{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:4GXJQ36Z4HIL6LOPZNJ23ZD2L3","short_pith_number":"pith:4GXJQ36Z","canonical_record":{"source":{"id":"2506.21286","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-26T14:06:41Z","cross_cats_sorted":[],"title_canon_sha256":"a3860b949e4649c665738f37b7c286d1545e4ca97ea2033ff9e5c7f50545f7c5","abstract_canon_sha256":"86350bceb778400d646af4329078ae8517510ba2ff14f584a3faa8746d59bda0"},"schema_version":"1.0"},"canonical_sha256":"e1ae986fd9e1d0bf2dcfcb53ade47a5ed236673d23f37137be43a2d9b5ab24fb","source":{"kind":"arxiv","id":"2506.21286","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.21286","created_at":"2026-07-05T11:36:56Z"},{"alias_kind":"arxiv_version","alias_value":"2506.21286v2","created_at":"2026-07-05T11:36:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.21286","created_at":"2026-07-05T11:36:56Z"},{"alias_kind":"pith_short_12","alias_value":"4GXJQ36Z4HIL","created_at":"2026-07-05T11:36:56Z"},{"alias_kind":"pith_short_16","alias_value":"4GXJQ36Z4HIL6LOP","created_at":"2026-07-05T11:36:56Z"},{"alias_kind":"pith_short_8","alias_value":"4GXJQ36Z","created_at":"2026-07-05T11:36:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:4GXJQ36Z4HIL6LOPZNJ23ZD2L3","target":"record","payload":{"canonical_record":{"source":{"id":"2506.21286","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-26T14:06:41Z","cross_cats_sorted":[],"title_canon_sha256":"a3860b949e4649c665738f37b7c286d1545e4ca97ea2033ff9e5c7f50545f7c5","abstract_canon_sha256":"86350bceb778400d646af4329078ae8517510ba2ff14f584a3faa8746d59bda0"},"schema_version":"1.0"},"canonical_sha256":"e1ae986fd9e1d0bf2dcfcb53ade47a5ed236673d23f37137be43a2d9b5ab24fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:36:56.251918Z","signature_b64":"+oF89B0jjCGTUtQjqWBAiSYFf3aMfbXQS1iDF9+RCqBLvk2kH13p9nXpOwoFLObPdll2iENYM9BkjRnbItgaBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1ae986fd9e1d0bf2dcfcb53ade47a5ed236673d23f37137be43a2d9b5ab24fb","last_reissued_at":"2026-07-05T11:36:56.251346Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:36:56.251346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.21286","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":"2026-07-05T11:36:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"di0lH6RC33+jFZazBSL+KKkAcoeffQNBlOYPZJFbdSEag6cLWVkIF0QO0S9C5d1B3eiusRAa+VJ9CDi4078MAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T19:48:42.281035Z"},"content_sha256":"cd906fbd6a183a5cccd0149dff9d89d18aa5270824f7c0c70a622d8fed779d97","schema_version":"1.0","event_id":"sha256:cd906fbd6a183a5cccd0149dff9d89d18aa5270824f7c0c70a622d8fed779d97"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:4GXJQ36Z4HIL6LOPZNJ23ZD2L3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Infinitely many counterexamples to a conjecture of Lov\\'asz","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aida Abiad, Christoph Spiegel, Frederik Garbe, Xavier Povill","submitted_at":"2025-06-26T14:06:41Z","abstract_excerpt":"Motivated by the well-known conjecture of Ryser which relates maximum matchings to minimum vertex covers in $r$-partite $r$-uniform hypergraphs, Lov\\'asz formulated a stronger conjecture. It states that one can always reduce the matching number by removing $r-1$ vertices. This conjecture was very recently disproven for $r=3$ by Clow, Haxell, and Mohar using the line graph of a $3$-regular graph of order $102$. Building on this, we describe a simple infinite family of counterexamples based on generalized Petersen graphs for the case $r=3$ and give specific counterexamples for $r=4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.21286","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/2506.21286/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":"2026-07-05T11:36:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D7iDULXujTGLmiTy3ohbJKxkdBV/QG8ywfvThj53snNdcESygbt3oF2k5aRRxO5UVWu71B7wHmuO0RHyl50hCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T19:48:42.281545Z"},"content_sha256":"125cfb95d6bd5140219fb3dafd5e725c9c5e29fa37223874ad9f8ffe497497b6","schema_version":"1.0","event_id":"sha256:125cfb95d6bd5140219fb3dafd5e725c9c5e29fa37223874ad9f8ffe497497b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4GXJQ36Z4HIL6LOPZNJ23ZD2L3/bundle.json","state_url":"https://