{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:USMOLNZ4YUG3RVMJMPBQY5CRMO","short_pith_number":"pith:USMOLNZ4","canonical_record":{"source":{"id":"2605.20691","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-05-20T04:38:23Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"718d2b7c6ae157ed789a059ce916069f28abc950944245811bc9184399adcbd7","abstract_canon_sha256":"87943d5d03fc39361a8fcb409d869708d632fd2738ead36d41a11c902f4a8d15"},"schema_version":"1.0"},"canonical_sha256":"a498e5b73cc50db8d58963c30c745163bbb4be7920d97723beef585bfeb52108","source":{"kind":"arxiv","id":"2605.20691","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.20691","created_at":"2026-05-21T01:04:49Z"},{"alias_kind":"arxiv_version","alias_value":"2605.20691v1","created_at":"2026-05-21T01:04:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20691","created_at":"2026-05-21T01:04:49Z"},{"alias_kind":"pith_short_12","alias_value":"USMOLNZ4YUG3","created_at":"2026-05-21T01:04:49Z"},{"alias_kind":"pith_short_16","alias_value":"USMOLNZ4YUG3RVMJ","created_at":"2026-05-21T01:04:49Z"},{"alias_kind":"pith_short_8","alias_value":"USMOLNZ4","created_at":"2026-05-21T01:04:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:USMOLNZ4YUG3RVMJMPBQY5CRMO","target":"record","payload":{"canonical_record":{"source":{"id":"2605.20691","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-05-20T04:38:23Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"718d2b7c6ae157ed789a059ce916069f28abc950944245811bc9184399adcbd7","abstract_canon_sha256":"87943d5d03fc39361a8fcb409d869708d632fd2738ead36d41a11c902f4a8d15"},"schema_version":"1.0"},"canonical_sha256":"a498e5b73cc50db8d58963c30c745163bbb4be7920d97723beef585bfeb52108","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:04:49.418439Z","signature_b64":"UGzHGLBxep1sPDgDsClkbVPrkqz9w+HlFhQNnbVy0cRw6Q/VI4ZJNSqbX9rolxWlhlQbzAvfLbNc7c7tl+eWAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a498e5b73cc50db8d58963c30c745163bbb4be7920d97723beef585bfeb52108","last_reissued_at":"2026-05-21T01:04:49.417821Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:04:49.417821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.20691","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":"2026-05-21T01:04:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bqvJbtFvVSTwtvYqZ0OC02K8M5MXJ0wsCS9+gI+F1g8bBU2so2xGZ9ZfVhCPm5ULh63QKDuN+lTUwN+isKaHAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T12:37:41.441232Z"},"content_sha256":"1aab075c4c3294478f0571c0e5421732f53bd7801734c3209e341a5b1d3bd107","schema_version":"1.0","event_id":"sha256:1aab075c4c3294478f0571c0e5421732f53bd7801734c3209e341a5b1d3bd107"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:USMOLNZ4YUG3RVMJMPBQY5CRMO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"String C-groups of 2-power order project onto a common string C-group","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Dong-Dong Hou, Egon Schulte","submitted_at":"2026-05-20T04:38:23Z","abstract_excerpt":"String C-groups are precisely the automorphism groups of abstract regular polytopes. A certain regular d-polytope C_d with an automorphism group of order 2^{2d-1}, discovered by Conder and shown to have the smallest number of flags among all regular d-polytopes of high ranks, also has the important extremal property to be the unique minimal d-polytope, with respect to combinatorial covering, among all finite regular d-polytopes with 2-power automorphism groups. In other words, the automorphism group of C_d is a quotient group of every finite string C-group of rank d and 2-power order; and ever"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20691","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.20691/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-21T01:04:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vV7+3IJRcQSWnmdznM7W+Sysf/ix75lkKfWOR2d5uIRqVLpM6jq6vVJqjJj55BzW+KQ5hOZkOffp1pAKOKgDAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T12:37:41.441993Z"},"content_sha256":"4b6d5681b48dd9593af86fc76cf815bdc0530e2d52b17456083a7386d1ad3558","schema_version":"1.0","event_id":"sha256:4b6d5681b48dd9593af86fc76cf815bdc0530e2d52b17456083a7386d1ad3558"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/USMOLNZ4YUG3RVMJMPBQY5CRMO/bundle.json","state_url":"https://pith.science