{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EIEGGKO7VIEZRP3JUER25EW36M","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":"4dc1049da5f57b3ff0538bdbce1d5fad870db3d90a7d732076b8193f44b75ec0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-09-30T23:47:23Z","title_canon_sha256":"047edb61a961c20942b0fd86cd42e4630bcc1a92a414511679dfa7ea565f2874"},"schema_version":"1.0","source":{"id":"1310.0095","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0095","created_at":"2026-05-18T03:11:45Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0095v1","created_at":"2026-05-18T03:11:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0095","created_at":"2026-05-18T03:11:45Z"},{"alias_kind":"pith_short_12","alias_value":"EIEGGKO7VIEZ","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EIEGGKO7VIEZRP3J","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EIEGGKO7","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:8a6f489c5fad199f0a11034ce2501c4c7d224135a0d5d556f362f3efda27111f","target":"graph","created_at":"2026-05-18T03:11:45Z","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":"For a field $\\K$ of characteristic zero, we introduce a cohomologically symplectic poset structure ${\\mathcal P}_{\\K}(X)$ on a simply connected space $X$ from the viewpoint of $\\K$-homotopy theory. It is given by the poset of inclusions of subgroups preserving c-symplectic structures in the group ${\\mathcal E}(X_{\\K})$ of $\\K$-homotopy classes of $\\K$-homotopy self-equivalences of $X$, which is defined by the $\\K$-Sullivan model of $X$. We observe that the height of the Hasse diagram of ${\\mathcal P}_{\\K}(X)$ added by 1, denoted by c-s-${\\rm depth}_{\\K}(X)$, is finite and often depends on the ","authors_text":"Kazuya Hamada, Shoji Yokura, Toshihiro Yamaguchi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-09-30T23:47:23Z","title":"C-symplectic poset structure on a simply connected space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0095","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":"sha256:952fa1b65d736e256657fab399f89737a5d62c883735e06cd18ed98276a8f8ee","target":"record","created_at":"2026-05-18T03:11:45Z","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":"4dc1049da5f57b3ff0538bdbce1d5fad870db3d90a7d732076b8193f44b75ec0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-09-30T23:47:23Z","title_canon_sha256":"047edb61a961c20942b0fd86cd42e4630bcc1a92a414511679dfa7ea565f2874"},"schema_version":"1.0","source":{"id":"1310.0095","kind":"arxiv","version":1}},"canonical_sha256":"22086329dfaa0998bf69a123ae92dbf3039dbf5c7543df19cebf04571228cfd5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22086329dfaa0998bf69a123ae92dbf3039dbf5c7543df19cebf04571228cfd5","first_computed_at":"2026-05-18T03:11:45.655194Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:45.655194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lD04n2SKfzmoooyQksF1qV6HKqW42rYzNQAYEf3s3Qq4wAzkZxoynLrbMV2U4Q1N+Hw6jN3GlZmVAhJwO0zgBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:45.655923Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.0095","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:952fa1b65d736e256657fab399f89737a5d62c883735e06cd18ed98276a8f8ee","sha256:8a6f489c5fad199f0a11034ce2501c4c7d224135a0d5d556f362f3efda27111f"],"state_sha256":"6631b565bab41c65310c98a3b9b59ce45dc926a47cc6bf9b08129b586c34a893"}