pith.science/pith/4GXJQ36Z4HIL6LOPZNJ23ZD2L3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4GXJQ36Z4HIL6LOPZNJ23ZD2L3/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":"2026-08-09T19:48:42Z","links":{"resolver":"https://pith.science/pith/4GXJQ36Z4HIL6LOPZNJ23ZD2L3","bundle":"https://pith.science/pith/4GXJQ36Z4HIL6LOPZNJ23ZD2L3/bundle.json","state":"https://pith.science/pith/4GXJQ36Z4HIL6LOPZNJ23ZD2L3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4GXJQ36Z4HIL6LOPZNJ23ZD2L3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:4GXJQ36Z4HIL6LOPZNJ23ZD2L3","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":"86350bceb778400d646af4329078ae8517510ba2ff14f584a3faa8746d59bda0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-26T14:06:41Z","title_canon_sha256":"a3860b949e4649c665738f37b7c286d1545e4ca97ea2033ff9e5c7f50545f7c5"},"schema_version":"1.0","source":{"id":"2506.21286","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.21286","created_at":"2026-07-05T11:36:56Z"},{"alias_kind":"arxiv_version","alias_value":"2506.21286v2","created_at":"2026-07-05T11:36:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.21286","created_at":"2026-07-05T11:36:56Z"},{"alias_kind":"pith_short_12","alias_value":"4GXJQ36Z4HIL","created_at":"2026-07-05T11:36:56Z"},{"alias_kind":"pith_short_16","alias_value":"4GXJQ36Z4HIL6LOP","created_at":"2026-07-05T11:36:56Z"},{"alias_kind":"pith_short_8","alias_value":"4GXJQ36Z","created_at":"2026-07-05T11:36:56Z"}],"graph_snapshots":[{"event_id":"sha256:125cfb95d6bd5140219fb3dafd5e725c9c5e29fa37223874ad9f8ffe497497b6","target":"graph","created_at":"2026-07-05T11:36:56Z","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/2506.21286/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Motivated by the well-known conjecture of Ryser which relates maximum matchings to minimum vertex covers in $r$-partite $r$-uniform hypergraphs, Lov\\'asz formulated a stronger conjecture. It states that one can always reduce the matching number by removing $r-1$ vertices. This conjecture was very recently disproven for $r=3$ by Clow, Haxell, and Mohar using the line graph of a $3$-regular graph of order $102$. Building on this, we describe a simple infinite family of counterexamples based on generalized Petersen graphs for the case $r=3$ and give specific counterexamples for $r=4$.","authors_text":"Aida Abiad, Christoph Spiegel, Frederik Garbe, Xavier Povill","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-26T14:06:41Z","title":"Infinitely many counterexamples to a conjecture of Lov\\'asz"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.21286","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:cd906fbd6a183a5cccd0149dff9d89d18aa5270824f7c0c70a622d8fed779d97","target":"record","created_at":"2026-07-05T11:36:56Z","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":"86350bceb778400d646af4329078ae8517510ba2ff14f584a3faa8746d59bda0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-26T14:06:41Z","title_canon_sha256":"a3860b949e4649c665738f37b7c286d1545e4ca97ea2033ff9e5c7f50545f7c5"},"schema_version":"1.0","source":{"id":"2506.21286","kind":"arxiv","version":2}},"canonical_sha256":"e1ae986fd9e1d0bf2dcfcb53ade47a5ed236673d23f37137be43a2d9b5ab24fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1ae986fd9e1d0bf2dcfcb53ade47a5ed236673d23f37137be43a2d9b5ab24fb","first_computed_at":"2026-07-05T11:36:56.251346Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:36:56.251346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+oF89B0jjCGTUtQjqWBAiSYFf3aMfbXQS1iDF9+RCqBLvk2kH13p9nXpOwoFLObPdll2iENYM9BkjRnbItgaBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:36:56.251918Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.21286","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd906fbd6a183a5cccd0149dff9d89d18aa5270824f7c0c70a622d8fed779d97","sha256:125cfb95d6bd5140219fb3dafd5e725c9c5e29fa37223874ad9f8ffe497497b6"],"state_sha256":"29f190fecac2334096bdcd9d1648fb718137d81a6ae95093365c70dfd63549fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7HlO/MC9XRcgTMNw9TwbdukTVRTiAiF3k0XJ0V4w0Yu5Lk3d0pVixnTOMnZmx+6fLGevI1eWKLNi3DgEVycMCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T19:48:42.286483Z","bundle_sha256":"bdb42b640b9fd1fda0d2ce143b9e6620708e9baea985995cece306afe02b33ac"}}