{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:P5THNU4XMTWBQTL65IYQ7AMBUF","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":"3efb28df2a6e9f19a72aaef1e51c6173ee0ac7fb6fe6eb395e344658f64fb335","cross_cats_sorted":["math-ph","math.MP","math.PR","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-01-18T10:15:52Z","title_canon_sha256":"2bca8630c1a5cfd83184c85036bd6020562acd56c3f2313b27ea57217af6b611"},"schema_version":"1.0","source":{"id":"1701.04998","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.04998","created_at":"2026-05-18T00:52:33Z"},{"alias_kind":"arxiv_version","alias_value":"1701.04998v1","created_at":"2026-05-18T00:52:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.04998","created_at":"2026-05-18T00:52:33Z"},{"alias_kind":"pith_short_12","alias_value":"P5THNU4XMTWB","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"P5THNU4XMTWBQTL6","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"P5THNU4X","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:cefc7983f1afc864609bc86179e48bc0822d39bb6f1a0cec6ffbf346b3515afc","target":"graph","created_at":"2026-05-18T00:52:33Z","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":"This paper is a contribution to semiclassical analysis for abstract Schr\\\"odinger type operators on locally compact spaces: Let $X$ be a metrizable seperable locally compact space, let $\\mu$ be a Radon measure on $X$ with a full support. Let $(t,x,y)\\mapsto p(t,x,y)$ be a strictly positive pointwise consistent $\\mu$-heat kernel, and assume that the generator $H_p\\geq 0$ of the corresponding self-adjoint contraction semigroup in $L^2(X,\\mu)$ induces a regular Dirichlet form. Then, given a function $\\Psi : (0,1)\\to (0,\\infty)$ such that the limit $\\lim_{t\\to 0+}p(t,x,x)\\Psi (t)$ exists for all $","authors_text":"Batu G\\\"uneysu","cross_cats":["math-ph","math.MP","math.PR","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-01-18T10:15:52Z","title":"On the geometry of semiclassical limits on Dirichlet spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04998","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":"sha256:7ced0e760850471fd2bddac6d33d342073c6a65955f57bd49da36ad978e0bed4","target":"record","created_at":"2026-05-18T00:52:33Z","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":"3efb28df2a6e9f19a72aaef1e51c6173ee0ac7fb6fe6eb395e344658f64fb335","cross_cats_sorted":["math-ph","math.MP","math.PR","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-01-18T10:15:52Z","title_canon_sha256":"2bca8630c1a5cfd83184c85036bd6020562acd56c3f2313b27ea57217af6b611"},"schema_version":"1.0","source":{"id":"1701.04998","kind":"arxiv","version":1}},"canonical_sha256":"7f6676d39764ec184d7eea310f8181a170b6e6c817e20012cedec60b8827d9bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f6676d39764ec184d7eea310f8181a170b6e6c817e20012cedec60b8827d9bf","first_computed_at":"2026-05-18T00:52:33.327201Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:33.327201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LLfN6OfJoC7vdmjuFbVYzguyHhQkUGZwAMsm9XbCWzbhs4OEAo1yk/+pdb3Ck3tQQcTIl1JR1gG72Joo7mh1DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:33.327586Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.04998","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ced0e760850471fd2bddac6d33d342073c6a65955f57bd49da36ad978e0bed4","sha256:cefc7983f1afc864609bc86179e48bc0822d39bb6f1a0cec6ffbf346b3515afc"],"state_sha256":"f2e19a00c96355668126251d6e3c38d948a1574a92008bebe3d221b02d00ec02"}