{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:62B4CQOUBEJVOIMMJ62CXWSVN7","short_pith_number":"pith:62B4CQOU","canonical_record":{"source":{"id":"2401.01241","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-01-02T15:18:07Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"25a40246dff8298e19c0f43da4a87fd52a44cc9920516ea96c10436c0850f669","abstract_canon_sha256":"fa557ef0e954c4ae808941cb2c1b203c3260537ee58349a69a3379d50f3040d4"},"schema_version":"1.0"},"canonical_sha256":"f683c141d4091357218c4fb42bda556fdc4461d3a4cd35fda9eab4f453ac6c21","source":{"kind":"arxiv","id":"2401.01241","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.01241","created_at":"2026-07-05T10:58:58Z"},{"alias_kind":"arxiv_version","alias_value":"2401.01241v2","created_at":"2026-07-05T10:58:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.01241","created_at":"2026-07-05T10:58:58Z"},{"alias_kind":"pith_short_12","alias_value":"62B4CQOUBEJV","created_at":"2026-07-05T10:58:58Z"},{"alias_kind":"pith_short_16","alias_value":"62B4CQOUBEJVOIMM","created_at":"2026-07-05T10:58:58Z"},{"alias_kind":"pith_short_8","alias_value":"62B4CQOU","created_at":"2026-07-05T10:58:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:62B4CQOUBEJVOIMMJ62CXWSVN7","target":"record","payload":{"canonical_record":{"source":{"id":"2401.01241","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-01-02T15:18:07Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"25a40246dff8298e19c0f43da4a87fd52a44cc9920516ea96c10436c0850f669","abstract_canon_sha256":"fa557ef0e954c4ae808941cb2c1b203c3260537ee58349a69a3379d50f3040d4"},"schema_version":"1.0"},"canonical_sha256":"f683c141d4091357218c4fb42bda556fdc4461d3a4cd35fda9eab4f453ac6c21","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:58:58.840576Z","signature_b64":"6urHV6QzOad/jpwwQsJIHszMH7bYRHqQP1avjR5Qng4o9wVpqWQEXSCCU1m97EAoU0YWJ12JysBmSsI5TFKcBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f683c141d4091357218c4fb42bda556fdc4461d3a4cd35fda9eab4f453ac6c21","last_reissued_at":"2026-07-05T10:58:58.840067Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:58:58.840067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2401.01241","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":"2026-07-05T10:58:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7f3IzBkYj00CN4zCciGlLnvmJAYFB1OPrviEr/hfOhBPimNx8biUtRIXTa7+B40kEb1wQUXcTKa8CPJENvR4CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T04:01:57.157714Z"},"content_sha256":"ee432e2ac5f3059dbf39abfd535b9d87c743bc09e38d9a311b4c48301e4dca90","schema_version":"1.0","event_id":"sha256:ee432e2ac5f3059dbf39abfd535b9d87c743bc09e38d9a311b4c48301e4dca90"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:62B4CQOUBEJVOIMMJ62CXWSVN7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial Fourier decay for fractal measures and their pushforwards","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Amlan Banaji, Simon Baker","submitted_at":"2024-01-02T15:18:07Z","abstract_excerpt":"We prove that the pushforwards of a very general class of fractal measures $\\mu$ on $\\mathbb{R}^d$ under a large family of non-linear maps $F \\colon \\mathbb{R}^d \\to \\mathbb{R}$ exhibit polynomial Fourier decay: there exist $C,\\eta>0$ such that $|\\widehat{F\\mu}(\\xi)|\\leq C|\\xi|^{-\\eta}$ for all $\\xi\\neq 0$. Using this, we prove that if $\\Phi = \\{ \\varphi_a \\colon [0,1] \\to [0,1] \\}_{a \\in \\mathcal{A}}$ is an iterated function system consisting of analytic contractions, and there exists $a \\in \\mathcal{A}$ such that $\\varphi_a$ is not an affine map, then every non-atomic self-conformal measure "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.01241","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/2401.01241/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":"2026-07-05T10:58:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"blU9uUS7xFURSeo8B1VSZD2kkLJmXTN91cIzWERUlct6bi7Cu0emqYrHvbRN2ufneKtCgx60jOTbIApaKT8LCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T04:01:57.158207Z"},"content_sha256":"9261f425e278e21774cb8f44a3fb5d1123304093c9fedb63048e9fe009d39ca2","schema_version":"1.0","event_id":"sha256:9261f425e278e21774cb8f44a3fb5d1123304093c9fedb63048e9fe009d39ca2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/62B4CQOUBEJVOIMMJ62CXWSVN7/bundle.json","state_url":"