{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:XJTFSVYSI6VTZOPYG2VGWZJ4TS","short_pith_number":"pith:XJTFSVYS","canonical_record":{"source":{"id":"1908.07104","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-19T23:22:42Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"89b35b45d0d4fb7eb6c033d8d2537244e4886de411fc848cfec6a4acf6c7dac1","abstract_canon_sha256":"9f8bc25f33a6d75e4811770a173efec8901cb3903d80ae4fa2c510aa723ac125"},"schema_version":"1.0"},"canonical_sha256":"ba6659571247ab3cb9f836aa6b653c9cbc587a92a8f86da64734f6e57460409e","source":{"kind":"arxiv","id":"1908.07104","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07104","created_at":"2026-07-05T01:17:57Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07104v2","created_at":"2026-07-05T01:17:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07104","created_at":"2026-07-05T01:17:57Z"},{"alias_kind":"pith_short_12","alias_value":"XJTFSVYSI6VT","created_at":"2026-07-05T01:17:57Z"},{"alias_kind":"pith_short_16","alias_value":"XJTFSVYSI6VTZOPY","created_at":"2026-07-05T01:17:57Z"},{"alias_kind":"pith_short_8","alias_value":"XJTFSVYS","created_at":"2026-07-05T01:17:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:XJTFSVYSI6VTZOPYG2VGWZJ4TS","target":"record","payload":{"canonical_record":{"source":{"id":"1908.07104","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-19T23:22:42Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"89b35b45d0d4fb7eb6c033d8d2537244e4886de411fc848cfec6a4acf6c7dac1","abstract_canon_sha256":"9f8bc25f33a6d75e4811770a173efec8901cb3903d80ae4fa2c510aa723ac125"},"schema_version":"1.0"},"canonical_sha256":"ba6659571247ab3cb9f836aa6b653c9cbc587a92a8f86da64734f6e57460409e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:17:57.583419Z","signature_b64":"jDZLcuQuKX4i8MOkG3t2Kc2qlXOgfkqFJHEGxArVeQcnrcycVkhRBhhBT+nBrvw3SvxVWfU02+Fc5HQjLjHxDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba6659571247ab3cb9f836aa6b653c9cbc587a92a8f86da64734f6e57460409e","last_reissued_at":"2026-07-05T01:17:57.582936Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:17:57.582936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.07104","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:17:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eD2SJ7EewNTS9ZdIgJCZj2QJvFgiGWZN5NUpcR726Kdqe1l/t6fmvEwSvNMXWYuxHpjHXuUERa0MdSKy/wDnAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T08:01:47.267323Z"},"content_sha256":"2732abfa9825b07705c8cf6eb9d405ccfc6a7d669d4bc72c90532ac8f549ba53","schema_version":"1.0","event_id":"sha256:2732abfa9825b07705c8cf6eb9d405ccfc6a7d669d4bc72c90532ac8f549ba53"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:XJTFSVYSI6VTZOPYG2VGWZJ4TS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the 486-vertex distance-regular graphs of Koolen--Riebeek and Soicher","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Daniel R. Hawtin, Robert F. Bailey","submitted_at":"2019-08-19T23:22:42Z","abstract_excerpt":"This paper considers three imprimitive distance-regular graphs with 486 vertices and diameter 4: the Koolen--Riebeek graph (which is bipartite), the Soicher graph (which is antipodal), and the incidence graph of a symmetric transversal design obtained from the affine geometry $\\mathrm{AG}(5,3)$ (which is both). It is shown that each of these is preserved by the same rank-9 action of the group $3^5:(2\\times M_{10})$, and the connection is explained using the ternary Golay code."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07104","kind":"arxiv","version":2},"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/1908.07104/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":"2026-07-05T01:17:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DBjoBNhKumL9rCd/2jlARW+xz2HAPEdZBkMzYJJgBSB+8PHOkmoapg/wTbn1PAcS8xhE95dAaT8/OVZrzPNDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T08:01:47.267836Z"},"content_sha256":"be8900a0a118c18172458f80726ad6c58971e716d2969a33fcb7ec005c668eb2","schema_version":"1.0","event_id":"sha256:be8900a0a118c18172458f80726ad6c58971e716d2969a33fcb7ec005c668eb2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XJTFSVYSI6VTZOPYG2VGWZJ4TS/bundle.json","state_url":"https://pith.science