{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:75H377E4P3IU73SWNNRLM2PV3P","short_pith_number":"pith:75H377E4","canonical_record":{"source":{"id":"1212.3816","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-12-16T18:48:15Z","cross_cats_sorted":["math.MP","math.PR","nlin.SI"],"title_canon_sha256":"5cc4f13d9a3daa2d405c89b73565837b325c3cce1b8b1bf5c5c1983cad81f0a6","abstract_canon_sha256":"4b19c37696d36a8588b0cb4a01a9f71899a3f1fcd75aeef49be92e76235b1ce2"},"schema_version":"1.0"},"canonical_sha256":"ff4fbffc9c7ed14fee566b62b669f5dbe77c86a8a2b6404828969b45c6738a4e","source":{"kind":"arxiv","id":"1212.3816","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3816","created_at":"2026-05-18T01:52:37Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3816v2","created_at":"2026-05-18T01:52:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3816","created_at":"2026-05-18T01:52:37Z"},{"alias_kind":"pith_short_12","alias_value":"75H377E4P3IU","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"75H377E4P3IU73SW","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"75H377E4","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:75H377E4P3IU73SWNNRLM2PV3P","target":"record","payload":{"canonical_record":{"source":{"id":"1212.3816","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-12-16T18:48:15Z","cross_cats_sorted":["math.MP","math.PR","nlin.SI"],"title_canon_sha256":"5cc4f13d9a3daa2d405c89b73565837b325c3cce1b8b1bf5c5c1983cad81f0a6","abstract_canon_sha256":"4b19c37696d36a8588b0cb4a01a9f71899a3f1fcd75aeef49be92e76235b1ce2"},"schema_version":"1.0"},"canonical_sha256":"ff4fbffc9c7ed14fee566b62b669f5dbe77c86a8a2b6404828969b45c6738a4e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:52:37.756608Z","signature_b64":"yqPej6ITPDe4vyTp6rt+1UX8fxDl5YK4jygwinHSJH3czREr87HrgbCeIvy9Au/lwvvJkmgsyxizB49Vst1zAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff4fbffc9c7ed14fee566b62b669f5dbe77c86a8a2b6404828969b45c6738a4e","last_reissued_at":"2026-05-18T01:52:37.756058Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:52:37.756058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.3816","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:52:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"npn8keFhu5qBNGQXfMg+R52qL77Okf1ki6kVPF2g6V66+wVJR7Emv5HxxQfsWgl318YLM8fdomLUvyA37ECWAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:01:44.074453Z"},"content_sha256":"6baeb1d3395e8ccb2b45f6cf04bd3d21205ef27e981782d0b8656372af3f0c62","schema_version":"1.0","event_id":"sha256:6baeb1d3395e8ccb2b45f6cf04bd3d21205ef27e981782d0b8656372af3f0c62"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:75H377E4P3IU73SWNNRLM2PV3P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tail decay for the distribution of the endpoint of a directed polymer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR","nlin.SI"],"primary_cat":"math-ph","authors_text":"Karl Liechty, Thomas Bothner","submitted_at":"2012-12-16T18:48:15Z","abstract_excerpt":"We obtain an asymptotic expansion for the tails of the random variable $\\tcal=\\arg\\max_{u\\in\\mathbb{R}}(\\mathcal{A}_2(u)-u^2)$ where $\\mathcal{A}_2$ is the Airy$_2$ process. Using the formula of Schehr \\cite{Sch} that connects the density function of $\\tcal$ to the Hastings-McLeod solution of the second Painlev\\'e equation, we prove that as $t\\rightarrow\\infty$, $\\mathbb{P}(|\\tcal|>t)=Ce^{-4/3\\varphi(t)}t^{-145/32}(1+O(t^{-3/4}))$, where $\\varphi(t)=t^3-2t^{3/2}+3t^{3/4}$, and the constant $C$ is given explicitly."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3816","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:52:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xaz+SQZgfYbXd+0NQOOBCGqudVFHRpqRRDErkAqjliweipa6i3MKuq5FRWhMP70MflJ+I1CABoMg8JJkcjZHAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:01:44.074805Z"},"content_sha256":"c18cadd4e9710844f68d299c78e620ce88746b189d6765e49c12d093f6b98de0","schema_version":"1.0","event_id":"sha256:c18cadd4e9710844f68d299c78e620ce88746b189d6765e49c12d093f6b98de0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/75H377E4P3IU73SWNNRLM2PV3P/bundle.json","state_url":"https://pith.science/pith