{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:AHBJSJLUVSMEY6IU5S7KAIKMDT","short_pith_number":"pith:AHBJSJLU","canonical_record":{"source":{"id":"1110.5977","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-27T03:48:43Z","cross_cats_sorted":[],"title_canon_sha256":"46c15a4af6cf6b258996670d78bc52764095023d3027c6703f6386b532ae129d","abstract_canon_sha256":"9b3a90abad251898e40af23b977340b88d842cf31dd8780ad95883a4dec48d3d"},"schema_version":"1.0"},"canonical_sha256":"01c2992574ac984c7914ecbea0214c1ce6573c2f6523123f62110a68cbed6a11","source":{"kind":"arxiv","id":"1110.5977","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5977","created_at":"2026-05-18T04:10:10Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5977v1","created_at":"2026-05-18T04:10:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5977","created_at":"2026-05-18T04:10:10Z"},{"alias_kind":"pith_short_12","alias_value":"AHBJSJLUVSME","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"AHBJSJLUVSMEY6IU","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"AHBJSJLU","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:AHBJSJLUVSMEY6IU5S7KAIKMDT","target":"record","payload":{"canonical_record":{"source":{"id":"1110.5977","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-27T03:48:43Z","cross_cats_sorted":[],"title_canon_sha256":"46c15a4af6cf6b258996670d78bc52764095023d3027c6703f6386b532ae129d","abstract_canon_sha256":"9b3a90abad251898e40af23b977340b88d842cf31dd8780ad95883a4dec48d3d"},"schema_version":"1.0"},"canonical_sha256":"01c2992574ac984c7914ecbea0214c1ce6573c2f6523123f62110a68cbed6a11","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:10.016173Z","signature_b64":"vQHHWpABpkN3GPDbWC8g+JkuZ12H4qrB23lMjny2XH2sXBDca3Zjqb1i4js1kMWdolmwLOSn4l603r1alY5uCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01c2992574ac984c7914ecbea0214c1ce6573c2f6523123f62110a68cbed6a11","last_reissued_at":"2026-05-18T04:10:10.015442Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:10.015442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.5977","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:10:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IsZMjMmQnb7js9OGyEq+6BlkFymgE3D7ye19pL8baUDHF3YHbS+P/6TW+zytHZVc09h7+pPynPP7TnZE0r1zCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T00:53:05.943671Z"},"content_sha256":"a738c123f6bd388ed14191b7f5453aa6d4534df2fe00f163cccc3be95a4c77dd","schema_version":"1.0","event_id":"sha256:a738c123f6bd388ed14191b7f5453aa6d4534df2fe00f163cccc3be95a4c77dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:AHBJSJLUVSMEY6IU5S7KAIKMDT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vertex-transitive maps with Schl\\\"afli type {3, 7}","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniel Pellicer","submitted_at":"2011-10-27T03:48:43Z","abstract_excerpt":"Among all equivelar vertex-transitive maps on a given closed surface S, the automorphism groups of maps with Schl\\\"afli types {3, 7} and {7, 3} allow the highest possible order. We describe a procedure to transform all such maps into 1- or 2-orbit maps, whose symmetry type has been previously studied. In so doing we provide a procedure to determine all vertex-transitive maps with Schl\\\"afli type {3, 7} which are neither regular or chiral. We determine all such maps on surfaces with Euler characteristic -1 \\geq \\c{hi} \\geq -40."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5977","kind":"arxiv","version":1},"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":"2026-05-18T04:10:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vb8kCYzo3hkoEqqjoUSSPaPvl0ykjy4sfdjqSYPUAfwy7ZOqCeQemEDbJAqevrL7zCwQH36m6B6Uvixe1xiYAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T00:53:05.944288Z"},"content_sha256":"e485ddb05816f271a0df213a70fc04233ed7de816b372b5ed6b679fe4d5124e3","schema_version":"1.0","event_id":"sha256:e485ddb05816f271a0df213a70fc04233ed7de816b372b5ed6b679fe4d5124e3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AHBJSJLUVSMEY6IU5S7KAIKMDT/bundle.json","state_url":"https