{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:C2DTM74DPROT3KEQ2AD5DDWKW3","short_pith_number":"pith:C2DTM74D","canonical_record":{"source":{"id":"2505.10666","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-05-15T19:17:09Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"ae005ecfd88c965845d2745aed055e662bb5ce844f50e3b6002f9860a560b779","abstract_canon_sha256":"de77ca815d1d1fc30db86080106f0b26497cd4db9c5fa33ac8ebaf8a6941a996"},"schema_version":"1.0"},"canonical_sha256":"1687367f837c5d3da890d007d18ecab6e79e58bca3d4150e0088a4d7b6ba56bb","source":{"kind":"arxiv","id":"2505.10666","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.10666","created_at":"2026-07-05T11:04:03Z"},{"alias_kind":"arxiv_version","alias_value":"2505.10666v1","created_at":"2026-07-05T11:04:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.10666","created_at":"2026-07-05T11:04:03Z"},{"alias_kind":"pith_short_12","alias_value":"C2DTM74DPROT","created_at":"2026-07-05T11:04:03Z"},{"alias_kind":"pith_short_16","alias_value":"C2DTM74DPROT3KEQ","created_at":"2026-07-05T11:04:03Z"},{"alias_kind":"pith_short_8","alias_value":"C2DTM74D","created_at":"2026-07-05T11:04:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:C2DTM74DPROT3KEQ2AD5DDWKW3","target":"record","payload":{"canonical_record":{"source":{"id":"2505.10666","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-05-15T19:17:09Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"ae005ecfd88c965845d2745aed055e662bb5ce844f50e3b6002f9860a560b779","abstract_canon_sha256":"de77ca815d1d1fc30db86080106f0b26497cd4db9c5fa33ac8ebaf8a6941a996"},"schema_version":"1.0"},"canonical_sha256":"1687367f837c5d3da890d007d18ecab6e79e58bca3d4150e0088a4d7b6ba56bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:04:03.311892Z","signature_b64":"z7tTn+K5VHbbDBgRWmA4b+gwVL8iNAQVyFFHZVSn9lTAwXIXYR96lD7t9BR1znVjY60opI14ux5HLviXG8xMDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1687367f837c5d3da890d007d18ecab6e79e58bca3d4150e0088a4d7b6ba56bb","last_reissued_at":"2026-07-05T11:04:03.311363Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:04:03.311363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.10666","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":"2026-07-05T11:04:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I5EnAGxN/Q2IYwRJHnEJegtedWSZ1iLEuac7T21lGOIpBydwLMoXwPHP3mi6XJvLEY/NqubCBUtSqKsG74UYAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T18:03:46.766360Z"},"content_sha256":"c9b4e573337dc93b99763e7f0991aba804e90a9874503a06653ff4b8eb04f2c3","schema_version":"1.0","event_id":"sha256:c9b4e573337dc93b99763e7f0991aba804e90a9874503a06653ff4b8eb04f2c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:C2DTM74DPROT3KEQ2AD5DDWKW3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantitative Carleson's conjecture for Ahlfors regular domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Emily Casey, Michele Villa, Xavier Tolsa","submitted_at":"2025-05-15T19:17:09Z","abstract_excerpt":"In this article, we prove a quantitative version of Carleson's $\\varepsilon^2$ conjecture in higher dimension: we characterise those Ahlfors-David regular domains in $\\mathbb{R}^{n+1}$ for which the Carleson's coefficients satisfy the so-called strong geometric lemma."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.10666","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/2505.10666/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":"2026-07-05T11:04:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2GK+MmY7dmvjtcH8Y/77Y3l5SuUKw5gjBAPghAjOt934lrkVjr5JeqH+E8z56UO/WIENfMy7I+oH/iVtW7SODw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T18:03:46.767436Z"},"content_sha256":"79d612b7fe9ea27798a1d9cb49b5a931d1b012a37edf7d213931b38c5dd0be2d","schema_version":"1.0","event_id":"sha256:79d612b7fe9ea27798a1d9cb49b5a931d1b012a37edf7d213931b38c5dd0be2d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C2DTM74DPROT3KEQ2AD5DDWKW3/bundle.json","state_url":