{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:W7KROLMZG342L2SEUACN6DLDAX","short_pith_number":"pith:W7KROLMZ","schema_version":"1.0","canonical_sha256":"b7d5172d9936f9a5ea44a004df0d6305d4cb9f9073da1272630f6f4735cc9e44","source":{"kind":"arxiv","id":"1606.02423","version":1},"attestation_state":"computed","paper":{"title":"Gaussian heat kernel estimates: from functions to forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adam Sikora, Baptiste Devyver, Thierry Coulhon","submitted_at":"2016-06-08T07:05:54Z","abstract_excerpt":"On a complete non-compact Riemannian manifold satisfying the volume doubling property, we give conditions on the negative part of the Ricci curvature that ensure that, unless there are harmonic one-forms, the Gaussian heat kernel upper estimate on functions transfers to one-forms. These conditions do no entail any constraint on the size of the Ricci curvature, only on its decay at infinity."},"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":"1606.02423","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-08T07:05:54Z","cross_cats_sorted":[],"title_canon_sha256":"2a6ddef8f3599732a2e9cc79c2ee24b11c8c753104423f9784c9430600099514","abstract_canon_sha256":"1e74879824dd167f67413da526455a4799e7c13a9fc36f9b0df4ac792b7b85a6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:41.403504Z","signature_b64":"DT+ozUftAY/0KztBv1mDOx59kdzPTEWLaa8M0DX4z+5cEas5k/DL5rbOeaIw0QNm8H3MeYdVxjR7dL+SktSaBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7d5172d9936f9a5ea44a004df0d6305d4cb9f9073da1272630f6f4735cc9e44","last_reissued_at":"2026-05-18T01:12:41.403030Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:41.403030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gaussian heat kernel estimates: from functions to forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adam Sikora, Baptiste Devyver, Thierry Coulhon","submitted_at":"2016-06-08T07:05:54Z","abstract_excerpt":"On a complete non-compact Riemannian manifold satisfying the volume doubling property, we give conditions on the negative part of the Ricci curvature that ensure that, unless there are harmonic one-forms, the Gaussian heat kernel upper estimate on functions transfers to one-forms. These conditions do no entail any constraint on the size of the Ricci curvature, only on its decay at infinity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02423","kind":"arxiv","version":1},"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":"1606.02423","created_at":"2026-05-18T01:12:41.403098+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.02423v1","created_at":"2026-05-18T01:12:41.403098+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02423","created_at":"2026-05-18T01:12:41.403098+00:00"},{"alias_kind":"pith_short_12","alias_value":"W7KROLMZG342","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"W7KROLMZG342L2SE","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"W7KROLMZ","created_at":"2026-05-18T12:30:48.956258+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/W7KROLMZG342L2SEUACN6DLDAX","json":"https://pith.science/pith/W7KROLMZG342L2SEUACN6DLDAX.json","graph_json":"https://pith.science/api/pith-number/W7KROLMZG342L2SEUACN6DLDAX/graph.json","events_json":"https://pith.science/api/pith-number/W7KROLMZG342L2SEUACN6DLDAX/events.json","paper":"https://pith.science/paper/W7KROLMZ"},"agent_actions":{"view_html":"https://pith.science/pith/W7KROLMZG342L2SEUACN6DLDAX","download_json":"https://pith.science/pith/W7KROLMZG342L2SEUACN6DLDAX.json","view_paper":"https://pith.science/paper/W7KROLMZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.02423&json=true","fetch_graph":"https://pith.science/api/pith-number/W7KROLMZG342L2SEUACN6DLDAX/graph.json","fetch_events":"https://pith.science/api/pith-number/W7KROLMZG342L2SEUACN6DLDAX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W7KROLMZG342L2SEUACN6DLDAX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W7KROLMZG342L2SEUACN6DLDAX/action/storage_attestation","attest_author":"https://pith.science/pith/W7KROLMZG342L2SEUACN6DLDAX/action/author_attestation","sign_citation":"https://pith.science/pith/W7KROLMZG342L2SEUACN6DLDAX/action/citation_signature","submit_replication":"https://pith.science/pith/W7KROLMZG342L2SEUACN6DLDAX/action/replication_record"}},"created_at":"2026-05-18T01:12:41.403098+00:00","updated_at":"2026-05-18T01:12:41.403098+00:00"}