{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:AQ4JJ7UN5QPZQAJWZUR5YI2MNO","short_pith_number":"pith:AQ4JJ7UN","canonical_record":{"source":{"id":"2607.18497","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-07-20T20:37:38Z","cross_cats_sorted":[],"title_canon_sha256":"22aed03c2fe4871b8e03a12f6a9ea79e0904a41d59679c328c6c9bcc960fad04","abstract_canon_sha256":"7042974462bcee75a64f3c4096da18040128450f47dad5efcc352bb435cb7fae"},"schema_version":"1.0"},"canonical_sha256":"043894fe8dec1f980136cd23dc234c6bb26c0f1d9b0834e95fcb44c109c61103","source":{"kind":"arxiv","id":"2607.18497","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.18497","created_at":"2026-07-22T00:22:51Z"},{"alias_kind":"arxiv_version","alias_value":"2607.18497v1","created_at":"2026-07-22T00:22:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.18497","created_at":"2026-07-22T00:22:51Z"},{"alias_kind":"pith_short_12","alias_value":"AQ4JJ7UN5QPZ","created_at":"2026-07-22T00:22:51Z"},{"alias_kind":"pith_short_16","alias_value":"AQ4JJ7UN5QPZQAJW","created_at":"2026-07-22T00:22:51Z"},{"alias_kind":"pith_short_8","alias_value":"AQ4JJ7UN","created_at":"2026-07-22T00:22:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:AQ4JJ7UN5QPZQAJWZUR5YI2MNO","target":"record","payload":{"canonical_record":{"source":{"id":"2607.18497","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-07-20T20:37:38Z","cross_cats_sorted":[],"title_canon_sha256":"22aed03c2fe4871b8e03a12f6a9ea79e0904a41d59679c328c6c9bcc960fad04","abstract_canon_sha256":"7042974462bcee75a64f3c4096da18040128450f47dad5efcc352bb435cb7fae"},"schema_version":"1.0"},"canonical_sha256":"043894fe8dec1f980136cd23dc234c6bb26c0f1d9b0834e95fcb44c109c61103","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-22T00:22:51.507799Z","signature_b64":"IgIZO9jzR5jbKMNu06l5EmKCipGVkKW1wd2FuzjymY002u1b25YqWgvOQ1WWJV54j2cbMWwKThY18uGr0d1HDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"043894fe8dec1f980136cd23dc234c6bb26c0f1d9b0834e95fcb44c109c61103","last_reissued_at":"2026-07-22T00:22:51.507031Z","signature_status":"signed_v1","first_computed_at":"2026-07-22T00:22:51.507031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.18497","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":"2026-07-22T00:22:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5y8nlfQPYWg1YlxxojBHA25F55oNoBtJBUFS5d6lnhvfbyCgEJeaSfkFqkkt4bHssLMTYthmWe07BTJRwMT5CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T09:42:38.667125Z"},"content_sha256":"644ee393d5d93425b7f340012cb1d2ceab44e153aa41362fe2df1a4b0a558960","schema_version":"1.0","event_id":"sha256:644ee393d5d93425b7f340012cb1d2ceab44e153aa41362fe2df1a4b0a558960"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:AQ4JJ7UN5QPZQAJWZUR5YI2MNO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cyclic covers and non-orbit 3-representation-finite symmetric algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Tor Kringeland","submitted_at":"2026-07-20T20:37:38Z","abstract_excerpt":"Over an algebraically closed field of characteristic zero, we exhibit two symmetric algebras that are 3-representation-finite but are not orbit algebras of repetitive categories. The first is a 36-dimensional characteristic-zero lift $A$ of $Q(3A)^2_2$, the quaternion-type algebra that B\\\"ohmler and Marczinzik proved 3-representation-finite in characteristic 2; we construct an explicit 3-cluster-tilting module. We show that any orbit presentation of a connected symmetric algebra forces the algebra, or a connected cyclic cover of it, to admit a half-dimensional square-zero grading. Such grading"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18497","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/2607.18497/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":"2026-07-22T00:22:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kSyaMbL6JH9PYLPdXt/NAEDUUAzMy6F+x4/8i47mZtmumt0KiPnbyfz22tIZ+2jNZ1xEtkLbjLGWeHyuTZMxDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T09:42:38.667524Z"},"content_sha256":"c7bff14702277dc28b5d8845a4e2ff503ab2a604f2dc8de1a0a0d5146a8a7be7","schema_version":"1.0","event_id":"sha256:c7bff14702277dc28b5d8845a4e2ff503ab2a604f2dc8de1a0a0d5146a8a7be7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AQ4JJ7UN5QPZQAJWZUR5YI2MNO/bundle.json","state_url":"https://pith