{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:M4RYY6PQ2CRHOBEOX2NPWBCORK","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":"5eef9548ec4268853b41cf9543baf7ff88adce066a478865713c528b25efa1c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-08-30T22:18:19Z","title_canon_sha256":"e4c25e73160452b4a7460aeb1bfe8fc5c5f39aaccb1132e634ff3903d0772f1a"},"schema_version":"1.0","source":{"id":"1409.0163","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0163","created_at":"2026-05-18T02:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0163v2","created_at":"2026-05-18T02:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0163","created_at":"2026-05-18T02:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"M4RYY6PQ2CRH","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"M4RYY6PQ2CRHOBEO","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"M4RYY6PQ","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:a8e66b4c51eeae24863e96010010b449668009947cc92c2f8b3a104f9d456634","target":"graph","created_at":"2026-05-18T02:20:49Z","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":"It is shown that the operad maps $E_n\\to E_{n+k}$ are formal over the reals for $k\\geq 2$ and non-formal for $k=1$. Furthermore we compute the cohomology of the deformation complex of the operad maps $E_{n}\\to E_{n+1}$, proving an algebraic version of the Cerf Lemma.","authors_text":"Thomas Willwacher, Victor Tourtchine","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-08-30T22:18:19Z","title":"Relative (non-)formality of the little cubes operads and the algebraic Cerf Lemma"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0163","kind":"arxiv","version":2},"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:cafec29ae8454c31228b8eb132ee6cfc989eb0acf3c9af550242868ef92b5d01","target":"record","created_at":"2026-05-18T02:20:49Z","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":"5eef9548ec4268853b41cf9543baf7ff88adce066a478865713c528b25efa1c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-08-30T22:18:19Z","title_canon_sha256":"e4c25e73160452b4a7460aeb1bfe8fc5c5f39aaccb1132e634ff3903d0772f1a"},"schema_version":"1.0","source":{"id":"1409.0163","kind":"arxiv","version":2}},"canonical_sha256":"67238c79f0d0a277048ebe9afb044e8a96287987844038c6ee867be2cc766e2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67238c79f0d0a277048ebe9afb044e8a96287987844038c6ee867be2cc766e2b","first_computed_at":"2026-05-18T02:20:49.598492Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:49.598492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cS9Pan4b06lQKbUWp9sYoXi+1AvcEn8ZgRy5cu/gTrWQWY1WXsmMH+RZSU8xmDS+99B7v+1vS4ZKeCrUOEZtAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:49.599104Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.0163","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cafec29ae8454c31228b8eb132ee6cfc989eb0acf3c9af550242868ef92b5d01","sha256:a8e66b4c51eeae24863e96010010b449668009947cc92c2f8b3a104f9d456634"],"state_sha256":"1e1504af5ca8f9ab57fac4825daf9a4b0e0659731c2cb498e3712cd93c3ccd17"}