{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:APE345DCEQOHUQYK4ISJ2Q3TUP","short_pith_number":"pith:APE345DC","canonical_record":{"source":{"id":"1807.02174","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-07-05T20:31:28Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"80e0dc0de28071bd8003e273cf6427f341e453fa2532aec6966879b6c1dd59cb","abstract_canon_sha256":"097fac6cc84c92cb76f9b8b4ba5167187f5c5c408a957b253be590d1399401e1"},"schema_version":"1.0"},"canonical_sha256":"03c9be7462241c7a430ae2249d4373a3d2a039f3bcd849cb9284d48f7201d5ac","source":{"kind":"arxiv","id":"1807.02174","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.02174","created_at":"2026-07-05T01:07:48Z"},{"alias_kind":"arxiv_version","alias_value":"1807.02174v1","created_at":"2026-07-05T01:07:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.02174","created_at":"2026-07-05T01:07:48Z"},{"alias_kind":"pith_short_12","alias_value":"APE345DCEQOH","created_at":"2026-07-05T01:07:48Z"},{"alias_kind":"pith_short_16","alias_value":"APE345DCEQOHUQYK","created_at":"2026-07-05T01:07:48Z"},{"alias_kind":"pith_short_8","alias_value":"APE345DC","created_at":"2026-07-05T01:07:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:APE345DCEQOHUQYK4ISJ2Q3TUP","target":"record","payload":{"canonical_record":{"source":{"id":"1807.02174","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-07-05T20:31:28Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"80e0dc0de28071bd8003e273cf6427f341e453fa2532aec6966879b6c1dd59cb","abstract_canon_sha256":"097fac6cc84c92cb76f9b8b4ba5167187f5c5c408a957b253be590d1399401e1"},"schema_version":"1.0"},"canonical_sha256":"03c9be7462241c7a430ae2249d4373a3d2a039f3bcd849cb9284d48f7201d5ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:07:48.067771Z","signature_b64":"AAmp4rtQQEVbcqrrMxFik45NmenOolaEedYAp+GEDpL5woqTY+0ZLFhb4m8msp1CfmsYY/xMesze1uvaLxG3Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03c9be7462241c7a430ae2249d4373a3d2a039f3bcd849cb9284d48f7201d5ac","last_reissued_at":"2026-07-05T01:07:48.067299Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:07:48.067299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.02174","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":"2026-07-05T01:07:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pe4nv7ucJxsKEKWyT2x+9lXeIHtO2KFmEdDCfbiEwbgsH1juCd5x8wr2UvkjID9abStjR+CRItEi+w/eKSt3AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T15:57:38.363919Z"},"content_sha256":"6186e5fd9a09a1a29ec89fe0349d548ef9580df89a17222a8b23a4c7da4f728c","schema_version":"1.0","event_id":"sha256:6186e5fd9a09a1a29ec89fe0349d548ef9580df89a17222a8b23a4c7da4f728c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:APE345DCEQOHUQYK4ISJ2Q3TUP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Locally $p$-admissible measures on $\\mathbb{R}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Anders Bjorn, Jana Bjorn, Nageswari Shanmugalingam","submitted_at":"2018-07-05T20:31:28Z","abstract_excerpt":"In this note we show that locally $p$-admissible measures on $\\mathbb{R}$ necessarily come from local Muckenhoupt $A_p$ weights. In the proof we employ the corresponding characterization of global $p$-admissible measures on $\\mathbb{R}$ in terms of global $A_p$ weights due to Bj\\\"orn, Buckley and Keith, together with tools from analysis in metric spaces, more specifically preservation of the doubling condition and Poincar\\'e inequalities under flattening, due to Durand-Cartagena and Li. As a consequence, the class of locally $p$-admissible weights on $\\mathbb{R}$ is invariant under addition an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02174","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/1807.02174/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":"2026-07-05T01:07:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2RQThbISCShFFHMjQBL9zub1FDDF2IsNPYyvgXHHZj568BFh+qiqs5v6cENPuxeTJpr/UFiM/UnP8lKrzyX7Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T15:57:38.364792Z"},"content_sha256":"81b0ecfda7b4c84f4e0ad39c101e2ea12a44bdd9dacfd7c096f5e9d45fd541b5","schema_version":"1.0","event_id":"sha256:81b0ecfda7b4c84f4e0ad39c101e2ea12a44bdd9dacfd7c096f5e9d45fd541b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/APE345DCEQOHUQYK4ISJ2Q3TUP/bundle.json","state_url":"https://