{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:RIRFVV4VIJUT2W6NCM5U655HAQ","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":"674003ebfcb2cdbce4785e168e02298a0d3c06d2ac89b3de8204a923e0896a78","cross_cats_sorted":["math.AT","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2025-07-07T19:38:51Z","title_canon_sha256":"17bed8f52fa31e763233b34f11042dd16cb2c9781b0eaad1992f02d8a0665fa9"},"schema_version":"1.0","source":{"id":"2507.05437","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.05437","created_at":"2026-07-05T12:04:37Z"},{"alias_kind":"arxiv_version","alias_value":"2507.05437v2","created_at":"2026-07-05T12:04:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.05437","created_at":"2026-07-05T12:04:37Z"},{"alias_kind":"pith_short_12","alias_value":"RIRFVV4VIJUT","created_at":"2026-07-05T12:04:37Z"},{"alias_kind":"pith_short_16","alias_value":"RIRFVV4VIJUT2W6N","created_at":"2026-07-05T12:04:37Z"},{"alias_kind":"pith_short_8","alias_value":"RIRFVV4V","created_at":"2026-07-05T12:04:37Z"}],"graph_snapshots":[{"event_id":"sha256:0d09eb469fc15dfe05b897cb199c17ec3fb946d9c72f8db42adcdd114837d5f8","target":"graph","created_at":"2026-07-05T12:04:37Z","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/2507.05437/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The d-Segal conditions of Dyckerhoff and Kapranov are exactness properties for simplicial objects based on the geometry of cyclic polytopes in d-dimensional Euclidean space. 2-Segal spaces are also known as decomposition spaces, and most activity has focused on this case. We study the interplay of these conditions with the partial groups of Chermak, a class of symmetric simplicial sets. The d-Segal conditions simplify for symmetric simplicial objects, and take a particularly explicit form for partial groups. We show partial groups provide a rich class of d-Segal sets for d > 2, by undertaking ","authors_text":"Justin Lynd, Philip Hackney","cross_cats":["math.AT","math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2025-07-07T19:38:51Z","title":"Higher Segal spaces and partial groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.05437","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":"sha256:98a58de940057cb04aefa686f07e2604bcc77c8fcc66974b2b90a90789bb99b3","target":"record","created_at":"2026-07-05T12:04:37Z","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":"674003ebfcb2cdbce4785e168e02298a0d3c06d2ac89b3de8204a923e0896a78","cross_cats_sorted":["math.AT","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2025-07-07T19:38:51Z","title_canon_sha256":"17bed8f52fa31e763233b34f11042dd16cb2c9781b0eaad1992f02d8a0665fa9"},"schema_version":"1.0","source":{"id":"2507.05437","kind":"arxiv","version":2}},"canonical_sha256":"8a225ad79542693d5bcd133b4f77a70434aa4365eba45df9c2b7e1e3baa96fec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a225ad79542693d5bcd133b4f77a70434aa4365eba45df9c2b7e1e3baa96fec","first_computed_at":"2026-07-05T12:04:37.377486Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:04:37.377486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YLZhUxMAEe2z8nhh2pQqghLeGem+wOZ+sYBv89XbD2h4IIz3kmAPE7cXoYXJPvzgqNjiACBM4VAPvicimTUAAg==","signature_status":"signed_v1","signed_at":"2026-07-05T12:04:37.378014Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.05437","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98a58de940057cb04aefa686f07e2604bcc77c8fcc66974b2b90a90789bb99b3","sha256:0d09eb469fc15dfe05b897cb199c17ec3fb946d9c72f8db42adcdd114837d5f8"],"state_sha256":"53f8ce82fe949206a25d102060835f30c063deab57740b2df736be13cd7436b3"}