"https://pith.science/pith/C2DTM74DPROT3KEQ2AD5DDWKW3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C2DTM74DPROT3KEQ2AD5DDWKW3/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":"2026-08-07T18:03:46Z","links":{"resolver":"https://pith.science/pith/C2DTM74DPROT3KEQ2AD5DDWKW3","bundle":"https://pith.science/pith/C2DTM74DPROT3KEQ2AD5DDWKW3/bundle.json","state":"https://pith.science/pith/C2DTM74DPROT3KEQ2AD5DDWKW3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C2DTM74DPROT3KEQ2AD5DDWKW3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:C2DTM74DPROT3KEQ2AD5DDWKW3","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":"de77ca815d1d1fc30db86080106f0b26497cd4db9c5fa33ac8ebaf8a6941a996","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-05-15T19:17:09Z","title_canon_sha256":"ae005ecfd88c965845d2745aed055e662bb5ce844f50e3b6002f9860a560b779"},"schema_version":"1.0","source":{"id":"2505.10666","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.10666","created_at":"2026-07-05T11:04:03Z"},{"alias_kind":"arxiv_version","alias_value":"2505.10666v1","created_at":"2026-07-05T11:04:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.10666","created_at":"2026-07-05T11:04:03Z"},{"alias_kind":"pith_short_12","alias_value":"C2DTM74DPROT","created_at":"2026-07-05T11:04:03Z"},{"alias_kind":"pith_short_16","alias_value":"C2DTM74DPROT3KEQ","created_at":"2026-07-05T11:04:03Z"},{"alias_kind":"pith_short_8","alias_value":"C2DTM74D","created_at":"2026-07-05T11:04:03Z"}],"graph_snapshots":[{"event_id":"sha256:79d612b7fe9ea27798a1d9cb49b5a931d1b012a37edf7d213931b38c5dd0be2d","target":"graph","created_at":"2026-07-05T11:04:03Z","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/2505.10666/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, we prove a quantitative version of Carleson's $\\varepsilon^2$ conjecture in higher dimension: we characterise those Ahlfors-David regular domains in $\\mathbb{R}^{n+1}$ for which the Carleson's coefficients satisfy the so-called strong geometric lemma.","authors_text":"Emily Casey, Michele Villa, Xavier Tolsa","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-05-15T19:17:09Z","title":"Quantitative Carleson's conjecture for Ahlfors regular domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.10666","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:c9b4e573337dc93b99763e7f0991aba804e90a9874503a06653ff4b8eb04f2c3","target":"record","created_at":"2026-07-05T11:04:03Z","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":"de77ca815d1d1fc30db86080106f0b26497cd4db9c5fa33ac8ebaf8a6941a996","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-05-15T19:17:09Z","title_canon_sha256":"ae005ecfd88c965845d2745aed055e662bb5ce844f50e3b6002f9860a560b779"},"schema_version":"1.0","source":{"id":"2505.10666","kind":"arxiv","version":1}},"canonical_sha256":"1687367f837c5d3da890d007d18ecab6e79e58bca3d4150e0088a4d7b6ba56bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1687367f837c5d3da890d007d18ecab6e79e58bca3d4150e0088a4d7b6ba56bb","first_computed_at":"2026-07-05T11:04:03.311363Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:04:03.311363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z7tTn+K5VHbbDBgRWmA4b+gwVL8iNAQVyFFHZVSn9lTAwXIXYR96lD7t9BR1znVjY60opI14ux5HLviXG8xMDA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:04:03.311892Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.10666","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9b4e573337dc93b99763e7f0991aba804e90a9874503a06653ff4b8eb04f2c3","sha256:79d612b7fe9ea27798a1d9cb49b5a931d1b012a37edf7d213931b38c5dd0be2d"],"state_sha256":"80a70bcfbe471cf9fc0ab7dd2a4d7b46a32527b556bfb8c53fed2a7df938e4c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pykm87F1hq4jZgypkJGH8tvVaa6TGceyqQ1rEpI2m3wcRO+cvkbDa/80mkbjgkKPLkz5wlD8YLwvZNuEVp60DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T18:03:46.777963Z","bundle_sha256":"d7da9372d9fd43fb90e77ff2764f2b7ba0dfb8c6d928296a522fe0fcf82b6e7d"}}