{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:VMGJGSG5RHHV4IX45QTKKYOZVE","short_pith_number":"pith:VMGJGSG5","schema_version":"1.0","canonical_sha256":"ab0c9348dd89cf5e22fcec26a561d9a912a0cc104ca5e4b2e54b2cfbd7815e96","source":{"kind":"arxiv","id":"2507.07321","version":1},"attestation_state":"computed","paper":{"title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CA","authors_text":"Amir Algom, Osama Khalil","submitted_at":"2025-07-09T22:45:19Z","abstract_excerpt":"Let $\\mu$ be a non-atomic self-similar measure on $\\mathbb{R}$, and let $\\nu$ be its pushforward to a non-degenerate curve in $\\mathbb{R}^d, d\\geq 1$. We show that for every $\\epsilon>0$, there is $p>1$, so that $\\left \\lVert \\hat{\\nu} \\right \\rVert_{L^p(B(R))}^p = O_\\epsilon(R^\\epsilon)$ for all $R>1$, where $B(R)$ is the $R$-ball about the origin. As a corollary, we show that convolution with $\\nu$ quantitatively improves $L^2$-dimension."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2507.07321","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-07-09T22:45:19Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"898de12b6d907160a0437b5adcea6ec149df2534af5e392cc3855054e83bf5f4","abstract_canon_sha256":"a649168fdcd84da8da0713c0cac70b206a6e02eac65ea60e36c25af9e33c0ce9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:34:55.780025Z","signature_b64":"EtV/FFtAdOa5WR3PRfU5Lh4KRdJzBa017H/+iDqlxuTXYFNoJ1DnbMK6jlpVqlBlojxcdwgPAnUBe7DOh76hAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab0c9348dd89cf5e22fcec26a561d9a912a0cc104ca5e4b2e54b2cfbd7815e96","last_reissued_at":"2026-07-05T11:34:55.779521Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:34:55.779521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CA","authors_text":"Amir Algom, Osama Khalil","submitted_at":"2025-07-09T22:45:19Z","abstract_excerpt":"Let $\\mu$ be a non-atomic self-similar measure on $\\mathbb{R}$, and let $\\nu$ be its pushforward to a non-degenerate curve in $\\mathbb{R}^d, d\\geq 1$. We show that for every $\\epsilon>0$, there is $p>1$, so that $\\left \\lVert \\hat{\\nu} \\right \\rVert_{L^p(B(R))}^p = O_\\epsilon(R^\\epsilon)$ for all $R>1$, where $B(R)$ is the $R$-ball about the origin. As a corollary, we show that convolution with $\\nu$ quantitatively improves $L^2$-dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.07321","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/2507.07321/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2507.07321","created_at":"2026-07-05T11:34:55.779581+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.07321v1","created_at":"2026-07-05T11:34:55.779581+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.07321","created_at":"2026-07-05T11:34:55.779581+00:00"},{"alias_kind":"pith_short_12","alias_value":"VMGJGSG5RHHV","created_at":"2026-07-05T11:34:55.779581+00:00"},{"alias_kind":"pith_short_16","alias_value":"VMGJGSG5RHHV4IX4","created_at":"2026-07-05T11:34:55.779581+00:00"},{"alias_kind":"pith_short_8","alias_value":"VMGJGSG5","created_at":"2026-07-05T11:34:55.779581+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.09743","citing_title":"Fourier transform of nonlinear images of self-similar measures: qualitative aspects","ref_index":6,"is_internal_anchor":false},{"citing_arxiv_id":"2606.13170","citing_title":"Quantitative flatness and obstructions in Fourier analysis","ref_index":2,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VMGJGSG5RHHV4IX45QTKKYOZVE","json":"https://pith.science/pith/VMGJGSG5RHHV4IX45QTKKYOZVE.json","graph_json":"https://pith.science/api/pith-number/VMGJGSG5RHHV4IX45QTKKYOZVE/graph.json","events_json":"https://pith.science/api/pith-number/VMGJGSG5RHHV4IX45QTKKYOZVE/events.json","paper":"https://pith.science/paper/VMGJGSG5"},"agent_actions":{"view_html":"https://pith.science/pith/VMGJGSG5RHHV4IX45QTKKYOZVE","download_json":"https://pith.science/pith/VMGJGSG5RHHV4IX45QTKKYOZVE.json","view_paper":"https://pith.science/paper/VMGJGSG5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.07321&json=true","fetch_graph":"https://pith.science/api/pith-number/VMGJGSG5RHHV4IX45QTKKYOZVE/graph.json","fetch_events":"https://pith.science/api/pith-number/VMGJGSG5RHHV4IX45QTKKYOZVE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VMGJGSG5RHHV4IX45QTKKYOZVE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VMGJGSG5RHHV4IX45QTKKYOZVE/action/storage_attestation","attest_author":"https://pith.science/pith/VMGJGSG5RHHV4IX45QTKKYOZVE/action/author_attestation","sign_citation":"https://pith.science/pith/VMGJGSG5RHHV4IX45QTKKYOZVE/action/citation_signature","submit_replication":"https://pith.science/pith/VMGJGSG5RHHV4IX45QTKKYOZVE/action/replication_record"}},"created_at":"2026-07-05T11:34:55.779581+00:00","updated_at":"2026-07-05T11:34:55.779581+00:00"}