/pith/USMOLNZ4YUG3RVMJMPBQY5CRMO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/USMOLNZ4YUG3RVMJMPBQY5CRMO/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":"2026-05-24T12:37:41Z","links":{"resolver":"https://pith.science/pith/USMOLNZ4YUG3RVMJMPBQY5CRMO","bundle":"https://pith.science/pith/USMOLNZ4YUG3RVMJMPBQY5CRMO/bundle.json","state":"https://pith.science/pith/USMOLNZ4YUG3RVMJMPBQY5CRMO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/USMOLNZ4YUG3RVMJMPBQY5CRMO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:USMOLNZ4YUG3RVMJMPBQY5CRMO","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":"87943d5d03fc39361a8fcb409d869708d632fd2738ead36d41a11c902f4a8d15","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-05-20T04:38:23Z","title_canon_sha256":"718d2b7c6ae157ed789a059ce916069f28abc950944245811bc9184399adcbd7"},"schema_version":"1.0","source":{"id":"2605.20691","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.20691","created_at":"2026-05-21T01:04:49Z"},{"alias_kind":"arxiv_version","alias_value":"2605.20691v1","created_at":"2026-05-21T01:04:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20691","created_at":"2026-05-21T01:04:49Z"},{"alias_kind":"pith_short_12","alias_value":"USMOLNZ4YUG3","created_at":"2026-05-21T01:04:49Z"},{"alias_kind":"pith_short_16","alias_value":"USMOLNZ4YUG3RVMJ","created_at":"2026-05-21T01:04:49Z"},{"alias_kind":"pith_short_8","alias_value":"USMOLNZ4","created_at":"2026-05-21T01:04:49Z"}],"graph_snapshots":[{"event_id":"sha256:4b6d5681b48dd9593af86fc76cf815bdc0530e2d52b17456083a7386d1ad3558","target":"graph","created_at":"2026-05-21T01:04:49Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.20691/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"String C-groups are precisely the automorphism groups of abstract regular polytopes. A certain regular d-polytope C_d with an automorphism group of order 2^{2d-1}, discovered by Conder and shown to have the smallest number of flags among all regular d-polytopes of high ranks, also has the important extremal property to be the unique minimal d-polytope, with respect to combinatorial covering, among all finite regular d-polytopes with 2-power automorphism groups. In other words, the automorphism group of C_d is a quotient group of every finite string C-group of rank d and 2-power order; and ever","authors_text":"Dong-Dong Hou, Egon Schulte","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-05-20T04:38:23Z","title":"String C-groups of 2-power order project onto a common string C-group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20691","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":"sha256:1aab075c4c3294478f0571c0e5421732f53bd7801734c3209e341a5b1d3bd107","target":"record","created_at":"2026-05-21T01:04:49Z","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":"87943d5d03fc39361a8fcb409d869708d632fd2738ead36d41a11c902f4a8d15","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-05-20T04:38:23Z","title_canon_sha256":"718d2b7c6ae157ed789a059ce916069f28abc950944245811bc9184399adcbd7"},"schema_version":"1.0","source":{"id":"2605.20691","kind":"arxiv","version":1}},"canonical_sha256":"a498e5b73cc50db8d58963c30c745163bbb4be7920d97723beef585bfeb52108","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a498e5b73cc50db8d58963c30c745163bbb4be7920d97723beef585bfeb52108","first_computed_at":"2026-05-21T01:04:49.417821Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:04:49.417821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UGzHGLBxep1sPDgDsClkbVPrkqz9w+HlFhQNnbVy0cRw6Q/VI4ZJNSqbX9rolxWlhlQbzAvfLbNc7c7tl+eWAw==","signature_status":"signed_v1","signed_at":"2026-05-21T01:04:49.418439Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.20691","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1aab075c4c3294478f0571c0e5421732f53bd7801734c3209e341a5b1d3bd107","sha256:4b6d5681b48dd9593af86fc76cf815bdc0530e2d52b17456083a7386d1ad3558"],"state_sha256":"befe75867652d4c0bdc51a9464daafd2252626034f5d8dd11f438463bf88c727"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uqefWChIyfdTbyQ9eAwSaQEmiJuoRQ00Il5RWJRdrdrVSfu4OseeZ4guB6bO1bp9f7KbtRyrHyf4jnB/T2d5Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T12:37:41.445788Z","bundle_sha256":"9bdec369d0ac66384f4d715e94525f024c22a94c5c5d2d5f39e66e66a6a0c3bd"}}