{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:HAIPYF6QSLTU6ZBH3IQCZ5GGQW","short_pith_number":"pith:HAIPYF6Q","canonical_record":{"source":{"id":"1105.3095","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-05-16T14:02:34Z","cross_cats_sorted":[],"title_canon_sha256":"ce92fdb92c91d94f2e1bf229de775e8ecf9b932604129c7a7b77bc2043c82d49","abstract_canon_sha256":"a3b0d51f3d4e7011acdfa12b4ac4a5d2f309b4d8e2ee50b05394a6cae539745e"},"schema_version":"1.0"},"canonical_sha256":"3810fc17d092e74f6427da202cf4c6859aeead0d8e03bd0e672a7c9b97813b96","source":{"kind":"arxiv","id":"1105.3095","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.3095","created_at":"2026-05-18T03:46:03Z"},{"alias_kind":"arxiv_version","alias_value":"1105.3095v2","created_at":"2026-05-18T03:46:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3095","created_at":"2026-05-18T03:46:03Z"},{"alias_kind":"pith_short_12","alias_value":"HAIPYF6QSLTU","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HAIPYF6QSLTU6ZBH","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HAIPYF6Q","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:HAIPYF6QSLTU6ZBH3IQCZ5GGQW","target":"record","payload":{"canonical_record":{"source":{"id":"1105.3095","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-05-16T14:02:34Z","cross_cats_sorted":[],"title_canon_sha256":"ce92fdb92c91d94f2e1bf229de775e8ecf9b932604129c7a7b77bc2043c82d49","abstract_canon_sha256":"a3b0d51f3d4e7011acdfa12b4ac4a5d2f309b4d8e2ee50b05394a6cae539745e"},"schema_version":"1.0"},"canonical_sha256":"3810fc17d092e74f6427da202cf4c6859aeead0d8e03bd0e672a7c9b97813b96","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:03.952610Z","signature_b64":"lXCpU+oSIp1sdFgVrtC1JOFv3J66x3A2QD3REgcZ9DYx87WCO+6FZZVwM2mEh9387+Go6NKT650SINFuykAIDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3810fc17d092e74f6427da202cf4c6859aeead0d8e03bd0e672a7c9b97813b96","last_reissued_at":"2026-05-18T03:46:03.951980Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:03.951980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.3095","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:46:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZnLPNM+sXwOwnwOYeTTfxhqswyV3wIQQR+JFIXOVZA7V8Y9angiWtkY5fA2iMlS7wGlLmM9MyshNYexFxROcAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:01:13.299607Z"},"content_sha256":"26442cae280f455ec20510fbfa07e6302492b8ba7cfdfc22926eb3e37600682e","schema_version":"1.0","event_id":"sha256:26442cae280f455ec20510fbfa07e6302492b8ba7cfdfc22926eb3e37600682e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:HAIPYF6QSLTU6ZBH3IQCZ5GGQW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Super-Poincar\\'e and Nash-type inequalities for Subordinated Semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ivan Gentil, Patrick Maheux","submitted_at":"2011-05-16T14:02:34Z","abstract_excerpt":"We prove that if a super-Poincar\\'e inequality is satisfied by an infinitesimal generator $-A$ of a symmetric contracting semigroup then it implies a corresponding super-Poincar\\'e inequality for $-g(A)$ with any Bernstein function $g$. We also study the converse statement. We deduce similar results for the Nash-type inequality. Our results applied to fractional powers of $A$ and to $\\log(I+A)$ and thus generalize some results of Biroli and Maheux, and Wang 2007. We provide several examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3095","kind":"arxiv","version":2},"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":"2026-05-18T03:46:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9MTQBLj29sRi9A4j0eg91lRMXrRxO46UhRYt5lMuGP4Nt5ao92wktNQwWaQdDLG77dBHeGdJV57OBmfTzYGVDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:01:13.299940Z"},"content_sha256":"af73671b1bdf7298bb321d3f1bc2092522cc1f6d676c932f3546be7385ea71a0","schema_version":"1.0","event_id":"sha256:af73671b1bdf7298bb321d3f1bc2092522cc1f6d676c932f3546be7385ea71a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HAIPYF6QSLTU6ZBH3IQCZ5GGQW/bundle.json","state_url":"https://pith.science/pith/