{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7DGCH4JDB24WN5BLRBIC355BRR","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":"98f0d7d951ea25ec34e261022c748bffb1588ade00701f3856ec1d842eea11a5","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-14T08:39:38Z","title_canon_sha256":"10773d0c52df51be35b4e59dd05b193eeeb01c17c25cc93a511ec911615d0db0"},"schema_version":"1.0","source":{"id":"1209.3125","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3125","created_at":"2026-05-18T03:34:16Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3125v3","created_at":"2026-05-18T03:34:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3125","created_at":"2026-05-18T03:34:16Z"},{"alias_kind":"pith_short_12","alias_value":"7DGCH4JDB24W","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7DGCH4JDB24WN5BL","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7DGCH4JD","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:c1606bbd2fca279130e8760fbcccd0503520daa094f32a7a055a9d906dde17d7","target":"graph","created_at":"2026-05-18T03:34:16Z","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":"The aim of this note is to show that Poincar\\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\\'e inequalities are considered, too. The proof is short and does not involve covering arguments.","authors_text":"Bart{\\l}omiej Dyda, Moritz Kassmann","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-14T08:39:38Z","title":"On weighted Poincar\\'e inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3125","kind":"arxiv","version":3},"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":"sha256:3f520c30199f72626d3ada50e65196ebd876799c27c2d57183f95097bfb14009","target":"record","created_at":"2026-05-18T03:34:16Z","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":"98f0d7d951ea25ec34e261022c748bffb1588ade00701f3856ec1d842eea11a5","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-14T08:39:38Z","title_canon_sha256":"10773d0c52df51be35b4e59dd05b193eeeb01c17c25cc93a511ec911615d0db0"},"schema_version":"1.0","source":{"id":"1209.3125","kind":"arxiv","version":3}},"canonical_sha256":"f8cc23f1230eb966f42b88502df7a18c75e3b3610da7e554c40c58574352e443","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8cc23f1230eb966f42b88502df7a18c75e3b3610da7e554c40c58574352e443","first_computed_at":"2026-05-18T03:34:16.065558Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:16.065558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0/I9iCOSf9t3DBD0r1La/xUCk0DDGeBmuy7XVDE+DLBX9V7CW1fusrj7QkwrQ+cKXngX9mF4kBliF1fFzM6cAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:16.066003Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.3125","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f520c30199f72626d3ada50e65196ebd876799c27c2d57183f95097bfb14009","sha256:c1606bbd2fca279130e8760fbcccd0503520daa094f32a7a055a9d906dde17d7"],"state_sha256":"a4e364b2257a67779d182373ea4a07dca83dc917c20737d98df2dc208310412f"}