{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:W3FURMH25AZ24B6MODNDDEY4LF","short_pith_number":"pith:W3FURMH2","canonical_record":{"source":{"id":"1503.08569","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-03-30T07:13:58Z","cross_cats_sorted":[],"title_canon_sha256":"585915644945bb28445eb9f1406a791b84c8c51ec48fe23aefaafa5092ee40c6","abstract_canon_sha256":"8cedae4ae0c716c03984ece6b35579c48003c8f5fbb18b1fb2e5e237ded121c1"},"schema_version":"1.0"},"canonical_sha256":"b6cb48b0fae833ae07cc70da31931c596399871f259ceac9c5747806823453d9","source":{"kind":"arxiv","id":"1503.08569","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.08569","created_at":"2026-05-18T02:20:01Z"},{"alias_kind":"arxiv_version","alias_value":"1503.08569v1","created_at":"2026-05-18T02:20:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08569","created_at":"2026-05-18T02:20:01Z"},{"alias_kind":"pith_short_12","alias_value":"W3FURMH25AZ2","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"W3FURMH25AZ24B6M","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"W3FURMH2","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:W3FURMH25AZ24B6MODNDDEY4LF","target":"record","payload":{"canonical_record":{"source":{"id":"1503.08569","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-03-30T07:13:58Z","cross_cats_sorted":[],"title_canon_sha256":"585915644945bb28445eb9f1406a791b84c8c51ec48fe23aefaafa5092ee40c6","abstract_canon_sha256":"8cedae4ae0c716c03984ece6b35579c48003c8f5fbb18b1fb2e5e237ded121c1"},"schema_version":"1.0"},"canonical_sha256":"b6cb48b0fae833ae07cc70da31931c596399871f259ceac9c5747806823453d9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:01.382971Z","signature_b64":"znQ0Z+f0qfMYBUDtvvfxQQ3bYapJze5UGDZ7LyRaYX7tR0AuUjPslDf6TA/E+1FOQvc2+DjXm4JoPqwViKxsAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6cb48b0fae833ae07cc70da31931c596399871f259ceac9c5747806823453d9","last_reissued_at":"2026-05-18T02:20:01.382419Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:01.382419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.08569","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":"2026-05-18T02:20:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BGyCMuffGY+ztttc8JgkcqgsnsSFN35qOUHSF6GCIm+2/VW7CHOT3Pzjc8fhIXJL/4qyfGJK57B+S1uc9uNtDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:51:45.557998Z"},"content_sha256":"1f362fe1d347efbcf62fcc10b1fe85cfc5d4c602447846b3cac1c53a152b0e85","schema_version":"1.0","event_id":"sha256:1f362fe1d347efbcf62fcc10b1fe85cfc5d4c602447846b3cac1c53a152b0e85"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:W3FURMH25AZ24B6MODNDDEY4LF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convolution estimates for measures on some complex curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Hyunuk Chung, Seheon Ham","submitted_at":"2015-03-30T07:13:58Z","abstract_excerpt":"We consider the convolution operator for a measure supported on complex curves. The measure which we consider here is an analogue of the affine arclength measure for real curves. By modifying a combinatorial argument called the band structure argument, we prove the (nearly) optimal Lorentz space estimates. This includes the optimal strong type estimates as special cases. The complex curves we consider here are the ones considered for the Fourier restriction estimates for complex curves in \\cite{BH}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08569","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":""},"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":"2026-05-18T02:20:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OTpvHaBw45/6M9oaJlt1t+HoTQU35RKDB4iu+m+kL/FKnelm1OxaVlEFtbBfbOZJR7r4dDp+5p7+Yb/XVoTiCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:51:45.558667Z"},"content_sha256":"71a6fd219d464c05ba42bb3f4a22eeddc822ae4692cb257d76b3dd7933e73cfb","schema_version":"1.0","event_id":"sha256:71a6fd219d464c05ba42bb3f4a22eeddc822ae4692cb257d76b3dd7933e73cfb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W3FURMH25AZ24B6MODNDDEY4LF/bundle.json","state_url":"https://