{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:CQKTPGLX7J46EAR4WWBEMW5WMQ","short_pith_number":"pith:CQKTPGLX","canonical_record":{"source":{"id":"2607.08461","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-07-09T13:20:12Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"0bc7244f68ed835bc34c65472fbce30ab362272cd6d6b809c6ac58183a6e5a31","abstract_canon_sha256":"f40564805fede0a7bf00a9017ce09f981e6bcddbc6aa2da8d45f93b952e0e189"},"schema_version":"1.0"},"canonical_sha256":"1415379977fa79e2023cb582465bb66436d408985cd0b74e341d664db4e18500","source":{"kind":"arxiv","id":"2607.08461","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.08461","created_at":"2026-07-10T01:19:51Z"},{"alias_kind":"arxiv_version","alias_value":"2607.08461v1","created_at":"2026-07-10T01:19:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.08461","created_at":"2026-07-10T01:19:51Z"},{"alias_kind":"pith_short_12","alias_value":"CQKTPGLX7J46","created_at":"2026-07-10T01:19:51Z"},{"alias_kind":"pith_short_16","alias_value":"CQKTPGLX7J46EAR4","created_at":"2026-07-10T01:19:51Z"},{"alias_kind":"pith_short_8","alias_value":"CQKTPGLX","created_at":"2026-07-10T01:19:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:CQKTPGLX7J46EAR4WWBEMW5WMQ","target":"record","payload":{"canonical_record":{"source":{"id":"2607.08461","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-07-09T13:20:12Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"0bc7244f68ed835bc34c65472fbce30ab362272cd6d6b809c6ac58183a6e5a31","abstract_canon_sha256":"f40564805fede0a7bf00a9017ce09f981e6bcddbc6aa2da8d45f93b952e0e189"},"schema_version":"1.0"},"canonical_sha256":"1415379977fa79e2023cb582465bb66436d408985cd0b74e341d664db4e18500","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-10T01:19:51.239414Z","signature_b64":"OHWkFo0jOnx4Lp5WMr2Xqzrjul5fr1EvOe6vJYDSK/4Gg6wN+3Wz1MIIMRcAtRJ5HJhjL6A+fJUAQQ7qkNyDDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1415379977fa79e2023cb582465bb66436d408985cd0b74e341d664db4e18500","last_reissued_at":"2026-07-10T01:19:51.238941Z","signature_status":"signed_v1","first_computed_at":"2026-07-10T01:19:51.238941Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.08461","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":"2026-07-10T01:19:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PvoY0JCNAiHHgh67cII0MlyGRb34QxjpYM6hrPNS73i4HD27ukpK6QnTCIaorFojjwMyobH2vlDHKg35w/9HDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T11:24:12.143071Z"},"content_sha256":"089ad789258da92cdc5d24964dce90668d706694d999041a96d7a315fdf7ef18","schema_version":"1.0","event_id":"sha256:089ad789258da92cdc5d24964dce90668d706694d999041a96d7a315fdf7ef18"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:CQKTPGLX7J46EAR4WWBEMW5WMQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two-ends Furstenberg inequality for transversal families and applications to Fourier decay","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.CA","authors_text":"Guangzeng Yi, Shukun Wu, William O'Regan","submitted_at":"2026-07-09T13:20:12Z","abstract_excerpt":"We generalise the recent two-ends Furstenberg inequality due to Wang and the second author from lines to a family of transversal curves, and give a much simplified proof. As an application, we present a result pertaining to the Fourier decay of fractal measures on convex curves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08461","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/2607.08461/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":"2026-07-10T01:19:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p7KEMLcjqO/kfeItvF4ULd00vjPwaz4U8Lxemq/BAmZxKo3vVX2WgIVYJ8+dy3hp4tKRXBlZ9LFZ+Tj4tkKbCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T11:24:12.143635Z"},"content_sha256":"03f8593f7cad49788e905df946c70708a68d000827871beec2e7de84aec6a680","schema_version":"1.0","event_id":"sha256:03f8593f7cad49788e905df946c70708a68d000827871beec2e7de84aec6a680"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CQKTPGLX7J46EAR4WWBEMW5WMQ/bundle.json","state_url