{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:IEQCJXI2WTQ72XHCXWM47BCPO6","short_pith_number":"pith:IEQCJXI2","canonical_record":{"source":{"id":"1810.03580","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-08T17:03:10Z","cross_cats_sorted":[],"title_canon_sha256":"fd0e425eb2f0ddf7f412f3f05593df2e877e906411d36080a670d47644a42bae","abstract_canon_sha256":"2d90f9e92fb530a5e09613df1223cd2621deaef9f1012da5fd76c9100537e2dd"},"schema_version":"1.0"},"canonical_sha256":"412024dd1ab4e1fd5ce2bd99cf844f77944e52f011698fb33fded091b66c290e","source":{"kind":"arxiv","id":"1810.03580","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03580","created_at":"2026-07-05T01:06:29Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03580v3","created_at":"2026-07-05T01:06:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03580","created_at":"2026-07-05T01:06:29Z"},{"alias_kind":"pith_short_12","alias_value":"IEQCJXI2WTQ7","created_at":"2026-07-05T01:06:29Z"},{"alias_kind":"pith_short_16","alias_value":"IEQCJXI2WTQ72XHC","created_at":"2026-07-05T01:06:29Z"},{"alias_kind":"pith_short_8","alias_value":"IEQCJXI2","created_at":"2026-07-05T01:06:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:IEQCJXI2WTQ72XHCXWM47BCPO6","target":"record","payload":{"canonical_record":{"source":{"id":"1810.03580","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-08T17:03:10Z","cross_cats_sorted":[],"title_canon_sha256":"fd0e425eb2f0ddf7f412f3f05593df2e877e906411d36080a670d47644a42bae","abstract_canon_sha256":"2d90f9e92fb530a5e09613df1223cd2621deaef9f1012da5fd76c9100537e2dd"},"schema_version":"1.0"},"canonical_sha256":"412024dd1ab4e1fd5ce2bd99cf844f77944e52f011698fb33fded091b66c290e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:06:29.749301Z","signature_b64":"3gc30A9kDxLU3kalWC1LJi/sbDTXdbCDW78Idlm5wHLdIMaa7Jj82oHvR9XC2qpgMN/8LgG+97tMykPR4CY2Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"412024dd1ab4e1fd5ce2bd99cf844f77944e52f011698fb33fded091b66c290e","last_reissued_at":"2026-07-05T01:06:29.748842Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:06:29.748842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.03580","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:06:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B1954nNkKe3Dhuva1hkHUQ/TYsqOpC3Fet4WZ8vt/Sfmk+vQ0cJ5UCO0XP0c/b/rza4jfm6JZv1/vvyyIS5bAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T21:10:53.121947Z"},"content_sha256":"605216b57175c3a25d6c2ee7c40bbaba3aaa9cdaa3a0296acb832b141d15fe30","schema_version":"1.0","event_id":"sha256:605216b57175c3a25d6c2ee7c40bbaba3aaa9cdaa3a0296acb832b141d15fe30"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:IEQCJXI2WTQ72XHCXWM47BCPO6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Busemann functions and Gibbs measures in directed polymer models on $\\mathbb{Z}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christopher Janjigian, Firas Rassoul-Agha","submitted_at":"2018-10-08T17:03:10Z","abstract_excerpt":"We consider random walk in a space-time random potential, also known as directed random polymer measures, on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices. We construct covariant cocycles and use them to prove new results on existence, uniqueness/non-uniqueness, and asymptotic directions of semi-infinite polymer measures (solutions to the Dobrushin-Lanford-Ruelle equations). We also prove non-existence of covariant or deterministically directed bi-infinite polymer measures. Along the way, we prove almost sure existence of Busemann function lim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03580","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/1810.03580/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:06:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kIjfIn2aTHjHlsr+SsxzOhPZbqWc26fhgDUtomFoLqTEQsymp/tEX7mGxaNz8aoSjMnoZAZvxD5b11NaINskCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T21:10:53.122532Z"},"content_sha256":"e22e1c401c233f839680032149c4fc356272388a0d33ae609a53be7b178e07a4","schema_version":"1.0","event_id":"sha256:e22e1c401c233f839680032149c4fc356272388a0d33ae609a53be7b178e07a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IEQCJXI2WTQ72XHCXWM47BCPO6/bundle.json","state_url":"https://pith.science/pith/IEQCJXI2WTQ72XHCXWM47BCPO6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IEQCJXI2WTQ72XHCXWM47BCPO6/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":"2026-08-16T21:10:53Z","links":{"resolver":"https://pith.science/pith/IEQCJXI2WTQ72XHCXWM47BCPO6","bundle":"https://pith.science/pith/IEQCJXI2WTQ72XHCXWM47BCPO6/bundle.json","state":"https://pith.science/pith/IEQCJXI2WTQ72XHCXWM47BCPO6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IEQCJXI2WTQ72XHCXWM47BCPO6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IEQCJXI2WTQ72XHCXWM47BCPO6","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":"2d90f9e92fb530a5e09613df1223cd2621deaef9f1012da5fd76c9100537e2dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-08T17:03:10Z","title_canon_sha256":"fd0e425eb2f0ddf7f412f3f05593df2e877e906411d36080a670d47644a42bae"},"schema_version":"1.0","source":{"id":"1810.03580","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03580","created_at":"2026-07-05T01:06:29Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03580v3","created_at":"2026-07-05T01:06:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03580","created_at":"2026-07-05T01:06:29Z"},{"alias_kind":"pith_short_12","alias_value":"IEQCJXI2WTQ7","created_at":"2026-07-05T01:06:29Z"},{"alias_kind":"pith_short_16","alias_value":"IEQCJXI2WTQ72XHC","created_at":"2026-07-05T01:06:29Z"},{"alias_kind":"pith_short_8","alias_value":"IEQCJXI2","created_at":"2026-07-05T01:06:29Z"}],"graph_snapshots":[{"event_id":"sha256:e22e1c401c233f839680032149c4fc356272388a0d33ae609a53be7b178e07a4","target":"graph","created_at":"2026-07-05T01:06:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1810.03580/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider random walk in a space-time random potential, also known as directed random polymer measures, on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices. We construct covariant cocycles and use them to prove new results on existence, uniqueness/non-uniqueness, and asymptotic directions of semi-infinite polymer measures (solutions to the Dobrushin-Lanford-Ruelle equations). We also prove non-existence of covariant or deterministically directed bi-infinite polymer measures. Along the way, we prove almost sure existence of Busemann function lim","authors_text":"Christopher Janjigian, Firas Rassoul-Agha","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-08T17:03:10Z","title":"Busemann functions and Gibbs measures in directed polymer models on $\\mathbb{Z}^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03580","kind":"arxiv","version":3},"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":"sha256:605216b57175c3a25d6c2ee7c40bbaba3aaa9cdaa3a0296acb832b141d15fe30","target":"record","created_at":"2026-07-05T01:06:29Z","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":"2d90f9e92fb530a5e09613df1223cd2621deaef9f1012da5fd76c9100537e2dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-08T17:03:10Z","title_canon_sha256":"fd0e425eb2f0ddf7f412f3f05593df2e877e906411d36080a670d47644a42bae"},"schema_version":"1.0","source":{"id":"1810.03580","kind":"arxiv","version":3}},"canonical_sha256":"412024dd1ab4e1fd5ce2bd99cf844f77944e52f011698fb33fded091b66c290e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"412024dd1ab4e1fd5ce2bd99cf844f77944e52f011698fb33fded091b66c290e","first_computed_at":"2026-07-05T01:06:29.748842Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:06:29.748842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3gc30A9kDxLU3kalWC1LJi/sbDTXdbCDW78Idlm5wHLdIMaa7Jj82oHvR9XC2qpgMN/8LgG+97tMykPR4CY2Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T01:06:29.749301Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.03580","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:605216b57175c3a25d6c2ee7c40bbaba3aaa9cdaa3a0296acb832b141d15fe30","sha256:e22e1c401c233f839680032149c4fc356272388a0d33ae609a53be7b178e07a4"],"state_sha256":"fa140b7fa6f6d4fe24b6a9dacef88969de604b58535814fc9095f28cb68cdff9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t0vxv4jP8DxHWBRj5apjoZDkzsjawfrVqq7GuwVXtrq1A06SyCKhScRZ47axV2J9wEgHNBdmVOrjNH3drk/XAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T21:10:53.126766Z","bundle_sha256":"214aca0ad081bfdfe324a79d53da83c236c1edb4943e33768cec56aa63109a61"}}