{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:MXNVTTPA6WWMCSM7DL6JXGJLK6","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":"de772762fe84d4d870121ee1a44679afc2e8a1aae9fc28a268c00a64013776be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-05-29T16:46:30Z","title_canon_sha256":"d59d312b564cab0d9799b2bd1b8cbc7ff696bdc77ab8e8628167c0145fbcc57a"},"schema_version":"1.0","source":{"id":"2405.19258","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.19258","created_at":"2026-06-03T14:05:45Z"},{"alias_kind":"arxiv_version","alias_value":"2405.19258v2","created_at":"2026-06-03T14:05:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.19258","created_at":"2026-06-03T14:05:45Z"},{"alias_kind":"pith_short_12","alias_value":"MXNVTTPA6WWM","created_at":"2026-06-03T14:05:45Z"},{"alias_kind":"pith_short_16","alias_value":"MXNVTTPA6WWMCSM7","created_at":"2026-06-03T14:05:45Z"},{"alias_kind":"pith_short_8","alias_value":"MXNVTTPA","created_at":"2026-06-03T14:05:45Z"}],"graph_snapshots":[{"event_id":"sha256:2e2ab58c1d8518ab2d6b3cfa0a9564b569b78597bd3f94b30c899f887b68eb9b","target":"graph","created_at":"2026-06-03T14:05:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2405.19258/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Dualising the construction of a polyhedral product, we introduce the notion of a polyhedral coproduct as a certain homotopy limit over the face poset of a simplicial complex. We begin a study of the basic properties of polyhedral coproducts, surveying the Eckmann-Hilton duals of various familiar examples and properties of polyhedral products. In particular, we show that polyhedral coproducts give a functorial interpolation between the wedge and cartesian product of spaces which differs from the one given by polyhedral products, and we establish a general loop space decomposition for these spac","authors_text":"Lewis Stanton, Steven Amelotte, William Hornslien","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-05-29T16:46:30Z","title":"Polyhedral coproducts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.19258","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":"sha256:70cd177f49e7a39df6f7979f4e4527c798525c23cd63aad2335a5bdd95e17e42","target":"record","created_at":"2026-06-03T14:05:45Z","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":"de772762fe84d4d870121ee1a44679afc2e8a1aae9fc28a268c00a64013776be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-05-29T16:46:30Z","title_canon_sha256":"d59d312b564cab0d9799b2bd1b8cbc7ff696bdc77ab8e8628167c0145fbcc57a"},"schema_version":"1.0","source":{"id":"2405.19258","kind":"arxiv","version":2}},"canonical_sha256":"65db59cde0f5acc1499f1afc9b992b57a579aa7206a935c9074b8608411a0608","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65db59cde0f5acc1499f1afc9b992b57a579aa7206a935c9074b8608411a0608","first_computed_at":"2026-06-03T14:05:45.061679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T14:05:45.061679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NNhWHjGJ09kwV8UbvG9kEJdvYDFxcFOCJy/kxf6mBUaOx06pidMXqNAc2JbGCN/+Sja9tT4JlAHQXMrYAYHqCQ==","signature_status":"signed_v1","signed_at":"2026-06-03T14:05:45.062173Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.19258","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70cd177f49e7a39df6f7979f4e4527c798525c23cd63aad2335a5bdd95e17e42","sha256:2e2ab58c1d8518ab2d6b3cfa0a9564b569b78597bd3f94b30c899f887b68eb9b"],"state_sha256":"8d6f80920a2ff2dc7725a980922b357ca0a89d5e4a47aa4acea2499c856febad"}