{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:IGIVXOUBO7WVJUJ3MJBNSFDPVM","short_pith_number":"pith:IGIVXOUB","canonical_record":{"source":{"id":"1609.01042","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-05T07:34:21Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"a6a891e2db388d54f11890d31402b7ea3cef96f16e6cf1d9854cea4e89d99aa1","abstract_canon_sha256":"64a2e1ffee9afef7d4b9c6337a39d70598b19e03c8834fa0747e94bc8c01f67d"},"schema_version":"1.0"},"canonical_sha256":"41915bba8177ed54d13b6242d9146fab270d838523a7dc09a73bbb690b515d75","source":{"kind":"arxiv","id":"1609.01042","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01042","created_at":"2026-05-18T00:33:44Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01042v2","created_at":"2026-05-18T00:33:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01042","created_at":"2026-05-18T00:33:44Z"},{"alias_kind":"pith_short_12","alias_value":"IGIVXOUBO7WV","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IGIVXOUBO7WVJUJ3","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IGIVXOUB","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:IGIVXOUBO7WVJUJ3MJBNSFDPVM","target":"record","payload":{"canonical_record":{"source":{"id":"1609.01042","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-05T07:34:21Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"a6a891e2db388d54f11890d31402b7ea3cef96f16e6cf1d9854cea4e89d99aa1","abstract_canon_sha256":"64a2e1ffee9afef7d4b9c6337a39d70598b19e03c8834fa0747e94bc8c01f67d"},"schema_version":"1.0"},"canonical_sha256":"41915bba8177ed54d13b6242d9146fab270d838523a7dc09a73bbb690b515d75","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:44.087372Z","signature_b64":"ta4Nog3cqoRYmmkyWSfuJwPqIAGxzQdX0Fkbba+9aIoQ7+2fn48d5EJpIkm1Yak8OYsrvlEA7SuEnJkbNgKuDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41915bba8177ed54d13b6242d9146fab270d838523a7dc09a73bbb690b515d75","last_reissued_at":"2026-05-18T00:33:44.086862Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:44.086862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.01042","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":"2026-05-18T00:33:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GQ621gwnMQf2srYLvH21LbEretDR8qo0xNA+dQTZkrOu+8PdzQfho4Vmtshbom1EaVPSwH8mtTG3tEvJNBHFBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:38:48.509876Z"},"content_sha256":"57243559f6582429949017c65c0d847c9e29dd111db11da3ed37d20e86f8271e","schema_version":"1.0","event_id":"sha256:57243559f6582429949017c65c0d847c9e29dd111db11da3ed37d20e86f8271e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:IGIVXOUBO7WVJUJ3MJBNSFDPVM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minimal obstructions for normal spanning trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CO","authors_text":"Max Pitz, Nathan Bowler, Stefan Geschke","submitted_at":"2016-09-05T07:34:21Z","abstract_excerpt":"Diestel and Leader have characterised connected graphs that admit a normal spanning tree via two classes of forbidden minors. One class are Halin's $(\\aleph_0,\\aleph_1)$-graphs: bipartite graphs with bipartition $(\\mathbb{N},B)$ such that $B$ is uncountable and every vertex of $B$ has infinite degree.\n  Our main result is that under Martin's Axiom and the failure of the Continuum Hypothesis, the class of forbidden $(\\aleph_0,\\aleph_1)$-graphs in Diestel and Leader's result can be replaced by one single instance of such a graph.\n  Under CH, however, the class of $(\\aleph_0,\\aleph_1)$-graphs con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01042","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":"2026-05-18T00:33:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4aBHumyGSeuBAGEMPvoIJw27AlFjP7NFd9xK7WrM+fik1/eEMtHsl/tzdf36/WToFvQdiFiEQpsA3SxhWzJ6Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:38:48.510486Z"},"content_sha256":"72c8e276376951e1f7f478e229d756bc6814fa90f97e50ad292a8eeef240d9be","schema_version":"1.0","event_id":"sha256:72c8e276376951e1f7f478e229d756bc6814fa90f97e50ad292a8eeef240d9be"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IGIVXOUBO7WVJUJ3MJBNSFDPVM/bundle.json","state_url":"https://