{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:W7YSV6QOSHWJYHZ22QBFYSJ3QJ","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":"0f1069dedaa44b94ec9559e93573cd48062664fdc74699e8c950b7d30aabc5af","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-29T04:00:21Z","title_canon_sha256":"fee2d5625b63216bb563674cfce0e305babc4e64af89a2ae79fe0010add441f9"},"schema_version":"1.0","source":{"id":"1212.6588","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6588","created_at":"2026-05-18T00:56:52Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6588v1","created_at":"2026-05-18T00:56:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6588","created_at":"2026-05-18T00:56:52Z"},{"alias_kind":"pith_short_12","alias_value":"W7YSV6QOSHWJ","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"W7YSV6QOSHWJYHZ2","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"W7YSV6QO","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:ab55bed5beb3fc9591419369e51b570f0dd8aefc5f6ed82ea2441eed849e1eb8","target":"graph","created_at":"2026-05-18T00:56:52Z","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 discuss a polyhedral embedding of the classical Fricke-Klein regular map of genus 5 in ordinary 3-space. This polyhedron was originally discovered by Grunbaum in 1999, but was recently rediscovered by Brehm and Wills. We establish isomorphism of the Grunbaum polyhedron with the Fricke-Klein map, and confirm its combinatorial regularity. The Grunbaum polyhedron is among the few currently known geometrically vertex-transitive polyhedra of genus g > 2, and is conjectured to be the only vertex-transitive polyhedron in this genus range that is also combinatorially regular. We also contribute ","authors_text":"Egon Schulte, Gabor Gevay, Jorg M. Wills","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-29T04:00:21Z","title":"The Regular Grunbaum Polyhedron of Genus 5"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6588","kind":"arxiv","version":1},"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:a10ed031ddbd244d2b22c9c135d413c97c989ea7a9b5024179c3b53570789dd1","target":"record","created_at":"2026-05-18T00:56:52Z","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":"0f1069dedaa44b94ec9559e93573cd48062664fdc74699e8c950b7d30aabc5af","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-29T04:00:21Z","title_canon_sha256":"fee2d5625b63216bb563674cfce0e305babc4e64af89a2ae79fe0010add441f9"},"schema_version":"1.0","source":{"id":"1212.6588","kind":"arxiv","version":1}},"canonical_sha256":"b7f12afa0e91ec9c1f3ad4025c493b82505f6657f7dc9a1327637f6acccb350f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7f12afa0e91ec9c1f3ad4025c493b82505f6657f7dc9a1327637f6acccb350f","first_computed_at":"2026-05-18T00:56:52.205530Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:52.205530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cQYUMKfVqq1AhJVcx+nIA2L8rr0Mh2QgmvPXKpgvTvvp2zAxN6e4M/UMngTSE6JsQH5dHjPQx+6DQ3K0CrQdBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:52.205991Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.6588","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a10ed031ddbd244d2b22c9c135d413c97c989ea7a9b5024179c3b53570789dd1","sha256:ab55bed5beb3fc9591419369e51b570f0dd8aefc5f6ed82ea2441eed849e1eb8"],"state_sha256":"38d001feabd3b1d5ec1ed5fc44ab71f4c612f01d16076d166d2c5b57c7a7dd90"}