{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:K5RA3ZI7DP6MAGVI3XIVQFCWDO","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":"43d7d9b054f095f4c115bd033b4f7202db0cc7c311c6851f09a0c5ee1542a436","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-09-13T10:04:09Z","title_canon_sha256":"001bd2ee67ff3541cfcdc7e91c946f81d87e6b9200d531a7b5c2ef70f96f736f"},"schema_version":"1.0","source":{"id":"1109.2728","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2728","created_at":"2026-05-18T04:10:36Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2728v2","created_at":"2026-05-18T04:10:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2728","created_at":"2026-05-18T04:10:36Z"},{"alias_kind":"pith_short_12","alias_value":"K5RA3ZI7DP6M","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"K5RA3ZI7DP6MAGVI","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"K5RA3ZI7","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:0f5dd8f46316194a64706176835223893ecebcb0c1121fafa0d0e336174fce7e","target":"graph","created_at":"2026-05-18T04:10:36Z","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":"We prove a conjecture of Bahri, Bendersky, Cohen and Gitler: if K is a shifted simplicial complex on n vertices, X_1,..., X_n are spaces and CX_i is the cone on X_i, then the polyhedral product determined by K and the pairs (CX_i,X_i) is homotopy equivalent to a wedge of suspensions of smashes of the X_i's. This generalises earlier work of the two authors in the special case where each X_i is a loop space. Connections are made to toric topology, combinatorics, and classical homotopy theory.","authors_text":"Jelena Grbic, Stephen Theriault","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-09-13T10:04:09Z","title":"The homotopy type of the polyhedral product for shifted complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2728","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":"sha256:2d11c7adeb486da76a0669f6fc5426e28d263710fa1ef3a9e197d5ce44688e42","target":"record","created_at":"2026-05-18T04:10:36Z","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":"43d7d9b054f095f4c115bd033b4f7202db0cc7c311c6851f09a0c5ee1542a436","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-09-13T10:04:09Z","title_canon_sha256":"001bd2ee67ff3541cfcdc7e91c946f81d87e6b9200d531a7b5c2ef70f96f736f"},"schema_version":"1.0","source":{"id":"1109.2728","kind":"arxiv","version":2}},"canonical_sha256":"57620de51f1bfcc01aa8ddd15814561bb228ead6103c639ff5f70ffcfa936d76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57620de51f1bfcc01aa8ddd15814561bb228ead6103c639ff5f70ffcfa936d76","first_computed_at":"2026-05-18T04:10:36.344637Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:36.344637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4QYeEPC0E77BS5mMtvCp9lorsUPThIt8iNzlyVL+KSCVhlY+i/33AESW45I7PsF1bse71GcaNrislE7thF1zBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:36.345389Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.2728","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d11c7adeb486da76a0669f6fc5426e28d263710fa1ef3a9e197d5ce44688e42","sha256:0f5dd8f46316194a64706176835223893ecebcb0c1121fafa0d0e336174fce7e"],"state_sha256":"5bd20bd41ee245e75ccf1e868f3340cebea07805f9fa7cdf125ada46ef619d9f"}