{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:7EBJP6IIZYLA2TJQ52SA7CLWUS","short_pith_number":"pith:7EBJP6II","canonical_record":{"source":{"id":"2002.11758","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2020-02-26T19:37:22Z","cross_cats_sorted":[],"title_canon_sha256":"e4095383a649b6c08014cedc6dbcea6283c0ddb3952a31ec9091f2cf1193b9a4","abstract_canon_sha256":"02e91d43b09878c885fdf61dab2b2aeab725ddcde9a98f6e50b518dd6234e5bd"},"schema_version":"1.0"},"canonical_sha256":"f90297f908ce160d4d30eea40f8976a4ba2d9677d18502f5602f505158c87120","source":{"kind":"arxiv","id":"2002.11758","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.11758","created_at":"2026-07-05T00:44:08Z"},{"alias_kind":"arxiv_version","alias_value":"2002.11758v1","created_at":"2026-07-05T00:44:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.11758","created_at":"2026-07-05T00:44:08Z"},{"alias_kind":"pith_short_12","alias_value":"7EBJP6IIZYLA","created_at":"2026-07-05T00:44:08Z"},{"alias_kind":"pith_short_16","alias_value":"7EBJP6IIZYLA2TJQ","created_at":"2026-07-05T00:44:08Z"},{"alias_kind":"pith_short_8","alias_value":"7EBJP6II","created_at":"2026-07-05T00:44:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:7EBJP6IIZYLA2TJQ52SA7CLWUS","target":"record","payload":{"canonical_record":{"source":{"id":"2002.11758","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2020-02-26T19:37:22Z","cross_cats_sorted":[],"title_canon_sha256":"e4095383a649b6c08014cedc6dbcea6283c0ddb3952a31ec9091f2cf1193b9a4","abstract_canon_sha256":"02e91d43b09878c885fdf61dab2b2aeab725ddcde9a98f6e50b518dd6234e5bd"},"schema_version":"1.0"},"canonical_sha256":"f90297f908ce160d4d30eea40f8976a4ba2d9677d18502f5602f505158c87120","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:44:08.663667Z","signature_b64":"U+gVierpTe5qWRalShF/EFBRzqcX3FYxsPc1hog3Mb2bDQIe/MdKb9ftsxr8HeEdjkJkP/DdHHGkvjTkmaiBDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f90297f908ce160d4d30eea40f8976a4ba2d9677d18502f5602f505158c87120","last_reissued_at":"2026-07-05T00:44:08.663203Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:44:08.663203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2002.11758","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":"2026-07-05T00:44:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d//JbXrV4X8egD/G4uxEPWlKeN2go3Q/7rEpx9dXIwkW6pW9h5U3/vhxI7Z9192lmIQ0LVYAVCBpmQ5BqvQmAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T12:01:46.342336Z"},"content_sha256":"6d103cd56d4db84fd7eee891f18c615438723f74f275b3ead6c8b4032292dc9d","schema_version":"1.0","event_id":"sha256:6d103cd56d4db84fd7eee891f18c615438723f74f275b3ead6c8b4032292dc9d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:7EBJP6IIZYLA2TJQ52SA7CLWUS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp $l^p$-improving estimates for the discrete paraboloid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Bartosz Langowski, Ciprian Demeter, Shival Dasu","submitted_at":"2020-02-26T19:37:22Z","abstract_excerpt":"We prove $l^p$-improving estimates for the averaging operator along the discrete paraboloid in the sharp range of $p$ in all dimensions $n\\ge 2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.11758","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/2002.11758/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":"2026-07-05T00:44:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TYskY6cxp/x6f8kxpdYBXyyIU81UNORLkOankhXcwEznp9P811Abd+WbBXiIBhzpIPMN6oLKVx7VWqMr26leCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T12:01:46.342880Z"},"content_sha256":"12cdb96f00e1a23a4c2da51970488ef39fbdedd7415cbff47f15e76bbaac09f4","schema_version":"1.0","event_id":"sha256:12cdb96f00e1a23a4c2da51970488ef39fbdedd7415cbff47f15e76bbaac09f4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7EBJP6IIZYLA2TJQ52SA7CLWUS/bundle.json","state_url":"https://pith.science