pith.science/pith/W3FURMH25AZ24B6MODNDDEY4LF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W3FURMH25AZ24B6MODNDDEY4LF/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":"2026-05-31T06:51:45Z","links":{"resolver":"https://pith.science/pith/W3FURMH25AZ24B6MODNDDEY4LF","bundle":"https://pith.science/pith/W3FURMH25AZ24B6MODNDDEY4LF/bundle.json","state":"https://pith.science/pith/W3FURMH25AZ24B6MODNDDEY4LF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W3FURMH25AZ24B6MODNDDEY4LF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:W3FURMH25AZ24B6MODNDDEY4LF","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":"8cedae4ae0c716c03984ece6b35579c48003c8f5fbb18b1fb2e5e237ded121c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-03-30T07:13:58Z","title_canon_sha256":"585915644945bb28445eb9f1406a791b84c8c51ec48fe23aefaafa5092ee40c6"},"schema_version":"1.0","source":{"id":"1503.08569","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.08569","created_at":"2026-05-18T02:20:01Z"},{"alias_kind":"arxiv_version","alias_value":"1503.08569v1","created_at":"2026-05-18T02:20:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08569","created_at":"2026-05-18T02:20:01Z"},{"alias_kind":"pith_short_12","alias_value":"W3FURMH25AZ2","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"W3FURMH25AZ24B6M","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"W3FURMH2","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:71a6fd219d464c05ba42bb3f4a22eeddc822ae4692cb257d76b3dd7933e73cfb","target":"graph","created_at":"2026-05-18T02:20:01Z","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"},"paper":{"abstract_excerpt":"We consider the convolution operator for a measure supported on complex curves. The measure which we consider here is an analogue of the affine arclength measure for real curves. By modifying a combinatorial argument called the band structure argument, we prove the (nearly) optimal Lorentz space estimates. This includes the optimal strong type estimates as special cases. The complex curves we consider here are the ones considered for the Fourier restriction estimates for complex curves in \\cite{BH}.","authors_text":"Hyunuk Chung, Seheon Ham","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-03-30T07:13:58Z","title":"Convolution estimates for measures on some complex curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08569","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":"sha256:1f362fe1d347efbcf62fcc10b1fe85cfc5d4c602447846b3cac1c53a152b0e85","target":"record","created_at":"2026-05-18T02:20:01Z","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":"8cedae4ae0c716c03984ece6b35579c48003c8f5fbb18b1fb2e5e237ded121c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-03-30T07:13:58Z","title_canon_sha256":"585915644945bb28445eb9f1406a791b84c8c51ec48fe23aefaafa5092ee40c6"},"schema_version":"1.0","source":{"id":"1503.08569","kind":"arxiv","version":1}},"canonical_sha256":"b6cb48b0fae833ae07cc70da31931c596399871f259ceac9c5747806823453d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6cb48b0fae833ae07cc70da31931c596399871f259ceac9c5747806823453d9","first_computed_at":"2026-05-18T02:20:01.382419Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:01.382419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"znQ0Z+f0qfMYBUDtvvfxQQ3bYapJze5UGDZ7LyRaYX7tR0AuUjPslDf6TA/E+1FOQvc2+DjXm4JoPqwViKxsAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:01.382971Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.08569","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f362fe1d347efbcf62fcc10b1fe85cfc5d4c602447846b3cac1c53a152b0e85","sha256:71a6fd219d464c05ba42bb3f4a22eeddc822ae4692cb257d76b3dd7933e73cfb"],"state_sha256":"5316501a714ec3733291a233276bb004aebfb286e215681eca398e9b2b63fa56"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d/BX90ADWmrrDiv86of66nR5OXxQLciQ8fmBQrgY/74fLQMRfonbTeBHQy6ZX0n5HyO/E+VC5xhu4EvIblejBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T06:51:45.565665Z","bundle_sha256":"d445a6079c76236159e424985147bf1b15cd41ad84e3ac276267587dbc5b7214"}}