{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:EA4UCUI7JBUR66GI64UYR26U6E","short_pith_number":"pith:EA4UCUI7","canonical_record":{"source":{"id":"2607.28900","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-07-30T23:43:20Z","cross_cats_sorted":[],"title_canon_sha256":"70c3faac677a5babbdf9811d214223cbab25ecddd66b90a9138c19916d50aa18","abstract_canon_sha256":"f2ca550a5110c30283e55c7fa67e3a30f4a22fff8ca35bf1df7ac6667a647b33"},"schema_version":"1.0"},"canonical_sha256":"203941511f48691f78c8f72988ebd4f1347ba3fd3fa747db0a15f48f1a7260cc","source":{"kind":"arxiv","id":"2607.28900","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.28900","created_at":"2026-08-03T01:17:27Z"},{"alias_kind":"arxiv_version","alias_value":"2607.28900v1","created_at":"2026-08-03T01:17:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28900","created_at":"2026-08-03T01:17:27Z"},{"alias_kind":"pith_short_12","alias_value":"EA4UCUI7JBUR","created_at":"2026-08-03T01:17:27Z"},{"alias_kind":"pith_short_16","alias_value":"EA4UCUI7JBUR66GI","created_at":"2026-08-03T01:17:27Z"},{"alias_kind":"pith_short_8","alias_value":"EA4UCUI7","created_at":"2026-08-03T01:17:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:EA4UCUI7JBUR66GI64UYR26U6E","target":"record","payload":{"canonical_record":{"source":{"id":"2607.28900","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-07-30T23:43:20Z","cross_cats_sorted":[],"title_canon_sha256":"70c3faac677a5babbdf9811d214223cbab25ecddd66b90a9138c19916d50aa18","abstract_canon_sha256":"f2ca550a5110c30283e55c7fa67e3a30f4a22fff8ca35bf1df7ac6667a647b33"},"schema_version":"1.0"},"canonical_sha256":"203941511f48691f78c8f72988ebd4f1347ba3fd3fa747db0a15f48f1a7260cc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-03T01:17:27.708240Z","signature_b64":"IEiqOCLxRFAZgb4BLhmAn1WiDppgdbNe/7srTP2MPjEU6/FTPpUQPhtJIj0p60x96QZoHw3mWKPtM5mgBb7UCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"203941511f48691f78c8f72988ebd4f1347ba3fd3fa747db0a15f48f1a7260cc","last_reissued_at":"2026-08-03T01:17:27.706775Z","signature_status":"signed_v1","first_computed_at":"2026-08-03T01:17:27.706775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.28900","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":"2026-08-03T01:17:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OaZU4VR1sB2HtQyP+DgkVa4ImoFlR1KJvFBDKSD8CrPczXE2Xk2T9UY0n/+j5EMOdz9SX5zHcoEO5gn3CuqJCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T02:33:57.692099Z"},"content_sha256":"58a2c1c3db07b2ca2671b4c8ba7e2a67552b927f36fa7a76cbf2cce3dbe38bc6","schema_version":"1.0","event_id":"sha256:58a2c1c3db07b2ca2671b4c8ba7e2a67552b927f36fa7a76cbf2cce3dbe38bc6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:EA4UCUI7JBUR66GI64UYR26U6E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finding 59:29 in the Monster","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Aluna Rizzoli, Anthony Pisani, Heiko Dietrich, Melissa Lee","submitted_at":"2026-07-30T23:43:20Z","abstract_excerpt":"The classification of the maximal subgroups of the Monster group has been completed recently, and explicit generators for each such subgroup (up to conjugacy) have been made available for the software mmgroup, with the exception of the maximal subgroup 59:29, see Dietrich et al. (Adv. Math., 2025; J Algebra, 2026). We provide explicit generators for this last maximal subgroup and comment on the extensive search that led to finding them. Our method is similar to, but significantly more involved than Bray et al.'s (London Math. Soc. J. Comput. Math., 2016) approach for constructing 47:23 in the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28900","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/2607.28900/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":"2026-08-03T01:17:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fgGAxTkaL73otWYDF0J3OGffSdIqbRKS5LMetb+7RZlUVlg8FAQU6WDhebby++Yhq2AoT5QXUBqeNZE1wDqmCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T02:33:57.693030Z"},"content_sha256":"f9377c4fdc84862464fffdc7f7ea2086a0e090c3b6e82163a881471b59925560","schema_version":"1.0","event_id":"sha256:f9377c4fdc84862464fffdc7f7ea2086a0e090c3b6e82163a881471b59925560"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EA4UCUI7JBUR66GI64UYR26U6E/bundle.json","state_url":"https