{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:SAS3I25LGL5LWTB64BQHEELQQ2","short_pith_number":"pith:SAS3I25L","schema_version":"1.0","canonical_sha256":"9025b46bab32fabb4c3ee0607211708691a6c6779f6c17e172efe5ad6be298ac","source":{"kind":"arxiv","id":"2208.11255","version":2},"attestation_state":"computed","paper":{"title":"The Green's function of the parabolic Anderson model and the continuum directed polymer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christopher Janjigian, Firas Rassoul-Agha, Timo Sepp\\\"al\\\"ainen, Tom Alberts","submitted_at":"2022-08-24T01:27:28Z","abstract_excerpt":"We build a regular version of the field $Z_{\\beta}(t,x|s,y)$ which describes the Green's function, or fundamental solution, of the parabolic Anderson model (PAM) with white noise forcing on $\\mathbb{R}^{1+1}$: $\\partial_t Z_{\\beta}(t,x | s,y) =$ $\\frac{1}{2}\\partial_{xx} Z_{\\beta}(t,x|s,y) + \\beta Z_{\\beta}(t,x | s,y)W(t,x)$, $Z_{\\beta}(s,x | s,y) = \\delta(x-y)$ for all $-\\infty < s \\leq t < \\infty$, all $x,y \\in \\mathbb{R}$, and all $\\beta \\in \\mathbb{R}$ simultaneously. Through the superposition principle, our construction gives a pointwise coupling of all solutions to the PAM with initial o"},"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":"2208.11255","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-08-24T01:27:28Z","cross_cats_sorted":[],"title_canon_sha256":"91bb5fc4789c5ff5ba6ce45fde4767936a5703224fa18c18513bb86ae0411347","abstract_canon_sha256":"e60ddeda3552b5625bc84de652c5df5f885e8129ad751d0a59976a730ac18aa3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:16:02.747185Z","signature_b64":"PzEK66ynYctSyVTe1/FVWsJbXiSNJqP5AWmNttyx0ho561YuGrOLZ+wYbV8Z14mSvhIUAEdhtNp2EGF/w00gCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9025b46bab32fabb4c3ee0607211708691a6c6779f6c17e172efe5ad6be298ac","last_reissued_at":"2026-07-05T05:16:02.746682Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:16:02.746682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Green's function of the parabolic Anderson model and the continuum directed polymer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christopher Janjigian, Firas Rassoul-Agha, Timo Sepp\\\"al\\\"ainen, Tom Alberts","submitted_at":"2022-08-24T01:27:28Z","abstract_excerpt":"We build a regular version of the field $Z_{\\beta}(t,x|s,y)$ which describes the Green's function, or fundamental solution, of the parabolic Anderson model (PAM) with white noise forcing on $\\mathbb{R}^{1+1}$: $\\partial_t Z_{\\beta}(t,x | s,y) =$ $\\frac{1}{2}\\partial_{xx} Z_{\\beta}(t,x|s,y) + \\beta Z_{\\beta}(t,x | s,y)W(t,x)$, $Z_{\\beta}(s,x | s,y) = \\delta(x-y)$ for all $-\\infty < s \\leq t < \\infty$, all $x,y \\in \\mathbb{R}$, and all $\\beta \\in \\mathbb{R}$ simultaneously. Through the superposition principle, our construction gives a pointwise coupling of all solutions to the PAM with initial o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.11255","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2208.11255/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2208.11255","created_at":"2026-07-05T05:16:02.746727+00:00"},{"alias_kind":"arxiv_version","alias_value":"2208.11255v2","created_at":"2026-07-05T05:16:02.746727+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.11255","created_at":"2026-07-05T05:16:02.746727+00:00"},{"alias_kind":"pith_short_12","alias_value":"SAS3I25LGL5L","created_at":"2026-07-05T05:16:02.746727+00:00"},{"alias_kind":"pith_short_16","alias_value":"SAS3I25LGL5LWTB6","created_at":"2026-07-05T05:16:02.746727+00:00"},{"alias_kind":"pith_short_8","alias_value":"SAS3I25L","created_at":"2026-07-05T05:16:02.746727+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.23065","citing_title":"Spatial decorrelation of KPZ from narrow wedge","ref_index":1,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SAS3I25LGL5LWTB64BQHEELQQ2","json":"https://pith.science/pith/SAS3I25LGL5LWTB64BQHEELQQ2.json","graph_json":"https://pith.science/api/pith-number/SAS3I25LGL5LWTB64BQHEELQQ2/graph.json","events_json":"https://pith.science/api/pith-number/SAS3I25LGL5LWTB64BQHEELQQ2/events.json","paper":"https://pith.science/paper/SAS3I25L"},"agent_actions":{"view_html":"https://pith.science/pith/SAS3I25LGL5LWTB64BQHEELQQ2","download_json":"https://pith.science/pith/SAS3I25LGL5LWTB64BQHEELQQ2.json","view_paper":"https://pith.science/paper/SAS3I25L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2208.11255&json=true","fetch_graph":"https://pith.science/api/pith-number/SAS3I25LGL5LWTB64BQHEELQQ2/graph.json","fetch_events":"https://pith.science/api/pith-number/SAS3I25LGL5LWTB64BQHEELQQ2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SAS3I25LGL5LWTB64BQHEELQQ2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SAS3I25LGL5LWTB64BQHEELQQ2/action/storage_attestation","attest_author":"https://pith.science/pith/SAS3I25LGL5LWTB64BQHEELQQ2/action/author_attestation","sign_citation":"https://pith.science/pith/SAS3I25LGL5LWTB64BQHEELQQ2/action/citation_signature","submit_replication":"https://pith.science/pith/SAS3I25LGL5LWTB64BQHEELQQ2/action/replication_record"}},"created_at":"2026-07-05T05:16:02.746727+00:00","updated_at":"2026-07-05T05:16:02.746727+00:00"}