{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:7LQGKDXNC2UNBITCY556MKTCLY","short_pith_number":"pith:7LQGKDXN","canonical_record":{"source":{"id":"2606.30048","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2026-06-29T09:41:18Z","cross_cats_sorted":[],"title_canon_sha256":"8d05c3a68e3a1c47ca0c3bd21e99cbf37f89d781315f1b06814b9d81a9d18648","abstract_canon_sha256":"aaca95bcea8d5c29b559257f37c3af2c0fe87cd707cc202b91a9f710978c78a1"},"schema_version":"1.0"},"canonical_sha256":"fae0650eed16a8d0a262c77be62a625e3629c8db1a2e5ae38f6ee0ecf4765ac8","source":{"kind":"arxiv","id":"2606.30048","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.30048","created_at":"2026-06-30T02:17:47Z"},{"alias_kind":"arxiv_version","alias_value":"2606.30048v1","created_at":"2026-06-30T02:17:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30048","created_at":"2026-06-30T02:17:47Z"},{"alias_kind":"pith_short_12","alias_value":"7LQGKDXNC2UN","created_at":"2026-06-30T02:17:47Z"},{"alias_kind":"pith_short_16","alias_value":"7LQGKDXNC2UNBITC","created_at":"2026-06-30T02:17:47Z"},{"alias_kind":"pith_short_8","alias_value":"7LQGKDXN","created_at":"2026-06-30T02:17:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:7LQGKDXNC2UNBITCY556MKTCLY","target":"record","payload":{"canonical_record":{"source":{"id":"2606.30048","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2026-06-29T09:41:18Z","cross_cats_sorted":[],"title_canon_sha256":"8d05c3a68e3a1c47ca0c3bd21e99cbf37f89d781315f1b06814b9d81a9d18648","abstract_canon_sha256":"aaca95bcea8d5c29b559257f37c3af2c0fe87cd707cc202b91a9f710978c78a1"},"schema_version":"1.0"},"canonical_sha256":"fae0650eed16a8d0a262c77be62a625e3629c8db1a2e5ae38f6ee0ecf4765ac8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T02:17:47.430371Z","signature_b64":"lc2ABf1ATL4B5aQl4iiXg0w/Yy1pkn72I5fpKX9DjzcP+teRrfNMKr/Ij5OT7XDzUpaK7fpOTtOEj6omcuDnAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fae0650eed16a8d0a262c77be62a625e3629c8db1a2e5ae38f6ee0ecf4765ac8","last_reissued_at":"2026-06-30T02:17:47.429730Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T02:17:47.429730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.30048","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":"2026-06-30T02:17:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uZGR+64i4e/jWnkanpAFn5Af0ElOv2lXlhCBKmJd6TFW3i89Ujl8nY6uo8SIta3fGzumQLwTEiz6/lvKzeWKCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T18:38:03.908462Z"},"content_sha256":"acafdb18c4cbc44dd0ed4adb8606ec1061ea49f08735185bbb619e4d4cdc5a2e","schema_version":"1.0","event_id":"sha256:acafdb18c4cbc44dd0ed4adb8606ec1061ea49f08735185bbb619e4d4cdc5a2e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:7LQGKDXNC2UNBITCY556MKTCLY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Axial Algebras: Questions and Conjectures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"I. Gorshkov, S. Shpectorov","submitted_at":"2026-06-29T09:41:18Z","abstract_excerpt":"Axial algebras are non-associative algebras generated by idempotents, called axes, whose adjoint action satisfies a fusion law. When this fusion law is graded, axes naturally lead to automorphisms of the algebra, and so such axial algebras are inextricably linked with groups.\n  This article is meant to complement the recent survey \\cite{ms} by significantly expanding the list of interesting open problems suggested by the specialists in the field, and providing a further discussion of the related concepts and available results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30048","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/2606.30048/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":"2026-06-30T02:17:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pYjOF5jrnzbgoAyo6PWZYzBe0T1xG2tayMHrfbGBEfVQF2fuA4xxWqj6/SQgh5TKBJct5YtLCFORjrFAZF64Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T18:38:03.909156Z"},"content_sha256":"7e52c33cae77b671bd0bbbc6ff59f855643fb870181d0b79e5c0dd66bee7e06f","schema_version":"1.0","event_id":"sha256:7e52c33cae77b671bd0bbbc6ff59f855643fb870181d0b79e5c0dd66bee7e06f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7LQGKDXNC2UNBITCY556MKTCLY/bundle.json","state_url":"https://pith.