{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:UQHPLUELS245JX4AKZX4YXVOUB","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":"d4a0ff3a222d015971321f1581c3bde4e595fc799c87ecde5d3cde511e731722","cross_cats_sorted":["hep-th","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-11T20:09:03Z","title_canon_sha256":"4c069191080d1698b71747263c543d065c63322b1c113d80311eb662b9d0f5e0"},"schema_version":"1.0","source":{"id":"1010.2218","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.2218","created_at":"2026-05-18T04:26:54Z"},{"alias_kind":"arxiv_version","alias_value":"1010.2218v1","created_at":"2026-05-18T04:26:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2218","created_at":"2026-05-18T04:26:54Z"},{"alias_kind":"pith_short_12","alias_value":"UQHPLUELS245","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UQHPLUELS245JX4A","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UQHPLUEL","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:855cfa1f45ca727d28b11c2e5d916694e9099faf163b2c775d5dabc28efff1c5","target":"graph","created_at":"2026-05-18T04:26:54Z","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":"We provide a construction procedure for complex root spaces invariant under antilinear transformations, which may be applied to any Coxeter group. The procedure is based on the factorisation of a chosen element of the Coxeter group into two factors. Each of the factors constitutes an involution and may therefore be deformed in an antilinear fashion. Having the importance of the E(8)-Coxeter group in mind, such as underlying a particular perturbation of the Ising model and the fact that for it no solution could be found previously, we exemplify the procedure for this particular case. As a concr","authors_text":"Andreas Fring, Monique Smith","cross_cats":["hep-th","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-11T20:09:03Z","title":"PT invariant complex E(8) root spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2218","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":"sha256:3f8a3f26bf1f69f9a44871e314237114356080260469fa2cfcdb0eda5626bb65","target":"record","created_at":"2026-05-18T04:26:54Z","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":"d4a0ff3a222d015971321f1581c3bde4e595fc799c87ecde5d3cde511e731722","cross_cats_sorted":["hep-th","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-11T20:09:03Z","title_canon_sha256":"4c069191080d1698b71747263c543d065c63322b1c113d80311eb662b9d0f5e0"},"schema_version":"1.0","source":{"id":"1010.2218","kind":"arxiv","version":1}},"canonical_sha256":"a40ef5d08b96b9d4df80566fcc5eaea076cfdb2436ea618aefed6380bf5d52ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a40ef5d08b96b9d4df80566fcc5eaea076cfdb2436ea618aefed6380bf5d52ef","first_computed_at":"2026-05-18T04:26:54.582912Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:54.582912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S3JMKT8M6QRKs/4/m+yTOtNJnJvSN9wYanFEGaQqoIFyAbiM+ten+D17qxIxoGYFCL056e+SbAnEZ3gX5vJqAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:54.583302Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.2218","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f8a3f26bf1f69f9a44871e314237114356080260469fa2cfcdb0eda5626bb65","sha256:855cfa1f45ca727d28b11c2e5d916694e9099faf163b2c775d5dabc28efff1c5"],"state_sha256":"54ebc9b7e6c53a2675ce6228a9650053d16407830e9042eedbd0b780a12aa684"}