{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:KX5ZU4IS44HMLDNVEHDQ72ZDIK","short_pith_number":"pith:KX5ZU4IS","canonical_record":{"source":{"id":"1810.00590","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-10-01T09:18:12Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"ab39e89334eb6ce84b089d842f578a372c046e36b8c1728616a1b800e4d7217a","abstract_canon_sha256":"4e245cc5768185fb6c2694d9b5a67913e760c48e44dfae84dc61241cd16b44e7"},"schema_version":"1.0"},"canonical_sha256":"55fb9a7112e70ec58db521c70feb234297b6eaac5092aadb1a20a1c7f92a58f2","source":{"kind":"arxiv","id":"1810.00590","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.00590","created_at":"2026-05-18T00:04:25Z"},{"alias_kind":"arxiv_version","alias_value":"1810.00590v1","created_at":"2026-05-18T00:04:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00590","created_at":"2026-05-18T00:04:25Z"},{"alias_kind":"pith_short_12","alias_value":"KX5ZU4IS44HM","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KX5ZU4IS44HMLDNV","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KX5ZU4IS","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:KX5ZU4IS44HMLDNVEHDQ72ZDIK","target":"record","payload":{"canonical_record":{"source":{"id":"1810.00590","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-10-01T09:18:12Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"ab39e89334eb6ce84b089d842f578a372c046e36b8c1728616a1b800e4d7217a","abstract_canon_sha256":"4e245cc5768185fb6c2694d9b5a67913e760c48e44dfae84dc61241cd16b44e7"},"schema_version":"1.0"},"canonical_sha256":"55fb9a7112e70ec58db521c70feb234297b6eaac5092aadb1a20a1c7f92a58f2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:25.325332Z","signature_b64":"KuOImnsxzmy2WWjD1IqGWjqtx85C7vIuBx7wJ/hqSdP9tqShN/0dh4U3QDpViosz/RbT9WDRbl1PeRi5l6AmCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55fb9a7112e70ec58db521c70feb234297b6eaac5092aadb1a20a1c7f92a58f2","last_reissued_at":"2026-05-18T00:04:25.324779Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:25.324779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.00590","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":"2026-05-18T00:04:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jedwgr5pXMPjcXoJjv16HAlcKJhscFT7In+qflCyCAP8uZHsckC1AkV8CRUmyBFanuKc1gozsXYKcuE7WS+0Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T17:30:32.213968Z"},"content_sha256":"86d7a29cb5bd990f9eff598afff035b43b53b9df698489f80293161908778879","schema_version":"1.0","event_id":"sha256:86d7a29cb5bd990f9eff598afff035b43b53b9df698489f80293161908778879"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:KX5ZU4IS44HMLDNVEHDQ72ZDIK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An infinite family of axial algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RA","authors_text":"Madeleine Whybrow","submitted_at":"2018-10-01T09:18:12Z","abstract_excerpt":"Axial algebras are non-associative algebras generated by semisimple idempotents, known as axes, that all obey a fusion rule. Axial algebras were introduced by Hall, Rehren and Shpectorov as a generalisation of the axioms of Majorana theory, which was in turn introduced by Ivanov as an axiomatisation of certain properties of the 2A-axes of the Griess algebra. Axial algebras of Monster type are axial algebras whose axes obey the Monster, or Majorana, fusion rule.\n  We construct an axial algebra of Monster type $M_{4A}$ over the polynomial ring $\\mathbb{R}[t]$ that is generated by six axes whose "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00590","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":"2026-05-18T00:04:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KSBLiiQ0j7TbL/BfLK+E/7hEHVWu7no7M6rc1sD1wqiQj0jmO0Vzjis3nCXxk1FQd60AXvEQRt/7ekqdHj5rAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T17:30:32.214691Z"},"content_sha256":"2deef9a7d88cc846c59db1831826ed1d20180a758bce71c3f6fd4037389fcded","schema_version":"1.0","event_id":"sha256:2deef9a7d88cc846c59db1831826ed1d20180a758bce71c3f6fd4037389fcded"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KX5ZU4IS44HMLDNVEHDQ72ZDIK/bundle.json","state_url":"https