{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:AXIRGFBWO33XNUXJFJ34J7WYTI","short_pith_number":"pith:AXIRGFBW","canonical_record":{"source":{"id":"2410.23080","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-10-30T14:54:07Z","cross_cats_sorted":[],"title_canon_sha256":"2a8b4dd293fd654a3ac77108b23e721f1ff23732762ecff0099a25529669aea7","abstract_canon_sha256":"d8076f7702f119eeb591acba46babf9d3853434a938c83a1f207c4e53ac7365a"},"schema_version":"1.0"},"canonical_sha256":"05d113143676f776d2e92a77c4fed89a0c27fdcfac6cfb058c6bd013e1a97c63","source":{"kind":"arxiv","id":"2410.23080","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.23080","created_at":"2026-07-05T09:28:40Z"},{"alias_kind":"arxiv_version","alias_value":"2410.23080v1","created_at":"2026-07-05T09:28:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.23080","created_at":"2026-07-05T09:28:40Z"},{"alias_kind":"pith_short_12","alias_value":"AXIRGFBWO33X","created_at":"2026-07-05T09:28:40Z"},{"alias_kind":"pith_short_16","alias_value":"AXIRGFBWO33XNUXJ","created_at":"2026-07-05T09:28:40Z"},{"alias_kind":"pith_short_8","alias_value":"AXIRGFBW","created_at":"2026-07-05T09:28:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:AXIRGFBWO33XNUXJFJ34J7WYTI","target":"record","payload":{"canonical_record":{"source":{"id":"2410.23080","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-10-30T14:54:07Z","cross_cats_sorted":[],"title_canon_sha256":"2a8b4dd293fd654a3ac77108b23e721f1ff23732762ecff0099a25529669aea7","abstract_canon_sha256":"d8076f7702f119eeb591acba46babf9d3853434a938c83a1f207c4e53ac7365a"},"schema_version":"1.0"},"canonical_sha256":"05d113143676f776d2e92a77c4fed89a0c27fdcfac6cfb058c6bd013e1a97c63","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:28:40.777751Z","signature_b64":"sBDVhtfRbtXQZhH5CAkHARRZ+X9iTo/8hVF/gYSc/2afXFOt6+L2n0cnDFJR3Dl1os5xcG5A/uEeNtAbpLzDDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05d113143676f776d2e92a77c4fed89a0c27fdcfac6cfb058c6bd013e1a97c63","last_reissued_at":"2026-07-05T09:28:40.777304Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:28:40.777304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.23080","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":"2026-07-05T09:28:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Qmusab8kKp9XkwyyrEFj5VNEvLaYzBSIn02tWNHPN4dbsrHEk4KedSuphcjdOULla04AR6uGbGLlSFAVuENDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:23:46.812724Z"},"content_sha256":"26667b0d1265a8dcd02c11c49df4f5af6f0f34aaec22896b71168f1625119b33","schema_version":"1.0","event_id":"sha256:26667b0d1265a8dcd02c11c49df4f5af6f0f34aaec22896b71168f1625119b33"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:AXIRGFBWO33XNUXJFJ34J7WYTI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On bounded energy of convolution of fractal measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Guangzeng Yi","submitted_at":"2024-10-30T14:54:07Z","abstract_excerpt":"For all $s\\in[0,1]$ and $t\\in(0,s]\\cup [2-s,2)$, we find the supremum of numbers $\\omega\\in(0,2)$ such that $\\text{I}_\\omega(\\mu\\ast\\sigma) \\lesssim 1$, where $\\mu$ is any Borel measure on $B(1)$ with $\\text{I}_t(\\mu)\\leq 1$ and $\\sigma$ is any $(s,1)$-Frostman measure on a $C^2$-graph with non-zero curvature. As an application, we use this to show the sharp $L^6$-decay of Fourier transform of $\\sigma$ when $s\\in [\\frac{2}{3}, 1]$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.23080","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/2410.23080/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":"2026-07-05T09:28:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I3uiJHqjzcipcbciV+3ULz3JCxFuuEPClU6voDh4DxXGd8OCZyhHwtfOzd4V07JjcBDgLmzUVB9tLgCp7hV5AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:23:46.813273Z"},"content_sha256":"a54bd482d4bde18115253391dad357fd1536108a1c7793ffa01cebddb1051170","schema_version":"1.0","event_id":"sha256:a54bd482d4bde18115253391dad357fd1536108a1c7793ffa01cebddb1051170"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AXIRGFBWO33XNUXJFJ34J7WYTI/bundle.json","state_url":"https://pith.science