{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FEJ34BJWRJMB7QW2A7WOZISBAX","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":"43caff5e6c51267d50f15d6e6c5a741defd91b7e5ca8cdde34499dd3559dccea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-20T09:24:10Z","title_canon_sha256":"2f3dfbe14281161656fa06a44f833e4e70cc0ebf968d3549142e7ada9a9565e5"},"schema_version":"1.0","source":{"id":"1501.04744","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04744","created_at":"2026-05-18T02:29:02Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04744v1","created_at":"2026-05-18T02:29:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04744","created_at":"2026-05-18T02:29:02Z"},{"alias_kind":"pith_short_12","alias_value":"FEJ34BJWRJMB","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FEJ34BJWRJMB7QW2","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FEJ34BJW","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:950f26c87062c4589154a6e2a1f70775b3e055e6ab3b2434ad2ce3c6b15574da","target":"graph","created_at":"2026-05-18T02:29:02Z","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":"A Platonic surface is a Riemann surface that underlies a regular map and so we can consider its vertices, edge-centres and face-centres. A symmetry (anticonformal involution) of the surface will fix a number of simple closed curves which we call mirrors. These mirrors must pass through the vertices, edge-centres and face-centres in some sequence which we call the pattern of the mirror. Here we investigate these patterns for various well-known families of Platonic surfaces, including genus 1 regular maps, and regular maps on Hurwitz surfaces and Fermat curves. The genesis of this paper is class","authors_text":"Adnan Meleko\\u{g}lu, David Singerman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-20T09:24:10Z","title":"The structure of mirrors on Platonic surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04744","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":"sha256:69fc4e1ea87f8beb1b77c841479aba183ec4d918a33fdee8c06219e1c54a9b3e","target":"record","created_at":"2026-05-18T02:29:02Z","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":"43caff5e6c51267d50f15d6e6c5a741defd91b7e5ca8cdde34499dd3559dccea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-20T09:24:10Z","title_canon_sha256":"2f3dfbe14281161656fa06a44f833e4e70cc0ebf968d3549142e7ada9a9565e5"},"schema_version":"1.0","source":{"id":"1501.04744","kind":"arxiv","version":1}},"canonical_sha256":"2913be05368a581fc2da07ececa24105f3d8feca688ba2f0ceb0adcb87b57b1f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2913be05368a581fc2da07ececa24105f3d8feca688ba2f0ceb0adcb87b57b1f","first_computed_at":"2026-05-18T02:29:02.948482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:02.948482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tINrglTa0ZZGFlQwNfR86LfcnyI0j4bBCCpGpkdNAYJ6+2b+E7Y97ubb4pUXvzchqgzYEiMGUB5VJO/maaOKDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:02.948965Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.04744","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69fc4e1ea87f8beb1b77c841479aba183ec4d918a33fdee8c06219e1c54a9b3e","sha256:950f26c87062c4589154a6e2a1f70775b3e055e6ab3b2434ad2ce3c6b15574da"],"state_sha256":"df115e438bb7d97a02927f5cea544298060975598f8eb8bcced68b1096248099"}