{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:Z27Q74S6CLYMYI2NLLDHNE76TY","short_pith_number":"pith:Z27Q74S6","canonical_record":{"source":{"id":"1202.1510","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-07T19:50:03Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"b467aeb0aab4bbe00029ca206540ad3c4bd968acd42bf1956fcc0b5305727389","abstract_canon_sha256":"bf6798e2cf3644e495aefce67d9888aa7f0e08ffd540265cd0a77d85dd223b2d"},"schema_version":"1.0"},"canonical_sha256":"cebf0ff25e12f0cc234d5ac67693fe9e3a57be8294e26dd086d972987856355c","source":{"kind":"arxiv","id":"1202.1510","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.1510","created_at":"2026-05-18T01:09:25Z"},{"alias_kind":"arxiv_version","alias_value":"1202.1510v4","created_at":"2026-05-18T01:09:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.1510","created_at":"2026-05-18T01:09:25Z"},{"alias_kind":"pith_short_12","alias_value":"Z27Q74S6CLYM","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"Z27Q74S6CLYMYI2N","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"Z27Q74S6","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:Z27Q74S6CLYMYI2NLLDHNE76TY","target":"record","payload":{"canonical_record":{"source":{"id":"1202.1510","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-07T19:50:03Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"b467aeb0aab4bbe00029ca206540ad3c4bd968acd42bf1956fcc0b5305727389","abstract_canon_sha256":"bf6798e2cf3644e495aefce67d9888aa7f0e08ffd540265cd0a77d85dd223b2d"},"schema_version":"1.0"},"canonical_sha256":"cebf0ff25e12f0cc234d5ac67693fe9e3a57be8294e26dd086d972987856355c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:25.090790Z","signature_b64":"oxo+fYiEdLQ5GQemlCZcvJDqMCMgXPEnbKT0nJa6SNSry2g+wyiY/kjJY0MXsJdzZQG6EMG65pTr7gI9Ztb7Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cebf0ff25e12f0cc234d5ac67693fe9e3a57be8294e26dd086d972987856355c","last_reissued_at":"2026-05-18T01:09:25.090080Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:25.090080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.1510","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:09:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c/wRnu8C51Hl4s1XtStZbKAYaS7tjzozMZJDzUbjHDGn5jdoHjkhm7QCzafULY51FJh2KNEztcJzM+kYNmpEDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:08:39.041351Z"},"content_sha256":"7eceac6fadcdf620d7735dec965ecd55d89c170c2defb336e87c500532eece7e","schema_version":"1.0","event_id":"sha256:7eceac6fadcdf620d7735dec965ecd55d89c170c2defb336e87c500532eece7e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:Z27Q74S6CLYMYI2NLLDHNE76TY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Poincar\\'{e} and logarithmic Sobolev inequalities by decomposition of the energy landscape","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.PR","authors_text":"Andr\\'e Schlichting, Georg Menz","submitted_at":"2012-02-07T19:50:03Z","abstract_excerpt":"We consider a diffusion on a potential landscape which is given by a smooth Hamiltonian $H:\\mathbb {R}^n\\to \\mathbb {R}$ in the regime of low temperature $\\varepsilon$. We proof the Eyring-Kramers formula for the optimal constant in the Poincar\\'{e} (PI) and logarithmic Sobolev inequality (LSI) for the associated generator $L=\\varepsilon \\Delta -\\nabla H\\cdot\\nabla$ of the diffusion. The proof is based on a refinement of the two-scale approach introduced by Grunewald et al. [Ann. Inst. Henri Poincar\\'{e} Probab. Stat. 45 (2009) 302-351] and of the mean-difference estimate introduced by Chafa\\\""},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1510","kind":"arxiv","version":4},"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":"2026-05-18T01:09:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aGCZMegntWlsAFiKY1aWFcxU/ojbafSW1E9amKJJ6B/ojZojbQucyvXZ9b5c+TuPII42mJ6Qur7JdXMUj+CvAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:08:39.041704Z"},"content_sha256":"ea99a6a7637ef1b48c87a8fcf7398f1f8cb95ae1ee7a025a75934ea88d8a2557","schema_version":"1.0","event_id":"sha256:ea99a6a7637ef1b48c87a8fcf7398f1f8cb95ae1ee7a025a75934ea88d8a2557"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z27Q74S6CLYMYI2NLLDHNE76TY/bundle.json","state_url":"https://pith.science/pith