{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:7DUXT3TBKOJOGKPYQKNWB277CY","short_pith_number":"pith:7DUXT3TB","canonical_record":{"source":{"id":"2211.08088","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2022-11-15T12:13:34Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"7aef3ce2c8c03f2620b4e92d81c9b8e30a4a47dc401461602e9c762543feef54","abstract_canon_sha256":"5c69dd240d41e66cd7328a028b9a643ee5f26d6552de4a877d44e6de880f3777"},"schema_version":"1.0"},"canonical_sha256":"f8e979ee615392e329f8829b60ebff163966e13c91b1dea07e74f2db2e60b9b6","source":{"kind":"arxiv","id":"2211.08088","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.08088","created_at":"2026-07-05T05:16:39Z"},{"alias_kind":"arxiv_version","alias_value":"2211.08088v1","created_at":"2026-07-05T05:16:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.08088","created_at":"2026-07-05T05:16:39Z"},{"alias_kind":"pith_short_12","alias_value":"7DUXT3TBKOJO","created_at":"2026-07-05T05:16:39Z"},{"alias_kind":"pith_short_16","alias_value":"7DUXT3TBKOJOGKPY","created_at":"2026-07-05T05:16:39Z"},{"alias_kind":"pith_short_8","alias_value":"7DUXT3TB","created_at":"2026-07-05T05:16:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:7DUXT3TBKOJOGKPYQKNWB277CY","target":"record","payload":{"canonical_record":{"source":{"id":"2211.08088","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2022-11-15T12:13:34Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"7aef3ce2c8c03f2620b4e92d81c9b8e30a4a47dc401461602e9c762543feef54","abstract_canon_sha256":"5c69dd240d41e66cd7328a028b9a643ee5f26d6552de4a877d44e6de880f3777"},"schema_version":"1.0"},"canonical_sha256":"f8e979ee615392e329f8829b60ebff163966e13c91b1dea07e74f2db2e60b9b6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:16:39.652227Z","signature_b64":"/hFDW0HvTPR4BSObohbVQLdXB/So3UwxjvJN+tVCcXQQ2emw/WHgimuW2X9zQCuAcnArDmu4DZB+hPOSb8vKCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8e979ee615392e329f8829b60ebff163966e13c91b1dea07e74f2db2e60b9b6","last_reissued_at":"2026-07-05T05:16:39.651823Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:16:39.651823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2211.08088","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":"2026-07-05T05:16:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KdPbZMw7L/aYcPTAUMoeoC29hIT8lJak4cpuSzUYyaAfFglW7qsGSgICK9bkoQIlDKywv14m91c/skwgJ9qRBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T03:03:09.464591Z"},"content_sha256":"122af1d7b16db728da34c71767d13fb3b4f4bd605199753604e96b5c996d2fd8","schema_version":"1.0","event_id":"sha256:122af1d7b16db728da34c71767d13fb3b4f4bd605199753604e96b5c996d2fd8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:7DUXT3TBKOJOGKPYQKNWB277CY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On oscillatory integrals with H\\\"older phases","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Ga\\'etan Leclerc","submitted_at":"2022-11-15T12:13:34Z","abstract_excerpt":"We exhibit a family of autosimilar H\\\"older maps that satisfies a fractal version of the Van Der Corput Lemma, despite not being absolutely continuous. The result is a direct consequence of a recent work of Sahlsten and Steven arXiv:2009.01703, which is based on a powerful theorem of Bourgain known as a sum-product phenomenon estimate. We give a substantially simpler proof of this fact in our particular context, using an elementary method inspired from arXiv:1704.02909 to check the non-concentration estimates that are needed to apply the sum-product phenomenon. This method allows us to gain ad"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.08088","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/2211.08088/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":"2026-07-05T05:16:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CTbtusohzr4DjYELCyDSgLSg4yqXZ8JRQo2Q0lOBZ35u+ZdAV6X4T3G2XKsdWzLF203HZF+vtLntFTgmyPhUCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T03:03:09.465572Z"},"content_sha256":"f4331ca7889dc3ac12cd092adf461a9693b17a1556fe3acd301be2782b131f64","schema_version":"1.0","event_id":"sha256:f4331ca7889dc3ac12cd092adf461a9693b17a1556fe3acd301be2782b131f64"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7DUXT3TBKOJOGKPYQKNWB277CY/bundle.json","state_url":"https://pith.science/pith/7DUXT3TBKOJOGKPYQKNWB