/pith/7EBJP6IIZYLA2TJQ52SA7CLWUS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7EBJP6IIZYLA2TJQ52SA7CLWUS/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":"2026-08-20T12:01:46Z","links":{"resolver":"https://pith.science/pith/7EBJP6IIZYLA2TJQ52SA7CLWUS","bundle":"https://pith.science/pith/7EBJP6IIZYLA2TJQ52SA7CLWUS/bundle.json","state":"https://pith.science/pith/7EBJP6IIZYLA2TJQ52SA7CLWUS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7EBJP6IIZYLA2TJQ52SA7CLWUS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:7EBJP6IIZYLA2TJQ52SA7CLWUS","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":"02e91d43b09878c885fdf61dab2b2aeab725ddcde9a98f6e50b518dd6234e5bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2020-02-26T19:37:22Z","title_canon_sha256":"e4095383a649b6c08014cedc6dbcea6283c0ddb3952a31ec9091f2cf1193b9a4"},"schema_version":"1.0","source":{"id":"2002.11758","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.11758","created_at":"2026-07-05T00:44:08Z"},{"alias_kind":"arxiv_version","alias_value":"2002.11758v1","created_at":"2026-07-05T00:44:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.11758","created_at":"2026-07-05T00:44:08Z"},{"alias_kind":"pith_short_12","alias_value":"7EBJP6IIZYLA","created_at":"2026-07-05T00:44:08Z"},{"alias_kind":"pith_short_16","alias_value":"7EBJP6IIZYLA2TJQ","created_at":"2026-07-05T00:44:08Z"},{"alias_kind":"pith_short_8","alias_value":"7EBJP6II","created_at":"2026-07-05T00:44:08Z"}],"graph_snapshots":[{"event_id":"sha256:12cdb96f00e1a23a4c2da51970488ef39fbdedd7415cbff47f15e76bbaac09f4","target":"graph","created_at":"2026-07-05T00:44:08Z","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/2002.11758/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove $l^p$-improving estimates for the averaging operator along the discrete paraboloid in the sharp range of $p$ in all dimensions $n\\ge 2$.","authors_text":"Bartosz Langowski, Ciprian Demeter, Shival Dasu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2020-02-26T19:37:22Z","title":"Sharp $l^p$-improving estimates for the discrete paraboloid"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.11758","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":"sha256:6d103cd56d4db84fd7eee891f18c615438723f74f275b3ead6c8b4032292dc9d","target":"record","created_at":"2026-07-05T00:44:08Z","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":"02e91d43b09878c885fdf61dab2b2aeab725ddcde9a98f6e50b518dd6234e5bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2020-02-26T19:37:22Z","title_canon_sha256":"e4095383a649b6c08014cedc6dbcea6283c0ddb3952a31ec9091f2cf1193b9a4"},"schema_version":"1.0","source":{"id":"2002.11758","kind":"arxiv","version":1}},"canonical_sha256":"f90297f908ce160d4d30eea40f8976a4ba2d9677d18502f5602f505158c87120","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f90297f908ce160d4d30eea40f8976a4ba2d9677d18502f5602f505158c87120","first_computed_at":"2026-07-05T00:44:08.663203Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:44:08.663203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U+gVierpTe5qWRalShF/EFBRzqcX3FYxsPc1hog3Mb2bDQIe/MdKb9ftsxr8HeEdjkJkP/DdHHGkvjTkmaiBDg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:44:08.663667Z","signed_message":"canonical_sha256_bytes"},"source_id":"2002.11758","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d103cd56d4db84fd7eee891f18c615438723f74f275b3ead6c8b4032292dc9d","sha256:12cdb96f00e1a23a4c2da51970488ef39fbdedd7415cbff47f15e76bbaac09f4"],"state_sha256":"8be2bdc0827f9b019a0348979f39dac74a50018e8d9bba7696fcf57a5d3b9d1a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i30k7sGXDKj6BoENfyrMkZaOArlpSlqY3CdfO/vN5aQ3lnoPhQuS1ZcmLT5q7WDvGLivHP8xYd0WNCzXZOw9Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T12:01:46.347663Z","bundle_sha256":"51d84475c446f05ed25a0a0cd6b7059736a613a76833804f363ee324be74b5dd"}}