{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:64ZHPPQLHC6XKOXQKEQGB2LDMY","short_pith_number":"pith:64ZHPPQL","canonical_record":{"source":{"id":"1111.7212","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-30T15:39:31Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"5e9a97ab658de045a1c03ba40796f4864e20a66d579143999ccdf2ffaf336f76","abstract_canon_sha256":"56f15e5c08b97307c28f9fc9880ff686b6a397b4b51854e58a0594647b2fa416"},"schema_version":"1.0"},"canonical_sha256":"f73277be0b38bd753af0512060e963663319206628854b007edd8eaae802420b","source":{"kind":"arxiv","id":"1111.7212","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.7212","created_at":"2026-05-18T01:09:25Z"},{"alias_kind":"arxiv_version","alias_value":"1111.7212v1","created_at":"2026-05-18T01:09:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.7212","created_at":"2026-05-18T01:09:25Z"},{"alias_kind":"pith_short_12","alias_value":"64ZHPPQLHC6X","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"64ZHPPQLHC6XKOXQ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"64ZHPPQL","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:64ZHPPQLHC6XKOXQKEQGB2LDMY","target":"record","payload":{"canonical_record":{"source":{"id":"1111.7212","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-30T15:39:31Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"5e9a97ab658de045a1c03ba40796f4864e20a66d579143999ccdf2ffaf336f76","abstract_canon_sha256":"56f15e5c08b97307c28f9fc9880ff686b6a397b4b51854e58a0594647b2fa416"},"schema_version":"1.0"},"canonical_sha256":"f73277be0b38bd753af0512060e963663319206628854b007edd8eaae802420b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:25.160189Z","signature_b64":"83kpqaK2dyu+BJgTxERce4ZKXhQhbOELlKTPkMICb6NPD152Gd8FDw4X2aKTpGm6MFWu0eg/pMM9ZIVsxVR+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f73277be0b38bd753af0512060e963663319206628854b007edd8eaae802420b","last_reissued_at":"2026-05-18T01:09:25.159593Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:25.159593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.7212","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":"2026-05-18T01:09:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4pRbrpfcfbSBd4DxPl7HmOKKDiUU4ybqnHqksQg1sfnmti/rtWOYra2+P8GMiVNDpJjVXiuJDhprXkF++LunBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:30:48.840662Z"},"content_sha256":"7f62714d7646df89cbccf764fcb9da9df5fee2ad3bfb9474cac69f716594b43f","schema_version":"1.0","event_id":"sha256:7f62714d7646df89cbccf764fcb9da9df5fee2ad3bfb9474cac69f716594b43f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:64ZHPPQLHC6XKOXQKEQGB2LDMY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Martingales and Sharp Bounds for Fourier multipliers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Adam O\\c{e}kowski, Rodrigo Ba\\~nuelos","submitted_at":"2011-11-30T15:39:31Z","abstract_excerpt":"Using the argument of Geiss, Montgomery-Smith and Saksman \\cite{GMSS}, and a new martingale inequality, the $L^p$--norms of certain Fourier multipliers in $\\R^d$, $d\\geq 2$, are identified. These include, among others, the second order Riesz transforms $R_j^2$, $j=1, 2,..., d$, and some of the L\\'evy multipliers studied in \\cite{BBB}, \\cite{BB}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.7212","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":"2026-05-18T01:09:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r53DmgMgdTaf8gqOcq5YL6/6Y/jdLIw6oKIi1f6WSNrKEE/3X/4JpLEJ2RBr64wuVstgTMufJopX06m8vvlUAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:30:48.840999Z"},"content_sha256":"4f0c9ccbfb71acd9657ec3c54e2bb0e38cb4f5a193473ae5f24c2ef910793d97","schema_version":"1.0","event_id":"sha256:4f0c9ccbfb71acd9657ec3c54e2bb0e38cb4f5a193473ae5f24c2ef910793d97"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/64ZHPPQLHC6XKOXQKEQGB2LDMY/bundle.json","state_url":"https://pith.science