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Although Soul\\'e vanishing guarantees that the map H^1(Gp, H_et) ---> H^1(Gp, Qp(1)^2) is bijective, the problem of constructing an explicit lifting of an arbitrary cocycle in H^1(Gp, Qp(1)^2) proves to be a challenge. We explain how we believe this problem should be analyzed, following an unpublished note by Romyar Sharifi, hereby making the original appendix to Explicit Chaba"},"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":"1403.4414","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-18T11:35:47Z","cross_cats_sorted":[],"title_canon_sha256":"68294ea3521aecdb08011b4c4451861bae83095b50dbe31e452d1463f24ebdaa","abstract_canon_sha256":"30ffda267d0eefaaad8e84e5114cf9b0500c8f6c62ea3d0799203bb9878b4c0e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:04.801909Z","signature_b64":"gwAiPZuMzDD4M77uFFXCXW5NKi+fGsZ85G8aDqu63ai2ByAa1KYWQ+R6CJ/GaD/eMGztP+gN0UDv6njS22OaBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1551dd28e50b5070a019d5b3c1fd1d26158d319201dec5ae11153513cec59451","last_reissued_at":"2026-05-18T02:56:04.801464Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:04.801464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Heisenberg coboundary equation: appendix to Explicit Chabauty-Kim theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ishai Dan-Cohen, Stefan Wewers","submitted_at":"2014-03-18T11:35:47Z","abstract_excerpt":"Let p be a regular prime number, let Gp denote the Galois group of the maximal unramified away from p extension of Q, and let H_et denote the Heisenberg group over Qp with Gp-action given by H_et = Qp(1)^2 \\oplus Qp(2). 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