{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:MWSHRFWJADXQUVPN2DJAELNVMR","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":"ba484f7778756e9a6c81f39bc380945a1a0408c189b7b71065cf04e45cecac49","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-09-20T21:00:54Z","title_canon_sha256":"546611079dd1c91094fd20a64a959b3ca3414daac00c08f50aadd0ab3b2b2147"},"schema_version":"1.0","source":{"id":"1109.4430","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4430","created_at":"2026-05-18T04:12:34Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4430v1","created_at":"2026-05-18T04:12:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4430","created_at":"2026-05-18T04:12:34Z"},{"alias_kind":"pith_short_12","alias_value":"MWSHRFWJADXQ","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"MWSHRFWJADXQUVPN","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"MWSHRFWJ","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:0d67d71298ed65aa9fc1ddc964d4c7e91cc1ded3f4498b3068bb5539e2b590f8","target":"graph","created_at":"2026-05-18T04:12:34Z","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":"To each simplicial reflexive polytope in Z^(n+1), we attach an n-dimensional space, Lambda^\\infty. It is the Legendrian boundary of a conic Lagrangian considered in work of the authors, Fang and Liu, and because of this it carries a sheaf of dg categories called the \"Kashiwara-Schapira sheaf.\" We discuss some conjectures and results about the role that Lambda^\\infty and the Kashiwara-Schapira sheaf should play in homological mirror symmetry.","authors_text":"David Treumann, Eric Zaslow","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-09-20T21:00:54Z","title":"Polytopes and Skeleta"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4430","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:f12dddda147e0779d61f0cea377fb51d20fda6a669806a1737022fb0bee199e4","target":"record","created_at":"2026-05-18T04:12:34Z","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":"ba484f7778756e9a6c81f39bc380945a1a0408c189b7b71065cf04e45cecac49","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-09-20T21:00:54Z","title_canon_sha256":"546611079dd1c91094fd20a64a959b3ca3414daac00c08f50aadd0ab3b2b2147"},"schema_version":"1.0","source":{"id":"1109.4430","kind":"arxiv","version":1}},"canonical_sha256":"65a47896c900ef0a55edd0d2022db5644b265f33d1f1136cf1f18dc7be63fc18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65a47896c900ef0a55edd0d2022db5644b265f33d1f1136cf1f18dc7be63fc18","first_computed_at":"2026-05-18T04:12:34.764201Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:34.764201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pFTmvZKT0FbfOvvfMdoqcRIR2gXbI+qpqMLaLHAHFLTdaGQ/wbuB3pVVr1cRbNpb4KZKXAhuSs0w5UwfBU0JAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:34.764774Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.4430","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f12dddda147e0779d61f0cea377fb51d20fda6a669806a1737022fb0bee199e4","sha256:0d67d71298ed65aa9fc1ddc964d4c7e91cc1ded3f4498b3068bb5539e2b590f8"],"state_sha256":"800fd8c269470cd30e74374c765be3925972fc2e23f283bb40e3fa847a01b73c"}