{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:3RNTLICSYGQLGG3RDDRAVYCS45","short_pith_number":"pith:3RNTLICS","canonical_record":{"source":{"id":"1608.08489","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-08-30T15:08:26Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"fffb9ca8c48a39923f3c8e12fe2db3aa7a03a309d345195f2b171eccf1310536","abstract_canon_sha256":"24835d673e2ecf38663b89c68c820a83d46ce40f4ccf35fcdd26108a16fce479"},"schema_version":"1.0"},"canonical_sha256":"dc5b35a052c1a0b31b7118e20ae052e764fd28367e5f1a7fdbd318cac80c3bbe","source":{"kind":"arxiv","id":"1608.08489","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08489","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08489v3","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08489","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"pith_short_12","alias_value":"3RNTLICSYGQL","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3RNTLICSYGQLGG3R","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3RNTLICS","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:3RNTLICSYGQLGG3RDDRAVYCS45","target":"record","payload":{"canonical_record":{"source":{"id":"1608.08489","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-08-30T15:08:26Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"fffb9ca8c48a39923f3c8e12fe2db3aa7a03a309d345195f2b171eccf1310536","abstract_canon_sha256":"24835d673e2ecf38663b89c68c820a83d46ce40f4ccf35fcdd26108a16fce479"},"schema_version":"1.0"},"canonical_sha256":"dc5b35a052c1a0b31b7118e20ae052e764fd28367e5f1a7fdbd318cac80c3bbe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:01.893299Z","signature_b64":"DNCZT46wALa+X5OOsAHEqqvSkFIwcmZaQg8U5aB8oPz5TS3zhswGgNK7B+YCdGrFLJy8E0WJZQyWtkBo9jLVAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc5b35a052c1a0b31b7118e20ae052e764fd28367e5f1a7fdbd318cac80c3bbe","last_reissued_at":"2026-05-18T00:29:01.892844Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:01.892844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.08489","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vnng92EkZ5twcmr7rgPQcnqEO377lW659Zn+Y2qQfIq/IST9dpw8wtt30h3sRUiSxxrQ1scs+r/leQZpK6ASCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T16:31:09.714468Z"},"content_sha256":"40adf02c475d19306fac7ca4fc6c8442a00c4b29823c2c0897921d5c8c0655f4","schema_version":"1.0","event_id":"sha256:40adf02c475d19306fac7ca4fc6c8442a00c4b29823c2c0897921d5c8c0655f4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:3RNTLICSYGQLGG3RDDRAVYCS45","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New refiners for permutation group search","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.GR","authors_text":"Christopher Jefferson, Markus Pfeiffer, Rebecca Waldecker","submitted_at":"2016-08-30T15:08:26Z","abstract_excerpt":"We describe how orbital graphs can be used to improve the practical performance of many algorithms for permutation groups, including intersection and stabilizer problems. First we explain how orbital graphs can be integrated in partition backtracking, the current state of the art algorithm for many permutation group problems. We then show how our algorithms perform in practice, demonstrating improvements of several orders of magnitude for some problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08489","kind":"arxiv","version":3},"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":"2026-05-18T00:29:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L7gY5Q4XxQANVjWPDaS/mG5CB8svhDMrlpERcTls6m+dhqKQ0J3z4Ffc2fJgxeOjXoxxjDR83JxP3cFKluarCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T16:31:09.715110Z"},"content_sha256":"cd8c5fe9e1f2d5d23bd8ccb9bcb92452741700e1ac37c06766696c5979225083","schema_version":"1.0","event_id":"sha256:cd8c5fe9e1f2d5d23bd8ccb9bcb92452741700e1ac37c06766696c5979225083"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3RNTLICSYGQLGG3RDDRAVYCS45/bundle.json","state_url":"https://pith.science/pith/3RNTLICSYGQLGG3RDDRAVYCS45/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3RNTLICSYGQLGG3RDDRAVYCS45/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":"2026-05-27T16:31:09Z","links":{"resolver":"https://pith.science/pith/3RNTLICSYGQLGG3RDDRAVYCS45","bundle":"https://pith.science/pith/3RNTLICSYGQLGG3RDDRAVYCS45/bundle.json","state":"https://pith.science/pith/3RNTLICSYGQLGG3RDDRAVYCS45/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3RNTLICSYGQLGG3RDDRAVYCS45/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3RNTLICSYGQLGG3RDDRAVYCS45","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":"24835d673e2ecf38663b89c68c820a83d46ce40f4ccf35fcdd26108a16fce479","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-08-30T15:08:26Z","title_canon_sha256":"fffb9ca8c48a39923f3c8e12fe2db3aa7a03a309d345195f2b171eccf1310536"},"schema_version":"1.0","source":{"id":"1608.08489","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08489","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08489v3","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08489","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"pith_short_12","alias_value":"3RNTLICSYGQL","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3RNTLICSYGQLGG3R","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3RNTLICS","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:cd8c5fe9e1f2d5d23bd8ccb9bcb92452741700e1ac37c06766696c5979225083","target":"graph","created_at":"2026-05-18T00:29:01Z","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 describe how orbital graphs can be used to improve the practical performance of many algorithms for permutation groups, including intersection and stabilizer problems. First we explain how orbital graphs can be integrated in partition backtracking, the current state of the art algorithm for many permutation group problems. We then show how our algorithms perform in practice, demonstrating improvements of several orders of magnitude for some problems.","authors_text":"Christopher Jefferson, Markus Pfeiffer, Rebecca Waldecker","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-08-30T15:08:26Z","title":"New refiners for permutation group search"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08489","kind":"arxiv","version":3},"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":"sha256:40adf02c475d19306fac7ca4fc6c8442a00c4b29823c2c0897921d5c8c0655f4","target":"record","created_at":"2026-05-18T00:29:01Z","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":"24835d673e2ecf38663b89c68c820a83d46ce40f4ccf35fcdd26108a16fce479","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-08-30T15:08:26Z","title_canon_sha256":"fffb9ca8c48a39923f3c8e12fe2db3aa7a03a309d345195f2b171eccf1310536"},"schema_version":"1.0","source":{"id":"1608.08489","kind":"arxiv","version":3}},"canonical_sha256":"dc5b35a052c1a0b31b7118e20ae052e764fd28367e5f1a7fdbd318cac80c3bbe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc5b35a052c1a0b31b7118e20ae052e764fd28367e5f1a7fdbd318cac80c3bbe","first_computed_at":"2026-05-18T00:29:01.892844Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:01.892844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DNCZT46wALa+X5OOsAHEqqvSkFIwcmZaQg8U5aB8oPz5TS3zhswGgNK7B+YCdGrFLJy8E0WJZQyWtkBo9jLVAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:01.893299Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.08489","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40adf02c475d19306fac7ca4fc6c8442a00c4b29823c2c0897921d5c8c0655f4","sha256:cd8c5fe9e1f2d5d23bd8ccb9bcb92452741700e1ac37c06766696c5979225083"],"state_sha256":"e774b5d5a276e848cbf2716b081f6d06872b44f75e09e1476c1cb28cb859b349"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b+F9UteY/WErOP9tJXIADj6wiIgD2Ice3cNL+aibtntKUt97h/2jZO4w1p1g2dySNocI2sznVgXwfPSyWkDrAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T16:31:09.718658Z","bundle_sha256":"6cc820b4e2074a61753062092e730e713010af4f3c9fbc85b6a28e39fb6e2a66"}}