{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:NWV4YT5PXLFOTU2DVARNXRS5K7","short_pith_number":"pith:NWV4YT5P","schema_version":"1.0","canonical_sha256":"6dabcc4fafbacae9d343a822dbc65d57cd86604f5b5a52af90be03878432ef22","source":{"kind":"arxiv","id":"1212.6665","version":2},"attestation_state":"computed","paper":{"title":"Uniform Gaussian bounds for subelliptic heat kernels and an application to the total variation flow of graphs over Carnot groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MG"],"primary_cat":"math.AP","authors_text":"Giovanna Citti, Luca Capogna, Maria Manfredini","submitted_at":"2012-12-29T21:49:57Z","abstract_excerpt":"In this paper we study heat kernels associated to a Carnot group $G$, endowed with a family of collapsing left-invariant Riemannian metrics $\\sigma_\\e$ which converge in the Gromov-Hausdorff sense to a sub-Riemannian structure on $G$ as $\\e\\to 0$. The main new contribution are Gaussian-type bounds on the heat kernel for the $\\sigma_\\e$ metrics which are stable as $\\e\\to 0$ and extend the previous time-independent estimates in \\cite{CiMa-F}. As an application we study well posedness of the total variation flow of graph surfaces over a bounded domain in $(G,\\s_\\e)$. We establish interior and bou"},"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":"1212.6665","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-29T21:49:57Z","cross_cats_sorted":["math.DG","math.MG"],"title_canon_sha256":"0157670f8fd0e345f6646a052344835eba8bf3a003b4fd36e9509ef947ee5171","abstract_canon_sha256":"58896a89a774e7c5ab562e3e09a895553af966354b3f1202391fcb9400b0a7c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:06.229146Z","signature_b64":"pP4YGw1Y2/kpX6ewxbF/z3idk1dN17E62HeX/9EiIhR5xgmGCXWlSZsaSZvPpN53X9O+qTzb2YlutTp9yC2gAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6dabcc4fafbacae9d343a822dbc65d57cd86604f5b5a52af90be03878432ef22","last_reissued_at":"2026-05-18T03:18:06.228591Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:06.228591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniform Gaussian bounds for subelliptic heat kernels and an application to the total variation flow of graphs over Carnot groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MG"],"primary_cat":"math.AP","authors_text":"Giovanna Citti, Luca Capogna, Maria Manfredini","submitted_at":"2012-12-29T21:49:57Z","abstract_excerpt":"In this paper we study heat kernels associated to a Carnot group $G$, endowed with a family of collapsing left-invariant Riemannian metrics $\\sigma_\\e$ which converge in the Gromov-Hausdorff sense to a sub-Riemannian structure on $G$ as $\\e\\to 0$. The main new contribution are Gaussian-type bounds on the heat kernel for the $\\sigma_\\e$ metrics which are stable as $\\e\\to 0$ and extend the previous time-independent estimates in \\cite{CiMa-F}. As an application we study well posedness of the total variation flow of graph surfaces over a bounded domain in $(G,\\s_\\e)$. We establish interior and bou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6665","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":"1212.6665","created_at":"2026-05-18T03:18:06.228682+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.6665v2","created_at":"2026-05-18T03:18:06.228682+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6665","created_at":"2026-05-18T03:18:06.228682+00:00"},{"alias_kind":"pith_short_12","alias_value":"NWV4YT5PXLFO","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"NWV4YT5PXLFOTU2D","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"NWV4YT5P","created_at":"2026-05-18T12:27:16.716162+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/NWV4YT5PXLFOTU2DVARNXRS5K7","json":"https://pith.science/pith/NWV4YT5PXLFOTU2DVARNXRS5K7.json","graph_json":"https://pith.science/api/pith-number/NWV4YT5PXLFOTU2DVARNXRS5K7/graph.json","events_json":"https://pith.science/api/pith-number/NWV4YT5PXLFOTU2DVARNXRS5K7/events.json","paper":"https://pith.science/paper/NWV4YT5P"},"agent_actions":{"view_html":"https://pith.science/pith/NWV4YT5PXLFOTU2DVARNXRS5K7","download_json":"https://pith.science/pith/NWV4YT5PXLFOTU2DVARNXRS5K7.json","view_paper":"https://pith.science/paper/NWV4YT5P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.6665&json=true","fetch_graph":"https://pith.science/api/pith-number/NWV4YT5PXLFOTU2DVARNXRS5K7/graph.json","fetch_events":"https://pith.science/api/pith-number/NWV4YT5PXLFOTU2DVARNXRS5K7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NWV4YT5PXLFOTU2DVARNXRS5K7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NWV4YT5PXLFOTU2DVARNXRS5K7/action/storage_attestation","attest_author":"https://pith.science/pith/NWV4YT5PXLFOTU2DVARNXRS5K7/action/author_attestation","sign_citation":"https://pith.science/pith/NWV4YT5PXLFOTU2DVARNXRS5K7/action/citation_signature","submit_replication":"https://pith.science/pith/NWV4YT5PXLFOTU2DVARNXRS5K7/action/replication_record"}},"created_at":"2026-05-18T03:18:06.228682+00:00","updated_at":"2026-05-18T03:18:06.228682+00:00"}