{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:26WEHD6XOXYVZVCXSAZ7556Z3E","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":"0c19f16eb1791754d242df0b189a0ea1f35401190fdcf08f90ea431b00a99aef","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-29T12:49:56Z","title_canon_sha256":"bf1d620f1dbbdbf501bc3e44b0ad0657e9da51f00dcfe78743e694a87245f9d5"},"schema_version":"1.0","source":{"id":"1703.10011","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.10011","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"arxiv_version","alias_value":"1703.10011v2","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10011","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"pith_short_12","alias_value":"26WEHD6XOXYV","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"26WEHD6XOXYVZVCX","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"26WEHD6X","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:83a7e2be067c378421f003604ec1b40b7ea86acbc06537d90dde21e3e1ba839e","target":"graph","created_at":"2026-05-18T00:47:37Z","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":"A study is made of an integral identity of Helffer and Sj{\\\"o}strand, which for some class of probability measures yields a formula for the covariance of two functions (of a stochastic variable). In comparison with the Brascamp--Lieb inequality, this formula is a more flexible and in some contexts stronger means for the analysis of correlation asymptotics in statistical mechanics. Using a fine version of the Closed Range Theorem, the identity's validity is shown to be equivalent to some explicitly given spectral properties of Witten-Laplacians on Euclidean space, and the formula is moreover de","authors_text":"Jon Johnsen","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-29T12:49:56Z","title":"On the spectral properties of Witten-Laplacians, their range projections and Brascamp-Lieb's inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10011","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:b04f80954fc53a0fe4151685f7abea9baecc8666b10f0ae9f07740a5f4e0c6bf","target":"record","created_at":"2026-05-18T00:47:37Z","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":"0c19f16eb1791754d242df0b189a0ea1f35401190fdcf08f90ea431b00a99aef","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-29T12:49:56Z","title_canon_sha256":"bf1d620f1dbbdbf501bc3e44b0ad0657e9da51f00dcfe78743e694a87245f9d5"},"schema_version":"1.0","source":{"id":"1703.10011","kind":"arxiv","version":2}},"canonical_sha256":"d7ac438fd775f15cd4579033fef7d9d908f0aa85b55abc62f9f06df037d0e43a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7ac438fd775f15cd4579033fef7d9d908f0aa85b55abc62f9f06df037d0e43a","first_computed_at":"2026-05-18T00:47:37.709543Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:37.709543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MtuKeJ2/GZpeiNAnY43y1jv/o7HcbmVQ4AqgAsPnNljh2pwzq4BsYR5tipvk6JG2aTtpx41s9o9EJqBCuDfqAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:37.710202Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.10011","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b04f80954fc53a0fe4151685f7abea9baecc8666b10f0ae9f07740a5f4e0c6bf","sha256:83a7e2be067c378421f003604ec1b40b7ea86acbc06537d90dde21e3e1ba839e"],"state_sha256":"378b604eb778237619154f7da430b6055e6f16812ec76e5f14feb1eb62cfe188"}