{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:QQX4FX3JSVUCFDSKX6BSXLX677","short_pith_number":"pith:QQX4FX3J","canonical_record":{"source":{"id":"2508.14332","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-08-20T01:04:11Z","cross_cats_sorted":[],"title_canon_sha256":"5598160e10f91fb77939b41f9b26a192c45bab0c87b2f447595fdcc1a1f918a1","abstract_canon_sha256":"9f447f9e973b51a5ed05776864d4c6138c3e85cae1af0b11c991fbdf997ff69a"},"schema_version":"1.0"},"canonical_sha256":"842fc2df699568228e4abf832baefefff73d429f6b4ee0b04c659f1a73418c62","source":{"kind":"arxiv","id":"2508.14332","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:QQX4FX3JSVUCFDSKX6BSXLX677","target":"record","payload":{"canonical_record":{"source":{"id":"2508.14332","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-08-20T01:04:11Z","cross_cats_sorted":[],"title_canon_sha256":"5598160e10f91fb77939b41f9b26a192c45bab0c87b2f447595fdcc1a1f918a1","abstract_canon_sha256":"9f447f9e973b51a5ed05776864d4c6138c3e85cae1af0b11c991fbdf997ff69a"},"schema_version":"1.0"},"canonical_sha256":"842fc2df699568228e4abf832baefefff73d429f6b4ee0b04c659f1a73418c62","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:56:29.974353Z","signature_b64":"3VDIzttzDy7MNLow2YT3CDUp2yjUNQ5Kd0QxZVOtNjvLemX7+zZJe8ALh9sm/26n6wzup14c550U13zptrfmDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"842fc2df699568228e4abf832baefefff73d429f6b4ee0b04c659f1a73418c62","last_reissued_at":"2026-07-05T11:56:29.973896Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:56:29.973896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2508.14332","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":"2026-07-05T11:56:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WCAgrwH/NoZB6QHjAJMX0r6S3fTqqc9RcIOWJhuWVm0wNNkaorLA/uVBGj/kBdvb27nqBhvhckEORp8lR6wVAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T13:42:53.474172Z"},"content_sha256":"1b530a19cdbecc50ad906decb32cf316524a8f25be52943da54bf029e89ad5b2","schema_version":"1.0","event_id":"sha256:1b530a19cdbecc50ad906decb32cf316524a8f25be52943da54bf029e89ad5b2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:QQX4FX3JSVUCFDSKX6BSXLX677","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic structure. IV. A counterexample to the weak coarse Menger conjecture","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alex Scott, Paul Seymour, Tung Nguyen","submitted_at":"2025-08-20T01:04:11Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.14332","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/2508.14332/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":"2026-07-05T11:56:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a3tL2Fuh3dqvG8abOcwuIrmXhqK9pBcRFlxXKdWjNU2Jq08FPLCKdjAJtyaNFRirhNFKdOuFyL2h9YHHVSvUDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T13:42:53.474675Z"},"content_sha256":"a32565a843b123ef385b1c34be8c4d629a4dce8a4f5b8dbe3273d4e40ed00c33","schema_version":"1.0","event_id":"sha256:a32565a843b123ef385b1c34be8c4d629a4dce8a4f5b8dbe3273d4e40ed00c33"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QQX4FX3JSVUCFDSKX6BSXLX677/bundle.json","state_url":"https://pith.science/pith/QQX4FX3JSVUCFDSKX6BSXLX677/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QQX4FX3JSVUCFDSKX6BSXLX677/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":"2026-08-05T13:42:53Z","links":{"resolver":"https://pith.science/pith/QQX4FX3JSVUCFDSKX6BSXLX677","bundle":"https://pith.science/pith/QQX4FX3JSVUCFDSKX6BSXLX677/bundle.json","state":"https://pith.science/pith/QQX4FX3JSVUCFDSKX6BSXLX677/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QQX4FX3JSVUCFDSKX6BSXLX677/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t7xNh1wkefpQhGkhK80u2LaAdfbvVgAEX5moRhwu4nXVKdG27GTAVilI/EqgzYCFEEptGGHocY9lCEJzl3QzBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T13:42:53.480527Z","bundle_sha256":"c6a1bebc01b537ea0a784ec20e383200a220b39ac61981866f3591720ca17482"}}