https://pith.science/pith/62B4CQOUBEJVOIMMJ62CXWSVN7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/62B4CQOUBEJVOIMMJ62CXWSVN7/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":"2026-08-09T04:01:57Z","links":{"resolver":"https://pith.science/pith/62B4CQOUBEJVOIMMJ62CXWSVN7","bundle":"https://pith.science/pith/62B4CQOUBEJVOIMMJ62CXWSVN7/bundle.json","state":"https://pith.science/pith/62B4CQOUBEJVOIMMJ62CXWSVN7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/62B4CQOUBEJVOIMMJ62CXWSVN7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:62B4CQOUBEJVOIMMJ62CXWSVN7","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":"fa557ef0e954c4ae808941cb2c1b203c3260537ee58349a69a3379d50f3040d4","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-01-02T15:18:07Z","title_canon_sha256":"25a40246dff8298e19c0f43da4a87fd52a44cc9920516ea96c10436c0850f669"},"schema_version":"1.0","source":{"id":"2401.01241","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.01241","created_at":"2026-07-05T10:58:58Z"},{"alias_kind":"arxiv_version","alias_value":"2401.01241v2","created_at":"2026-07-05T10:58:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.01241","created_at":"2026-07-05T10:58:58Z"},{"alias_kind":"pith_short_12","alias_value":"62B4CQOUBEJV","created_at":"2026-07-05T10:58:58Z"},{"alias_kind":"pith_short_16","alias_value":"62B4CQOUBEJVOIMM","created_at":"2026-07-05T10:58:58Z"},{"alias_kind":"pith_short_8","alias_value":"62B4CQOU","created_at":"2026-07-05T10:58:58Z"}],"graph_snapshots":[{"event_id":"sha256:9261f425e278e21774cb8f44a3fb5d1123304093c9fedb63048e9fe009d39ca2","target":"graph","created_at":"2026-07-05T10:58:58Z","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/2401.01241/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that the pushforwards of a very general class of fractal measures $\\mu$ on $\\mathbb{R}^d$ under a large family of non-linear maps $F \\colon \\mathbb{R}^d \\to \\mathbb{R}$ exhibit polynomial Fourier decay: there exist $C,\\eta>0$ such that $|\\widehat{F\\mu}(\\xi)|\\leq C|\\xi|^{-\\eta}$ for all $\\xi\\neq 0$. Using this, we prove that if $\\Phi = \\{ \\varphi_a \\colon [0,1] \\to [0,1] \\}_{a \\in \\mathcal{A}}$ is an iterated function system consisting of analytic contractions, and there exists $a \\in \\mathcal{A}$ such that $\\varphi_a$ is not an affine map, then every non-atomic self-conformal measure ","authors_text":"Amlan Banaji, Simon Baker","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-01-02T15:18:07Z","title":"Polynomial Fourier decay for fractal measures and their pushforwards"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.01241","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:ee432e2ac5f3059dbf39abfd535b9d87c743bc09e38d9a311b4c48301e4dca90","target":"record","created_at":"2026-07-05T10:58:58Z","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":"fa557ef0e954c4ae808941cb2c1b203c3260537ee58349a69a3379d50f3040d4","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-01-02T15:18:07Z","title_canon_sha256":"25a40246dff8298e19c0f43da4a87fd52a44cc9920516ea96c10436c0850f669"},"schema_version":"1.0","source":{"id":"2401.01241","kind":"arxiv","version":2}},"canonical_sha256":"f683c141d4091357218c4fb42bda556fdc4461d3a4cd35fda9eab4f453ac6c21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f683c141d4091357218c4fb42bda556fdc4461d3a4cd35fda9eab4f453ac6c21","first_computed_at":"2026-07-05T10:58:58.840067Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:58:58.840067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6urHV6QzOad/jpwwQsJIHszMH7bYRHqQP1avjR5Qng4o9wVpqWQEXSCCU1m97EAoU0YWJ12JysBmSsI5TFKcBg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:58:58.840576Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.01241","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee432e2ac5f3059dbf39abfd535b9d87c743bc09e38d9a311b4c48301e4dca90","sha256:9261f425e278e21774cb8f44a3fb5d1123304093c9fedb63048e9fe009d39ca2"],"state_sha256":"8a638c9cc30ef80ff5e68ec835098083a566682e1052a2ef49f336bb0dcc44ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2VtY42tO4ssv6g+/JoHuPmd0OwnOJB12VLuup5I+19zGspYeiBk9pPrbOTkZlPB9mmiYehbyDNvNhcXpZOJOCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T04:01:57.161578Z","bundle_sha256":"df2cd5c21ad7a8303e748578a69f3b265f2df07864d0a7f3dd338cd7dba07d59"}}