277CY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7DUXT3TBKOJOGKPYQKNWB277CY/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":"2026-08-09T03:03:09Z","links":{"resolver":"https://pith.science/pith/7DUXT3TBKOJOGKPYQKNWB277CY","bundle":"https://pith.science/pith/7DUXT3TBKOJOGKPYQKNWB277CY/bundle.json","state":"https://pith.science/pith/7DUXT3TBKOJOGKPYQKNWB277CY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7DUXT3TBKOJOGKPYQKNWB277CY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:7DUXT3TBKOJOGKPYQKNWB277CY","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":"5c69dd240d41e66cd7328a028b9a643ee5f26d6552de4a877d44e6de880f3777","cross_cats_sorted":["math.CA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2022-11-15T12:13:34Z","title_canon_sha256":"7aef3ce2c8c03f2620b4e92d81c9b8e30a4a47dc401461602e9c762543feef54"},"schema_version":"1.0","source":{"id":"2211.08088","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.08088","created_at":"2026-07-05T05:16:39Z"},{"alias_kind":"arxiv_version","alias_value":"2211.08088v1","created_at":"2026-07-05T05:16:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.08088","created_at":"2026-07-05T05:16:39Z"},{"alias_kind":"pith_short_12","alias_value":"7DUXT3TBKOJO","created_at":"2026-07-05T05:16:39Z"},{"alias_kind":"pith_short_16","alias_value":"7DUXT3TBKOJOGKPY","created_at":"2026-07-05T05:16:39Z"},{"alias_kind":"pith_short_8","alias_value":"7DUXT3TB","created_at":"2026-07-05T05:16:39Z"}],"graph_snapshots":[{"event_id":"sha256:f4331ca7889dc3ac12cd092adf461a9693b17a1556fe3acd301be2782b131f64","target":"graph","created_at":"2026-07-05T05:16:39Z","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/2211.08088/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We exhibit a family of autosimilar H\\\"older maps that satisfies a fractal version of the Van Der Corput Lemma, despite not being absolutely continuous. The result is a direct consequence of a recent work of Sahlsten and Steven arXiv:2009.01703, which is based on a powerful theorem of Bourgain known as a sum-product phenomenon estimate. We give a substantially simpler proof of this fact in our particular context, using an elementary method inspired from arXiv:1704.02909 to check the non-concentration estimates that are needed to apply the sum-product phenomenon. This method allows us to gain ad","authors_text":"Ga\\'etan Leclerc","cross_cats":["math.CA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2022-11-15T12:13:34Z","title":"On oscillatory integrals with H\\\"older phases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.08088","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":"sha256:122af1d7b16db728da34c71767d13fb3b4f4bd605199753604e96b5c996d2fd8","target":"record","created_at":"2026-07-05T05:16:39Z","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":"5c69dd240d41e66cd7328a028b9a643ee5f26d6552de4a877d44e6de880f3777","cross_cats_sorted":["math.CA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2022-11-15T12:13:34Z","title_canon_sha256":"7aef3ce2c8c03f2620b4e92d81c9b8e30a4a47dc401461602e9c762543feef54"},"schema_version":"1.0","source":{"id":"2211.08088","kind":"arxiv","version":1}},"canonical_sha256":"f8e979ee615392e329f8829b60ebff163966e13c91b1dea07e74f2db2e60b9b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8e979ee615392e329f8829b60ebff163966e13c91b1dea07e74f2db2e60b9b6","first_computed_at":"2026-07-05T05:16:39.651823Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:16:39.651823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/hFDW0HvTPR4BSObohbVQLdXB/So3UwxjvJN+tVCcXQQ2emw/WHgimuW2X9zQCuAcnArDmu4DZB+hPOSb8vKCg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:16:39.652227Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.08088","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:122af1d7b16db728da34c71767d13fb3b4f4bd605199753604e96b5c996d2fd8","sha256:f4331ca7889dc3ac12cd092adf461a9693b17a1556fe3acd301be2782b131f64"],"state_sha256":"5fd3d25b5e047708210d84632f5e72baaf98d2e323ca2e7952eddcd4d4f831d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7nKjKKt5qKvZPFFsDsG4RP+gkkKeeyM7bcNifsorYSXSE2VXJGJzFhj/BsSHoWCEEnhaP9u8bMLW3RqYDTYSDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T03:03:09.472224Z","bundle_sha256":"3461d702f8998b55ccf1e935be66eaca436723578436f6a10a90e1f50eb306f7"}}