{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:TD4A6IW7A5YKGIM3QZCVFW6YR7","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":"ae19d2fdf3d74318f606d2136fa93c6ea2487861b2843f8ce31ac751ae21c207","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-01-12T16:22:43Z","title_canon_sha256":"cd6e330339b103723007fa3e2def665aa5b70b84ef21b586ea60a637af71b6ff"},"schema_version":"1.0","source":{"id":"0901.1604","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.1604","created_at":"2026-05-18T04:32:22Z"},{"alias_kind":"arxiv_version","alias_value":"0901.1604v3","created_at":"2026-05-18T04:32:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.1604","created_at":"2026-05-18T04:32:22Z"},{"alias_kind":"pith_short_12","alias_value":"TD4A6IW7A5YK","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"TD4A6IW7A5YKGIM3","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"TD4A6IW7","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:d7c177dd46546e96804358b82cb549432ff52f4e098420658b354ccbdbb05e65","target":"graph","created_at":"2026-05-18T04:32:22Z","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":"In this short note, we compute the Betti numbers of the moduli stack of flat SU(3)-bundles over a Klein bottle. We also handle the general compact group case over RP^2. In all cases the cohomology is found to be equivariantly formal, supporting a conjecture from the author's doctoral thesis. Our results also verify conjectural formulas obtained by Ho-Liu using Yang-Mills Morse theory.","authors_text":"Thomas Baird","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-01-12T16:22:43Z","title":"Moduli of flat SU(3)-bundles over a Klein bottle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.1604","kind":"arxiv","version":3},"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:e988bfd0ce27eaf5718debe3aef1504bb9521816255306e14fc29975db273cea","target":"record","created_at":"2026-05-18T04:32:22Z","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":"ae19d2fdf3d74318f606d2136fa93c6ea2487861b2843f8ce31ac751ae21c207","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-01-12T16:22:43Z","title_canon_sha256":"cd6e330339b103723007fa3e2def665aa5b70b84ef21b586ea60a637af71b6ff"},"schema_version":"1.0","source":{"id":"0901.1604","kind":"arxiv","version":3}},"canonical_sha256":"98f80f22df0770a3219b864552dbd88fe02f372baa884cfed2ceaa13a0ee543f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98f80f22df0770a3219b864552dbd88fe02f372baa884cfed2ceaa13a0ee543f","first_computed_at":"2026-05-18T04:32:22.222065Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:22.222065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ds4GVK6g8qJZk9Z1sEaYAp/ODeZjwV9btWwuOH28XWEsLfPHw5oaR+mwiFKtbAyB6EV3+phNHJ4mmiAkI4jYDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:22.222808Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.1604","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e988bfd0ce27eaf5718debe3aef1504bb9521816255306e14fc29975db273cea","sha256:d7c177dd46546e96804358b82cb549432ff52f4e098420658b354ccbdbb05e65"],"state_sha256":"9077e5024d5c2dcf57e6702a140a6b4f546589dfb0f7aaa1f91f45f30275835e"}