{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:QINLETCPGMMIPTWTBT7PH23CLP","short_pith_number":"pith:QINLETCP","canonical_record":{"source":{"id":"1111.0606","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-02T18:53:28Z","cross_cats_sorted":[],"title_canon_sha256":"d9c71fb110f1ada05018686d31ea0e071115d84408218bc6b8c01e250ee23a14","abstract_canon_sha256":"611cb629e1895e79e9cc34c76ed94e1dd0aec5855737a6d90c1ef1bebfa9920e"},"schema_version":"1.0"},"canonical_sha256":"821ab24c4f331887ced30cfef3eb625bdbbb9997929515df34dc1fb7a1c5504f","source":{"kind":"arxiv","id":"1111.0606","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.0606","created_at":"2026-05-18T03:51:35Z"},{"alias_kind":"arxiv_version","alias_value":"1111.0606v2","created_at":"2026-05-18T03:51:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0606","created_at":"2026-05-18T03:51:35Z"},{"alias_kind":"pith_short_12","alias_value":"QINLETCPGMMI","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QINLETCPGMMIPTWT","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QINLETCP","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:QINLETCPGMMIPTWTBT7PH23CLP","target":"record","payload":{"canonical_record":{"source":{"id":"1111.0606","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-02T18:53:28Z","cross_cats_sorted":[],"title_canon_sha256":"d9c71fb110f1ada05018686d31ea0e071115d84408218bc6b8c01e250ee23a14","abstract_canon_sha256":"611cb629e1895e79e9cc34c76ed94e1dd0aec5855737a6d90c1ef1bebfa9920e"},"schema_version":"1.0"},"canonical_sha256":"821ab24c4f331887ced30cfef3eb625bdbbb9997929515df34dc1fb7a1c5504f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:35.707935Z","signature_b64":"bVuLP0NdmAdL0uIBzQNbszHMBJrGDuGUTN0Pnw2/PPdBMroP9mOgrg7DrRUZYtW4AzFnjvrHk3EFnmDVQA85Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"821ab24c4f331887ced30cfef3eb625bdbbb9997929515df34dc1fb7a1c5504f","last_reissued_at":"2026-05-18T03:51:35.707442Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:35.707442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.0606","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":"2026-05-18T03:51:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7O6aPJprfPghQ48MLLjPHVUyTpB1HfuW6sJJKRx5O3UvPZ9wYsdUkL6ok/LD/0Ym5Ll2On76+kEVjUMZpgbTCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:35:45.915098Z"},"content_sha256":"11c66bde899e64275717017f6224582cd6e36ca257e5481ab9626d11839dfda5","schema_version":"1.0","event_id":"sha256:11c66bde899e64275717017f6224582cd6e36ca257e5481ab9626d11839dfda5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:QINLETCPGMMIPTWTBT7PH23CLP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the intersection of infinite matroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Elad Aigner-Horev, Jan-Oliver Fr\\\"ohlich, Johannes Carmesin","submitted_at":"2011-11-02T18:53:28Z","abstract_excerpt":"We show that the infinite matroid intersection conjecture of Nash-Williams implies the infinite Menger theorem proved recently by Aharoni and Berger.\n  We prove that this conjecture is true whenever one matroid is nearly finitary and the second is the dual of a nearly finitary matroid, where the nearly finitary matroids form a superclass of the finitary matroids.\n  In particular, this proves the infinite matroid intersection conjecture for finite-cycle matroids of 2-connected, locally finite graphs with only a finite number of vertex-disjoint rays."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0606","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":""},"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":"2026-05-18T03:51:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YzV5rRvsWmtSicGJi9mScecjyo/YGqP+Q9kxsr9N9VNNJT0hjTveb5LLBAyPJc400/oN8PLusdG1egBsBsLpDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:35:45.915460Z"},"content_sha256":"33b011a2ace7a073dcc5c9c2738386bb0f89f31ebe33c551337f7be9604151bf","schema_version":"1.0","event_id":"sha256:33b011a2ace7a073dcc5c9c2738386bb0f89f31ebe33c551337f7be9604151bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QINLETCPGMMIPTWTBT7PH23CLP/bundle.json","state_url":"https://