{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:RBRMX4A3CXFQ3DA3Y6JVI2FXJX","short_pith_number":"pith:RBRMX4A3","canonical_record":{"source":{"id":"1610.01307","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-05T08:41:59Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"f36973332d623e9b7508466b899629643a1522921e122238b962f46c8a51945c","abstract_canon_sha256":"ddfcedf0dafc670917be194e8f6f3b97cf5e97643dc801997cd060b3d5229fdd"},"schema_version":"1.0"},"canonical_sha256":"8862cbf01b15cb0d8c1bc7935468b74dca92463396df6f618c8ed32775415c2e","source":{"kind":"arxiv","id":"1610.01307","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.01307","created_at":"2026-05-18T01:03:11Z"},{"alias_kind":"arxiv_version","alias_value":"1610.01307v1","created_at":"2026-05-18T01:03:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01307","created_at":"2026-05-18T01:03:11Z"},{"alias_kind":"pith_short_12","alias_value":"RBRMX4A3CXFQ","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RBRMX4A3CXFQ3DA3","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RBRMX4A3","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:RBRMX4A3CXFQ3DA3Y6JVI2FXJX","target":"record","payload":{"canonical_record":{"source":{"id":"1610.01307","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-05T08:41:59Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"f36973332d623e9b7508466b899629643a1522921e122238b962f46c8a51945c","abstract_canon_sha256":"ddfcedf0dafc670917be194e8f6f3b97cf5e97643dc801997cd060b3d5229fdd"},"schema_version":"1.0"},"canonical_sha256":"8862cbf01b15cb0d8c1bc7935468b74dca92463396df6f618c8ed32775415c2e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:11.187917Z","signature_b64":"DxgzqCfQs9+2m6Rmb3vRjte4f6qZNzWz0YKb3YdKtk4zUrYDY47RISVgBvIFqnultTOK8PGFwSs+nu73FHt5CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8862cbf01b15cb0d8c1bc7935468b74dca92463396df6f618c8ed32775415c2e","last_reissued_at":"2026-05-18T01:03:11.187305Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:11.187305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.01307","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":"2026-05-18T01:03:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q8IjufMucDYHm3OTlD52w9yoIfz4jmwvCOcKxEo9/Py30vW0OmBZfEgG8bmN0WG54akNQrHeLd0NTIfqN/RODw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T07:54:08.796496Z"},"content_sha256":"bce3e57e3dee9b9f5cd0ccce17e5c219997a7a7b2b70f65b3bc715b848b141f6","schema_version":"1.0","event_id":"sha256:bce3e57e3dee9b9f5cd0ccce17e5c219997a7a7b2b70f65b3bc715b848b141f6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:RBRMX4A3CXFQ3DA3Y6JVI2FXJX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Miyamoto involutions in axial algebras of Jordan type half","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.GR","authors_text":"J. I. Hall, S. Shpectorov, Y. Segev","submitted_at":"2016-10-05T08:41:59Z","abstract_excerpt":"Nonassociative commutative algebras $A$ generated by idempotents $e$ whose adjoint operators ${\\rm ad}_e\\colon A \\rightarrow A$, given by $x \\mapsto xe$, are diagonalizable and have few eigenvalues are of recent interest. When certain fusion (multiplication) rules between the associated eigenspaces are imposed, the structure of these algebras remains rich yet rather rigid. For example vertex operator algebras give rise to such algebras. The connection between the Monster algebra and Monster group extends to many axial algebras which then have interesting groups of automorphisms.\n  Axial algebr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01307","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":""},"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":"2026-05-18T01:03:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BGu9kbldB6VTAQZRI8l0OpmT+WIq/7bAt0tUeHatjpk0R7BHs/M6QJsZBcQA8E8VtWgWCkx7Vg2KMDe5H6R3Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T07:54:08.797268Z"},"content_sha256":"f73fabb10b50407ccf38c80eee29d3488bc67325ee1a6b659fcc7396444fe84e","schema_version":"1.0","event_id":"sha256:f73fabb10b50407ccf38c80eee29d3488bc67325ee1a6b659fcc7396444fe84e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RBRMX4A3CXFQ3DA3Y6JVI