{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1999:CQQM55OR7IABPDPQ2CMQCS4DIT","short_pith_number":"pith:CQQM55OR","schema_version":"1.0","canonical_sha256":"1420cef5d1fa00178df0d099014b8344e6e404de88169a1630da0b89e86d3db9","source":{"kind":"arxiv","id":"gr-qc/9902007","version":1},"attestation_state":"computed","paper":{"title":"On the factor ordering problem in stochastic inflation","license":"","headline":"","cross_cats":["hep-ph","hep-th"],"primary_cat":"gr-qc","authors_text":"Alexander Vilenkin (Tufts University)","submitted_at":"1999-02-01T19:54:53Z","abstract_excerpt":"The stochastic approach to inflation suffers from ambiguities due to the arbitrary choice of the time variable and due to the choice of the factor ordering in the corresponding Fokker-Planck equation. Here it is shown that both ambiguities can be removed if we require that the factor ordering should be set in such a way that physical results are invariant with respect to time reparametrizations. This requirement uniquely selects the so-called Ito factor ordering. Additional ambiguities associated with non-trivial kinetic terms of the scalar fields are also discussed, as well as ways of constra"},"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":"gr-qc/9902007","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"1999-02-01T19:54:53Z","cross_cats_sorted":["hep-ph","hep-th"],"title_canon_sha256":"86ebfac690fb28161c2c4b85488a99db76bdeed57f972183da87879624492f58","abstract_canon_sha256":"7d2556a9e4bfb31e81927013feb9d9ad79523374afd5433d77cae29ada28e24c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:01.152383Z","signature_b64":"ESkkbXNsUMyd9VUIMMiN9Y0kiTucM6BeG7SgaVtMvU08Lmnd6DYJBG/gpE6FzOzJ5qqG2HkwBZYMH5sAqBHGAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1420cef5d1fa00178df0d099014b8344e6e404de88169a1630da0b89e86d3db9","last_reissued_at":"2026-05-18T01:08:01.152011Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:01.152011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the factor ordering problem in stochastic inflation","license":"","headline":"","cross_cats":["hep-ph","hep-th"],"primary_cat":"gr-qc","authors_text":"Alexander Vilenkin (Tufts University)","submitted_at":"1999-02-01T19:54:53Z","abstract_excerpt":"The stochastic approach to inflation suffers from ambiguities due to the arbitrary choice of the time variable and due to the choice of the factor ordering in the corresponding Fokker-Planck equation. Here it is shown that both ambiguities can be removed if we require that the factor ordering should be set in such a way that physical results are invariant with respect to time reparametrizations. This requirement uniquely selects the so-called Ito factor ordering. Additional ambiguities associated with non-trivial kinetic terms of the scalar fields are also discussed, as well as ways of constra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/9902007","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":"gr-qc/9902007","created_at":"2026-05-18T01:08:01.152067+00:00"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/9902007v1","created_at":"2026-05-18T01:08:01.152067+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/9902007","created_at":"2026-05-18T01:08:01.152067+00:00"},{"alias_kind":"pith_short_12","alias_value":"CQQM55OR7IAB","created_at":"2026-05-18T12:25:49.038998+00:00"},{"alias_kind":"pith_short_16","alias_value":"CQQM55OR7IABPDPQ","created_at":"2026-05-18T12:25:49.038998+00:00"},{"alias_kind":"pith_short_8","alias_value":"CQQM55OR","created_at":"2026-05-18T12:25:49.038998+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.12465","citing_title":"It\\^{o}, Stratonovich, and zoom-in schemes in stochastic inflation","ref_index":57,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CQQM55OR7IABPDPQ2CMQCS4DIT","json":"https://pith.science/pith/CQQM55OR7IABPDPQ2CMQCS4DIT.json","graph_json":"https://pith.science/api/pith-number/CQQM55OR7IABPDPQ2CMQCS4DIT/graph.json","events_json":"https://pith.science/api/pith-number/CQQM55OR7IABPDPQ2CMQCS4DIT/events.json","paper":"https://pith.science/paper/CQQM55OR"},"agent_actions":{"view_html":"https://pith.science/pith/CQQM55OR7IABPDPQ2CMQCS4DIT","download_json":"https://pith.science/pith/CQQM55OR7IABPDPQ2CMQCS4DIT.json","view_paper":"https://pith.science/paper/CQQM55OR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=gr-qc/9902007&json=true","fetch_graph":"https://pith.science/api/pith-number/CQQM55OR7IABPDPQ2CMQCS4DIT/graph.json","fetch_events":"https://pith.science/api/pith-number/CQQM55OR7IABPDPQ2CMQCS4DIT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CQQM55OR7IABPDPQ2CMQCS4DIT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CQQM55OR7IABPDPQ2CMQCS4DIT/action/storage_attestation","attest_author":"https://pith.science/pith/CQQM55OR7IABPDPQ2CMQCS4DIT/action/author_attestation","sign_citation":"https://pith.science/pith/CQQM55OR7IABPDPQ2CMQCS4DIT/action/citation_signature","submit_replication":"https://pith.science/pith/CQQM55OR7IABPDPQ2CMQCS4DIT/action/replication_record"}},"created_at":"2026-05-18T01:08:01.152067+00:00","updated_at":"2026-05-18T01:08:01.152067+00:00"}