{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:L2ZNBSA5YNCZXXGZBQFP2HN3OV","short_pith_number":"pith:L2ZNBSA5","canonical_record":{"source":{"id":"2505.04517","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-05-07T15:44:38Z","cross_cats_sorted":[],"title_canon_sha256":"8ea1f6456511173be9d3e723c5f70e86e5bb41e8ee313be2cba477d6620c0638","abstract_canon_sha256":"b860465061f64b6cec808c88eda0e06e488efa6716d1be531f720cb835404718"},"schema_version":"1.0"},"canonical_sha256":"5eb2d0c81dc3459bdcd90c0afd1dbb756cc3ff0e57d1c704c4d1459de5470ca7","source":{"kind":"arxiv","id":"2505.04517","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.04517","created_at":"2026-07-05T10:59:52Z"},{"alias_kind":"arxiv_version","alias_value":"2505.04517v1","created_at":"2026-07-05T10:59:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.04517","created_at":"2026-07-05T10:59:52Z"},{"alias_kind":"pith_short_12","alias_value":"L2ZNBSA5YNCZ","created_at":"2026-07-05T10:59:52Z"},{"alias_kind":"pith_short_16","alias_value":"L2ZNBSA5YNCZXXGZ","created_at":"2026-07-05T10:59:52Z"},{"alias_kind":"pith_short_8","alias_value":"L2ZNBSA5","created_at":"2026-07-05T10:59:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:L2ZNBSA5YNCZXXGZBQFP2HN3OV","target":"record","payload":{"canonical_record":{"source":{"id":"2505.04517","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-05-07T15:44:38Z","cross_cats_sorted":[],"title_canon_sha256":"8ea1f6456511173be9d3e723c5f70e86e5bb41e8ee313be2cba477d6620c0638","abstract_canon_sha256":"b860465061f64b6cec808c88eda0e06e488efa6716d1be531f720cb835404718"},"schema_version":"1.0"},"canonical_sha256":"5eb2d0c81dc3459bdcd90c0afd1dbb756cc3ff0e57d1c704c4d1459de5470ca7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:59:52.878091Z","signature_b64":"0mSQlNLPlrf5Ww0I7Q0poh7gr7toBtxycv68xo70K5tu4VjYOCvWg6Gbpl1HAU/SwTwMGLlHbt+fSS5vzRF2CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5eb2d0c81dc3459bdcd90c0afd1dbb756cc3ff0e57d1c704c4d1459de5470ca7","last_reissued_at":"2026-07-05T10:59:52.877612Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:59:52.877612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.04517","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":"2026-07-05T10:59:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U5FIf/QkqODbGu6vrxHMiDoT1tHgWrsNVjY10pvgWLN4F4U/kt8nCmrSWG2ncxTNKaP4Y/W9VqRamn+9LbK5Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T22:46:55.252282Z"},"content_sha256":"dd16d64af387072ff45d1839d2af000e998b2dabdfa0b6301ba50b74bd119998","schema_version":"1.0","event_id":"sha256:dd16d64af387072ff45d1839d2af000e998b2dabdfa0b6301ba50b74bd119998"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:L2ZNBSA5YNCZXXGZBQFP2HN3OV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on bilinear multipliers with convex singularities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Valentina Ciccone","submitted_at":"2025-05-07T15:44:38Z","abstract_excerpt":"We study bounds in the local $L^2$ range of exponents for bilinear multipliers whose symbol is the characteristic function of the epigraph of certain convex curves. We realize these bounds as a consequence of estimates that we establish, via simple arguments, for the associated exotic paraproducts. As a further application, we observe bounds beyond the local $L^2$ range for bilinear multipliers whose symbol is the characteristic function of the epigraph of convex polygonal curves associated with these paraproducts."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.04517","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/2505.04517/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":"2026-07-05T10:59:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uMus0whhj+1TAoyG+7hE+p5KOb0ifObZLTGUxsjxXktPMj2eKD9iP4gijBcwYk9eYjtDghzsrdRrCPOcvxiFDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T22:46:55.252858Z"},"content_sha256":"637e4c0a65403fa96c213c88866c5d87eec5f2e8fc0a7856a51f675f39da63f1","schema_version":"1.0","event_id":"sha256:637e4c0a65403fa96c213c88866c5d87eec5f2e8fc0a7856a51f675f39da63f1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L2ZNBSA5YNCZXXGZBQFP2HN3OV/bundle.json","state_url":"https://pith