2FXJX/bundle.json","state_url":"https://pith.science/pith/RBRMX4A3CXFQ3DA3Y6JVI2FXJX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RBRMX4A3CXFQ3DA3Y6JVI2FXJX/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":"2026-06-10T07:54:08Z","links":{"resolver":"https://pith.science/pith/RBRMX4A3CXFQ3DA3Y6JVI2FXJX","bundle":"https://pith.science/pith/RBRMX4A3CXFQ3DA3Y6JVI2FXJX/bundle.json","state":"https://pith.science/pith/RBRMX4A3CXFQ3DA3Y6JVI2FXJX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RBRMX4A3CXFQ3DA3Y6JVI2FXJX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RBRMX4A3CXFQ3DA3Y6JVI2FXJX","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":"ddfcedf0dafc670917be194e8f6f3b97cf5e97643dc801997cd060b3d5229fdd","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-05T08:41:59Z","title_canon_sha256":"f36973332d623e9b7508466b899629643a1522921e122238b962f46c8a51945c"},"schema_version":"1.0","source":{"id":"1610.01307","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.01307","created_at":"2026-05-18T01:03:11Z"},{"alias_kind":"arxiv_version","alias_value":"1610.01307v1","created_at":"2026-05-18T01:03:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01307","created_at":"2026-05-18T01:03:11Z"},{"alias_kind":"pith_short_12","alias_value":"RBRMX4A3CXFQ","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RBRMX4A3CXFQ3DA3","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RBRMX4A3","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:f73fabb10b50407ccf38c80eee29d3488bc67325ee1a6b659fcc7396444fe84e","target":"graph","created_at":"2026-05-18T01:03:11Z","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":"Nonassociative commutative algebras $A$ generated by idempotents $e$ whose adjoint operators ${\\rm ad}_e\\colon A \\rightarrow A$, given by $x \\mapsto xe$, are diagonalizable and have few eigenvalues are of recent interest. When certain fusion (multiplication) rules between the associated eigenspaces are imposed, the structure of these algebras remains rich yet rather rigid. For example vertex operator algebras give rise to such algebras. The connection between the Monster algebra and Monster group extends to many axial algebras which then have interesting groups of automorphisms.\n  Axial algebr","authors_text":"J. I. Hall, S. Shpectorov, Y. Segev","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-05T08:41:59Z","title":"Miyamoto involutions in axial algebras of Jordan type half"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01307","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:bce3e57e3dee9b9f5cd0ccce17e5c219997a7a7b2b70f65b3bc715b848b141f6","target":"record","created_at":"2026-05-18T01:03:11Z","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":"ddfcedf0dafc670917be194e8f6f3b97cf5e97643dc801997cd060b3d5229fdd","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-05T08:41:59Z","title_canon_sha256":"f36973332d623e9b7508466b899629643a1522921e122238b962f46c8a51945c"},"schema_version":"1.0","source":{"id":"1610.01307","kind":"arxiv","version":1}},"canonical_sha256":"8862cbf01b15cb0d8c1bc7935468b74dca92463396df6f618c8ed32775415c2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8862cbf01b15cb0d8c1bc7935468b74dca92463396df6f618c8ed32775415c2e","first_computed_at":"2026-05-18T01:03:11.187305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:11.187305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DxgzqCfQs9+2m6Rmb3vRjte4f6qZNzWz0YKb3YdKtk4zUrYDY47RISVgBvIFqnultTOK8PGFwSs+nu73FHt5CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:11.187917Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.01307","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bce3e57e3dee9b9f5cd0ccce17e5c219997a7a7b2b70f65b3bc715b848b141f6","sha256:f73fabb10b50407ccf38c80eee29d3488bc67325ee1a6b659fcc7396444fe84e"],"state_sha256":"e4887d97a4feb141be85e800b3b8a2f407f96b9910b55e5bc4d96802ea509cb8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GKdRuuKVnV+a1TH6FD5YOC7ghvuTpnOsaHJAoZ+Qpd5y7V1Nn/EYbope8V4OPxWrHE915PybleVyJ9BQAy+HDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T07:54:08.801457Z","bundle_sha256":"b1741d39d3bf0e92eba1e1c68e7254f2a43f753169431d295fa9c06db166ceca"}}