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The strict tangent-module analogue, obtained from \\([T_{\\mathbb R}\\CP^3\\otimes\\C]\\), vanishes because \\[ \\operatorname{ch}_3(T^{1,0}\\CP^3)+ \\operatorname{ch}_3(T^{0,1}\\CP^3)=0. \\] By contrast, "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.04054","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-06-02T09:41:00Z","cross_cats_sorted":["hep-th","math-ph","math.MP","math.RT"],"title_canon_sha256":"0f036a6d63997fc3e07b6481852a5aed08d470f33062a5e9ef7bf304b084064b","abstract_canon_sha256":"eaf0d502b808fc9b62966d129f8b5c60db0e2a3d8e171e7c8335d057460823b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T00:06:45.352774Z","signature_b64":"t0OisTSVQsdE0HVCe5vI/Qnxl4iWV3IiMa4VmCHjnL17l7Rbe7cg+FJ7wq50enKZGFCKAHUm7/gdnQI4COucCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2192300b859e9bf0866e8317250aed44878562f59610b3c599a1764154226a78","last_reissued_at":"2026-06-04T00:06:45.352357Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T00:06:45.352357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cyclic source pairings for Penrose--Sparling non-Hausdorff twistor spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","math.RT"],"primary_cat":"math.DG","authors_text":"Ioannis P. 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The strict tangent-module analogue, obtained from \\([T_{\\mathbb R}\\CP^3\\otimes\\C]\\), vanishes because \\[ \\operatorname{ch}_3(T^{1,0}\\CP^3)+ \\operatorname{ch}_3(T^{0,1}\\CP^3)=0. \\] By contrast, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04054","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/2606.04054/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.04054","created_at":"2026-06-04T00:06:45.352415+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.04054v1","created_at":"2026-06-04T00:06:45.352415+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04054","created_at":"2026-06-04T00:06:45.352415+00:00"},{"alias_kind":"pith_short_12","alias_value":"EGJDAC4FT2N7","created_at":"2026-06-04T00:06:45.352415+00:00"},{"alias_kind":"pith_short_16","alias_value":"EGJDAC4FT2N7BBTO","created_at":"2026-06-04T00:06:45.352415+00:00"},{"alias_kind":"pith_short_8","alias_value":"EGJDAC4F","created_at":"2026-06-04T00:06:45.352415+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EGJDAC4FT2N7BBTOQMLSKCXNIS","json":"https://pith.science/pith/EGJDAC4FT2N7BBTOQMLSKCXNIS.json","graph_json":"https://pith.science/api/pith-number/EGJDAC4FT2N7BBTOQMLSKCXNIS/graph.json","events_json":"https://pith.science/api/pith-number/EGJDAC4FT2N7BBTOQMLSKCXNIS/events.json","paper":"https://pith.science/paper/EGJDAC4F"},"agent_actions":{"view_html":"https://pith.science/pith/EGJDAC4FT2N7BBTOQMLSKCXNIS","download_json":"https://pith.science/pith/EGJDAC4FT2N7BBTOQMLSKCXNIS.json","view_paper":"https://pith.science/paper/EGJDAC4F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.04054&json=true","fetch_graph":"https://pith.science/api/pith-number/EGJDAC4FT2N7BBTOQMLSKCXNIS/graph.json","fetch_events":"https://pith.science/api/pith-number/EGJDAC4FT2N7BBTOQMLSKCXNIS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EGJDAC4FT2N7BBTOQMLSKCXNIS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EGJDAC4FT2N7BBTOQMLSKCXNIS/action/storage_attestation","attest_author":"https://pith.science/pith/EGJDAC4FT2N7BBTOQMLSKCXNIS/action/author_attestation","sign_citation":"https://pith.science/pith/EGJDAC4FT2N7BBTOQMLSKCXNIS/action/citation_signature","submit_replication":"https://pith.science/pith/EGJDAC4FT2N7BBTOQMLSKCXNIS/action/replication_record"}},"created_at":"2026-06-04T00:06:45.352415+00:00","updated_at":"2026-06-04T00:06:45.352415+00:00"}