{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:47V4PUMOHOGPRV6RJ5DFBM3R42","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":"c1debed4f73483ace55f09afcf39b22c46c5118b0cb20a794ebd0349ebfd7fe2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-04-24T19:54:12Z","title_canon_sha256":"2a966654e0e0f93bf80695508f57116833c4f8ad60760b15ed24dcee62ab5f34"},"schema_version":"1.0","source":{"id":"1804.09230","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.09230","created_at":"2026-05-17T23:52:24Z"},{"alias_kind":"arxiv_version","alias_value":"1804.09230v2","created_at":"2026-05-17T23:52:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09230","created_at":"2026-05-17T23:52:24Z"},{"alias_kind":"pith_short_12","alias_value":"47V4PUMOHOGP","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"47V4PUMOHOGPRV6R","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"47V4PUMO","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:9c5b650deecea177368c53c4eaf920de0d326d8399e1f330c52e0a207033eaf5","target":"graph","created_at":"2026-05-17T23:52:24Z","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":"This is the third in a series of papers studying the vertex-algebraic structure of principal subspaces of twisted modules for lattice vertex operator algebras. We focus primarily on lattices $L$ whose Gram matrix contains only non-negative entries. We develop further ideas originally presented by Calinescu, Lepowsky, and Milas to find presentations (generators and relations) of the principal subspace of a certain natural twisted module for the vertex operator algebra $V_L$. We then use these presentations to construct exact sequences involving this principal subspace, which give a set of recur","authors_text":"Christopher Sadowski, Gautam Webb, Michael Penn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-04-24T19:54:12Z","title":"Principal subspaces of twisted modules for certain lattice vertex operator algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09230","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":"sha256:4594ebcb151c147ab709f0022105fed88bea849f2f9b7d2a0e1c05a7e7563361","target":"record","created_at":"2026-05-17T23:52:24Z","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":"c1debed4f73483ace55f09afcf39b22c46c5118b0cb20a794ebd0349ebfd7fe2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-04-24T19:54:12Z","title_canon_sha256":"2a966654e0e0f93bf80695508f57116833c4f8ad60760b15ed24dcee62ab5f34"},"schema_version":"1.0","source":{"id":"1804.09230","kind":"arxiv","version":2}},"canonical_sha256":"e7ebc7d18e3b8cf8d7d14f4650b371e6b0551539911b52b21bfcff08d51453d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7ebc7d18e3b8cf8d7d14f4650b371e6b0551539911b52b21bfcff08d51453d5","first_computed_at":"2026-05-17T23:52:24.446184Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:24.446184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n18XBCkGeVgkR85z9kBDFxoLhleBFVcgRvJcfBvovtnTZrVFLyaDom23VmdTYVfVmxOYAVnK39/8ELeUmyctAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:24.447126Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.09230","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4594ebcb151c147ab709f0022105fed88bea849f2f9b7d2a0e1c05a7e7563361","sha256:9c5b650deecea177368c53c4eaf920de0d326d8399e1f330c52e0a207033eaf5"],"state_sha256":"436dee4e239083510384947fa8531b4c3a357c74037f79e42508d6a85ddb4eb7"}