{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:LFC5IGCUDTYTO3GOYBYTI4ZZPU","short_pith_number":"pith:LFC5IGCU","schema_version":"1.0","canonical_sha256":"5945d418541cf1376ccec0713473397d0f77090ec38103ec0e21a0483839bec8","source":{"kind":"arxiv","id":"1112.6159","version":1},"attestation_state":"computed","paper":{"title":"Geometric Ergodicity of a Hypoelliptic Diffusion Modelling The Melt-Spinning Process of Nonwoven Materials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.SP"],"primary_cat":"math.PR","authors_text":"Achim Wubker, Martin Kolb, Mladen Savov","submitted_at":"2011-12-28T18:07:24Z","abstract_excerpt":"We analyze the large time behavior of a stochastic model for the lay-down of fibers on a conveyor belt in the production process of nonwovens. It is shown, that under weak conditions this degenerate diffusion process is strong mixing, confirming a conjecture of Grothaus and Klar. Moreover, under some additional assumptions even geometric ergodicity is established using probabilistic tools -- described in the book of Meyn and Tweedie -- in combination with methods from stochastic analysis."},"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":"1112.6159","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-12-28T18:07:24Z","cross_cats_sorted":["math.AP","math.SP"],"title_canon_sha256":"3e1b3f25d232d590f1dfe128d2e9e27a02653e723eada54e959bd72620ce6f8d","abstract_canon_sha256":"6674e450a30c684ca8669d57a1d43ee1fd5fa48941f255106f249cabebe07752"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:36.622965Z","signature_b64":"lpw1Z/Tqd2kw5uGOqbXjiKh040LWaWvMLSn/EhHZJwNC1QG71aeWGcySQLEC7Of6OSB0uDVbPvQgitoleFUgAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5945d418541cf1376ccec0713473397d0f77090ec38103ec0e21a0483839bec8","last_reissued_at":"2026-05-18T04:05:36.622466Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:36.622466Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometric Ergodicity of a Hypoelliptic Diffusion Modelling The Melt-Spinning Process of Nonwoven Materials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.SP"],"primary_cat":"math.PR","authors_text":"Achim Wubker, Martin Kolb, Mladen Savov","submitted_at":"2011-12-28T18:07:24Z","abstract_excerpt":"We analyze the large time behavior of a stochastic model for the lay-down of fibers on a conveyor belt in the production process of nonwovens. It is shown, that under weak conditions this degenerate diffusion process is strong mixing, confirming a conjecture of Grothaus and Klar. Moreover, under some additional assumptions even geometric ergodicity is established using probabilistic tools -- described in the book of Meyn and Tweedie -- in combination with methods from stochastic analysis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.6159","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":"1112.6159","created_at":"2026-05-18T04:05:36.622553+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.6159v1","created_at":"2026-05-18T04:05:36.622553+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.6159","created_at":"2026-05-18T04:05:36.622553+00:00"},{"alias_kind":"pith_short_12","alias_value":"LFC5IGCUDTYT","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"LFC5IGCUDTYTO3GO","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"LFC5IGCU","created_at":"2026-05-18T12:26:34.985390+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/LFC5IGCUDTYTO3GOYBYTI4ZZPU","json":"https://pith.science/pith/LFC5IGCUDTYTO3GOYBYTI4ZZPU.json","graph_json":"https://pith.science/api/pith-number/LFC5IGCUDTYTO3GOYBYTI4ZZPU/graph.json","events_json":"https://pith.science/api/pith-number/LFC5IGCUDTYTO3GOYBYTI4ZZPU/events.json","paper":"https://pith.science/paper/LFC5IGCU"},"agent_actions":{"view_html":"https://pith.science/pith/LFC5IGCUDTYTO3GOYBYTI4ZZPU","download_json":"https://pith.science/pith/LFC5IGCUDTYTO3GOYBYTI4ZZPU.json","view_paper":"https://pith.science/paper/LFC5IGCU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.6159&json=true","fetch_graph":"https://pith.science/api/pith-number/LFC5IGCUDTYTO3GOYBYTI4ZZPU/graph.json","fetch_events":"https://pith.science/api/pith-number/LFC5IGCUDTYTO3GOYBYTI4ZZPU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LFC5IGCUDTYTO3GOYBYTI4ZZPU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LFC5IGCUDTYTO3GOYBYTI4ZZPU/action/storage_attestation","attest_author":"https://pith.science/pith/LFC5IGCUDTYTO3GOYBYTI4ZZPU/action/author_attestation","sign_citation":"https://pith.science/pith/LFC5IGCUDTYTO3GOYBYTI4ZZPU/action/citation_signature","submit_replication":"https://pith.science/pith/LFC5IGCUDTYTO3GOYBYTI4ZZPU/action/replication_record"}},"created_at":"2026-05-18T04:05:36.622553+00:00","updated_at":"2026-05-18T04:05:36.622553+00:00"}