{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:IC6M76MKABLH2NRG4TQF4VVIIH","short_pith_number":"pith:IC6M76MK","canonical_record":{"source":{"id":"2606.09743","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-08T17:05:29Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"1526e845b8f0b3bfbed31318e7d2d0dc03fe8d243c5f2cdef84fcbeafbf8ad78","abstract_canon_sha256":"b8905c905325643274312a9bc7b73dafe2816421fca27ef6d07b40bf268e1e8a"},"schema_version":"1.0"},"canonical_sha256":"40bccff98a00567d3626e4e05e56a841fe403e2c4a58363f9f8f7c5b93f70775","source":{"kind":"arxiv","id":"2606.09743","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.09743","created_at":"2026-06-09T02:09:07Z"},{"alias_kind":"arxiv_version","alias_value":"2606.09743v1","created_at":"2026-06-09T02:09:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.09743","created_at":"2026-06-09T02:09:07Z"},{"alias_kind":"pith_short_12","alias_value":"IC6M76MKABLH","created_at":"2026-06-09T02:09:07Z"},{"alias_kind":"pith_short_16","alias_value":"IC6M76MKABLH2NRG","created_at":"2026-06-09T02:09:07Z"},{"alias_kind":"pith_short_8","alias_value":"IC6M76MK","created_at":"2026-06-09T02:09:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:IC6M76MKABLH2NRG4TQF4VVIIH","target":"record","payload":{"canonical_record":{"source":{"id":"2606.09743","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-08T17:05:29Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"1526e845b8f0b3bfbed31318e7d2d0dc03fe8d243c5f2cdef84fcbeafbf8ad78","abstract_canon_sha256":"b8905c905325643274312a9bc7b73dafe2816421fca27ef6d07b40bf268e1e8a"},"schema_version":"1.0"},"canonical_sha256":"40bccff98a00567d3626e4e05e56a841fe403e2c4a58363f9f8f7c5b93f70775","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:09:07.191963Z","signature_b64":"lVCn6MCyscxKZ5BCe+xkvQrt2l6mnCg7ULytpEueDmzgihaBm8Ira/EutQFLfuIvjefiUm8JC7fz0+HmHfz8BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40bccff98a00567d3626e4e05e56a841fe403e2c4a58363f9f8f7c5b93f70775","last_reissued_at":"2026-06-09T02:09:07.190935Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:09:07.190935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.09743","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":"2026-06-09T02:09:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"etLP1IRutt5R+AgumXe2bildUPMw/hEF4vgTlriXdofVFaj/PKFAeJgQFmPaul3MUPf6moPNgFcFMuIBv1FFAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:15:30.383115Z"},"content_sha256":"23e460779d7dee3be153fee3f314fedb4dbcde32ed6cbac67c53ac28cbd2c7dd","schema_version":"1.0","event_id":"sha256:23e460779d7dee3be153fee3f314fedb4dbcde32ed6cbac67c53ac28cbd2c7dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:IC6M76MKABLH2NRG4TQF4VVIIH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fourier transform of nonlinear images of self-similar measures: qualitative aspects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Amlan Banaji, Han Yu","submitted_at":"2026-06-08T17:05:29Z","abstract_excerpt":"The goal of this paper is to establish polynomial Fourier decay for images of self-similar measures $\\mu$ on $\\mathbb{R}^k$ under sufficiently nonlinear real-analytic maps $f \\colon \\mathbb{R}^k \\to \\mathbb{R}^d$. For example, we prove that if $f$ is analytic on $\\mathbb{R}^k$, its graph does not lie in an affine hyperplane in $\\mathbb{R}^{k+d}$, and $\\mu$ is not supported in an affine hyperplane in $\\mathbb{R}^k$, then the image measure has polynomial Fourier decay. Key steps in the proof include establishing a uniform Lojasiewicz-type inequality for self-similar measures, and using the decay"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09743","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/2606.09743/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":"2026-06-09T02:09:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gfKSBvIiJcAOUZmykjyuRLVtnVQQ0nvLM7GZGqaEAZ7N+sARwXATXZnbo1j7/ywgGf7DxkwKgtJ/RrX7X7kXBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:15:30.383537Z"},"content_sha256":"4ee9698b7faab9d58f1d09154d44c39f7780d04a555b0bb2e9242928213407d2","schema_version":"1.0","event_id":"sha256:4ee9698b7faab9d58f1d09154d44c39f7780d04a555b0bb2e9242928213407d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IC6M76MKABLH2NRG4TQF4VVIIH/bundle.json","state_url":"https://pith.science