pith.science/pith/QINLETCPGMMIPTWTBT7PH23CLP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QINLETCPGMMIPTWTBT7PH23CLP/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":"2026-06-22T23:35:45Z","links":{"resolver":"https://pith.science/pith/QINLETCPGMMIPTWTBT7PH23CLP","bundle":"https://pith.science/pith/QINLETCPGMMIPTWTBT7PH23CLP/bundle.json","state":"https://pith.science/pith/QINLETCPGMMIPTWTBT7PH23CLP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QINLETCPGMMIPTWTBT7PH23CLP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QINLETCPGMMIPTWTBT7PH23CLP","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":"611cb629e1895e79e9cc34c76ed94e1dd0aec5855737a6d90c1ef1bebfa9920e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-02T18:53:28Z","title_canon_sha256":"d9c71fb110f1ada05018686d31ea0e071115d84408218bc6b8c01e250ee23a14"},"schema_version":"1.0","source":{"id":"1111.0606","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.0606","created_at":"2026-05-18T03:51:35Z"},{"alias_kind":"arxiv_version","alias_value":"1111.0606v2","created_at":"2026-05-18T03:51:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0606","created_at":"2026-05-18T03:51:35Z"},{"alias_kind":"pith_short_12","alias_value":"QINLETCPGMMI","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QINLETCPGMMIPTWT","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QINLETCP","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:33b011a2ace7a073dcc5c9c2738386bb0f89f31ebe33c551337f7be9604151bf","target":"graph","created_at":"2026-05-18T03:51:35Z","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"},"paper":{"abstract_excerpt":"We show that the infinite matroid intersection conjecture of Nash-Williams implies the infinite Menger theorem proved recently by Aharoni and Berger.\n  We prove that this conjecture is true whenever one matroid is nearly finitary and the second is the dual of a nearly finitary matroid, where the nearly finitary matroids form a superclass of the finitary matroids.\n  In particular, this proves the infinite matroid intersection conjecture for finite-cycle matroids of 2-connected, locally finite graphs with only a finite number of vertex-disjoint rays.","authors_text":"Elad Aigner-Horev, Jan-Oliver Fr\\\"ohlich, Johannes Carmesin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-02T18:53:28Z","title":"On the intersection of infinite matroids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0606","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":"sha256:11c66bde899e64275717017f6224582cd6e36ca257e5481ab9626d11839dfda5","target":"record","created_at":"2026-05-18T03:51:35Z","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":"611cb629e1895e79e9cc34c76ed94e1dd0aec5855737a6d90c1ef1bebfa9920e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-02T18:53:28Z","title_canon_sha256":"d9c71fb110f1ada05018686d31ea0e071115d84408218bc6b8c01e250ee23a14"},"schema_version":"1.0","source":{"id":"1111.0606","kind":"arxiv","version":2}},"canonical_sha256":"821ab24c4f331887ced30cfef3eb625bdbbb9997929515df34dc1fb7a1c5504f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"821ab24c4f331887ced30cfef3eb625bdbbb9997929515df34dc1fb7a1c5504f","first_computed_at":"2026-05-18T03:51:35.707442Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:35.707442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bVuLP0NdmAdL0uIBzQNbszHMBJrGDuGUTN0Pnw2/PPdBMroP9mOgrg7DrRUZYtW4AzFnjvrHk3EFnmDVQA85Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:35.707935Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.0606","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11c66bde899e64275717017f6224582cd6e36ca257e5481ab9626d11839dfda5","sha256:33b011a2ace7a073dcc5c9c2738386bb0f89f31ebe33c551337f7be9604151bf"],"state_sha256":"b465e53a32d591d37b5eabf796567f8856916225ce9ab56454640968a30339ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xlCmL/b1Ey04RE+Y/Yi75PAtI+Mznc8hOjBZ+/NGoVxSuTE6OyJ9vO2Xbjtgod3wUgYfGm38Q4BFbAMdQJfEDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T23:35:45.917449Z","bundle_sha256":"6b7e7cb49269286d0c0fc3e5bc8d461447bf67d77ab323cd0d084842197b1bc2"}}