{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:AQMOGEQKA7RNTHDODB42OTPREZ","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":"6976d4bd857fbc68dd16deb7652fe54a82b9cafa61d7c6723a830189ba6e137f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-06-04T07:33:03Z","title_canon_sha256":"75b970ecfe556c6220d1cbd4a16933b2aa38ec264e827f92f29ea20ad69beaca"},"schema_version":"1.0","source":{"id":"2606.05802","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.05802","created_at":"2026-06-05T01:15:03Z"},{"alias_kind":"arxiv_version","alias_value":"2606.05802v1","created_at":"2026-06-05T01:15:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.05802","created_at":"2026-06-05T01:15:03Z"},{"alias_kind":"pith_short_12","alias_value":"AQMOGEQKA7RN","created_at":"2026-06-05T01:15:03Z"},{"alias_kind":"pith_short_16","alias_value":"AQMOGEQKA7RNTHDO","created_at":"2026-06-05T01:15:03Z"},{"alias_kind":"pith_short_8","alias_value":"AQMOGEQK","created_at":"2026-06-05T01:15:03Z"}],"graph_snapshots":[{"event_id":"sha256:fbe74162ab2b14c900193adad8301a1940a1d457503317efabf761e80ac1b1ae","target":"graph","created_at":"2026-06-05T01:15:03Z","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/2606.05802/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct cubic Dirac operators and relative cubic Dirac operators for infinite-dimensional quadratic $\\mathbb{Z}$-graded color Lie algebras with finite-dimensional components. These operators are defined in completions of the quantum Weil algebra determined by the $\\mathbb{Z}$-grading. The same grading fixes the normal-ordering convention. The failure of the normally ordered Casimir to be central, and of the normally ordered cubic Dirac operator to be $\\mathfrak{g}$-invariant, is measured by a color analogue of the Kac-Peterson class. If this class is trivial, the Casimir admits a central ","authors_text":"Konstantin Wernli, Steffen Schmidt","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-06-04T07:33:03Z","title":"Dirac operators for infinite-dimensional color Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05802","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:fc576123ec19019672f714c5aee03463c5f8c1856185992d6d793c38d0890eee","target":"record","created_at":"2026-06-05T01:15:03Z","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":"6976d4bd857fbc68dd16deb7652fe54a82b9cafa61d7c6723a830189ba6e137f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-06-04T07:33:03Z","title_canon_sha256":"75b970ecfe556c6220d1cbd4a16933b2aa38ec264e827f92f29ea20ad69beaca"},"schema_version":"1.0","source":{"id":"2606.05802","kind":"arxiv","version":1}},"canonical_sha256":"0418e3120a07e2d99c6e1879a74df12646a125dc3bcdad84cd3cc4e3cf5d249f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0418e3120a07e2d99c6e1879a74df12646a125dc3bcdad84cd3cc4e3cf5d249f","first_computed_at":"2026-06-05T01:15:03.826825Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-05T01:15:03.826825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6d+IM4EaSHK1Xc5e9hyUinJ/EMMr3a1NFvo41oPeT9x/nh2boX1PzWfaqxCErcfRz+Mw/f2fRlGBE7nrN6DoBw==","signature_status":"signed_v1","signed_at":"2026-06-05T01:15:03.827382Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.05802","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc576123ec19019672f714c5aee03463c5f8c1856185992d6d793c38d0890eee","sha256:fbe74162ab2b14c900193adad8301a1940a1d457503317efabf761e80ac1b1ae"],"state_sha256":"362c73e0e9641e53f210e634a9d783c90232ea96570760a6163d9a78678357cb"}