/pith/IC6M76MKABLH2NRG4TQF4VVIIH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IC6M76MKABLH2NRG4TQF4VVIIH/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":"2026-06-10T21:15:30Z","links":{"resolver":"https://pith.science/pith/IC6M76MKABLH2NRG4TQF4VVIIH","bundle":"https://pith.science/pith/IC6M76MKABLH2NRG4TQF4VVIIH/bundle.json","state":"https://pith.science/pith/IC6M76MKABLH2NRG4TQF4VVIIH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IC6M76MKABLH2NRG4TQF4VVIIH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:IC6M76MKABLH2NRG4TQF4VVIIH","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":"b8905c905325643274312a9bc7b73dafe2816421fca27ef6d07b40bf268e1e8a","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-08T17:05:29Z","title_canon_sha256":"1526e845b8f0b3bfbed31318e7d2d0dc03fe8d243c5f2cdef84fcbeafbf8ad78"},"schema_version":"1.0","source":{"id":"2606.09743","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.09743","created_at":"2026-06-09T02:09:07Z"},{"alias_kind":"arxiv_version","alias_value":"2606.09743v1","created_at":"2026-06-09T02:09:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.09743","created_at":"2026-06-09T02:09:07Z"},{"alias_kind":"pith_short_12","alias_value":"IC6M76MKABLH","created_at":"2026-06-09T02:09:07Z"},{"alias_kind":"pith_short_16","alias_value":"IC6M76MKABLH2NRG","created_at":"2026-06-09T02:09:07Z"},{"alias_kind":"pith_short_8","alias_value":"IC6M76MK","created_at":"2026-06-09T02:09:07Z"}],"graph_snapshots":[{"event_id":"sha256:4ee9698b7faab9d58f1d09154d44c39f7780d04a555b0bb2e9242928213407d2","target":"graph","created_at":"2026-06-09T02:09:07Z","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/2606.09743/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The goal of this paper is to establish polynomial Fourier decay for images of self-similar measures $\\mu$ on $\\mathbb{R}^k$ under sufficiently nonlinear real-analytic maps $f \\colon \\mathbb{R}^k \\to \\mathbb{R}^d$. For example, we prove that if $f$ is analytic on $\\mathbb{R}^k$, its graph does not lie in an affine hyperplane in $\\mathbb{R}^{k+d}$, and $\\mu$ is not supported in an affine hyperplane in $\\mathbb{R}^k$, then the image measure has polynomial Fourier decay. Key steps in the proof include establishing a uniform Lojasiewicz-type inequality for self-similar measures, and using the decay","authors_text":"Amlan Banaji, Han Yu","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-08T17:05:29Z","title":"Fourier transform of nonlinear images of self-similar measures: qualitative aspects"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09743","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":"sha256:23e460779d7dee3be153fee3f314fedb4dbcde32ed6cbac67c53ac28cbd2c7dd","target":"record","created_at":"2026-06-09T02:09:07Z","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":"b8905c905325643274312a9bc7b73dafe2816421fca27ef6d07b40bf268e1e8a","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-08T17:05:29Z","title_canon_sha256":"1526e845b8f0b3bfbed31318e7d2d0dc03fe8d243c5f2cdef84fcbeafbf8ad78"},"schema_version":"1.0","source":{"id":"2606.09743","kind":"arxiv","version":1}},"canonical_sha256":"40bccff98a00567d3626e4e05e56a841fe403e2c4a58363f9f8f7c5b93f70775","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40bccff98a00567d3626e4e05e56a841fe403e2c4a58363f9f8f7c5b93f70775","first_computed_at":"2026-06-09T02:09:07.190935Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:09:07.190935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lVCn6MCyscxKZ5BCe+xkvQrt2l6mnCg7ULytpEueDmzgihaBm8Ira/EutQFLfuIvjefiUm8JC7fz0+HmHfz8BQ==","signature_status":"signed_v1","signed_at":"2026-06-09T02:09:07.191963Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.09743","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23e460779d7dee3be153fee3f314fedb4dbcde32ed6cbac67c53ac28cbd2c7dd","sha256:4ee9698b7faab9d58f1d09154d44c39f7780d04a555b0bb2e9242928213407d2"],"state_sha256":"4eeba3d301eb779939203514ae0eb1e049863d53f86b51d160f93f60dc70676d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e2xtj6CUhd4mfA4IX5aVsXLet+fYERkvtTVSsjlfCzhjUc83cjyDFn+hu6K391AxXRyYcSXaq6ZPHRSeLJxaCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T21:15:30.385775Z","bundle_sha256":"779230b6ef280c00467f8cd157baf8f631f96b8cf3fe59d5cefbf6a78ff61f2b"}}