.science/pith/AQ4JJ7UN5QPZQAJWZUR5YI2MNO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AQ4JJ7UN5QPZQAJWZUR5YI2MNO/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":"2026-08-21T09:42:38Z","links":{"resolver":"https://pith.science/pith/AQ4JJ7UN5QPZQAJWZUR5YI2MNO","bundle":"https://pith.science/pith/AQ4JJ7UN5QPZQAJWZUR5YI2MNO/bundle.json","state":"https://pith.science/pith/AQ4JJ7UN5QPZQAJWZUR5YI2MNO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AQ4JJ7UN5QPZQAJWZUR5YI2MNO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:AQ4JJ7UN5QPZQAJWZUR5YI2MNO","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":"7042974462bcee75a64f3c4096da18040128450f47dad5efcc352bb435cb7fae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-07-20T20:37:38Z","title_canon_sha256":"22aed03c2fe4871b8e03a12f6a9ea79e0904a41d59679c328c6c9bcc960fad04"},"schema_version":"1.0","source":{"id":"2607.18497","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.18497","created_at":"2026-07-22T00:22:51Z"},{"alias_kind":"arxiv_version","alias_value":"2607.18497v1","created_at":"2026-07-22T00:22:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.18497","created_at":"2026-07-22T00:22:51Z"},{"alias_kind":"pith_short_12","alias_value":"AQ4JJ7UN5QPZ","created_at":"2026-07-22T00:22:51Z"},{"alias_kind":"pith_short_16","alias_value":"AQ4JJ7UN5QPZQAJW","created_at":"2026-07-22T00:22:51Z"},{"alias_kind":"pith_short_8","alias_value":"AQ4JJ7UN","created_at":"2026-07-22T00:22:51Z"}],"graph_snapshots":[{"event_id":"sha256:c7bff14702277dc28b5d8845a4e2ff503ab2a604f2dc8de1a0a0d5146a8a7be7","target":"graph","created_at":"2026-07-22T00:22:51Z","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/2607.18497/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Over an algebraically closed field of characteristic zero, we exhibit two symmetric algebras that are 3-representation-finite but are not orbit algebras of repetitive categories. The first is a 36-dimensional characteristic-zero lift $A$ of $Q(3A)^2_2$, the quaternion-type algebra that B\\\"ohmler and Marczinzik proved 3-representation-finite in characteristic 2; we construct an explicit 3-cluster-tilting module. We show that any orbit presentation of a connected symmetric algebra forces the algebra, or a connected cyclic cover of it, to admit a half-dimensional square-zero grading. Such grading","authors_text":"Tor Kringeland","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-07-20T20:37:38Z","title":"Cyclic covers and non-orbit 3-representation-finite symmetric algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18497","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":"sha256:644ee393d5d93425b7f340012cb1d2ceab44e153aa41362fe2df1a4b0a558960","target":"record","created_at":"2026-07-22T00:22:51Z","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":"7042974462bcee75a64f3c4096da18040128450f47dad5efcc352bb435cb7fae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-07-20T20:37:38Z","title_canon_sha256":"22aed03c2fe4871b8e03a12f6a9ea79e0904a41d59679c328c6c9bcc960fad04"},"schema_version":"1.0","source":{"id":"2607.18497","kind":"arxiv","version":1}},"canonical_sha256":"043894fe8dec1f980136cd23dc234c6bb26c0f1d9b0834e95fcb44c109c61103","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"043894fe8dec1f980136cd23dc234c6bb26c0f1d9b0834e95fcb44c109c61103","first_computed_at":"2026-07-22T00:22:51.507031Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-22T00:22:51.507031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IgIZO9jzR5jbKMNu06l5EmKCipGVkKW1wd2FuzjymY002u1b25YqWgvOQ1WWJV54j2cbMWwKThY18uGr0d1HDw==","signature_status":"signed_v1","signed_at":"2026-07-22T00:22:51.507799Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.18497","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:644ee393d5d93425b7f340012cb1d2ceab44e153aa41362fe2df1a4b0a558960","sha256:c7bff14702277dc28b5d8845a4e2ff503ab2a604f2dc8de1a0a0d5146a8a7be7"],"state_sha256":"607ee6d5e6baf6be44f6ead3742fc387d96bded7f874d7f80bdb3d903b40912c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fBoviq9UJ5CS0U1wtmswscszONVpA9XSK+IrlmNo84GLuzf/5oN8s/2+qroGWHUK2MYQGxAt/eVowOuxCUM6Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T09:42:38.670022Z","bundle_sha256":"bc0a6bcf3c1bdcf338c9a510e9daa893757c6d7bf4aa9fd31008516595b20a43"}}