{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:3QBAL4RJQL3K3SETAWSAR53O3F","short_pith_number":"pith:3QBAL4RJ","schema_version":"1.0","canonical_sha256":"dc0205f22982f6adc89305a408f76ed96ee246150a32482cc6c1686e1f8cb5f0","source":{"kind":"arxiv","id":"1802.01734","version":4},"attestation_state":"computed","paper":{"title":"Stochastic parabolic Anderson model with time-homogeneous generalized potential: Mild formulation of solution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hyun-Jung Kim","submitted_at":"2018-02-05T23:43:47Z","abstract_excerpt":"A mild formulation for stochastic parabolic Anderson model with time-homogeneous Gaussian potential suggests a way of defining a solution to obtain its optimal regularity. Two different interpretations in the equation or in the mild formulation are possible with usual pathwise product and the Wick product: the usual pathwise interpretation is mainly discussed. We emphasize that a modified version of parabolic Schauder estimates is a key idea for the existence and uniqueness of a mild solution. In particular, the mild formulation is crucial to investigate a relation between the equation with us"},"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":"1802.01734","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-05T23:43:47Z","cross_cats_sorted":[],"title_canon_sha256":"02dce0fa18608bf0f8e5826df7bf724b1c3174d2b5ac9b8eee209938a9a781d9","abstract_canon_sha256":"da7d842e8856297787481f37fb961a0dfaa0c4bc4e11f78f0ff93978568e8452"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:39.388419Z","signature_b64":"dG/IG4G6dbXzrtNxErMlop7EtrBQrGVNR2BA5p+78GvWR4bfLwAWzFXmrWwoOpB0e8OoDmCe6YU/UIp0k2tADQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc0205f22982f6adc89305a408f76ed96ee246150a32482cc6c1686e1f8cb5f0","last_reissued_at":"2026-05-18T00:05:39.387984Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:39.387984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stochastic parabolic Anderson model with time-homogeneous generalized potential: Mild formulation of solution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hyun-Jung Kim","submitted_at":"2018-02-05T23:43:47Z","abstract_excerpt":"A mild formulation for stochastic parabolic Anderson model with time-homogeneous Gaussian potential suggests a way of defining a solution to obtain its optimal regularity. Two different interpretations in the equation or in the mild formulation are possible with usual pathwise product and the Wick product: the usual pathwise interpretation is mainly discussed. We emphasize that a modified version of parabolic Schauder estimates is a key idea for the existence and uniqueness of a mild solution. In particular, the mild formulation is crucial to investigate a relation between the equation with us"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01734","kind":"arxiv","version":4},"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":"1802.01734","created_at":"2026-05-18T00:05:39.388056+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.01734v4","created_at":"2026-05-18T00:05:39.388056+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.01734","created_at":"2026-05-18T00:05:39.388056+00:00"},{"alias_kind":"pith_short_12","alias_value":"3QBAL4RJQL3K","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"3QBAL4RJQL3K3SET","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"3QBAL4RJ","created_at":"2026-05-18T12:32:02.567920+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/3QBAL4RJQL3K3SETAWSAR53O3F","json":"https://pith.science/pith/3QBAL4RJQL3K3SETAWSAR53O3F.json","graph_json":"https://pith.science/api/pith-number/3QBAL4RJQL3K3SETAWSAR53O3F/graph.json","events_json":"https://pith.science/api/pith-number/3QBAL4RJQL3K3SETAWSAR53O3F/events.json","paper":"https://pith.science/paper/3QBAL4RJ"},"agent_actions":{"view_html":"https://pith.science/pith/3QBAL4RJQL3K3SETAWSAR53O3F","download_json":"https://pith.science/pith/3QBAL4RJQL3K3SETAWSAR53O3F.json","view_paper":"https://pith.science/paper/3QBAL4RJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.01734&json=true","fetch_graph":"https://pith.science/api/pith-number/3QBAL4RJQL3K3SETAWSAR53O3F/graph.json","fetch_events":"https://pith.science/api/pith-number/3QBAL4RJQL3K3SETAWSAR53O3F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3QBAL4RJQL3K3SETAWSAR53O3F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3QBAL4RJQL3K3SETAWSAR53O3F/action/storage_attestation","attest_author":"https://pith.science/pith/3QBAL4RJQL3K3SETAWSAR53O3F/action/author_attestation","sign_citation":"https://pith.science/pith/3QBAL4RJQL3K3SETAWSAR53O3F/action/citation_signature","submit_replication":"https://pith.science/pith/3QBAL4RJQL3K3SETAWSAR53O3F/action/replication_record"}},"created_at":"2026-05-18T00:05:39.388056+00:00","updated_at":"2026-05-18T00:05:39.388056+00:00"}