{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QQX4FX3JSVUCFDSKX6BSXLX677","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":"9f447f9e973b51a5ed05776864d4c6138c3e85cae1af0b11c991fbdf997ff69a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-08-20T01:04:11Z","title_canon_sha256":"5598160e10f91fb77939b41f9b26a192c45bab0c87b2f447595fdcc1a1f918a1"},"schema_version":"1.0","source":{"id":"2508.14332","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.14332","created_at":"2026-07-05T11:56:29Z"},{"alias_kind":"arxiv_version","alias_value":"2508.14332v1","created_at":"2026-07-05T11:56:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.14332","created_at":"2026-07-05T11:56:29Z"},{"alias_kind":"pith_short_12","alias_value":"QQX4FX3JSVUC","created_at":"2026-07-05T11:56:29Z"},{"alias_kind":"pith_short_16","alias_value":"QQX4FX3JSVUCFDSK","created_at":"2026-07-05T11:56:29Z"},{"alias_kind":"pith_short_8","alias_value":"QQX4FX3J","created_at":"2026-07-05T11:56:29Z"}],"graph_snapshots":[{"event_id":"sha256:a32565a843b123ef385b1c34be8c4d629a4dce8a4f5b8dbe3273d4e40ed00c33","target":"graph","created_at":"2026-07-05T11:56:29Z","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/2508.14332/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Coarse graph theory concerns finding 'coarse' analogues of graph theory theorems, replacing disjointness with being far apart. One of the most interesting open questions is to find a coarse analogue of Menger's theorem, which characterizes when there are $k$ vertex-disjoint paths between two given sets $S,T$ of vertices of a graph. We showed in an earlier paper that the most natural such analogue is false, but a weaker statement remained as a popular open question. Here we show that the weaker statement is also false.\n  More exactly, suppose that $S,T$ are sets of vertices of a graph $G$, and ","authors_text":"Alex Scott, Paul Seymour, Tung Nguyen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-08-20T01:04:11Z","title":"Asymptotic structure. IV. A counterexample to the weak coarse Menger conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.14332","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":"sha256:1b530a19cdbecc50ad906decb32cf316524a8f25be52943da54bf029e89ad5b2","target":"record","created_at":"2026-07-05T11:56:29Z","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":"9f447f9e973b51a5ed05776864d4c6138c3e85cae1af0b11c991fbdf997ff69a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-08-20T01:04:11Z","title_canon_sha256":"5598160e10f91fb77939b41f9b26a192c45bab0c87b2f447595fdcc1a1f918a1"},"schema_version":"1.0","source":{"id":"2508.14332","kind":"arxiv","version":1}},"canonical_sha256":"842fc2df699568228e4abf832baefefff73d429f6b4ee0b04c659f1a73418c62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"842fc2df699568228e4abf832baefefff73d429f6b4ee0b04c659f1a73418c62","first_computed_at":"2026-07-05T11:56:29.973896Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:56:29.973896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3VDIzttzDy7MNLow2YT3CDUp2yjUNQ5Kd0QxZVOtNjvLemX7+zZJe8ALh9sm/26n6wzup14c550U13zptrfmDw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:56:29.974353Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.14332","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b530a19cdbecc50ad906decb32cf316524a8f25be52943da54bf029e89ad5b2","sha256:a32565a843b123ef385b1c34be8c4d629a4dce8a4f5b8dbe3273d4e40ed00c33"],"state_sha256":"156980ae3d8af158373a5aad2dc1986d25548476e0d7df7e1bed63add063e15f"}