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When the action is more general, we partially compute these boundary maps. Via obstructions of Jordan Ellenberg, this implies that pi_1 sections of P^1_k-{0,1,infty} satisfy the condition that associated nth order Massey products in Galois cohomology vanish. For the pi_1 sections coming from rational points, these conditions imply that < (1-x)^"},"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":"1107.1790","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-07-09T15:20:53Z","cross_cats_sorted":["math.AG","math.NT"],"title_canon_sha256":"ff82175e6d48f3309ccc0e4033b1c86d648a2df0022fa31f680cd5b886126ec4","abstract_canon_sha256":"1ee5a57eeace247db4e2c53fb3491669c03dbdc94a69cf19cac422aa0104deb7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:34.142430Z","signature_b64":"4sg3Zxsdtnx3z49C5Q+H7XMZPb607PH27z11JR+V4QctgVJi8pxIRYt6hbuSpVqbgpsIX+Ubk7A0l58yrTX3DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0fd5702cf72ed3e424c1e8caea6dcfef07653e285f874fa2ffd44e4f3243b3eb","last_reissued_at":"2026-05-18T04:18:34.141996Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:34.141996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"n-Nilpotent Obstructions to pi_1 Sections of P^1-{0,1,infty} and Massey Products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.NT"],"primary_cat":"math.AT","authors_text":"Kirsten Wickelgren","submitted_at":"2011-07-09T15:20:53Z","abstract_excerpt":"Let pi be a pro-l completion of a free group, and let G be a profinite group acting continuously on pi. 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