pith.science/pith/IGIVXOUBO7WVJUJ3MJBNSFDPVM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IGIVXOUBO7WVJUJ3MJBNSFDPVM/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":"2026-05-31T05:38:48Z","links":{"resolver":"https://pith.science/pith/IGIVXOUBO7WVJUJ3MJBNSFDPVM","bundle":"https://pith.science/pith/IGIVXOUBO7WVJUJ3MJBNSFDPVM/bundle.json","state":"https://pith.science/pith/IGIVXOUBO7WVJUJ3MJBNSFDPVM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IGIVXOUBO7WVJUJ3MJBNSFDPVM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IGIVXOUBO7WVJUJ3MJBNSFDPVM","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":"64a2e1ffee9afef7d4b9c6337a39d70598b19e03c8834fa0747e94bc8c01f67d","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-05T07:34:21Z","title_canon_sha256":"a6a891e2db388d54f11890d31402b7ea3cef96f16e6cf1d9854cea4e89d99aa1"},"schema_version":"1.0","source":{"id":"1609.01042","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01042","created_at":"2026-05-18T00:33:44Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01042v2","created_at":"2026-05-18T00:33:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01042","created_at":"2026-05-18T00:33:44Z"},{"alias_kind":"pith_short_12","alias_value":"IGIVXOUBO7WV","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IGIVXOUBO7WVJUJ3","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IGIVXOUB","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:72c8e276376951e1f7f478e229d756bc6814fa90f97e50ad292a8eeef240d9be","target":"graph","created_at":"2026-05-18T00:33:44Z","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":"Diestel and Leader have characterised connected graphs that admit a normal spanning tree via two classes of forbidden minors. One class are Halin's $(\\aleph_0,\\aleph_1)$-graphs: bipartite graphs with bipartition $(\\mathbb{N},B)$ such that $B$ is uncountable and every vertex of $B$ has infinite degree.\n  Our main result is that under Martin's Axiom and the failure of the Continuum Hypothesis, the class of forbidden $(\\aleph_0,\\aleph_1)$-graphs in Diestel and Leader's result can be replaced by one single instance of such a graph.\n  Under CH, however, the class of $(\\aleph_0,\\aleph_1)$-graphs con","authors_text":"Max Pitz, Nathan Bowler, Stefan Geschke","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-05T07:34:21Z","title":"Minimal obstructions for normal spanning trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01042","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":"sha256:57243559f6582429949017c65c0d847c9e29dd111db11da3ed37d20e86f8271e","target":"record","created_at":"2026-05-18T00:33:44Z","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":"64a2e1ffee9afef7d4b9c6337a39d70598b19e03c8834fa0747e94bc8c01f67d","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-05T07:34:21Z","title_canon_sha256":"a6a891e2db388d54f11890d31402b7ea3cef96f16e6cf1d9854cea4e89d99aa1"},"schema_version":"1.0","source":{"id":"1609.01042","kind":"arxiv","version":2}},"canonical_sha256":"41915bba8177ed54d13b6242d9146fab270d838523a7dc09a73bbb690b515d75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41915bba8177ed54d13b6242d9146fab270d838523a7dc09a73bbb690b515d75","first_computed_at":"2026-05-18T00:33:44.086862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:44.086862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ta4Nog3cqoRYmmkyWSfuJwPqIAGxzQdX0Fkbba+9aIoQ7+2fn48d5EJpIkm1Yak8OYsrvlEA7SuEnJkbNgKuDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:44.087372Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.01042","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57243559f6582429949017c65c0d847c9e29dd111db11da3ed37d20e86f8271e","sha256:72c8e276376951e1f7f478e229d756bc6814fa90f97e50ad292a8eeef240d9be"],"state_sha256":"f16f7636079bdaaef4932563ed283f5a44e3df1dd3dbe3b7d13746ca88478534"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BW1UkQr5CgoxXgX+FfooI55+yS8YFUbErG3kPAU573w9OH7TJ9/vMi6JMafYOJwjNO6KTLNxP4htnFb9ogoJBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T05:38:48.514308Z","bundle_sha256":"c6bf85bda826ec076ee4bbc5b00bf0ff1b4adeaa54afbf5396ac6e0b939f6c42"}}