{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:ZVDN2E3VCMB2GFXCWLO2RIDNU4","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":"c188af2c0d9118e7e9e0d0a22623224e3666b8c07799dc5ed3105a2e72443d89","cross_cats_sorted":["math.PR","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-10-25T21:16:54Z","title_canon_sha256":"3b21ffd26552c1b15b8f8944e0868a7b2897610cf235fb68e72af6b8d4a6bf29"},"schema_version":"1.0","source":{"id":"0910.4768","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.4768","created_at":"2026-05-18T04:31:11Z"},{"alias_kind":"arxiv_version","alias_value":"0910.4768v1","created_at":"2026-05-18T04:31:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.4768","created_at":"2026-05-18T04:31:11Z"},{"alias_kind":"pith_short_12","alias_value":"ZVDN2E3VCMB2","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"ZVDN2E3VCMB2GFXC","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"ZVDN2E3V","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:b1e726abeb6badacf82ff8b3acf5ca9e4bb4dcbb6400849419d88976f40a002f","target":"graph","created_at":"2026-05-18T04:31:11Z","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":"We prove some results about the super Poincar\\'e inequality (SPI) and its relation to the spectrum of an operator: we show that it can be alternatively written with Orlicz norms instead of L1 norms, and we use this to give an alternative proof that a bound on the bottom of the essential spectrum implies a SPI. Finally, we apply these ideas to give a spectral proof of the log Sobolev inequality for the Gaussian measure.","authors_text":"Pierre-Andr\\'e Zitt (IMB)","cross_cats":["math.PR","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-10-25T21:16:54Z","title":"Super Poincar\\'e inequalities, Orlicz norms and essential spectrum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.4768","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":"sha256:967f86b5150b8f6cd3f3c0625c9bbbaf46fab732b33673bb896015610ef526eb","target":"record","created_at":"2026-05-18T04:31:11Z","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":"c188af2c0d9118e7e9e0d0a22623224e3666b8c07799dc5ed3105a2e72443d89","cross_cats_sorted":["math.PR","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-10-25T21:16:54Z","title_canon_sha256":"3b21ffd26552c1b15b8f8944e0868a7b2897610cf235fb68e72af6b8d4a6bf29"},"schema_version":"1.0","source":{"id":"0910.4768","kind":"arxiv","version":1}},"canonical_sha256":"cd46dd13751303a316e2b2dda8a06da712a59954c9cfdeffc21b57c3d168c455","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd46dd13751303a316e2b2dda8a06da712a59954c9cfdeffc21b57c3d168c455","first_computed_at":"2026-05-18T04:31:11.996180Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:11.996180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OiaJHxWdaBmskBQQPI4Ni75xAIbDydb1iFbRFuFxObRv61+Ek4aBPvjPuzGdPf5BBYK/CfmORA+6nKMzIrIkDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:11.996723Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.4768","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:967f86b5150b8f6cd3f3c0625c9bbbaf46fab732b33673bb896015610ef526eb","sha256:b1e726abeb6badacf82ff8b3acf5ca9e4bb4dcbb6400849419d88976f40a002f"],"state_sha256":"dbb8c010e79041f0cedbc694d5d462f3719b680ab10262a37c92b7511464aa37"}