{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:M2SY2XKW7OCP5BMW7PGR3543VI","short_pith_number":"pith:M2SY2XKW","canonical_record":{"source":{"id":"1510.01897","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-07T11:21:13Z","cross_cats_sorted":[],"title_canon_sha256":"afa2607b8b856d338cdd74b2086ff5c729a518ea3e86addd5f1040f5ab90650a","abstract_canon_sha256":"0f310bf65e3fe0db89140544bbb2441e040d04860d8034e461863bda638a1726"},"schema_version":"1.0"},"canonical_sha256":"66a58d5d56fb84fe8596fbcd1df79baa0800234aeb7795d01bcb797c545007cf","source":{"kind":"arxiv","id":"1510.01897","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.01897","created_at":"2026-05-18T00:54:48Z"},{"alias_kind":"arxiv_version","alias_value":"1510.01897v2","created_at":"2026-05-18T00:54:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01897","created_at":"2026-05-18T00:54:48Z"},{"alias_kind":"pith_short_12","alias_value":"M2SY2XKW7OCP","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"M2SY2XKW7OCP5BMW","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"M2SY2XKW","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:M2SY2XKW7OCP5BMW7PGR3543VI","target":"record","payload":{"canonical_record":{"source":{"id":"1510.01897","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-07T11:21:13Z","cross_cats_sorted":[],"title_canon_sha256":"afa2607b8b856d338cdd74b2086ff5c729a518ea3e86addd5f1040f5ab90650a","abstract_canon_sha256":"0f310bf65e3fe0db89140544bbb2441e040d04860d8034e461863bda638a1726"},"schema_version":"1.0"},"canonical_sha256":"66a58d5d56fb84fe8596fbcd1df79baa0800234aeb7795d01bcb797c545007cf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:48.111137Z","signature_b64":"+0qj/5g/eIgRQ6QC+yWUNPDcoXS1Et1skeruspz6WAJiW98dX6X3wugElKHFRzaso33zcKOTh9SHaEQPJ+PqDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66a58d5d56fb84fe8596fbcd1df79baa0800234aeb7795d01bcb797c545007cf","last_reissued_at":"2026-05-18T00:54:48.110561Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:48.110561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.01897","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:54:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NR5GfDkzib4VFpINP42UQpKjZgHIKS+euJw1RMly0LHSLb0uB9sQKxKguLH+13l1Zhfc0cBo76A3frqkvX52CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:48:12.810730Z"},"content_sha256":"918a297bc7f14fdcf05b805b2c4b81425ef5af672cbff98ef53ecba80ba41b79","schema_version":"1.0","event_id":"sha256:918a297bc7f14fdcf05b805b2c4b81425ef5af672cbff98ef53ecba80ba41b79"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:M2SY2XKW7OCP5BMW7PGR3543VI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Subdyadic square functions and applications to weighted harmonic analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"David Beltran, Jonathan Bennett","submitted_at":"2015-10-07T11:21:13Z","abstract_excerpt":"Through the study of novel variants of the classical Littlewood-Paley-Stein $g$-functions, we obtain pointwise estimates for broad classes of highly-singular Fourier multipliers on $\\mathbb{R}^d$ satisfying regularity hypotheses adapted to fine (subdyadic) scales. In particular, this allows us to efficiently bound such multipliers by geometrically-defined maximal operators via general weighted $L^2$ inequalities, in the spirit of a well-known conjecture of Stein. Our framework applies to solution operators for dispersive PDE, such as the time-dependent free Schr\\\"odinger equation, and other hi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01897","kind":"arxiv","version":2},"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":"2026-05-18T00:54:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3O9bhR6pU9ULZw0q2vvh1C0HUTcohC4N4uRIBNspu0wD/UrP/wy/z7jkvxdt7ca4IU+jxPiNtuocSKOMIyb/Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:48:12.811469Z"},"content_sha256":"c16df88f8aad7f023c3226bcb1d6c990491d33fb189f67de6341961424e59573","schema_version":"1.0","event_id":"sha256:c16df88f8aad7f023c3226bcb1d6c990491d33fb189f67de6341961424e59573"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M2SY2XKW7OCP5BMW7PGR3543VI/bundle.json","state_url":"https://pith.science/pith/M2SY2