://pith.science/pith/AHBJSJLUVSMEY6IU5S7KAIKMDT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AHBJSJLUVSMEY6IU5S7KAIKMDT/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":"2026-05-23T00:53:05Z","links":{"resolver":"https://pith.science/pith/AHBJSJLUVSMEY6IU5S7KAIKMDT","bundle":"https://pith.science/pith/AHBJSJLUVSMEY6IU5S7KAIKMDT/bundle.json","state":"https://pith.science/pith/AHBJSJLUVSMEY6IU5S7KAIKMDT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AHBJSJLUVSMEY6IU5S7KAIKMDT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:AHBJSJLUVSMEY6IU5S7KAIKMDT","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":"9b3a90abad251898e40af23b977340b88d842cf31dd8780ad95883a4dec48d3d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-27T03:48:43Z","title_canon_sha256":"46c15a4af6cf6b258996670d78bc52764095023d3027c6703f6386b532ae129d"},"schema_version":"1.0","source":{"id":"1110.5977","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5977","created_at":"2026-05-18T04:10:10Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5977v1","created_at":"2026-05-18T04:10:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5977","created_at":"2026-05-18T04:10:10Z"},{"alias_kind":"pith_short_12","alias_value":"AHBJSJLUVSME","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"AHBJSJLUVSMEY6IU","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"AHBJSJLU","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:e485ddb05816f271a0df213a70fc04233ed7de816b372b5ed6b679fe4d5124e3","target":"graph","created_at":"2026-05-18T04:10:10Z","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":"Among all equivelar vertex-transitive maps on a given closed surface S, the automorphism groups of maps with Schl\\\"afli types {3, 7} and {7, 3} allow the highest possible order. We describe a procedure to transform all such maps into 1- or 2-orbit maps, whose symmetry type has been previously studied. In so doing we provide a procedure to determine all vertex-transitive maps with Schl\\\"afli type {3, 7} which are neither regular or chiral. We determine all such maps on surfaces with Euler characteristic -1 \\geq \\c{hi} \\geq -40.","authors_text":"Daniel Pellicer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-27T03:48:43Z","title":"Vertex-transitive maps with Schl\\\"afli type {3, 7}"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5977","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:a738c123f6bd388ed14191b7f5453aa6d4534df2fe00f163cccc3be95a4c77dd","target":"record","created_at":"2026-05-18T04:10:10Z","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":"9b3a90abad251898e40af23b977340b88d842cf31dd8780ad95883a4dec48d3d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-27T03:48:43Z","title_canon_sha256":"46c15a4af6cf6b258996670d78bc52764095023d3027c6703f6386b532ae129d"},"schema_version":"1.0","source":{"id":"1110.5977","kind":"arxiv","version":1}},"canonical_sha256":"01c2992574ac984c7914ecbea0214c1ce6573c2f6523123f62110a68cbed6a11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01c2992574ac984c7914ecbea0214c1ce6573c2f6523123f62110a68cbed6a11","first_computed_at":"2026-05-18T04:10:10.015442Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:10.015442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vQHHWpABpkN3GPDbWC8g+JkuZ12H4qrB23lMjny2XH2sXBDca3Zjqb1i4js1kMWdolmwLOSn4l603r1alY5uCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:10.016173Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.5977","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a738c123f6bd388ed14191b7f5453aa6d4534df2fe00f163cccc3be95a4c77dd","sha256:e485ddb05816f271a0df213a70fc04233ed7de816b372b5ed6b679fe4d5124e3"],"state_sha256":"5156ff98d0746cada6b11d00d8de58518dfc5c60e9a086df73b6a85dcbccf95d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cJxMUBMyWb1/GWwe7uz+muOyQ+nxo8DoldSDSJgmDWyMvthFUUUp8MjvpBtKYaqb0u+djrDHDt+7qydznzEXAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T00:53:05.947768Z","bundle_sha256":"b848a3eafb18cd13f88690d9b4a97e9712b48bdcc55168a458e2073af658654c"}}