{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:LLTP46EBDMWOCA2DOQ55ZNF7KP","short_pith_number":"pith:LLTP46EB","schema_version":"1.0","canonical_sha256":"5ae6fe78811b2ce10343743bdcb4bf53cb8f6cb59ccc1f5798e3b5408b54a5ea","source":{"kind":"arxiv","id":"1211.3623","version":2},"attestation_state":"computed","paper":{"title":"Reflecting Diffusion Process on Time-Inhomogeneous Manifolds with Boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kun Zhang, Li-Juan Cheng","submitted_at":"2012-11-15T14:56:44Z","abstract_excerpt":"Let $L_t:=\\Delta_t+Z_t$ for a $C^{1,1}$-vector field $Z$ on a differential manifold $M$ with boundary $\\partial M$, where $\\Delta_t$ is the Laplacian induced by a time dependent metric $g_t$ differentiable in $t\\in [0,T_c)$. We first introduce the reflecting diffusion process generated by $L_t$ and establish the derivative formula for the associated diffusion semigroup; then construct the couplings for the reflecting $L_t$-diffusion processes by parallel and reflecting displacement, which implies the gradient estimates of the associated heat semigroup; and finally, present a number of equivale"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1211.3623","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-15T14:56:44Z","cross_cats_sorted":[],"title_canon_sha256":"184b98da9271f9ccbe5bc1fa968c496f8cb5c8053c01ec10cf8623a0ab1319e5","abstract_canon_sha256":"f5f46c8221580fc51b2858324ec225b045d707363f9d03d32b10222d1c8e5dc5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:57.740937Z","signature_b64":"A0PlD+rfgQrC+uxkJvf3PBC6bvP/Iphob2V2rnbLROyTjnqLFLaqtsWVykyWQFv3ISzuctT9w3q/D8oXwFlDBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ae6fe78811b2ce10343743bdcb4bf53cb8f6cb59ccc1f5798e3b5408b54a5ea","last_reissued_at":"2026-05-18T00:37:57.740544Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:57.740544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reflecting Diffusion Process on Time-Inhomogeneous Manifolds with Boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kun Zhang, Li-Juan Cheng","submitted_at":"2012-11-15T14:56:44Z","abstract_excerpt":"Let $L_t:=\\Delta_t+Z_t$ for a $C^{1,1}$-vector field $Z$ on a differential manifold $M$ with boundary $\\partial M$, where $\\Delta_t$ is the Laplacian induced by a time dependent metric $g_t$ differentiable in $t\\in [0,T_c)$. We first introduce the reflecting diffusion process generated by $L_t$ and establish the derivative formula for the associated diffusion semigroup; then construct the couplings for the reflecting $L_t$-diffusion processes by parallel and reflecting displacement, which implies the gradient estimates of the associated heat semigroup; and finally, present a number of equivale"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3623","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1211.3623","created_at":"2026-05-18T00:37:57.740603+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.3623v2","created_at":"2026-05-18T00:37:57.740603+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.3623","created_at":"2026-05-18T00:37:57.740603+00:00"},{"alias_kind":"pith_short_12","alias_value":"LLTP46EBDMWO","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"LLTP46EBDMWOCA2D","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"LLTP46EB","created_at":"2026-05-18T12:27:14.488303+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LLTP46EBDMWOCA2DOQ55ZNF7KP","json":"https://pith.science/pith/LLTP46EBDMWOCA2DOQ55ZNF7KP.json","graph_json":"https://pith.science/api/pith-number/LLTP46EBDMWOCA2DOQ55ZNF7KP/graph.json","events_json":"https://pith.science/api/pith-number/LLTP46EBDMWOCA2DOQ55ZNF7KP/events.json","paper":"https://pith.science/paper/LLTP46EB"},"agent_actions":{"view_html":"https://pith.science/pith/LLTP46EBDMWOCA2DOQ55ZNF7KP","download_json":"https://pith.science/pith/LLTP46EBDMWOCA2DOQ55ZNF7KP.json","view_paper":"https://pith.science/paper/LLTP46EB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.3623&json=true","fetch_graph":"https://pith.science/api/pith-number/LLTP46EBDMWOCA2DOQ55ZNF7KP/graph.json","fetch_events":"https://pith.science/api/pith-number/LLTP46EBDMWOCA2DOQ55ZNF7KP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LLTP46EBDMWOCA2DOQ55ZNF7KP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LLTP46EBDMWOCA2DOQ55ZNF7KP/action/storage_attestation","attest_author":"https://pith.science/pith/LLTP46EBDMWOCA2DOQ55ZNF7KP/action/author_attestation","sign_citation":"https://pith.science/pith/LLTP46EBDMWOCA2DOQ55ZNF7KP/action/citation_signature","submit_replication":"https://pith.science/pith/LLTP46EBDMWOCA2DOQ55ZNF7KP/action/replication_record"}},"created_at":"2026-05-18T00:37:57.740603+00:00","updated_at":"2026-05-18T00:37:57.740603+00:00"}