/75H377E4P3IU73SWNNRLM2PV3P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/75H377E4P3IU73SWNNRLM2PV3P/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T17:01:44Z","links":{"resolver":"https://pith.science/pith/75H377E4P3IU73SWNNRLM2PV3P","bundle":"https://pith.science/pith/75H377E4P3IU73SWNNRLM2PV3P/bundle.json","state":"https://pith.science/pith/75H377E4P3IU73SWNNRLM2PV3P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/75H377E4P3IU73SWNNRLM2PV3P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:75H377E4P3IU73SWNNRLM2PV3P","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4b19c37696d36a8588b0cb4a01a9f71899a3f1fcd75aeef49be92e76235b1ce2","cross_cats_sorted":["math.MP","math.PR","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-12-16T18:48:15Z","title_canon_sha256":"5cc4f13d9a3daa2d405c89b73565837b325c3cce1b8b1bf5c5c1983cad81f0a6"},"schema_version":"1.0","source":{"id":"1212.3816","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3816","created_at":"2026-05-18T01:52:37Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3816v2","created_at":"2026-05-18T01:52:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3816","created_at":"2026-05-18T01:52:37Z"},{"alias_kind":"pith_short_12","alias_value":"75H377E4P3IU","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"75H377E4P3IU73SW","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"75H377E4","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:c18cadd4e9710844f68d299c78e620ce88746b189d6765e49c12d093f6b98de0","target":"graph","created_at":"2026-05-18T01:52:37Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We obtain an asymptotic expansion for the tails of the random variable $\\tcal=\\arg\\max_{u\\in\\mathbb{R}}(\\mathcal{A}_2(u)-u^2)$ where $\\mathcal{A}_2$ is the Airy$_2$ process. Using the formula of Schehr \\cite{Sch} that connects the density function of $\\tcal$ to the Hastings-McLeod solution of the second Painlev\\'e equation, we prove that as $t\\rightarrow\\infty$, $\\mathbb{P}(|\\tcal|>t)=Ce^{-4/3\\varphi(t)}t^{-145/32}(1+O(t^{-3/4}))$, where $\\varphi(t)=t^3-2t^{3/2}+3t^{3/4}$, and the constant $C$ is given explicitly.","authors_text":"Karl Liechty, Thomas Bothner","cross_cats":["math.MP","math.PR","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-12-16T18:48:15Z","title":"Tail decay for the distribution of the endpoint of a directed polymer"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3816","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6baeb1d3395e8ccb2b45f6cf04bd3d21205ef27e981782d0b8656372af3f0c62","target":"record","created_at":"2026-05-18T01:52:37Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4b19c37696d36a8588b0cb4a01a9f71899a3f1fcd75aeef49be92e76235b1ce2","cross_cats_sorted":["math.MP","math.PR","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-12-16T18:48:15Z","title_canon_sha256":"5cc4f13d9a3daa2d405c89b73565837b325c3cce1b8b1bf5c5c1983cad81f0a6"},"schema_version":"1.0","source":{"id":"1212.3816","kind":"arxiv","version":2}},"canonical_sha256":"ff4fbffc9c7ed14fee566b62b669f5dbe77c86a8a2b6404828969b45c6738a4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff4fbffc9c7ed14fee566b62b669f5dbe77c86a8a2b6404828969b45c6738a4e","first_computed_at":"2026-05-18T01:52:37.756058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:52:37.756058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yqPej6ITPDe4vyTp6rt+1UX8fxDl5YK4jygwinHSJH3czREr87HrgbCeIvy9Au/lwvvJkmgsyxizB49Vst1zAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:52:37.756608Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.3816","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6baeb1d3395e8ccb2b45f6cf04bd3d21205ef27e981782d0b8656372af3f0c62","sha256:c18cadd4e9710844f68d299c78e620ce88746b189d6765e49c12d093f6b98de0"],"state_sha256":"1516f38251cc4efa646d94ff7980fd73bc3f57af876962c53899640d8dbdcbdd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nRrBXe18/27uEagHUcpdHlgT+zqAPp7/KdskVfeffMqUnokIaXu2N8UQ4rX43KSw54ttYP8R0XmtCGOyptjSCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T17:01:44.076791Z","bundle_sha256":"a9d1c17527c9ca1157483b2f6aaa278895cb65ef14ae95c9cb382aceebb35024"}}