{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:2FSMZZX3GF7Y4DIBAN3C32GTX4","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":"6072cd3b151bfa877330820e214fbfc569d8c040a2b268381fe266f8f86abe78","cross_cats_sorted":["math.AC","math.DG","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2023-10-30T13:04:06Z","title_canon_sha256":"aa45c29f1801e7971be58af6688b684ffea547ae8304e4074dff66a5da8906ab"},"schema_version":"1.0","source":{"id":"2310.19506","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.19506","created_at":"2026-07-05T10:41:10Z"},{"alias_kind":"arxiv_version","alias_value":"2310.19506v6","created_at":"2026-07-05T10:41:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.19506","created_at":"2026-07-05T10:41:10Z"},{"alias_kind":"pith_short_12","alias_value":"2FSMZZX3GF7Y","created_at":"2026-07-05T10:41:10Z"},{"alias_kind":"pith_short_16","alias_value":"2FSMZZX3GF7Y4DIB","created_at":"2026-07-05T10:41:10Z"},{"alias_kind":"pith_short_8","alias_value":"2FSMZZX3","created_at":"2026-07-05T10:41:10Z"}],"graph_snapshots":[{"event_id":"sha256:85ba517cf2f08978e38a3c58e0289b345cf6cdb4e05b471d07cb5c85dfbedb87","target":"graph","created_at":"2026-07-05T10:41:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2310.19506/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We encode the real homotopy type of an $n$-dimensional $(r-1)$-connected compact manifold $M$, $ r\\ge 2$ into a minimal unital $C_\\infty$-structure on $H^* (M,\\mathbb R)$, obtained via homotopy transfer of the unital DGCA structure of the small quotient algebra associated with a Hodge decomposition of the de Rham algebra $\\mathcal A^*(M)$, which has been proposed by Fiorenza-Kawai-L\\^e-Schwachh\\\"ofer in [Ann. Sc. Norm. Super Pisa (5), vol. XXII (2021), 79-107]. We prove that if $n \\le \\ell (r-1) +2$, with $\\ell \\geq 4$, the multiplication $\\mu_k$ on the minimal unital $C_\\infty$-algebra $H^*(M","authors_text":"Domenico Fiorenza, H\\^ong V\\^an L\\^e","cross_cats":["math.AC","math.DG","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2023-10-30T13:04:06Z","title":"Unital $C_\\infty$-algebras and the real homotopy type of $(r-1)$-connected compact manifolds of dimension $\\le \\ell(r-1)+2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.19506","kind":"arxiv","version":6},"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:b0642302887fd49974d772939f98eb598bc3b1e9be5527ca62d124fc5729c597","target":"record","created_at":"2026-07-05T10:41:10Z","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":"6072cd3b151bfa877330820e214fbfc569d8c040a2b268381fe266f8f86abe78","cross_cats_sorted":["math.AC","math.DG","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2023-10-30T13:04:06Z","title_canon_sha256":"aa45c29f1801e7971be58af6688b684ffea547ae8304e4074dff66a5da8906ab"},"schema_version":"1.0","source":{"id":"2310.19506","kind":"arxiv","version":6}},"canonical_sha256":"d164cce6fb317f8e0d0103762de8d3bf20f0a0551f09702f5a72cc12bd6bc097","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d164cce6fb317f8e0d0103762de8d3bf20f0a0551f09702f5a72cc12bd6bc097","first_computed_at":"2026-07-05T10:41:10.940984Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:41:10.940984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LZ+sVJxySDGtmn6+VmWuRepKnxWnZjrYw9myRfaCDF1k9j+QSb1v6L2FnzoE3J+65FQ7Cqo/UZ5d5SaoWxLjDA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:41:10.941446Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.19506","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0642302887fd49974d772939f98eb598bc3b1e9be5527ca62d124fc5729c597","sha256:85ba517cf2f08978e38a3c58e0289b345cf6cdb4e05b471d07cb5c85dfbedb87"],"state_sha256":"c1373ed70da545c24885a390b409a3487a37a310ebd52680288f7a42c5c0d52a"}