{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ZL5U66IDSL2HP3AHSVZQ6PQHLI","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":"c321441e80370582384e108b81ec5d7b3a8c5a04c35204e6cadd9f9ff99850ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-01-08T03:34:36Z","title_canon_sha256":"84c989fbf80eaa79236a8eda36a1d29a4c558bce4a5891ed67745c0adabcb3d4"},"schema_version":"1.0","source":{"id":"2401.03647","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.03647","created_at":"2026-07-05T07:31:12Z"},{"alias_kind":"arxiv_version","alias_value":"2401.03647v1","created_at":"2026-07-05T07:31:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.03647","created_at":"2026-07-05T07:31:12Z"},{"alias_kind":"pith_short_12","alias_value":"ZL5U66IDSL2H","created_at":"2026-07-05T07:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"ZL5U66IDSL2HP3AH","created_at":"2026-07-05T07:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"ZL5U66ID","created_at":"2026-07-05T07:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:cb9e3f10d4aa563ffecbe373854cc3de9736083ca48bbd3555785aa8237679ed","target":"graph","created_at":"2026-07-05T07:31:12Z","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/2401.03647/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The half-orthant model is a partially oriented model of a random medium involving a parameter $p\\in [0,1]$, for which there is a critical value $p_c(d)$ (depending on the dimension $d$) below which every point is reachable from the origin. We prove a limit theorem for the graph-distance (or \"chemical distance\") for this model when $p<p_c(2)$, and also when $1-p$ is larger than the critical parameter for site percolation in $\\mathbb{Z}^d$. The proof involves an application of the subadditive ergodic theorem. Novel arguments herein include the method of proving that the expected number of steps ","authors_text":"Mark Holmes, Nicholas Beaton, Xin Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-01-08T03:34:36Z","title":"Chemical distance for the half-orthant model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.03647","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":"sha256:03a57ef7353b145cbe438a801023786b9f58e5c419c3e49009d0a9e2160bc41b","target":"record","created_at":"2026-07-05T07:31:12Z","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":"c321441e80370582384e108b81ec5d7b3a8c5a04c35204e6cadd9f9ff99850ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-01-08T03:34:36Z","title_canon_sha256":"84c989fbf80eaa79236a8eda36a1d29a4c558bce4a5891ed67745c0adabcb3d4"},"schema_version":"1.0","source":{"id":"2401.03647","kind":"arxiv","version":1}},"canonical_sha256":"cafb4f790392f477ec0795730f3e075a0b7cd812f0a3c46478ac417d027805b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cafb4f790392f477ec0795730f3e075a0b7cd812f0a3c46478ac417d027805b0","first_computed_at":"2026-07-05T07:31:12.079972Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:31:12.079972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f5rTtnzqc9BpVZUQ3psc0LHIr8JxAgZwZ3nOtw9AUBjaqdw/ujFmwTfI/ifQlB1kNdvXOue8bmrYDm3MRQsNAg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:31:12.080461Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.03647","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03a57ef7353b145cbe438a801023786b9f58e5c419c3e49009d0a9e2160bc41b","sha256:cb9e3f10d4aa563ffecbe373854cc3de9736083ca48bbd3555785aa8237679ed"],"state_sha256":"879260d6874cf051498275086b9e241096ecac3cb3fa9d5c991036ff50bf13a6"}