/pith/AXIRGFBWO33XNUXJFJ34J7WYTI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AXIRGFBWO33XNUXJFJ34J7WYTI/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":"2026-08-09T07:23:46Z","links":{"resolver":"https://pith.science/pith/AXIRGFBWO33XNUXJFJ34J7WYTI","bundle":"https://pith.science/pith/AXIRGFBWO33XNUXJFJ34J7WYTI/bundle.json","state":"https://pith.science/pith/AXIRGFBWO33XNUXJFJ34J7WYTI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AXIRGFBWO33XNUXJFJ34J7WYTI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:AXIRGFBWO33XNUXJFJ34J7WYTI","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":"d8076f7702f119eeb591acba46babf9d3853434a938c83a1f207c4e53ac7365a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-10-30T14:54:07Z","title_canon_sha256":"2a8b4dd293fd654a3ac77108b23e721f1ff23732762ecff0099a25529669aea7"},"schema_version":"1.0","source":{"id":"2410.23080","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.23080","created_at":"2026-07-05T09:28:40Z"},{"alias_kind":"arxiv_version","alias_value":"2410.23080v1","created_at":"2026-07-05T09:28:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.23080","created_at":"2026-07-05T09:28:40Z"},{"alias_kind":"pith_short_12","alias_value":"AXIRGFBWO33X","created_at":"2026-07-05T09:28:40Z"},{"alias_kind":"pith_short_16","alias_value":"AXIRGFBWO33XNUXJ","created_at":"2026-07-05T09:28:40Z"},{"alias_kind":"pith_short_8","alias_value":"AXIRGFBW","created_at":"2026-07-05T09:28:40Z"}],"graph_snapshots":[{"event_id":"sha256:a54bd482d4bde18115253391dad357fd1536108a1c7793ffa01cebddb1051170","target":"graph","created_at":"2026-07-05T09:28:40Z","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/2410.23080/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For all $s\\in[0,1]$ and $t\\in(0,s]\\cup [2-s,2)$, we find the supremum of numbers $\\omega\\in(0,2)$ such that $\\text{I}_\\omega(\\mu\\ast\\sigma) \\lesssim 1$, where $\\mu$ is any Borel measure on $B(1)$ with $\\text{I}_t(\\mu)\\leq 1$ and $\\sigma$ is any $(s,1)$-Frostman measure on a $C^2$-graph with non-zero curvature. As an application, we use this to show the sharp $L^6$-decay of Fourier transform of $\\sigma$ when $s\\in [\\frac{2}{3}, 1]$.","authors_text":"Guangzeng Yi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-10-30T14:54:07Z","title":"On bounded energy of convolution of fractal measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.23080","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":"sha256:26667b0d1265a8dcd02c11c49df4f5af6f0f34aaec22896b71168f1625119b33","target":"record","created_at":"2026-07-05T09:28:40Z","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":"d8076f7702f119eeb591acba46babf9d3853434a938c83a1f207c4e53ac7365a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-10-30T14:54:07Z","title_canon_sha256":"2a8b4dd293fd654a3ac77108b23e721f1ff23732762ecff0099a25529669aea7"},"schema_version":"1.0","source":{"id":"2410.23080","kind":"arxiv","version":1}},"canonical_sha256":"05d113143676f776d2e92a77c4fed89a0c27fdcfac6cfb058c6bd013e1a97c63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05d113143676f776d2e92a77c4fed89a0c27fdcfac6cfb058c6bd013e1a97c63","first_computed_at":"2026-07-05T09:28:40.777304Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:28:40.777304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sBDVhtfRbtXQZhH5CAkHARRZ+X9iTo/8hVF/gYSc/2afXFOt6+L2n0cnDFJR3Dl1os5xcG5A/uEeNtAbpLzDDg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:28:40.777751Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.23080","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26667b0d1265a8dcd02c11c49df4f5af6f0f34aaec22896b71168f1625119b33","sha256:a54bd482d4bde18115253391dad357fd1536108a1c7793ffa01cebddb1051170"],"state_sha256":"00a2ecaff9a3fa37f33e07c1745a6912c3ee68bf1cac8de6809dda16a7a3bb2f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zvLi0a11QWvcO2EodrclTiVqXyrQSMjHN7Llq4taBL2VOIJcPmP2kCsM0gU71I6kF8Al3NBnsmQ4OMv3GgOLAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T07:23:46.816892Z","bundle_sha256":"b1b3394249538dcfb837fb8a837bbea1e42c3b9de402b86dd1d2427f11178a3f"}}