{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:P7OWKNQBJFZU5LED6RA6BSVLHM","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":"81ef63c60a702a097e5639a5e6aa1035e057fcbab83afbd3d1d7d8582df0e5aa","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-05-15T19:00:06Z","title_canon_sha256":"2ab2df5f9f84707eeb836174297ca808f298c1aa28eecd0ccc21de51015b779a"},"schema_version":"1.0","source":{"id":"2605.16558","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.16558","created_at":"2026-05-20T00:02:29Z"},{"alias_kind":"arxiv_version","alias_value":"2605.16558v1","created_at":"2026-05-20T00:02:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.16558","created_at":"2026-05-20T00:02:29Z"},{"alias_kind":"pith_short_12","alias_value":"P7OWKNQBJFZU","created_at":"2026-05-20T00:02:29Z"},{"alias_kind":"pith_short_16","alias_value":"P7OWKNQBJFZU5LED","created_at":"2026-05-20T00:02:29Z"},{"alias_kind":"pith_short_8","alias_value":"P7OWKNQB","created_at":"2026-05-20T00:02:29Z"}],"graph_snapshots":[{"event_id":"sha256:b1dd6ca8eadc2c0f2b935003389093ec2abe321f1697a2639299107137829957","target":"graph","created_at":"2026-05-20T00:02:29Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"unlike classical tangent bundle cases, the hyperbolic frame bundle admits lifting without any topological obstruction. This leads to the possibility of always defining spinor structures in hyperbolic Clifford bundles."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The particularities arising from the Whitney sum in the hyperbolic setting eliminate the topological obstructions to lifting that exist in classical tangent bundle cases, based on a general analysis of obstruction classes."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Hyperbolic Clifford algebra bundles admit frame bundle lifts without topological obstructions, enabling consistent spinor structures unlike classical tangent bundles."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Hyperbolic Clifford algebra bundles allow spinor structures to be defined without topological obstructions."}],"snapshot_sha256":"fa600265147bb0355f6fcf7d6b86c88766c659436ebf84db2391d5fbbe21adfc"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T22:01:23.120295Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T21:41:14.028568Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T19:21:56.887072Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.628772Z","status":"skipped","version":"1.0.0"}],"endpoint":"/pith/2605.16558/integrity.json","findings":[],"snapshot_sha256":"a14ff13766f896db01ead53b19dd78c6015545db219324d5f8a58e6d145fb1a2","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Starting from a general analysis of obstruction classes, we develop the investigation of obstructions associated with the bundle structure of the hyperbolic Clifford algebra. By taking into account particularities arising from the Whitney sum, it is shown that, unlike classical tangent bundle cases, the hyperbolic frame bundle admits lifting without any topological obstruction. This leads to the possibility of always defining spinor structures in hyperbolic Clifford bundles.","authors_text":"E. Notte-Cuello, J. M. Hoff da Silva","cross_cats":["hep-th","math.MP"],"headline":"Hyperbolic Clifford algebra bundles allow spinor structures to be defined without topological obstructions.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-05-15T19:00:06Z","title":"Notes on obstructions in the hyperbolic Clifford algebra bundle structure"},"references":{"count":12,"internal_anchors":0,"resolved_work":12,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"W. Greub and H. R. Petry,On the lifting of structure groups, in Differential Geometrical Methods in Mathematical Physics, II, Lecture Notes in Mathematics, Springer, New York (1978)","work_id":"cfbb99e0-d1e1-4b76-b523-789e3c4700e4","year":1978},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"H. Osborn,Vector Bundles, Vol. I, Academic Press, New York (1982)","work_id":"c093625d-8b01-4d54-9d2f-c17c1bf36381","year":1982},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"R. Geroch,Spinor structure of space-times in General Relativity I, J. Math. Phys. 9, 1739–1744 (1968)","work_id":"95d2472c-b438-4b7d-8faa-7342cb010198","year":1968},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"R. Geroch,Spinor structure of space-times in General Relativity II, J. Math. Phys. 11, 343–348 (1970)","work_id":"32506170-9316-4db7-af13-1bc712361f2e","year":1970},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"W. Greub, S. Halperin, and J. Van Stone,Connections, Curvature and Cohomology, Academic Press, New York (1973)","work_id":"b82d7b0a-d046-4cbb-ba03-ef2113c33f7b","year":1973}],"snapshot_sha256":"9d428eac50dab05c63537de62e3cab73bf9785d71aca845b094dd4581b204fe4"},"source":{"id":"2605.16558","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T21:27:20.227277Z","id":"7c083fd1-912c-4d26-a4c7-015667cdcc2f","model_set":{"reader":"grok-4.3"},"one_line_summary":"Hyperbolic Clifford algebra bundles admit frame bundle lifts without topological obstructions, enabling consistent spinor structures unlike classical tangent bundles.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Hyperbolic Clifford algebra bundles allow spinor structures to be defined without topological obstructions.","strongest_claim":"unlike classical tangent bundle cases, the hyperbolic frame bundle admits lifting without any topological obstruction. This leads to the possibility of always defining spinor structures in hyperbolic Clifford bundles.","weakest_assumption":"The particularities arising from the Whitney sum in the hyperbolic setting eliminate the topological obstructions to lifting that exist in classical tangent bundle cases, based on a general analysis of obstruction classes."}},"verdict_id":"7c083fd1-912c-4d26-a4c7-015667cdcc2f"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7990549162fc04d887bc99a62a539b88b3184b8759d9c324f49235aa6a54bc70","target":"record","created_at":"2026-05-20T00:02:29Z","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":"81ef63c60a702a097e5639a5e6aa1035e057fcbab83afbd3d1d7d8582df0e5aa","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-05-15T19:00:06Z","title_canon_sha256":"2ab2df5f9f84707eeb836174297ca808f298c1aa28eecd0ccc21de51015b779a"},"schema_version":"1.0","source":{"id":"2605.16558","kind":"arxiv","version":1}},"canonical_sha256":"7fdd65360149734eac83f441e0caab3b19e9eefd5822fd08be679f2984c93a52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fdd65360149734eac83f441e0caab3b19e9eefd5822fd08be679f2984c93a52","first_computed_at":"2026-05-20T00:02:29.059471Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:02:29.059471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"err7nB7DVOmgM9b5BxA2D5289u5FlGl0RrA2YRH9itd6759C/qy2wme9E8i0VFws+DUcBKKXqaRaERFymns8DQ==","signature_status":"signed_v1","signed_at":"2026-05-20T00:02:29.060207Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.16558","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7990549162fc04d887bc99a62a539b88b3184b8759d9c324f49235aa6a54bc70","sha256:b1dd6ca8eadc2c0f2b935003389093ec2abe321f1697a2639299107137829957"],"state_sha256":"b3f82e545a8154ab30b1b4ef553d55a02259d22b4ec3ad209d2f8f85287d8f81"}