{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:HKVWH4DTQEL5XVUVRVXQIEHKDH","short_pith_number":"pith:HKVWH4DT","canonical_record":{"source":{"id":"2401.06685","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-01-12T16:48:37Z","cross_cats_sorted":[],"title_canon_sha256":"96f02fa4451da3dd9e86c9aa327daaa14ce5a2aa170fee3d003a5c756dd136d7","abstract_canon_sha256":"1a935e1a4ddacbf043ae526e58e516f9f29aa81a561faed570f56da268c7b1d6"},"schema_version":"1.0"},"canonical_sha256":"3aab63f0738117dbd6958d6f0410ea19e2d2605cdb584e0954afd4b83d9a58b2","source":{"kind":"arxiv","id":"2401.06685","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.06685","created_at":"2026-07-05T10:01:11Z"},{"alias_kind":"arxiv_version","alias_value":"2401.06685v2","created_at":"2026-07-05T10:01:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.06685","created_at":"2026-07-05T10:01:11Z"},{"alias_kind":"pith_short_12","alias_value":"HKVWH4DTQEL5","created_at":"2026-07-05T10:01:11Z"},{"alias_kind":"pith_short_16","alias_value":"HKVWH4DTQEL5XVUV","created_at":"2026-07-05T10:01:11Z"},{"alias_kind":"pith_short_8","alias_value":"HKVWH4DT","created_at":"2026-07-05T10:01:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:HKVWH4DTQEL5XVUVRVXQIEHKDH","target":"record","payload":{"canonical_record":{"source":{"id":"2401.06685","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-01-12T16:48:37Z","cross_cats_sorted":[],"title_canon_sha256":"96f02fa4451da3dd9e86c9aa327daaa14ce5a2aa170fee3d003a5c756dd136d7","abstract_canon_sha256":"1a935e1a4ddacbf043ae526e58e516f9f29aa81a561faed570f56da268c7b1d6"},"schema_version":"1.0"},"canonical_sha256":"3aab63f0738117dbd6958d6f0410ea19e2d2605cdb584e0954afd4b83d9a58b2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:01:11.438071Z","signature_b64":"G0pN1YIjR83iSDMbWBjnysuBmLkaKmZ95Rso6IfTBXJGDmcL1A/S41JiVlZaT1877eC+eRzauauDKS13tH8IBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3aab63f0738117dbd6958d6f0410ea19e2d2605cdb584e0954afd4b83d9a58b2","last_reissued_at":"2026-07-05T10:01:11.437658Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:01:11.437658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2401.06685","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:01:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LQL0XJZCoYH5j93PKHLlmV2R7MtNnOB4lx+VkqQR3l2QBJjgE9WLROPAL7HjdOTD6IV46Z15UhvzaFSxR6DSBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T01:21:18.735946Z"},"content_sha256":"73c17750f171c294d33b3633958136c3b7e4929f796d16fdb62bbda500ae035d","schema_version":"1.0","event_id":"sha256:73c17750f171c294d33b3633958136c3b7e4929f796d16fdb62bbda500ae035d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:HKVWH4DTQEL5XVUVRVXQIEHKDH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A counterexample to the 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":"2024-01-12T16:48:37Z","abstract_excerpt":"Menger's well-known theorem from 1927 characterizes when it is possible to find $k$ vertex-disjoint paths between two sets of vertices in a graph $G$. Recently, Georgakopoulos and Papasoglu and, independently, Albrechtsen, Huynh, Jacobs, Knappe and Wollan conjectured a coarse analogue of Menger's theorem, when the $k$ paths are required to be pairwise at some distance at least $d$. The result is known for $k\\le 2$, but we will show that it is false for all $k\\ge 3$, even if $G$ is constrained to have maximum degree at most three. We also give a simpler proof of the result when $k=2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.06685","kind":"arxiv","version":2},"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/2401.06685/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":"2026-07-05T10:01:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BFt4orluoqYKIo37w5GejeOcQlAYlALQ/frNF1pMdp64iKpyMO8VQksviDkCCiH4VgRrIPuJ3vu0HY6+dl2aBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T01:21:18.736696Z"},"content_sha256":"0237565989562246f46ce95c4969be07fa0d6e99eb4f6ef2a0659304a49b89de","schema_version":"1.0","event_id":"sha256:0237565989562246f46ce95c4969be07fa0d6e99eb4f6ef2a0659304a49b89de"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HKVWH4DTQEL5XVUVRVXQIEHKDH/bundle.json","state_url":"https://pith.science/pith/HKVWH