.science/pith/L2ZNBSA5YNCZXXGZBQFP2HN3OV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L2ZNBSA5YNCZXXGZBQFP2HN3OV/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":"2026-08-19T22:46:55Z","links":{"resolver":"https://pith.science/pith/L2ZNBSA5YNCZXXGZBQFP2HN3OV","bundle":"https://pith.science/pith/L2ZNBSA5YNCZXXGZBQFP2HN3OV/bundle.json","state":"https://pith.science/pith/L2ZNBSA5YNCZXXGZBQFP2HN3OV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L2ZNBSA5YNCZXXGZBQFP2HN3OV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:L2ZNBSA5YNCZXXGZBQFP2HN3OV","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":"b860465061f64b6cec808c88eda0e06e488efa6716d1be531f720cb835404718","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-05-07T15:44:38Z","title_canon_sha256":"8ea1f6456511173be9d3e723c5f70e86e5bb41e8ee313be2cba477d6620c0638"},"schema_version":"1.0","source":{"id":"2505.04517","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.04517","created_at":"2026-07-05T10:59:52Z"},{"alias_kind":"arxiv_version","alias_value":"2505.04517v1","created_at":"2026-07-05T10:59:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.04517","created_at":"2026-07-05T10:59:52Z"},{"alias_kind":"pith_short_12","alias_value":"L2ZNBSA5YNCZ","created_at":"2026-07-05T10:59:52Z"},{"alias_kind":"pith_short_16","alias_value":"L2ZNBSA5YNCZXXGZ","created_at":"2026-07-05T10:59:52Z"},{"alias_kind":"pith_short_8","alias_value":"L2ZNBSA5","created_at":"2026-07-05T10:59:52Z"}],"graph_snapshots":[{"event_id":"sha256:637e4c0a65403fa96c213c88866c5d87eec5f2e8fc0a7856a51f675f39da63f1","target":"graph","created_at":"2026-07-05T10:59:52Z","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/2505.04517/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study bounds in the local $L^2$ range of exponents for bilinear multipliers whose symbol is the characteristic function of the epigraph of certain convex curves. We realize these bounds as a consequence of estimates that we establish, via simple arguments, for the associated exotic paraproducts. As a further application, we observe bounds beyond the local $L^2$ range for bilinear multipliers whose symbol is the characteristic function of the epigraph of convex polygonal curves associated with these paraproducts.","authors_text":"Valentina Ciccone","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-05-07T15:44:38Z","title":"A note on bilinear multipliers with convex singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.04517","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:dd16d64af387072ff45d1839d2af000e998b2dabdfa0b6301ba50b74bd119998","target":"record","created_at":"2026-07-05T10:59:52Z","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":"b860465061f64b6cec808c88eda0e06e488efa6716d1be531f720cb835404718","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2025-05-07T15:44:38Z","title_canon_sha256":"8ea1f6456511173be9d3e723c5f70e86e5bb41e8ee313be2cba477d6620c0638"},"schema_version":"1.0","source":{"id":"2505.04517","kind":"arxiv","version":1}},"canonical_sha256":"5eb2d0c81dc3459bdcd90c0afd1dbb756cc3ff0e57d1c704c4d1459de5470ca7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5eb2d0c81dc3459bdcd90c0afd1dbb756cc3ff0e57d1c704c4d1459de5470ca7","first_computed_at":"2026-07-05T10:59:52.877612Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:59:52.877612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0mSQlNLPlrf5Ww0I7Q0poh7gr7toBtxycv68xo70K5tu4VjYOCvWg6Gbpl1HAU/SwTwMGLlHbt+fSS5vzRF2CA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:59:52.878091Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.04517","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd16d64af387072ff45d1839d2af000e998b2dabdfa0b6301ba50b74bd119998","sha256:637e4c0a65403fa96c213c88866c5d87eec5f2e8fc0a7856a51f675f39da63f1"],"state_sha256":"ca6374b6971a339505f45ae12e710650966399cea110beecf86327dddaa68da9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wmKLhIn7znu/b+xgrhTJ7XhvYkGfNrpVbq8WewAEIYKW/MO8cXRruEZ7uw1Th3gO+Whf++n1rMUQOntO3Pj4Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T22:46:55.258838Z","bundle_sha256":"d0802130da45f8d98135d7c70c4284998a7717c2001ca89b480f5ea7f66b8ef5"}}