://pith.science/pith/EA4UCUI7JBUR66GI64UYR26U6E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EA4UCUI7JBUR66GI64UYR26U6E/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":"2026-08-09T02:33:57Z","links":{"resolver":"https://pith.science/pith/EA4UCUI7JBUR66GI64UYR26U6E","bundle":"https://pith.science/pith/EA4UCUI7JBUR66GI64UYR26U6E/bundle.json","state":"https://pith.science/pith/EA4UCUI7JBUR66GI64UYR26U6E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EA4UCUI7JBUR66GI64UYR26U6E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:EA4UCUI7JBUR66GI64UYR26U6E","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":"f2ca550a5110c30283e55c7fa67e3a30f4a22fff8ca35bf1df7ac6667a647b33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-07-30T23:43:20Z","title_canon_sha256":"70c3faac677a5babbdf9811d214223cbab25ecddd66b90a9138c19916d50aa18"},"schema_version":"1.0","source":{"id":"2607.28900","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.28900","created_at":"2026-08-03T01:17:27Z"},{"alias_kind":"arxiv_version","alias_value":"2607.28900v1","created_at":"2026-08-03T01:17:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28900","created_at":"2026-08-03T01:17:27Z"},{"alias_kind":"pith_short_12","alias_value":"EA4UCUI7JBUR","created_at":"2026-08-03T01:17:27Z"},{"alias_kind":"pith_short_16","alias_value":"EA4UCUI7JBUR66GI","created_at":"2026-08-03T01:17:27Z"},{"alias_kind":"pith_short_8","alias_value":"EA4UCUI7","created_at":"2026-08-03T01:17:27Z"}],"graph_snapshots":[{"event_id":"sha256:f9377c4fdc84862464fffdc7f7ea2086a0e090c3b6e82163a881471b59925560","target":"graph","created_at":"2026-08-03T01:17:27Z","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/2607.28900/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The classification of the maximal subgroups of the Monster group has been completed recently, and explicit generators for each such subgroup (up to conjugacy) have been made available for the software mmgroup, with the exception of the maximal subgroup 59:29, see Dietrich et al. (Adv. Math., 2025; J Algebra, 2026). We provide explicit generators for this last maximal subgroup and comment on the extensive search that led to finding them. Our method is similar to, but significantly more involved than Bray et al.'s (London Math. Soc. J. Comput. Math., 2016) approach for constructing 47:23 in the ","authors_text":"Aluna Rizzoli, Anthony Pisani, Heiko Dietrich, Melissa Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-07-30T23:43:20Z","title":"Finding 59:29 in the Monster"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28900","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":"sha256:58a2c1c3db07b2ca2671b4c8ba7e2a67552b927f36fa7a76cbf2cce3dbe38bc6","target":"record","created_at":"2026-08-03T01:17:27Z","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":"f2ca550a5110c30283e55c7fa67e3a30f4a22fff8ca35bf1df7ac6667a647b33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-07-30T23:43:20Z","title_canon_sha256":"70c3faac677a5babbdf9811d214223cbab25ecddd66b90a9138c19916d50aa18"},"schema_version":"1.0","source":{"id":"2607.28900","kind":"arxiv","version":1}},"canonical_sha256":"203941511f48691f78c8f72988ebd4f1347ba3fd3fa747db0a15f48f1a7260cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"203941511f48691f78c8f72988ebd4f1347ba3fd3fa747db0a15f48f1a7260cc","first_computed_at":"2026-08-03T01:17:27.706775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-03T01:17:27.706775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IEiqOCLxRFAZgb4BLhmAn1WiDppgdbNe/7srTP2MPjEU6/FTPpUQPhtJIj0p60x96QZoHw3mWKPtM5mgBb7UCg==","signature_status":"signed_v1","signed_at":"2026-08-03T01:17:27.708240Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.28900","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58a2c1c3db07b2ca2671b4c8ba7e2a67552b927f36fa7a76cbf2cce3dbe38bc6","sha256:f9377c4fdc84862464fffdc7f7ea2086a0e090c3b6e82163a881471b59925560"],"state_sha256":"81068e8509b493106f236759cd458b28ea8c70abe39fca9db63061d3e915b5a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MmgICZfY7ZwH/GNy4+rxUAqStdJ8B+eerbgdXw1L+c329YspI3WPlYaDMQSzprm3/uKMhMau1lYBHUQpoGM1Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T02:33:57.699674Z","bundle_sha256":"439d657dccd4d1a0a0b6870b1f0c43812e2c1c3e9e18695b477c4f12eeee7e3f"}}