{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:KKT3JFKKCIR3OYI46CAIWU5ETV","short_pith_number":"pith:KKT3JFKK","schema_version":"1.0","canonical_sha256":"52a7b4954a1223b7611cf0808b53a49d51ea67ba98f651b61546660a9bd7adb1","source":{"kind":"arxiv","id":"2303.04224","version":3},"attestation_state":"computed","paper":{"title":"Differentiability of the Shape Function for Directed Polymers in Continuous Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Douglas Dow, Yuri Bakhtin","submitted_at":"2023-03-07T20:34:06Z","abstract_excerpt":"For directed polymers, the shape function computes the limiting average energy accrued by paths with a given average slope. We prove that, for a large family of directed polymer models in discrete time and continuous space in dimension $1+1$, for positive and zero temperature, the shape function is differentiable with respect to the slope on the entire real line."},"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":"2303.04224","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-03-07T20:34:06Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"fda8076f9321a9fbd8808910144a8c7e841cbd9d200fa9d22901da84240868e2","abstract_canon_sha256":"24046cf9f1616fddd1724548a0febecdd8207a2ec72996f0d121022ff60afc61"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:23:02.333455Z","signature_b64":"zD71iuS4KAgp5Fk+ioMJKoqW0RDnh+I/Arhu0EFNi6Qg2/tUyIbc6MT0C+TQXAolFu9OtFDd/r7iMfX+C+0LDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52a7b4954a1223b7611cf0808b53a49d51ea67ba98f651b61546660a9bd7adb1","last_reissued_at":"2026-07-05T06:23:02.333078Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:23:02.333078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Differentiability of the Shape Function for Directed Polymers in Continuous Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Douglas Dow, Yuri Bakhtin","submitted_at":"2023-03-07T20:34:06Z","abstract_excerpt":"For directed polymers, the shape function computes the limiting average energy accrued by paths with a given average slope. We prove that, for a large family of directed polymer models in discrete time and continuous space in dimension $1+1$, for positive and zero temperature, the shape function is differentiable with respect to the slope on the entire real line."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.04224","kind":"arxiv","version":3},"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/2303.04224/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":"2303.04224","created_at":"2026-07-05T06:23:02.333126+00:00"},{"alias_kind":"arxiv_version","alias_value":"2303.04224v3","created_at":"2026-07-05T06:23:02.333126+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.04224","created_at":"2026-07-05T06:23:02.333126+00:00"},{"alias_kind":"pith_short_12","alias_value":"KKT3JFKKCIR3","created_at":"2026-07-05T06:23:02.333126+00:00"},{"alias_kind":"pith_short_16","alias_value":"KKT3JFKKCIR3OYI4","created_at":"2026-07-05T06:23:02.333126+00:00"},{"alias_kind":"pith_short_8","alias_value":"KKT3JFKK","created_at":"2026-07-05T06:23:02.333126+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.13030","citing_title":"Classification of the limit shape for 1+1-dimensional FPP","ref_index":19,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KKT3JFKKCIR3OYI46CAIWU5ETV","json":"https://pith.science/pith/KKT3JFKKCIR3OYI46CAIWU5ETV.json","graph_json":"https://pith.science/api/pith-number/KKT3JFKKCIR3OYI46CAIWU5ETV/graph.json","events_json":"https://pith.science/api/pith-number/KKT3JFKKCIR3OYI46CAIWU5ETV/events.json","paper":"https://pith.science/paper/KKT3JFKK"},"agent_actions":{"view_html":"https://pith.science/pith/KKT3JFKKCIR3OYI46CAIWU5ETV","download_json":"https://pith.science/pith/KKT3JFKKCIR3OYI46CAIWU5ETV.json","view_paper":"https://pith.science/paper/KKT3JFKK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2303.04224&json=true","fetch_graph":"https://pith.science/api/pith-number/KKT3JFKKCIR3OYI46CAIWU5ETV/graph.json","fetch_events":"https://pith.science/api/pith-number/KKT3JFKKCIR3OYI46CAIWU5ETV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KKT3JFKKCIR3OYI46CAIWU5ETV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KKT3JFKKCIR3OYI46CAIWU5ETV/action/storage_attestation","attest_author":"https://pith.science/pith/KKT3JFKKCIR3OYI46CAIWU5ETV/action/author_attestation","sign_citation":"https://pith.science/pith/KKT3JFKKCIR3OYI46CAIWU5ETV/action/citation_signature","submit_replication":"https://pith.science/pith/KKT3JFKKCIR3OYI46CAIWU5ETV/action/replication_record"}},"created_at":"2026-07-05T06:23:02.333126+00:00","updated_at":"2026-07-05T06:23:02.333126+00:00"}