/pith/XJTFSVYSI6VTZOPYG2VGWZJ4TS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XJTFSVYSI6VTZOPYG2VGWZJ4TS/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":"2026-08-16T08:01:47Z","links":{"resolver":"https://pith.science/pith/XJTFSVYSI6VTZOPYG2VGWZJ4TS","bundle":"https://pith.science/pith/XJTFSVYSI6VTZOPYG2VGWZJ4TS/bundle.json","state":"https://pith.science/pith/XJTFSVYSI6VTZOPYG2VGWZJ4TS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XJTFSVYSI6VTZOPYG2VGWZJ4TS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:XJTFSVYSI6VTZOPYG2VGWZJ4TS","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":"9f8bc25f33a6d75e4811770a173efec8901cb3903d80ae4fa2c510aa723ac125","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-19T23:22:42Z","title_canon_sha256":"89b35b45d0d4fb7eb6c033d8d2537244e4886de411fc848cfec6a4acf6c7dac1"},"schema_version":"1.0","source":{"id":"1908.07104","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07104","created_at":"2026-07-05T01:17:57Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07104v2","created_at":"2026-07-05T01:17:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07104","created_at":"2026-07-05T01:17:57Z"},{"alias_kind":"pith_short_12","alias_value":"XJTFSVYSI6VT","created_at":"2026-07-05T01:17:57Z"},{"alias_kind":"pith_short_16","alias_value":"XJTFSVYSI6VTZOPY","created_at":"2026-07-05T01:17:57Z"},{"alias_kind":"pith_short_8","alias_value":"XJTFSVYS","created_at":"2026-07-05T01:17:57Z"}],"graph_snapshots":[{"event_id":"sha256:be8900a0a118c18172458f80726ad6c58971e716d2969a33fcb7ec005c668eb2","target":"graph","created_at":"2026-07-05T01:17:57Z","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/1908.07104/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper considers three imprimitive distance-regular graphs with 486 vertices and diameter 4: the Koolen--Riebeek graph (which is bipartite), the Soicher graph (which is antipodal), and the incidence graph of a symmetric transversal design obtained from the affine geometry $\\mathrm{AG}(5,3)$ (which is both). It is shown that each of these is preserved by the same rank-9 action of the group $3^5:(2\\times M_{10})$, and the connection is explained using the ternary Golay code.","authors_text":"Daniel R. Hawtin, Robert F. Bailey","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-19T23:22:42Z","title":"On the 486-vertex distance-regular graphs of Koolen--Riebeek and Soicher"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07104","kind":"arxiv","version":2},"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":"sha256:2732abfa9825b07705c8cf6eb9d405ccfc6a7d669d4bc72c90532ac8f549ba53","target":"record","created_at":"2026-07-05T01:17:57Z","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":"9f8bc25f33a6d75e4811770a173efec8901cb3903d80ae4fa2c510aa723ac125","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-19T23:22:42Z","title_canon_sha256":"89b35b45d0d4fb7eb6c033d8d2537244e4886de411fc848cfec6a4acf6c7dac1"},"schema_version":"1.0","source":{"id":"1908.07104","kind":"arxiv","version":2}},"canonical_sha256":"ba6659571247ab3cb9f836aa6b653c9cbc587a92a8f86da64734f6e57460409e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba6659571247ab3cb9f836aa6b653c9cbc587a92a8f86da64734f6e57460409e","first_computed_at":"2026-07-05T01:17:57.582936Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:17:57.582936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jDZLcuQuKX4i8MOkG3t2Kc2qlXOgfkqFJHEGxArVeQcnrcycVkhRBhhBT+nBrvw3SvxVWfU02+Fc5HQjLjHxDA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:17:57.583419Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.07104","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2732abfa9825b07705c8cf6eb9d405ccfc6a7d669d4bc72c90532ac8f549ba53","sha256:be8900a0a118c18172458f80726ad6c58971e716d2969a33fcb7ec005c668eb2"],"state_sha256":"23bced8c3aa318cad3fd078a1978426227007eeb7f3db35a284d814b0edac9c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zE7pRNuEkKeocx2AFWH2yecvMeBu5xnTG63Kod8DN3D4KQ19Le6FuOg0tiX8MoOcoXhEMfcVr1GKNJLuEHo3Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T08:01:47.272260Z","bundle_sha256":"d8f9f8f1b511a027074befe661e75a5b536d85c3897ef068d7497c8721d8b403"}}