{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:5ZMSBCP3VMSX3SQYNQRDNSFOKE","short_pith_number":"pith:5ZMSBCP3","schema_version":"1.0","canonical_sha256":"ee592089fbab257dca186c2236c8ae5100e709687c00c0c5a901dc0ee1cb3724","source":{"kind":"arxiv","id":"2308.07312","version":1},"attestation_state":"computed","paper":{"title":"Geodesic trees in last passage percolation and some related problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"M\\'arton Bal\\'azs, Riddhipratim Basu, Sudeshna Bhattacharjee","submitted_at":"2023-08-14T17:57:37Z","abstract_excerpt":"For the exactly solvable model of exponential last passage percolation on $\\mathbb{Z}^2$, it is known that given any non-axial direction, all the semi-infinite geodesics starting from points in $\\mathbb{Z}^2$ in that direction almost surely coalesce, thereby forming a geodesic tree which has only one end. It is widely understood that the geodesic trees are important objects in understanding the geometry of the LPP landscape. In this paper we study several natural questions about these geodesic trees and their intersections. In particular, we obtain optimal (up to constants) upper and lower bou"},"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":"2308.07312","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-08-14T17:57:37Z","cross_cats_sorted":[],"title_canon_sha256":"74ce1bbdbbfb78c8346810aa7681daad1ed7617c45ba5731dcc650b28f6d89e7","abstract_canon_sha256":"1e7b3ebc3b8047b332147ebcf673d69040840060a7ef897693387721aa9108f0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:40:59.076340Z","signature_b64":"tMWtGaRw+o2kvGmtRojJPtCVl4UxEmz9rFAQKxwYHGBH9+v26ZTtU8oT7bsWwk4/0JFS1+8zcEqcmZgGeeSODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee592089fbab257dca186c2236c8ae5100e709687c00c0c5a901dc0ee1cb3724","last_reissued_at":"2026-07-05T06:40:59.075863Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:40:59.075863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geodesic trees in last passage percolation and some related problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"M\\'arton Bal\\'azs, Riddhipratim Basu, Sudeshna Bhattacharjee","submitted_at":"2023-08-14T17:57:37Z","abstract_excerpt":"For the exactly solvable model of exponential last passage percolation on $\\mathbb{Z}^2$, it is known that given any non-axial direction, all the semi-infinite geodesics starting from points in $\\mathbb{Z}^2$ in that direction almost surely coalesce, thereby forming a geodesic tree which has only one end. It is widely understood that the geodesic trees are important objects in understanding the geometry of the LPP landscape. In this paper we study several natural questions about these geodesic trees and their intersections. In particular, we obtain optimal (up to constants) upper and lower bou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.07312","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2308.07312/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":"2308.07312","created_at":"2026-07-05T06:40:59.075916+00:00"},{"alias_kind":"arxiv_version","alias_value":"2308.07312v1","created_at":"2026-07-05T06:40:59.075916+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.07312","created_at":"2026-07-05T06:40:59.075916+00:00"},{"alias_kind":"pith_short_12","alias_value":"5ZMSBCP3VMSX","created_at":"2026-07-05T06:40:59.075916+00:00"},{"alias_kind":"pith_short_16","alias_value":"5ZMSBCP3VMSX3SQY","created_at":"2026-07-05T06:40:59.075916+00:00"},{"alias_kind":"pith_short_8","alias_value":"5ZMSBCP3","created_at":"2026-07-05T06:40:59.075916+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2412.03067","citing_title":"Geodesic Trees and Exceptional Directions in FPP on Hyperbolic Groups","ref_index":6,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5ZMSBCP3VMSX3SQYNQRDNSFOKE","json":"https://pith.science/pith/5ZMSBCP3VMSX3SQYNQRDNSFOKE.json","graph_json":"https://pith.science/api/pith-number/5ZMSBCP3VMSX3SQYNQRDNSFOKE/graph.json","events_json":"https://pith.science/api/pith-number/5ZMSBCP3VMSX3SQYNQRDNSFOKE/events.json","paper":"https://pith.science/paper/5ZMSBCP3"},"agent_actions":{"view_html":"https://pith.science/pith/5ZMSBCP3VMSX3SQYNQRDNSFOKE","download_json":"https://pith.science/pith/5ZMSBCP3VMSX3SQYNQRDNSFOKE.json","view_paper":"https://pith.science/paper/5ZMSBCP3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2308.07312&json=true","fetch_graph":"https://pith.science/api/pith-number/5ZMSBCP3VMSX3SQYNQRDNSFOKE/graph.json","fetch_events":"https://pith.science/api/pith-number/5ZMSBCP3VMSX3SQYNQRDNSFOKE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5ZMSBCP3VMSX3SQYNQRDNSFOKE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5ZMSBCP3VMSX3SQYNQRDNSFOKE/action/storage_attestation","attest_author":"https://pith.science/pith/5ZMSBCP3VMSX3SQYNQRDNSFOKE/action/author_attestation","sign_citation":"https://pith.science/pith/5ZMSBCP3VMSX3SQYNQRDNSFOKE/action/citation_signature","submit_replication":"https://pith.science/pith/5ZMSBCP3VMSX3SQYNQRDNSFOKE/action/replication_record"}},"created_at":"2026-07-05T06:40:59.075916+00:00","updated_at":"2026-07-05T06:40:59.075916+00:00"}