{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:4FL5Y4SCFOVPS5M2YBQGSDP4N3","short_pith_number":"pith:4FL5Y4SC","canonical_record":{"source":{"id":"math/0606296","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2006-06-13T19:21:46Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0efc1c7a40cdd6469d34e985e1e94d97c633b21d3dd2648aaace86bda25ab51f","abstract_canon_sha256":"ac588aefb84efdb0f0561efa7920ed5633cc98a675fb166fd9f92eef99741f4f"},"schema_version":"1.0"},"canonical_sha256":"e157dc72422baaf9759ac060690dfc6efe1d778504f87c35d1f9a8af862e38c5","source":{"kind":"arxiv","id":"math/0606296","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0606296","created_at":"2026-05-18T03:34:00Z"},{"alias_kind":"arxiv_version","alias_value":"math/0606296v1","created_at":"2026-05-18T03:34:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0606296","created_at":"2026-05-18T03:34:00Z"},{"alias_kind":"pith_short_12","alias_value":"4FL5Y4SCFOVP","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"4FL5Y4SCFOVPS5M2","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"4FL5Y4SC","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:4FL5Y4SCFOVPS5M2YBQGSDP4N3","target":"record","payload":{"canonical_record":{"source":{"id":"math/0606296","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2006-06-13T19:21:46Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0efc1c7a40cdd6469d34e985e1e94d97c633b21d3dd2648aaace86bda25ab51f","abstract_canon_sha256":"ac588aefb84efdb0f0561efa7920ed5633cc98a675fb166fd9f92eef99741f4f"},"schema_version":"1.0"},"canonical_sha256":"e157dc72422baaf9759ac060690dfc6efe1d778504f87c35d1f9a8af862e38c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:00.443588Z","signature_b64":"lksLhg24/BBrGXBuxADWzOPenimfqafhnY7iv61QUVc42yRq0N/aqicW290a8g2JaVDs9pndOuGW2Yjt+wCdBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e157dc72422baaf9759ac060690dfc6efe1d778504f87c35d1f9a8af862e38c5","last_reissued_at":"2026-05-18T03:34:00.442704Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:00.442704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0606296","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:34:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9+Bc+0tHq30e9ZilXabXSBcfEBuH6pTlC2ZTOsGGnENJPhq0BGYywmdR4YUctzvJkraS++9DMoLK7CcUwEVZCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:13:44.771605Z"},"content_sha256":"af71ca781cbb6fa41ccbeef9b64b886460d1b9411499db0404f5d1341371aeac","schema_version":"1.0","event_id":"sha256:af71ca781cbb6fa41ccbeef9b64b886460d1b9411499db0404f5d1341371aeac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:4FL5Y4SCFOVPS5M2YBQGSDP4N3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the free energy of a directed polymer in a Brownian environment","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"John Moriarty, Neil O'Connell","submitted_at":"2006-06-13T19:21:46Z","abstract_excerpt":"We prove a formula conjectured in O'Connell and Yor (2001) for the free energy density of a directed polymer in a Brownian environment in 1+1 dimensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606296","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:34:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pkINohpbXVHsyHXltdFIPiNlWa0FYS3RYN1PzFmdhK/bODslDjQ7JXz17LLPfdUhWpEkyd+2yTPZgSKgmG67CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:13:44.772227Z"},"content_sha256":"03a83dabfd80713e4f40003a0988c5bf44427474f81a9f3d52aaf066c89112e7","schema_version":"1.0","event_id":"sha256:03a83dabfd80713e4f40003a0988c5bf44427474f81a9f3d52aaf066c89112e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4FL5Y4SCFOVPS5M2YBQGSDP4N3/bundle.json","state_url":"https://pith.science/pith/4FL5Y4SCFOVPS5M2YBQGSDP4N3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4FL5Y4SCFOVPS5M2YBQGSDP4N3/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":"2026-05-31T01:13:44Z","links":{"resolver":"https://pith.science/pith/4FL5Y4SCFOVPS5M2YBQGSDP4N3","bundle":"https://pith.science/pith/4FL5Y4SCFOVPS5M2YBQGSDP4N3/bundle.json","state":"https://pith.science/pith/4FL5Y4SCFOVPS5M2YBQGSDP4N3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4FL5Y4SCFOVPS5M2YBQGSDP4N3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:4FL5Y4SCFOVPS5M2YBQGSDP4N3","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":"ac588aefb84efdb0f0561efa7920ed5633cc98a675fb166fd9f92eef99741f4f","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.PR","submitted_at":"2006-06-13T19:21:46Z","title_canon_sha256":"0efc1c7a40cdd6469d34e985e1e94d97c633b21d3dd2648aaace86bda25ab51f"},"schema_version":"1.0","source":{"id":"math/0606296","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0606296","created_at":"2026-05-18T03:34:00Z"},{"alias_kind":"arxiv_version","alias_value":"math/0606296v1","created_at":"2026-05-18T03:34:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0606296","created_at":"2026-05-18T03:34:00Z"},{"alias_kind":"pith_short_12","alias_value":"4FL5Y4SCFOVP","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"4FL5Y4SCFOVPS5M2","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"4FL5Y4SC","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:03a83dabfd80713e4f40003a0988c5bf44427474f81a9f3d52aaf066c89112e7","target":"graph","created_at":"2026-05-18T03:34:00Z","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 prove a formula conjectured in O'Connell and Yor (2001) for the free energy density of a directed polymer in a Brownian environment in 1+1 dimensions.","authors_text":"John Moriarty, Neil O'Connell","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2006-06-13T19:21:46Z","title":"On the free energy of a directed polymer in a Brownian environment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606296","kind":"arxiv","version":1},"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:af71ca781cbb6fa41ccbeef9b64b886460d1b9411499db0404f5d1341371aeac","target":"record","created_at":"2026-05-18T03:34:00Z","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":"ac588aefb84efdb0f0561efa7920ed5633cc98a675fb166fd9f92eef99741f4f","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.PR","submitted_at":"2006-06-13T19:21:46Z","title_canon_sha256":"0efc1c7a40cdd6469d34e985e1e94d97c633b21d3dd2648aaace86bda25ab51f"},"schema_version":"1.0","source":{"id":"math/0606296","kind":"arxiv","version":1}},"canonical_sha256":"e157dc72422baaf9759ac060690dfc6efe1d778504f87c35d1f9a8af862e38c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e157dc72422baaf9759ac060690dfc6efe1d778504f87c35d1f9a8af862e38c5","first_computed_at":"2026-05-18T03:34:00.442704Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:00.442704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lksLhg24/BBrGXBuxADWzOPenimfqafhnY7iv61QUVc42yRq0N/aqicW290a8g2JaVDs9pndOuGW2Yjt+wCdBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:00.443588Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0606296","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af71ca781cbb6fa41ccbeef9b64b886460d1b9411499db0404f5d1341371aeac","sha256:03a83dabfd80713e4f40003a0988c5bf44427474f81a9f3d52aaf066c89112e7"],"state_sha256":"c21310d544a4baf26fac7b28dd3e38b914098f400902b4529ad4f3233294656b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F9kczPw5ATYc4uVNmzv5yqqor1X/pYn1f96CKWrYtqp/5oP9Raxv8Qoixx7fPVs45QZHDP7oqygZ0NZzl4yYDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T01:13:44.776660Z","bundle_sha256":"94b77edb28ee31dd05c1194a00995e998c8aaaf5b605c8d902397eb4fb704f3a"}}