{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:YXXM5AAGBIOVGGFKMJZKFBQSY5","short_pith_number":"pith:YXXM5AAG","canonical_record":{"source":{"id":"2403.15784","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2024-03-23T10:09:07Z","cross_cats_sorted":[],"title_canon_sha256":"4f05adef6c8af2d34faa4ee4dcdb18859fcee6049bb0629e65c3e4c59bd28cba","abstract_canon_sha256":"c11b42ce55a01d52a64666e8ec1778ce9d797fda3ce31e450547a7fc37f222d8"},"schema_version":"1.0"},"canonical_sha256":"c5eece80060a1d5318aa6272a28612c74ce982c872982a46194474592dc1cf9a","source":{"kind":"arxiv","id":"2403.15784","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.15784","created_at":"2026-07-05T09:45:45Z"},{"alias_kind":"arxiv_version","alias_value":"2403.15784v2","created_at":"2026-07-05T09:45:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.15784","created_at":"2026-07-05T09:45:45Z"},{"alias_kind":"pith_short_12","alias_value":"YXXM5AAGBIOV","created_at":"2026-07-05T09:45:45Z"},{"alias_kind":"pith_short_16","alias_value":"YXXM5AAGBIOVGGFK","created_at":"2026-07-05T09:45:45Z"},{"alias_kind":"pith_short_8","alias_value":"YXXM5AAG","created_at":"2026-07-05T09:45:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:YXXM5AAGBIOVGGFKMJZKFBQSY5","target":"record","payload":{"canonical_record":{"source":{"id":"2403.15784","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2024-03-23T10:09:07Z","cross_cats_sorted":[],"title_canon_sha256":"4f05adef6c8af2d34faa4ee4dcdb18859fcee6049bb0629e65c3e4c59bd28cba","abstract_canon_sha256":"c11b42ce55a01d52a64666e8ec1778ce9d797fda3ce31e450547a7fc37f222d8"},"schema_version":"1.0"},"canonical_sha256":"c5eece80060a1d5318aa6272a28612c74ce982c872982a46194474592dc1cf9a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:45:45.617843Z","signature_b64":"GaaPNGj0DdLHALQGRrltJNe11tpXja8IR/M3GoAF2QVl4agEn5Hyrzd+WFdwLGfttd9pIN563NPBXF9CZJQ/Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5eece80060a1d5318aa6272a28612c74ce982c872982a46194474592dc1cf9a","last_reissued_at":"2026-07-05T09:45:45.617397Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:45:45.617397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.15784","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":"2026-07-05T09:45:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"il2aqN8cmYjCqOdoJn3LwYspr0wA1UsvVLAiICQFiggrp//EBDrZOgFCgXQ5mYFLpev//VcQ7QRV9/swLjEmCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T00:35:53.719272Z"},"content_sha256":"7b189936c5e21c249c1ab3be0ee190f3d4cf6f0ef6b057d4fd8dd044fa73a44b","schema_version":"1.0","event_id":"sha256:7b189936c5e21c249c1ab3be0ee190f3d4cf6f0ef6b057d4fd8dd044fa73a44b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:YXXM5AAGBIOVGGFKMJZKFBQSY5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Orthogonal projection, dual Furstenberg problem, and discretized sum-product","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Bochen Liu, Longhui Li","submitted_at":"2024-03-23T10:09:07Z","abstract_excerpt":"In this paper we come up with a dual version of the Furstenberg problem and obtain partial results via $L^p$ estimates of orthogonal projections. Examples are also discussed. Moreover, compared with general sets, we find that special structure like Cartesian product has better $L^p$-behavior. This leads to improvement on some discretized sum-product estimates."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.15784","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.15784/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":"2026-07-05T09:45:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7PwlX8jzYQAiS6shG1aWP7AcEcn9psB71Izvb9KesSOlEOFWOSYc1ktbnVWOlYZXGnLoMP6CW64kLHVO8yoDAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T00:35:53.719767Z"},"content_sha256":"ea456c634ca3327f59813efb9c3a87d9781736904215b3d22b7f2009acdd3ea0","schema_version":"1.0","event_id":"sha256:ea456c634ca3327f59813efb9c3a87d9781736904215b3d22b7f2009acdd3ea0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YXXM5AAGBIOVGGFKMJZKFBQSY5/bundle.json","state_url":"https://