/Z27Q74S6CLYMYI2NLLDHNE76TY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z27Q74S6CLYMYI2NLLDHNE76TY/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":"2026-06-26T01:08:39Z","links":{"resolver":"https://pith.science/pith/Z27Q74S6CLYMYI2NLLDHNE76TY","bundle":"https://pith.science/pith/Z27Q74S6CLYMYI2NLLDHNE76TY/bundle.json","state":"https://pith.science/pith/Z27Q74S6CLYMYI2NLLDHNE76TY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z27Q74S6CLYMYI2NLLDHNE76TY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Z27Q74S6CLYMYI2NLLDHNE76TY","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":"bf6798e2cf3644e495aefce67d9888aa7f0e08ffd540265cd0a77d85dd223b2d","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-07T19:50:03Z","title_canon_sha256":"b467aeb0aab4bbe00029ca206540ad3c4bd968acd42bf1956fcc0b5305727389"},"schema_version":"1.0","source":{"id":"1202.1510","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.1510","created_at":"2026-05-18T01:09:25Z"},{"alias_kind":"arxiv_version","alias_value":"1202.1510v4","created_at":"2026-05-18T01:09:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.1510","created_at":"2026-05-18T01:09:25Z"},{"alias_kind":"pith_short_12","alias_value":"Z27Q74S6CLYM","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"Z27Q74S6CLYMYI2N","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"Z27Q74S6","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:ea99a6a7637ef1b48c87a8fcf7398f1f8cb95ae1ee7a025a75934ea88d8a2557","target":"graph","created_at":"2026-05-18T01:09:25Z","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 consider a diffusion on a potential landscape which is given by a smooth Hamiltonian $H:\\mathbb {R}^n\\to \\mathbb {R}$ in the regime of low temperature $\\varepsilon$. We proof the Eyring-Kramers formula for the optimal constant in the Poincar\\'{e} (PI) and logarithmic Sobolev inequality (LSI) for the associated generator $L=\\varepsilon \\Delta -\\nabla H\\cdot\\nabla$ of the diffusion. The proof is based on a refinement of the two-scale approach introduced by Grunewald et al. [Ann. Inst. Henri Poincar\\'{e} Probab. Stat. 45 (2009) 302-351] and of the mean-difference estimate introduced by Chafa\\\"","authors_text":"Andr\\'e Schlichting, Georg Menz","cross_cats":["math-ph","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-07T19:50:03Z","title":"Poincar\\'{e} and logarithmic Sobolev inequalities by decomposition of the energy landscape"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1510","kind":"arxiv","version":4},"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":"sha256:7eceac6fadcdf620d7735dec965ecd55d89c170c2defb336e87c500532eece7e","target":"record","created_at":"2026-05-18T01:09:25Z","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":"bf6798e2cf3644e495aefce67d9888aa7f0e08ffd540265cd0a77d85dd223b2d","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-07T19:50:03Z","title_canon_sha256":"b467aeb0aab4bbe00029ca206540ad3c4bd968acd42bf1956fcc0b5305727389"},"schema_version":"1.0","source":{"id":"1202.1510","kind":"arxiv","version":4}},"canonical_sha256":"cebf0ff25e12f0cc234d5ac67693fe9e3a57be8294e26dd086d972987856355c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cebf0ff25e12f0cc234d5ac67693fe9e3a57be8294e26dd086d972987856355c","first_computed_at":"2026-05-18T01:09:25.090080Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:25.090080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oxo+fYiEdLQ5GQemlCZcvJDqMCMgXPEnbKT0nJa6SNSry2g+wyiY/kjJY0MXsJdzZQG6EMG65pTr7gI9Ztb7Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:25.090790Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.1510","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7eceac6fadcdf620d7735dec965ecd55d89c170c2defb336e87c500532eece7e","sha256:ea99a6a7637ef1b48c87a8fcf7398f1f8cb95ae1ee7a025a75934ea88d8a2557"],"state_sha256":"dd9d67db90b93cdcf5e2f0052642145942ca44bb1ebc608fbf4d47a8e7c1f831"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"md/RlB6CZs2r995IWoXskUkPhXEPL5WSgfPZiusrnH54KgBQ2ZXRwOcpWXitRW/txxyOX/Ygj1kXi8aq2CKIAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T01:08:39.043647Z","bundle_sha256":"a4efbecf5bdcd569b1d45bbd158927f9b05c56a50e1203464c0db26e2b5168a9"}}