HAIPYF6QSLTU6ZBH3IQCZ5GGQW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HAIPYF6QSLTU6ZBH3IQCZ5GGQW/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":"2026-06-25T18:01:13Z","links":{"resolver":"https://pith.science/pith/HAIPYF6QSLTU6ZBH3IQCZ5GGQW","bundle":"https://pith.science/pith/HAIPYF6QSLTU6ZBH3IQCZ5GGQW/bundle.json","state":"https://pith.science/pith/HAIPYF6QSLTU6ZBH3IQCZ5GGQW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HAIPYF6QSLTU6ZBH3IQCZ5GGQW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HAIPYF6QSLTU6ZBH3IQCZ5GGQW","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":"a3b0d51f3d4e7011acdfa12b4ac4a5d2f309b4d8e2ee50b05394a6cae539745e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-05-16T14:02:34Z","title_canon_sha256":"ce92fdb92c91d94f2e1bf229de775e8ecf9b932604129c7a7b77bc2043c82d49"},"schema_version":"1.0","source":{"id":"1105.3095","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.3095","created_at":"2026-05-18T03:46:03Z"},{"alias_kind":"arxiv_version","alias_value":"1105.3095v2","created_at":"2026-05-18T03:46:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3095","created_at":"2026-05-18T03:46:03Z"},{"alias_kind":"pith_short_12","alias_value":"HAIPYF6QSLTU","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HAIPYF6QSLTU6ZBH","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HAIPYF6Q","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:af73671b1bdf7298bb321d3f1bc2092522cc1f6d676c932f3546be7385ea71a0","target":"graph","created_at":"2026-05-18T03:46:03Z","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 that if a super-Poincar\\'e inequality is satisfied by an infinitesimal generator $-A$ of a symmetric contracting semigroup then it implies a corresponding super-Poincar\\'e inequality for $-g(A)$ with any Bernstein function $g$. We also study the converse statement. We deduce similar results for the Nash-type inequality. Our results applied to fractional powers of $A$ and to $\\log(I+A)$ and thus generalize some results of Biroli and Maheux, and Wang 2007. We provide several examples.","authors_text":"Ivan Gentil, Patrick Maheux","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-05-16T14:02:34Z","title":"Super-Poincar\\'e and Nash-type inequalities for Subordinated Semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3095","kind":"arxiv","version":2},"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":"sha256:26442cae280f455ec20510fbfa07e6302492b8ba7cfdfc22926eb3e37600682e","target":"record","created_at":"2026-05-18T03:46:03Z","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":"a3b0d51f3d4e7011acdfa12b4ac4a5d2f309b4d8e2ee50b05394a6cae539745e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-05-16T14:02:34Z","title_canon_sha256":"ce92fdb92c91d94f2e1bf229de775e8ecf9b932604129c7a7b77bc2043c82d49"},"schema_version":"1.0","source":{"id":"1105.3095","kind":"arxiv","version":2}},"canonical_sha256":"3810fc17d092e74f6427da202cf4c6859aeead0d8e03bd0e672a7c9b97813b96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3810fc17d092e74f6427da202cf4c6859aeead0d8e03bd0e672a7c9b97813b96","first_computed_at":"2026-05-18T03:46:03.951980Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:03.951980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lXCpU+oSIp1sdFgVrtC1JOFv3J66x3A2QD3REgcZ9DYx87WCO+6FZZVwM2mEh9387+Go6NKT650SINFuykAIDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:03.952610Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.3095","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26442cae280f455ec20510fbfa07e6302492b8ba7cfdfc22926eb3e37600682e","sha256:af73671b1bdf7298bb321d3f1bc2092522cc1f6d676c932f3546be7385ea71a0"],"state_sha256":"924b37f9d1d37f3ecb3cc52f4f62e8ea053d6ac79695be7d29ac80d12215e4f1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U2qbWL05Y/QCE0VO5vWYHRCindbpUkYUAYNlzapnvbdwznrEJpvclnJByoi/8LDYua2GGQiBMVmblU1oS5doCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T18:01:13.301805Z","bundle_sha256":"582754da53e119fc6726a3efa2f6afe01099ac79f3c7b7654a7c38e0a8c45bf3"}}