":"https://pith.science/pith/CQKTPGLX7J46EAR4WWBEMW5WMQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CQKTPGLX7J46EAR4WWBEMW5WMQ/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":"2026-08-08T11:24:12Z","links":{"resolver":"https://pith.science/pith/CQKTPGLX7J46EAR4WWBEMW5WMQ","bundle":"https://pith.science/pith/CQKTPGLX7J46EAR4WWBEMW5WMQ/bundle.json","state":"https://pith.science/pith/CQKTPGLX7J46EAR4WWBEMW5WMQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CQKTPGLX7J46EAR4WWBEMW5WMQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CQKTPGLX7J46EAR4WWBEMW5WMQ","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":"f40564805fede0a7bf00a9017ce09f981e6bcddbc6aa2da8d45f93b952e0e189","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-07-09T13:20:12Z","title_canon_sha256":"0bc7244f68ed835bc34c65472fbce30ab362272cd6d6b809c6ac58183a6e5a31"},"schema_version":"1.0","source":{"id":"2607.08461","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.08461","created_at":"2026-07-10T01:19:51Z"},{"alias_kind":"arxiv_version","alias_value":"2607.08461v1","created_at":"2026-07-10T01:19:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.08461","created_at":"2026-07-10T01:19:51Z"},{"alias_kind":"pith_short_12","alias_value":"CQKTPGLX7J46","created_at":"2026-07-10T01:19:51Z"},{"alias_kind":"pith_short_16","alias_value":"CQKTPGLX7J46EAR4","created_at":"2026-07-10T01:19:51Z"},{"alias_kind":"pith_short_8","alias_value":"CQKTPGLX","created_at":"2026-07-10T01:19:51Z"}],"graph_snapshots":[{"event_id":"sha256:03f8593f7cad49788e905df946c70708a68d000827871beec2e7de84aec6a680","target":"graph","created_at":"2026-07-10T01:19:51Z","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/2607.08461/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We generalise the recent two-ends Furstenberg inequality due to Wang and the second author from lines to a family of transversal curves, and give a much simplified proof. As an application, we present a result pertaining to the Fourier decay of fractal measures on convex curves.","authors_text":"Guangzeng Yi, Shukun Wu, William O'Regan","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-07-09T13:20:12Z","title":"Two-ends Furstenberg inequality for transversal families and applications to Fourier decay"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08461","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":"sha256:089ad789258da92cdc5d24964dce90668d706694d999041a96d7a315fdf7ef18","target":"record","created_at":"2026-07-10T01:19:51Z","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":"f40564805fede0a7bf00a9017ce09f981e6bcddbc6aa2da8d45f93b952e0e189","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-07-09T13:20:12Z","title_canon_sha256":"0bc7244f68ed835bc34c65472fbce30ab362272cd6d6b809c6ac58183a6e5a31"},"schema_version":"1.0","source":{"id":"2607.08461","kind":"arxiv","version":1}},"canonical_sha256":"1415379977fa79e2023cb582465bb66436d408985cd0b74e341d664db4e18500","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1415379977fa79e2023cb582465bb66436d408985cd0b74e341d664db4e18500","first_computed_at":"2026-07-10T01:19:51.238941Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-10T01:19:51.238941Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OHWkFo0jOnx4Lp5WMr2Xqzrjul5fr1EvOe6vJYDSK/4Gg6wN+3Wz1MIIMRcAtRJ5HJhjL6A+fJUAQQ7qkNyDDA==","signature_status":"signed_v1","signed_at":"2026-07-10T01:19:51.239414Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.08461","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:089ad789258da92cdc5d24964dce90668d706694d999041a96d7a315fdf7ef18","sha256:03f8593f7cad49788e905df946c70708a68d000827871beec2e7de84aec6a680"],"state_sha256":"f729899b01860e9e3104c7c19da5c5d00fdc178a389800d5f57425127dd53b1b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F2V6gZ8evOAyXLaOlcIELtZpHL4nmcyKeXfyb4g9ZAECpyXA0vwoywM/0c6fXGKu+h720CK6Tjxk2E85f343CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T11:24:12.147171Z","bundle_sha256":"106303ae13dd94eac7e16ddb557b4e6b90f02d77f0eef0e1da2c724f798ec56a"}}