pith.science/pith/YXXM5AAGBIOVGGFKMJZKFBQSY5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YXXM5AAGBIOVGGFKMJZKFBQSY5/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":"2026-08-20T00:35:53Z","links":{"resolver":"https://pith.science/pith/YXXM5AAGBIOVGGFKMJZKFBQSY5","bundle":"https://pith.science/pith/YXXM5AAGBIOVGGFKMJZKFBQSY5/bundle.json","state":"https://pith.science/pith/YXXM5AAGBIOVGGFKMJZKFBQSY5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YXXM5AAGBIOVGGFKMJZKFBQSY5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:YXXM5AAGBIOVGGFKMJZKFBQSY5","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":"c11b42ce55a01d52a64666e8ec1778ce9d797fda3ce31e450547a7fc37f222d8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2024-03-23T10:09:07Z","title_canon_sha256":"4f05adef6c8af2d34faa4ee4dcdb18859fcee6049bb0629e65c3e4c59bd28cba"},"schema_version":"1.0","source":{"id":"2403.15784","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.15784","created_at":"2026-07-05T09:45:45Z"},{"alias_kind":"arxiv_version","alias_value":"2403.15784v2","created_at":"2026-07-05T09:45:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.15784","created_at":"2026-07-05T09:45:45Z"},{"alias_kind":"pith_short_12","alias_value":"YXXM5AAGBIOV","created_at":"2026-07-05T09:45:45Z"},{"alias_kind":"pith_short_16","alias_value":"YXXM5AAGBIOVGGFK","created_at":"2026-07-05T09:45:45Z"},{"alias_kind":"pith_short_8","alias_value":"YXXM5AAG","created_at":"2026-07-05T09:45:45Z"}],"graph_snapshots":[{"event_id":"sha256:ea456c634ca3327f59813efb9c3a87d9781736904215b3d22b7f2009acdd3ea0","target":"graph","created_at":"2026-07-05T09:45:45Z","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/2403.15784/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we come up with a dual version of the Furstenberg problem and obtain partial results via $L^p$ estimates of orthogonal projections. Examples are also discussed. Moreover, compared with general sets, we find that special structure like Cartesian product has better $L^p$-behavior. This leads to improvement on some discretized sum-product estimates.","authors_text":"Bochen Liu, Longhui Li","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2024-03-23T10:09:07Z","title":"Orthogonal projection, dual Furstenberg problem, and discretized sum-product"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.15784","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":"sha256:7b189936c5e21c249c1ab3be0ee190f3d4cf6f0ef6b057d4fd8dd044fa73a44b","target":"record","created_at":"2026-07-05T09:45:45Z","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":"c11b42ce55a01d52a64666e8ec1778ce9d797fda3ce31e450547a7fc37f222d8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2024-03-23T10:09:07Z","title_canon_sha256":"4f05adef6c8af2d34faa4ee4dcdb18859fcee6049bb0629e65c3e4c59bd28cba"},"schema_version":"1.0","source":{"id":"2403.15784","kind":"arxiv","version":2}},"canonical_sha256":"c5eece80060a1d5318aa6272a28612c74ce982c872982a46194474592dc1cf9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5eece80060a1d5318aa6272a28612c74ce982c872982a46194474592dc1cf9a","first_computed_at":"2026-07-05T09:45:45.617397Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:45:45.617397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GaaPNGj0DdLHALQGRrltJNe11tpXja8IR/M3GoAF2QVl4agEn5Hyrzd+WFdwLGfttd9pIN563NPBXF9CZJQ/Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:45:45.617843Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.15784","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b189936c5e21c249c1ab3be0ee190f3d4cf6f0ef6b057d4fd8dd044fa73a44b","sha256:ea456c634ca3327f59813efb9c3a87d9781736904215b3d22b7f2009acdd3ea0"],"state_sha256":"cedd406384791aac1dc0bb8db2c5b3eed8fb09856c4df0b6b32e9fb47012a4da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JJweTNgzfEwqmvgDJ36ifUBE7ftnOawKddTQpogkBubdVWJ6kxicQ3vJZp7bkXBLpyvRUmy2qjWxYUQlU2JLAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T00:35:53.723565Z","bundle_sha256":"8acf9e8d95cd59a5afff6848fa58041acea46b3ce85e0c6759b84ad72cb89407"}}