/pith/64ZHPPQLHC6XKOXQKEQGB2LDMY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/64ZHPPQLHC6XKOXQKEQGB2LDMY/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":"2026-06-01T08:30:48Z","links":{"resolver":"https://pith.science/pith/64ZHPPQLHC6XKOXQKEQGB2LDMY","bundle":"https://pith.science/pith/64ZHPPQLHC6XKOXQKEQGB2LDMY/bundle.json","state":"https://pith.science/pith/64ZHPPQLHC6XKOXQKEQGB2LDMY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/64ZHPPQLHC6XKOXQKEQGB2LDMY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:64ZHPPQLHC6XKOXQKEQGB2LDMY","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":"56f15e5c08b97307c28f9fc9880ff686b6a397b4b51854e58a0594647b2fa416","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-30T15:39:31Z","title_canon_sha256":"5e9a97ab658de045a1c03ba40796f4864e20a66d579143999ccdf2ffaf336f76"},"schema_version":"1.0","source":{"id":"1111.7212","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.7212","created_at":"2026-05-18T01:09:25Z"},{"alias_kind":"arxiv_version","alias_value":"1111.7212v1","created_at":"2026-05-18T01:09:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.7212","created_at":"2026-05-18T01:09:25Z"},{"alias_kind":"pith_short_12","alias_value":"64ZHPPQLHC6X","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"64ZHPPQLHC6XKOXQ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"64ZHPPQL","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:4f0c9ccbfb71acd9657ec3c54e2bb0e38cb4f5a193473ae5f24c2ef910793d97","target":"graph","created_at":"2026-05-18T01:09:25Z","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":"Using the argument of Geiss, Montgomery-Smith and Saksman \\cite{GMSS}, and a new martingale inequality, the $L^p$--norms of certain Fourier multipliers in $\\R^d$, $d\\geq 2$, are identified. These include, among others, the second order Riesz transforms $R_j^2$, $j=1, 2,..., d$, and some of the L\\'evy multipliers studied in \\cite{BBB}, \\cite{BB}","authors_text":"Adam O\\c{e}kowski, Rodrigo Ba\\~nuelos","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-30T15:39:31Z","title":"Martingales and Sharp Bounds for Fourier multipliers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.7212","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":"sha256:7f62714d7646df89cbccf764fcb9da9df5fee2ad3bfb9474cac69f716594b43f","target":"record","created_at":"2026-05-18T01:09:25Z","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":"56f15e5c08b97307c28f9fc9880ff686b6a397b4b51854e58a0594647b2fa416","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-30T15:39:31Z","title_canon_sha256":"5e9a97ab658de045a1c03ba40796f4864e20a66d579143999ccdf2ffaf336f76"},"schema_version":"1.0","source":{"id":"1111.7212","kind":"arxiv","version":1}},"canonical_sha256":"f73277be0b38bd753af0512060e963663319206628854b007edd8eaae802420b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f73277be0b38bd753af0512060e963663319206628854b007edd8eaae802420b","first_computed_at":"2026-05-18T01:09:25.159593Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:25.159593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"83kpqaK2dyu+BJgTxERce4ZKXhQhbOELlKTPkMICb6NPD152Gd8FDw4X2aKTpGm6MFWu0eg/pMM9ZIVsxVR+CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:25.160189Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.7212","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f62714d7646df89cbccf764fcb9da9df5fee2ad3bfb9474cac69f716594b43f","sha256:4f0c9ccbfb71acd9657ec3c54e2bb0e38cb4f5a193473ae5f24c2ef910793d97"],"state_sha256":"3ff45e620cf681db9b77dcc470e26e0573c17b1d374a6262b54bedf942114ca5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UhR6t/aoEfRZcwbn9NHL5sUVlqm0QswYV4IoS9z6JLhxlxkyW3VaNkZcvvZZeu18jENckqKphxPprX21Js5cCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T08:30:48.842873Z","bundle_sha256":"6c429461a1926f786c20a2924830fbdbcbc870574d546d52e315bd072bcd0950"}}