{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:AVFFEJXGLWFGLDPLP76WGPRDQR","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":"1e687f5aca874422eb477d7e0d143dc2690eb7108ff42dab006730811e880be4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-09T12:19:38Z","title_canon_sha256":"500d7e93997fdb686a907341bfcb7765d9712f3aab71d160b6682d1d7f581de8"},"schema_version":"1.0","source":{"id":"1809.02960","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.02960","created_at":"2026-05-18T00:06:10Z"},{"alias_kind":"arxiv_version","alias_value":"1809.02960v1","created_at":"2026-05-18T00:06:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02960","created_at":"2026-05-18T00:06:10Z"},{"alias_kind":"pith_short_12","alias_value":"AVFFEJXGLWFG","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AVFFEJXGLWFGLDPL","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AVFFEJXG","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:63ed6dcc0a59e0b0cba1acd76ff0df02e44e67c0e6de820928e96be909820b07","target":"graph","created_at":"2026-05-18T00:06:10Z","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 paper further investigates \\emph{Laplacian simplices}. A construction by Braun and the first author associates to a simple connected graph $G$ a simplex $\\cP_G$ whose vertices are the rows of the Laplacian matrix of $G$. In this paper we associate to a reflexive $\\cP_G$ a duality-preserving linear code $\\cC(\\cP_G)$. This new perspective allows us to build upon previous results relating graphical properties of $G$ to properties of the polytope $\\cP_G$. In particular, we make progress towards a graphical characterization of reflexive $\\cP_G$ using techniques from Ehrhart theory. We provide ","authors_text":"Marie Meyer, Tefjol Pllaha","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-09T12:19:38Z","title":"Laplacian Simplices II: A Coding Theoretic Approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02960","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":"sha256:378a4fd8c89ebf6a8c18523aa01feb8ec0ace47b7d62377f046f7443fb23d8ca","target":"record","created_at":"2026-05-18T00:06:10Z","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":"1e687f5aca874422eb477d7e0d143dc2690eb7108ff42dab006730811e880be4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-09T12:19:38Z","title_canon_sha256":"500d7e93997fdb686a907341bfcb7765d9712f3aab71d160b6682d1d7f581de8"},"schema_version":"1.0","source":{"id":"1809.02960","kind":"arxiv","version":1}},"canonical_sha256":"054a5226e65d8a658deb7ffd633e23846922854586edef9b6dae8f04c16d7263","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"054a5226e65d8a658deb7ffd633e23846922854586edef9b6dae8f04c16d7263","first_computed_at":"2026-05-18T00:06:10.492546Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:10.492546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7KwUFzW5nA/KgwaBQ05cv5uo0U3B6+kPEi4PePB0JitwXYN95uyftpcdfmz9heBisltkgD2OAf0RHZuAxCHPDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:10.493200Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.02960","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:378a4fd8c89ebf6a8c18523aa01feb8ec0ace47b7d62377f046f7443fb23d8ca","sha256:63ed6dcc0a59e0b0cba1acd76ff0df02e44e67c0e6de820928e96be909820b07"],"state_sha256":"098fd6523aa70030a128942a04b682f85a34b6eb61bbb928ca77670df784f029"}