pith.science/pith/APE345DCEQOHUQYK4ISJ2Q3TUP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/APE345DCEQOHUQYK4ISJ2Q3TUP/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":"2026-08-17T15:57:38Z","links":{"resolver":"https://pith.science/pith/APE345DCEQOHUQYK4ISJ2Q3TUP","bundle":"https://pith.science/pith/APE345DCEQOHUQYK4ISJ2Q3TUP/bundle.json","state":"https://pith.science/pith/APE345DCEQOHUQYK4ISJ2Q3TUP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/APE345DCEQOHUQYK4ISJ2Q3TUP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:APE345DCEQOHUQYK4ISJ2Q3TUP","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":"097fac6cc84c92cb76f9b8b4ba5167187f5c5c408a957b253be590d1399401e1","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-07-05T20:31:28Z","title_canon_sha256":"80e0dc0de28071bd8003e273cf6427f341e453fa2532aec6966879b6c1dd59cb"},"schema_version":"1.0","source":{"id":"1807.02174","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.02174","created_at":"2026-07-05T01:07:48Z"},{"alias_kind":"arxiv_version","alias_value":"1807.02174v1","created_at":"2026-07-05T01:07:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.02174","created_at":"2026-07-05T01:07:48Z"},{"alias_kind":"pith_short_12","alias_value":"APE345DCEQOH","created_at":"2026-07-05T01:07:48Z"},{"alias_kind":"pith_short_16","alias_value":"APE345DCEQOHUQYK","created_at":"2026-07-05T01:07:48Z"},{"alias_kind":"pith_short_8","alias_value":"APE345DC","created_at":"2026-07-05T01:07:48Z"}],"graph_snapshots":[{"event_id":"sha256:81b0ecfda7b4c84f4e0ad39c101e2ea12a44bdd9dacfd7c096f5e9d45fd541b5","target":"graph","created_at":"2026-07-05T01:07:48Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1807.02174/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this note we show that locally $p$-admissible measures on $\\mathbb{R}$ necessarily come from local Muckenhoupt $A_p$ weights. In the proof we employ the corresponding characterization of global $p$-admissible measures on $\\mathbb{R}$ in terms of global $A_p$ weights due to Bj\\\"orn, Buckley and Keith, together with tools from analysis in metric spaces, more specifically preservation of the doubling condition and Poincar\\'e inequalities under flattening, due to Durand-Cartagena and Li. As a consequence, the class of locally $p$-admissible weights on $\\mathbb{R}$ is invariant under addition an","authors_text":"Anders Bjorn, Jana Bjorn, Nageswari Shanmugalingam","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-07-05T20:31:28Z","title":"Locally $p$-admissible measures on $\\mathbb{R}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02174","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":"sha256:6186e5fd9a09a1a29ec89fe0349d548ef9580df89a17222a8b23a4c7da4f728c","target":"record","created_at":"2026-07-05T01:07:48Z","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":"097fac6cc84c92cb76f9b8b4ba5167187f5c5c408a957b253be590d1399401e1","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-07-05T20:31:28Z","title_canon_sha256":"80e0dc0de28071bd8003e273cf6427f341e453fa2532aec6966879b6c1dd59cb"},"schema_version":"1.0","source":{"id":"1807.02174","kind":"arxiv","version":1}},"canonical_sha256":"03c9be7462241c7a430ae2249d4373a3d2a039f3bcd849cb9284d48f7201d5ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03c9be7462241c7a430ae2249d4373a3d2a039f3bcd849cb9284d48f7201d5ac","first_computed_at":"2026-07-05T01:07:48.067299Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:07:48.067299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AAmp4rtQQEVbcqrrMxFik45NmenOolaEedYAp+GEDpL5woqTY+0ZLFhb4m8msp1CfmsYY/xMesze1uvaLxG3Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:07:48.067771Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.02174","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6186e5fd9a09a1a29ec89fe0349d548ef9580df89a17222a8b23a4c7da4f728c","sha256:81b0ecfda7b4c84f4e0ad39c101e2ea12a44bdd9dacfd7c096f5e9d45fd541b5"],"state_sha256":"1c6067ed448d567bdab0eb96c14a359e4dd0270b32f8ce1b229c3f7dbd6ee5be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EqDec4/Ul73I2Pw/eWNIVOaKaP2q5fcKy2+3c5piS6xVmFvgmmZTHhFnyhPS1AwSbBGJ3kEfGPvY5aRy5p3eCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T15:57:38.371408Z","bundle_sha256":"4342413c2aa3d1aae7bbc4e85a5d79b1b506a0091300027636d1a28ff862ff78"}}