{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:MXNVTTPA6WWMCSM7DL6JXGJLK6","short_pith_number":"pith:MXNVTTPA","schema_version":"1.0","canonical_sha256":"65db59cde0f5acc1499f1afc9b992b57a579aa7206a935c9074b8608411a0608","source":{"kind":"arxiv","id":"2405.19258","version":2},"attestation_state":"computed","paper":{"title":"Polyhedral coproducts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Lewis Stanton, Steven Amelotte, William Hornslien","submitted_at":"2024-05-29T16:46:30Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2405.19258","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-05-29T16:46:30Z","cross_cats_sorted":[],"title_canon_sha256":"d59d312b564cab0d9799b2bd1b8cbc7ff696bdc77ab8e8628167c0145fbcc57a","abstract_canon_sha256":"de772762fe84d4d870121ee1a44679afc2e8a1aae9fc28a268c00a64013776be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T14:05:45.062173Z","signature_b64":"NNhWHjGJ09kwV8UbvG9kEJdvYDFxcFOCJy/kxf6mBUaOx06pidMXqNAc2JbGCN/+Sja9tT4JlAHQXMrYAYHqCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65db59cde0f5acc1499f1afc9b992b57a579aa7206a935c9074b8608411a0608","last_reissued_at":"2026-06-03T14:05:45.061679Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T14:05:45.061679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polyhedral coproducts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Lewis Stanton, Steven Amelotte, William Hornslien","submitted_at":"2024-05-29T16:46:30Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.19258","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.19258/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2405.19258","created_at":"2026-06-03T14:05:45.061737+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.19258v2","created_at":"2026-06-03T14:05:45.061737+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.19258","created_at":"2026-06-03T14:05:45.061737+00:00"},{"alias_kind":"pith_short_12","alias_value":"MXNVTTPA6WWM","created_at":"2026-06-03T14:05:45.061737+00:00"},{"alias_kind":"pith_short_16","alias_value":"MXNVTTPA6WWMCSM7","created_at":"2026-06-03T14:05:45.061737+00:00"},{"alias_kind":"pith_short_8","alias_value":"MXNVTTPA","created_at":"2026-06-03T14:05:45.061737+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MXNVTTPA6WWMCSM7DL6JXGJLK6","json":"https://pith.science/pith/MXNVTTPA6WWMCSM7DL6JXGJLK6.json","graph_json":"https://pith.science/api/pith-number/MXNVTTPA6WWMCSM7DL6JXGJLK6/graph.json","events_json":"https://pith.science/api/pith-number/MXNVTTPA6WWMCSM7DL6JXGJLK6/events.json","paper":"https://pith.science/paper/MXNVTTPA"},"agent_actions":{"view_html":"https://pith.science/pith/MXNVTTPA6WWMCSM7DL6JXGJLK6","download_json":"https://pith.science/pith/MXNVTTPA6WWMCSM7DL6JXGJLK6.json","view_paper":"https://pith.science/paper/MXNVTTPA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.19258&json=true","fetch_graph":"https://pith.science/api/pith-number/MXNVTTPA6WWMCSM7DL6JXGJLK6/graph.json","fetch_events":"https://pith.science/api/pith-number/MXNVTTPA6WWMCSM7DL6JXGJLK6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MXNVTTPA6WWMCSM7DL6JXGJLK6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MXNVTTPA6WWMCSM7DL6JXGJLK6/action/storage_attestation","attest_author":"https://pith.science/pith/MXNVTTPA6WWMCSM7DL6JXGJLK6/action/author_attestation","sign_citation":"https://pith.science/pith/MXNVTTPA6WWMCSM7DL6JXGJLK6/action/citation_signature","submit_replication":"https://pith.science/pith/MXNVTTPA6WWMCSM7DL6JXGJLK6/action/replication_record"}},"created_at":"2026-06-03T14:05:45.061737+00:00","updated_at":"2026-06-03T14:05:45.061737+00:00"}