science/pith/7LQGKDXNC2UNBITCY556MKTCLY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7LQGKDXNC2UNBITCY556MKTCLY/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":"2026-08-05T18:38:03Z","links":{"resolver":"https://pith.science/pith/7LQGKDXNC2UNBITCY556MKTCLY","bundle":"https://pith.science/pith/7LQGKDXNC2UNBITCY556MKTCLY/bundle.json","state":"https://pith.science/pith/7LQGKDXNC2UNBITCY556MKTCLY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7LQGKDXNC2UNBITCY556MKTCLY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:7LQGKDXNC2UNBITCY556MKTCLY","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":"aaca95bcea8d5c29b559257f37c3af2c0fe87cd707cc202b91a9f710978c78a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2026-06-29T09:41:18Z","title_canon_sha256":"8d05c3a68e3a1c47ca0c3bd21e99cbf37f89d781315f1b06814b9d81a9d18648"},"schema_version":"1.0","source":{"id":"2606.30048","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.30048","created_at":"2026-06-30T02:17:47Z"},{"alias_kind":"arxiv_version","alias_value":"2606.30048v1","created_at":"2026-06-30T02:17:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30048","created_at":"2026-06-30T02:17:47Z"},{"alias_kind":"pith_short_12","alias_value":"7LQGKDXNC2UN","created_at":"2026-06-30T02:17:47Z"},{"alias_kind":"pith_short_16","alias_value":"7LQGKDXNC2UNBITC","created_at":"2026-06-30T02:17:47Z"},{"alias_kind":"pith_short_8","alias_value":"7LQGKDXN","created_at":"2026-06-30T02:17:47Z"}],"graph_snapshots":[{"event_id":"sha256:7e52c33cae77b671bd0bbbc6ff59f855643fb870181d0b79e5c0dd66bee7e06f","target":"graph","created_at":"2026-06-30T02:17:47Z","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/2606.30048/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Axial algebras are non-associative algebras generated by idempotents, called axes, whose adjoint action satisfies a fusion law. When this fusion law is graded, axes naturally lead to automorphisms of the algebra, and so such axial algebras are inextricably linked with groups.\n  This article is meant to complement the recent survey \\cite{ms} by significantly expanding the list of interesting open problems suggested by the specialists in the field, and providing a further discussion of the related concepts and available results.","authors_text":"I. Gorshkov, S. Shpectorov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2026-06-29T09:41:18Z","title":"Axial Algebras: Questions and Conjectures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30048","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:acafdb18c4cbc44dd0ed4adb8606ec1061ea49f08735185bbb619e4d4cdc5a2e","target":"record","created_at":"2026-06-30T02:17:47Z","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":"aaca95bcea8d5c29b559257f37c3af2c0fe87cd707cc202b91a9f710978c78a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2026-06-29T09:41:18Z","title_canon_sha256":"8d05c3a68e3a1c47ca0c3bd21e99cbf37f89d781315f1b06814b9d81a9d18648"},"schema_version":"1.0","source":{"id":"2606.30048","kind":"arxiv","version":1}},"canonical_sha256":"fae0650eed16a8d0a262c77be62a625e3629c8db1a2e5ae38f6ee0ecf4765ac8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fae0650eed16a8d0a262c77be62a625e3629c8db1a2e5ae38f6ee0ecf4765ac8","first_computed_at":"2026-06-30T02:17:47.429730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T02:17:47.429730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lc2ABf1ATL4B5aQl4iiXg0w/Yy1pkn72I5fpKX9DjzcP+teRrfNMKr/Ij5OT7XDzUpaK7fpOTtOEj6omcuDnAg==","signature_status":"signed_v1","signed_at":"2026-06-30T02:17:47.430371Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.30048","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:acafdb18c4cbc44dd0ed4adb8606ec1061ea49f08735185bbb619e4d4cdc5a2e","sha256:7e52c33cae77b671bd0bbbc6ff59f855643fb870181d0b79e5c0dd66bee7e06f"],"state_sha256":"326c929459457a9e0fa4a3bcd2c5edf151021991c7c8e10884c5747c31781ddc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SDhXUVVJbeiuXB+MG5uKBLGlfaU3SQkviQZ0FKabYtoMqW/zRvU2citGHQoUsrONmE+OVKTviX9VZI5NwWNBBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T18:38:03.914005Z","bundle_sha256":"281c02fafd39448ab11bdecf2d775687317fcd5145ebd15dfcc5c900c833fef8"}}