w6nHJL0k//d2xJanf+0OdyDpmHn8TUzW8NsqOFSsBq0yToSoSnYF+vwll4HPJxy9ho3UBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:29.781521Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.2690","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77bd830113e558c35a3de51a0ad6979f62a2210fbd5fce2c5044ce0f7e6beeb7","sha256:f691822d54b397ed8437eeae35965c6eb5eb5a9e491108f717b30298a44f63ce"],"state_sha256":"50435fc151aae4585ebc36b19e0aa20bbe2105fc3467f5d31f531d084bc77d23"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tp/RU8M6D7tYf6EYR8jeoa6e/1Vr6o432dw2y2MPWHrQP6doe0PPDYpR86dhJLXOWq5b1SvSkEIJzLmhGGz6Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T01:34:16.219424Z","bundle_sha256":"fc610e769257dd1c8ca092d2944aa373167e57d89671a59efb087aea17e0aba3"}}