{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VQOO6JZAXWUWXLDP3OUICXYGWB","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":"325f5cc4481370f3c3b16cabe64509bc99786d2b28cf41a553c9f8d104c259ab","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-06-22T20:19:54Z","title_canon_sha256":"215d448aee2b4ba556fd8d923990323fe7ec9a8593e24062f11cabeec76fba1e"},"schema_version":"1.0","source":{"id":"1506.06779","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06779","created_at":"2026-05-18T01:40:55Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06779v1","created_at":"2026-05-18T01:40:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06779","created_at":"2026-05-18T01:40:55Z"},{"alias_kind":"pith_short_12","alias_value":"VQOO6JZAXWUW","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VQOO6JZAXWUWXLDP","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VQOO6JZA","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:17cd4fb0e9faa51b1fa662587a5b7d53c199e5da64bd48ea3840bfa0046ab174","target":"graph","created_at":"2026-05-18T01:40:55Z","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":"A rationality result previously proved for Robertson-Walker metrics is extended to a homogeneous anisotropic cosmological model, namely the Bianchi type-IX minisuperspace. It is shown that the Seeley-de Witt coefficients appearing in the expansion of the spectral action for the Bianchi type-IX geometry are expressed in terms of polynomials with rational coefficients in the cosmic evolution factors $w_1(t), w_2(t), w_3(t),$ and their higher derivates with respect to time. We begin with the computation of the Dirac operator of this geometry and calculate the coefficients $a_0, a_2, a_4$ of the s","authors_text":"Farzad Fathizadeh, Matilde Marcolli, Wentao Fan","cross_cats":["gr-qc","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-06-22T20:19:54Z","title":"Spectral Action for Bianchi Type-IX Cosmological Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06779","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":"sha256:7102b23f1e7d68694996026cacd8065d3ace3cf508bc3ae276c3dbfe76cdbda1","target":"record","created_at":"2026-05-18T01:40:55Z","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":"325f5cc4481370f3c3b16cabe64509bc99786d2b28cf41a553c9f8d104c259ab","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-06-22T20:19:54Z","title_canon_sha256":"215d448aee2b4ba556fd8d923990323fe7ec9a8593e24062f11cabeec76fba1e"},"schema_version":"1.0","source":{"id":"1506.06779","kind":"arxiv","version":1}},"canonical_sha256":"ac1cef2720bda96bac6fdba8815f06b072802c49c02e65df50e777c796d06306","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac1cef2720bda96bac6fdba8815f06b072802c49c02e65df50e777c796d06306","first_computed_at":"2026-05-18T01:40:55.974000Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:40:55.974000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wrj7icQ1SuuazrKhlyt89wCCadudSeOBDIk1EipefhfVLqyTcSpEsA15dggexVfow4jRovEQTUrE4adBWfd/CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:40:55.974726Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.06779","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7102b23f1e7d68694996026cacd8065d3ace3cf508bc3ae276c3dbfe76cdbda1","sha256:17cd4fb0e9faa51b1fa662587a5b7d53c199e5da64bd48ea3840bfa0046ab174"],"state_sha256":"5cc3eff31b916c7213064586c9023905b7e59d0ef23dd8344398c8e3ae2b13eb"}