://pith.science/pith/KX5ZU4IS44HMLDNVEHDQ72ZDIK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KX5ZU4IS44HMLDNVEHDQ72ZDIK/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":"2026-06-10T17:30:32Z","links":{"resolver":"https://pith.science/pith/KX5ZU4IS44HMLDNVEHDQ72ZDIK","bundle":"https://pith.science/pith/KX5ZU4IS44HMLDNVEHDQ72ZDIK/bundle.json","state":"https://pith.science/pith/KX5ZU4IS44HMLDNVEHDQ72ZDIK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KX5ZU4IS44HMLDNVEHDQ72ZDIK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KX5ZU4IS44HMLDNVEHDQ72ZDIK","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":"4e245cc5768185fb6c2694d9b5a67913e760c48e44dfae84dc61241cd16b44e7","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-10-01T09:18:12Z","title_canon_sha256":"ab39e89334eb6ce84b089d842f578a372c046e36b8c1728616a1b800e4d7217a"},"schema_version":"1.0","source":{"id":"1810.00590","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.00590","created_at":"2026-05-18T00:04:25Z"},{"alias_kind":"arxiv_version","alias_value":"1810.00590v1","created_at":"2026-05-18T00:04:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00590","created_at":"2026-05-18T00:04:25Z"},{"alias_kind":"pith_short_12","alias_value":"KX5ZU4IS44HM","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KX5ZU4IS44HMLDNV","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KX5ZU4IS","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:2deef9a7d88cc846c59db1831826ed1d20180a758bce71c3f6fd4037389fcded","target":"graph","created_at":"2026-05-18T00:04:25Z","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":"Axial algebras are non-associative algebras generated by semisimple idempotents, known as axes, that all obey a fusion rule. Axial algebras were introduced by Hall, Rehren and Shpectorov as a generalisation of the axioms of Majorana theory, which was in turn introduced by Ivanov as an axiomatisation of certain properties of the 2A-axes of the Griess algebra. Axial algebras of Monster type are axial algebras whose axes obey the Monster, or Majorana, fusion rule.\n  We construct an axial algebra of Monster type $M_{4A}$ over the polynomial ring $\\mathbb{R}[t]$ that is generated by six axes whose ","authors_text":"Madeleine Whybrow","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-10-01T09:18:12Z","title":"An infinite family of axial algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00590","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":"sha256:86d7a29cb5bd990f9eff598afff035b43b53b9df698489f80293161908778879","target":"record","created_at":"2026-05-18T00:04:25Z","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":"4e245cc5768185fb6c2694d9b5a67913e760c48e44dfae84dc61241cd16b44e7","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-10-01T09:18:12Z","title_canon_sha256":"ab39e89334eb6ce84b089d842f578a372c046e36b8c1728616a1b800e4d7217a"},"schema_version":"1.0","source":{"id":"1810.00590","kind":"arxiv","version":1}},"canonical_sha256":"55fb9a7112e70ec58db521c70feb234297b6eaac5092aadb1a20a1c7f92a58f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55fb9a7112e70ec58db521c70feb234297b6eaac5092aadb1a20a1c7f92a58f2","first_computed_at":"2026-05-18T00:04:25.324779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:25.324779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KuOImnsxzmy2WWjD1IqGWjqtx85C7vIuBx7wJ/hqSdP9tqShN/0dh4U3QDpViosz/RbT9WDRbl1PeRi5l6AmCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:25.325332Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.00590","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86d7a29cb5bd990f9eff598afff035b43b53b9df698489f80293161908778879","sha256:2deef9a7d88cc846c59db1831826ed1d20180a758bce71c3f6fd4037389fcded"],"state_sha256":"92e4e806268e2c2d9c1d542b9ee64ccced2441c1e9a3a8d6bf0707318f9dce22"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BhSy/iPNGd7ihgiNq2o+be0JWC4dAjz3hIXvEZ9ryAqXqqz4+xUUzCSV/XrnpQoDAb6tLtegVgApuDkvyq/7Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T17:30:32.219069Z","bundle_sha256":"7115c557bd25ff68b4c543347a45090e374e78edaf3bf1d5503faa006bbc8ace"}}