{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:MNGWSGKK4XW352EIZIYFKZNG4T","short_pith_number":"pith:MNGWSGKK","schema_version":"1.0","canonical_sha256":"634d69194ae5edbee888ca305565a6e4c3c5c3e1385fc7f6e1cbebeb1f8d322a","source":{"kind":"arxiv","id":"1211.0992","version":1},"attestation_state":"computed","paper":{"title":"The scaling relation chi = 2 xi - 1 for directed polymers in a random environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Antonio Auffinger, Michael Damron","submitted_at":"2012-11-05T20:33:51Z","abstract_excerpt":"We prove the scaling relation chi = 2 xi - 1 between the transversal exponent xi and the fluctuation exponent chi for directed polymers in a random environment in d dimensions. The definition of these exponents is similar to that proposed by S. Chatterjee in first-passage percolation. The proof presented here also establishes the relation in the zero temperature version of the model, known as last-passage percolation."},"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":"1211.0992","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-05T20:33:51Z","cross_cats_sorted":[],"title_canon_sha256":"e339a32c0c941f7889e53013eb0324097eb163a60a14fbbff0aacf2b90ef6e28","abstract_canon_sha256":"c9cee0115407cd5fc0e93455934a424214bc8adc5af416792c4bbae854bcfe21"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:01.129394Z","signature_b64":"WAjqT0Noj1+1BYZXB/F456puhDJ7pxiZB3yw+2G/t8RUtb8KmFHJcHF8IhT2+Pe9WzSLi1YB3sk3DsdXjSWABA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"634d69194ae5edbee888ca305565a6e4c3c5c3e1385fc7f6e1cbebeb1f8d322a","last_reissued_at":"2026-05-18T03:00:01.128611Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:01.128611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The scaling relation chi = 2 xi - 1 for directed polymers in a random environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Antonio Auffinger, Michael Damron","submitted_at":"2012-11-05T20:33:51Z","abstract_excerpt":"We prove the scaling relation chi = 2 xi - 1 between the transversal exponent xi and the fluctuation exponent chi for directed polymers in a random environment in d dimensions. The definition of these exponents is similar to that proposed by S. Chatterjee in first-passage percolation. The proof presented here also establishes the relation in the zero temperature version of the model, known as last-passage percolation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0992","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":"1211.0992","created_at":"2026-05-18T03:00:01.128731+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.0992v1","created_at":"2026-05-18T03:00:01.128731+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0992","created_at":"2026-05-18T03:00:01.128731+00:00"},{"alias_kind":"pith_short_12","alias_value":"MNGWSGKK4XW3","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"MNGWSGKK4XW352EI","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"MNGWSGKK","created_at":"2026-05-18T12:27:14.488303+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/MNGWSGKK4XW352EIZIYFKZNG4T","json":"https://pith.science/pith/MNGWSGKK4XW352EIZIYFKZNG4T.json","graph_json":"https://pith.science/api/pith-number/MNGWSGKK4XW352EIZIYFKZNG4T/graph.json","events_json":"https://pith.science/api/pith-number/MNGWSGKK4XW352EIZIYFKZNG4T/events.json","paper":"https://pith.science/paper/MNGWSGKK"},"agent_actions":{"view_html":"https://pith.science/pith/MNGWSGKK4XW352EIZIYFKZNG4T","download_json":"https://pith.science/pith/MNGWSGKK4XW352EIZIYFKZNG4T.json","view_paper":"https://pith.science/paper/MNGWSGKK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.0992&json=true","fetch_graph":"https://pith.science/api/pith-number/MNGWSGKK4XW352EIZIYFKZNG4T/graph.json","fetch_events":"https://pith.science/api/pith-number/MNGWSGKK4XW352EIZIYFKZNG4T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MNGWSGKK4XW352EIZIYFKZNG4T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MNGWSGKK4XW352EIZIYFKZNG4T/action/storage_attestation","attest_author":"https://pith.science/pith/MNGWSGKK4XW352EIZIYFKZNG4T/action/author_attestation","sign_citation":"https://pith.science/pith/MNGWSGKK4XW352EIZIYFKZNG4T/action/citation_signature","submit_replication":"https://pith.science/pith/MNGWSGKK4XW352EIZIYFKZNG4T/action/replication_record"}},"created_at":"2026-05-18T03:00:01.128731+00:00","updated_at":"2026-05-18T03:00:01.128731+00:00"}