{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:3RQH5FRPARU4ODIWNMKN6MOETW","short_pith_number":"pith:3RQH5FRP","canonical_record":{"source":{"id":"2606.23004","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-06-22T08:17:54Z","cross_cats_sorted":[],"title_canon_sha256":"bbbbdf84439ce070c09f36ff897bd7c4981b34cd964c2dedf0ea23ac67d6aa9f","abstract_canon_sha256":"a5213869cdcac2b5623584ac6c2a063f9ecfe4b3a4201d231d7e4d3fafd01099"},"schema_version":"1.0"},"canonical_sha256":"dc607e962f0469c70d166b14df31c49dbc2803b081375020fd9bb51161c31393","source":{"kind":"arxiv","id":"2606.23004","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.23004","created_at":"2026-06-23T03:14:06Z"},{"alias_kind":"arxiv_version","alias_value":"2606.23004v1","created_at":"2026-06-23T03:14:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23004","created_at":"2026-06-23T03:14:06Z"},{"alias_kind":"pith_short_12","alias_value":"3RQH5FRPARU4","created_at":"2026-06-23T03:14:06Z"},{"alias_kind":"pith_short_16","alias_value":"3RQH5FRPARU4ODIW","created_at":"2026-06-23T03:14:06Z"},{"alias_kind":"pith_short_8","alias_value":"3RQH5FRP","created_at":"2026-06-23T03:14:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:3RQH5FRPARU4ODIWNMKN6MOETW","target":"record","payload":{"canonical_record":{"source":{"id":"2606.23004","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-06-22T08:17:54Z","cross_cats_sorted":[],"title_canon_sha256":"bbbbdf84439ce070c09f36ff897bd7c4981b34cd964c2dedf0ea23ac67d6aa9f","abstract_canon_sha256":"a5213869cdcac2b5623584ac6c2a063f9ecfe4b3a4201d231d7e4d3fafd01099"},"schema_version":"1.0"},"canonical_sha256":"dc607e962f0469c70d166b14df31c49dbc2803b081375020fd9bb51161c31393","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T03:14:06.493205Z","signature_b64":"QcKhHLCOjfmcpxrsqFaI0I4svOUrDRq+0dNjF/FMK31S+OJ2PqZ+kwp/3asBtfQoNYULdEpAhyJhpQSuJ6r0CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc607e962f0469c70d166b14df31c49dbc2803b081375020fd9bb51161c31393","last_reissued_at":"2026-06-23T03:14:06.492823Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T03:14:06.492823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.23004","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":"2026-06-23T03:14:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2SYigs77fvU2Wr9b+Yy5WhFmE/H5wkqitixL3Xdn6E06rdA1RP8dS2Z4yxT8ancY1Ahuv0FDHjVIOOw7xmmNDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T12:20:55.573887Z"},"content_sha256":"c3571553aeb902a2dca84d05bc1db635d8655079e7a88f155cc25c58cf1b6f84","schema_version":"1.0","event_id":"sha256:c3571553aeb902a2dca84d05bc1db635d8655079e7a88f155cc25c58cf1b6f84"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:3RQH5FRPARU4ODIWNMKN6MOETW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bicyclic biskew braces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Hal Simpson, Paul J. Truman","submitted_at":"2026-06-22T08:17:54Z","abstract_excerpt":"We study finite braces whose additive and multiplicative groups are both cyclic. We reinterpret the classification of these braces from the perspective of regular subgroups of permutation groups, and identify which of them are biskew braces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23004","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/2606.23004/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":"2026-06-23T03:14:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rqJTKwasQLgaD6zeO5HqPJ/+2WaPepcF9F4x7ZsrE/qB99coX9hsAsOj7gPNE2iGdqTW/iT3rKPkoVn/JW8IDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T12:20:55.574248Z"},"content_sha256":"9280e7b2988305b6d02bcf7f0e47ccfaddb3adaed4d5b9ca0430999037f4eac2","schema_version":"1.0","event_id":"sha256:9280e7b2988305b6d02bcf7f0e47ccfaddb3adaed4d5b9ca0430999037f4eac2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3RQH5FRPARU4ODIWNMKN6MOETW/bundle.json","state_url":"https://pith.science