4DTQEL5XVUVRVXQIEHKDH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HKVWH4DTQEL5XVUVRVXQIEHKDH/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":"2026-08-21T01:21:18Z","links":{"resolver":"https://pith.science/pith/HKVWH4DTQEL5XVUVRVXQIEHKDH","bundle":"https://pith.science/pith/HKVWH4DTQEL5XVUVRVXQIEHKDH/bundle.json","state":"https://pith.science/pith/HKVWH4DTQEL5XVUVRVXQIEHKDH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HKVWH4DTQEL5XVUVRVXQIEHKDH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:HKVWH4DTQEL5XVUVRVXQIEHKDH","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":"1a935e1a4ddacbf043ae526e58e516f9f29aa81a561faed570f56da268c7b1d6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-01-12T16:48:37Z","title_canon_sha256":"96f02fa4451da3dd9e86c9aa327daaa14ce5a2aa170fee3d003a5c756dd136d7"},"schema_version":"1.0","source":{"id":"2401.06685","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.06685","created_at":"2026-07-05T10:01:11Z"},{"alias_kind":"arxiv_version","alias_value":"2401.06685v2","created_at":"2026-07-05T10:01:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.06685","created_at":"2026-07-05T10:01:11Z"},{"alias_kind":"pith_short_12","alias_value":"HKVWH4DTQEL5","created_at":"2026-07-05T10:01:11Z"},{"alias_kind":"pith_short_16","alias_value":"HKVWH4DTQEL5XVUV","created_at":"2026-07-05T10:01:11Z"},{"alias_kind":"pith_short_8","alias_value":"HKVWH4DT","created_at":"2026-07-05T10:01:11Z"}],"graph_snapshots":[{"event_id":"sha256:0237565989562246f46ce95c4969be07fa0d6e99eb4f6ef2a0659304a49b89de","target":"graph","created_at":"2026-07-05T10:01:11Z","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/2401.06685/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Menger's well-known theorem from 1927 characterizes when it is possible to find $k$ vertex-disjoint paths between two sets of vertices in a graph $G$. Recently, Georgakopoulos and Papasoglu and, independently, Albrechtsen, Huynh, Jacobs, Knappe and Wollan conjectured a coarse analogue of Menger's theorem, when the $k$ paths are required to be pairwise at some distance at least $d$. The result is known for $k\\le 2$, but we will show that it is false for all $k\\ge 3$, even if $G$ is constrained to have maximum degree at most three. We also give a simpler proof of the result when $k=2$.","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":"2024-01-12T16:48:37Z","title":"A counterexample to the coarse Menger conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.06685","kind":"arxiv","version":2},"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":"sha256:73c17750f171c294d33b3633958136c3b7e4929f796d16fdb62bbda500ae035d","target":"record","created_at":"2026-07-05T10:01:11Z","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":"1a935e1a4ddacbf043ae526e58e516f9f29aa81a561faed570f56da268c7b1d6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-01-12T16:48:37Z","title_canon_sha256":"96f02fa4451da3dd9e86c9aa327daaa14ce5a2aa170fee3d003a5c756dd136d7"},"schema_version":"1.0","source":{"id":"2401.06685","kind":"arxiv","version":2}},"canonical_sha256":"3aab63f0738117dbd6958d6f0410ea19e2d2605cdb584e0954afd4b83d9a58b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3aab63f0738117dbd6958d6f0410ea19e2d2605cdb584e0954afd4b83d9a58b2","first_computed_at":"2026-07-05T10:01:11.437658Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:01:11.437658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G0pN1YIjR83iSDMbWBjnysuBmLkaKmZ95Rso6IfTBXJGDmcL1A/S41JiVlZaT1877eC+eRzauauDKS13tH8IBA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:01:11.438071Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.06685","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73c17750f171c294d33b3633958136c3b7e4929f796d16fdb62bbda500ae035d","sha256:0237565989562246f46ce95c4969be07fa0d6e99eb4f6ef2a0659304a49b89de"],"state_sha256":"9cff0bf5b399e825868ff2aa3500064787fc7422f4238bd9144153e02c74ee0f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zfmiLHQrCMn2OFHXHAcKeAw4tejdM7gWxMkx398qzB2jWZuzikwmomNgJBUB9d9604vx3+pzCoxjFVFBBswnCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T01:21:18.742279Z","bundle_sha256":"3f2fd3953bfe61b45e5d96fd1b7c0da6f19d3e6d9db485467f2a33d825f5f2ad"}}