{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LI3LPVC3LYHROS37427CXYSNIH","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":"acd471de09dae82389a611a1eded42f8bc002dfae4c327768a8515cfb61f1e7e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-07-20T20:32:08Z","title_canon_sha256":"56d32d2392fed14196979d5fcb43684cd9fded74428f74fbf00ea39073812291"},"schema_version":"1.0","source":{"id":"1107.4117","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4117","created_at":"2026-05-18T04:17:13Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4117v1","created_at":"2026-05-18T04:17:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4117","created_at":"2026-05-18T04:17:13Z"},{"alias_kind":"pith_short_12","alias_value":"LI3LPVC3LYHR","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LI3LPVC3LYHROS37","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LI3LPVC3","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:fbdf721ad42cdfa1e8241c79929197950ee566f8faa2681a8b120ccb71a8de5b","target":"graph","created_at":"2026-05-18T04:17:13Z","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":"There are two main approaches to the problem of realizing a $\\Pi$-algebra (a graded group $\\Lambda$ equipped with an action of the primary homotopy operations) as the homotopy groups of a space $X$. Both involve trying to realize an algebraic free simplicial resolution $G_\\bullet$ of $\\Lambda$ by a simplicial space $W_\\bullet$ and proceed by induction on the simplicial dimension. The first provides a sequence of Andr\\'{e}-Quillen cohomology classes in $H_{AQ}^{n+2}(\\Lambda;\\Omega^{n}\\Lambda)$ for $n \\geq 1$ as obstructions to the existence of successive Postnikov sections for $W_\\bullet$ by wo","authors_text":"David Blanc (U. Haifa), James M. Turner (Calvin College), Mark W. Johnson (Penn State Altoona)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-07-20T20:32:08Z","title":"Higher homotopy operations and Andr\\'{e}-Quillen cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4117","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":"sha256:32ee6dbcf0e971fc52aea49967b2b8c9e865964052c649e40eec651af456a698","target":"record","created_at":"2026-05-18T04:17:13Z","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":"acd471de09dae82389a611a1eded42f8bc002dfae4c327768a8515cfb61f1e7e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-07-20T20:32:08Z","title_canon_sha256":"56d32d2392fed14196979d5fcb43684cd9fded74428f74fbf00ea39073812291"},"schema_version":"1.0","source":{"id":"1107.4117","kind":"arxiv","version":1}},"canonical_sha256":"5a36b7d45b5e0f174b7fe6be2be24d41d18b48237f79e9275ace0675a0098d9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a36b7d45b5e0f174b7fe6be2be24d41d18b48237f79e9275ace0675a0098d9d","first_computed_at":"2026-05-18T04:17:13.197371Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:13.197371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8XUngYFjo2DQMnkU3UF4vN2f4RQSycyFsRloWdPN9Ld+aHyC+ScgTk0kZ+hvUoLhtt+GRD0aE+fomCQbEqVhAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:13.198002Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.4117","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32ee6dbcf0e971fc52aea49967b2b8c9e865964052c649e40eec651af456a698","sha256:fbdf721ad42cdfa1e8241c79929197950ee566f8faa2681a8b120ccb71a8de5b"],"state_sha256":"625ec06c48a77840fd15d842acc5aa9d161a375a88250859b37e15c980426f03"}