/pith/3RQH5FRPARU4ODIWNMKN6MOETW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3RQH5FRPARU4ODIWNMKN6MOETW/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":"2026-06-29T12:20:55Z","links":{"resolver":"https://pith.science/pith/3RQH5FRPARU4ODIWNMKN6MOETW","bundle":"https://pith.science/pith/3RQH5FRPARU4ODIWNMKN6MOETW/bundle.json","state":"https://pith.science/pith/3RQH5FRPARU4ODIWNMKN6MOETW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3RQH5FRPARU4ODIWNMKN6MOETW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:3RQH5FRPARU4ODIWNMKN6MOETW","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":"a5213869cdcac2b5623584ac6c2a063f9ecfe4b3a4201d231d7e4d3fafd01099","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-06-22T08:17:54Z","title_canon_sha256":"bbbbdf84439ce070c09f36ff897bd7c4981b34cd964c2dedf0ea23ac67d6aa9f"},"schema_version":"1.0","source":{"id":"2606.23004","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.23004","created_at":"2026-06-23T03:14:06Z"},{"alias_kind":"arxiv_version","alias_value":"2606.23004v1","created_at":"2026-06-23T03:14:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23004","created_at":"2026-06-23T03:14:06Z"},{"alias_kind":"pith_short_12","alias_value":"3RQH5FRPARU4","created_at":"2026-06-23T03:14:06Z"},{"alias_kind":"pith_short_16","alias_value":"3RQH5FRPARU4ODIW","created_at":"2026-06-23T03:14:06Z"},{"alias_kind":"pith_short_8","alias_value":"3RQH5FRP","created_at":"2026-06-23T03:14:06Z"}],"graph_snapshots":[{"event_id":"sha256:9280e7b2988305b6d02bcf7f0e47ccfaddb3adaed4d5b9ca0430999037f4eac2","target":"graph","created_at":"2026-06-23T03:14:06Z","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/2606.23004/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study finite braces whose additive and multiplicative groups are both cyclic. We reinterpret the classification of these braces from the perspective of regular subgroups of permutation groups, and identify which of them are biskew braces.","authors_text":"Hal Simpson, Paul J. Truman","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-06-22T08:17:54Z","title":"Bicyclic biskew braces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23004","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:c3571553aeb902a2dca84d05bc1db635d8655079e7a88f155cc25c58cf1b6f84","target":"record","created_at":"2026-06-23T03:14:06Z","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":"a5213869cdcac2b5623584ac6c2a063f9ecfe4b3a4201d231d7e4d3fafd01099","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-06-22T08:17:54Z","title_canon_sha256":"bbbbdf84439ce070c09f36ff897bd7c4981b34cd964c2dedf0ea23ac67d6aa9f"},"schema_version":"1.0","source":{"id":"2606.23004","kind":"arxiv","version":1}},"canonical_sha256":"dc607e962f0469c70d166b14df31c49dbc2803b081375020fd9bb51161c31393","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc607e962f0469c70d166b14df31c49dbc2803b081375020fd9bb51161c31393","first_computed_at":"2026-06-23T03:14:06.492823Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T03:14:06.492823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QcKhHLCOjfmcpxrsqFaI0I4svOUrDRq+0dNjF/FMK31S+OJ2PqZ+kwp/3asBtfQoNYULdEpAhyJhpQSuJ6r0CQ==","signature_status":"signed_v1","signed_at":"2026-06-23T03:14:06.493205Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.23004","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3571553aeb902a2dca84d05bc1db635d8655079e7a88f155cc25c58cf1b6f84","sha256:9280e7b2988305b6d02bcf7f0e47ccfaddb3adaed4d5b9ca0430999037f4eac2"],"state_sha256":"2777db52f56df24eab6fa1de793bbff88aa1fa2b3ff75bdec410cfac2d78588b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z3Dszv6wbJ1Gbh8A6oXhbJc5wAhIyff6NJjvtxwi9//aqzRhPMrAjR8fm7cFUduKujjBhhCVJIpvmXMTnLGfBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T12:20:55.576146Z","bundle_sha256":"bbdd8d300e5830d4f7c551a9b05a6c379feb511a1a3ebc6abef4fa758ee2cfed"}}