XKW7OCP5BMW7PGR3543VI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M2SY2XKW7OCP5BMW7PGR3543VI/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":"2026-05-25T20:48:12Z","links":{"resolver":"https://pith.science/pith/M2SY2XKW7OCP5BMW7PGR3543VI","bundle":"https://pith.science/pith/M2SY2XKW7OCP5BMW7PGR3543VI/bundle.json","state":"https://pith.science/pith/M2SY2XKW7OCP5BMW7PGR3543VI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M2SY2XKW7OCP5BMW7PGR3543VI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:M2SY2XKW7OCP5BMW7PGR3543VI","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":"0f310bf65e3fe0db89140544bbb2441e040d04860d8034e461863bda638a1726","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-07T11:21:13Z","title_canon_sha256":"afa2607b8b856d338cdd74b2086ff5c729a518ea3e86addd5f1040f5ab90650a"},"schema_version":"1.0","source":{"id":"1510.01897","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.01897","created_at":"2026-05-18T00:54:48Z"},{"alias_kind":"arxiv_version","alias_value":"1510.01897v2","created_at":"2026-05-18T00:54:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01897","created_at":"2026-05-18T00:54:48Z"},{"alias_kind":"pith_short_12","alias_value":"M2SY2XKW7OCP","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"M2SY2XKW7OCP5BMW","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"M2SY2XKW","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:c16df88f8aad7f023c3226bcb1d6c990491d33fb189f67de6341961424e59573","target":"graph","created_at":"2026-05-18T00:54:48Z","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":"Through the study of novel variants of the classical Littlewood-Paley-Stein $g$-functions, we obtain pointwise estimates for broad classes of highly-singular Fourier multipliers on $\\mathbb{R}^d$ satisfying regularity hypotheses adapted to fine (subdyadic) scales. In particular, this allows us to efficiently bound such multipliers by geometrically-defined maximal operators via general weighted $L^2$ inequalities, in the spirit of a well-known conjecture of Stein. Our framework applies to solution operators for dispersive PDE, such as the time-dependent free Schr\\\"odinger equation, and other hi","authors_text":"David Beltran, Jonathan Bennett","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-07T11:21:13Z","title":"Subdyadic square functions and applications to weighted harmonic analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01897","kind":"arxiv","version":2},"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":"sha256:918a297bc7f14fdcf05b805b2c4b81425ef5af672cbff98ef53ecba80ba41b79","target":"record","created_at":"2026-05-18T00:54:48Z","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":"0f310bf65e3fe0db89140544bbb2441e040d04860d8034e461863bda638a1726","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-07T11:21:13Z","title_canon_sha256":"afa2607b8b856d338cdd74b2086ff5c729a518ea3e86addd5f1040f5ab90650a"},"schema_version":"1.0","source":{"id":"1510.01897","kind":"arxiv","version":2}},"canonical_sha256":"66a58d5d56fb84fe8596fbcd1df79baa0800234aeb7795d01bcb797c545007cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66a58d5d56fb84fe8596fbcd1df79baa0800234aeb7795d01bcb797c545007cf","first_computed_at":"2026-05-18T00:54:48.110561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:48.110561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+0qj/5g/eIgRQ6QC+yWUNPDcoXS1Et1skeruspz6WAJiW98dX6X3wugElKHFRzaso33zcKOTh9SHaEQPJ+PqDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:48.111137Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.01897","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:918a297bc7f14fdcf05b805b2c4b81425ef5af672cbff98ef53ecba80ba41b79","sha256:c16df88f8aad7f023c3226bcb1d6c990491d33fb189f67de6341961424e59573"],"state_sha256":"1663352eae171df4a551ab1684121f1117e658bd94df51170c8f5aaf49feccb2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7/62q6v2U1p1kw6iQiq+r61efJfgSnme3mFR5d2btIBvMd5f3sgdFbdQCnG2An5f2AD5tQlMIG1KOuaNb34bBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T20:48:12.816117Z","bundle_sha256":"43a10151f4e5602d12e5764248175affaa23766ab0ce4bb35e48cec3a5594ca9"}}