{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DL5HW4AMKHS7CR3RHXQI2KV7XA","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":"63c09bbbe8a7c157d524eb17c40aae0b13139d738e7df73c60cbf0652f21f5dd","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-05-28T05:39:33Z","title_canon_sha256":"6e9d4b3fbf43fedb11065bd7c0850709c2d16b350e44bfb2c2b2563da782cd35"},"schema_version":"1.0","source":{"id":"1405.7118","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.7118","created_at":"2026-05-18T02:50:59Z"},{"alias_kind":"arxiv_version","alias_value":"1405.7118v1","created_at":"2026-05-18T02:50:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.7118","created_at":"2026-05-18T02:50:59Z"},{"alias_kind":"pith_short_12","alias_value":"DL5HW4AMKHS7","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DL5HW4AMKHS7CR3R","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DL5HW4AM","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:18fede67796e56978809339c5b406f2a5eca23e07ea0418c6fc8a31f796b83aa","target":"graph","created_at":"2026-05-18T02:50:59Z","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":"A unital $\\ell$-group is an abelian group equipped with a translation invariant lattice-order and with a distinguished strong unit, i.e. an element whose positive integer multiples eventually dominate every element of $G$.If $X$ is a compact subset of $R^n$, the set $M(X)$ of real-valued piecewise linear maps with integer coefficients, whose addition and lattice operations defined pointwise and whose distinguished element is the constant map $1$, is a unital $\\ell$-group.\n  In this paper we provide a geometric decription of finitely generated (regular) projective unital $\\ell$-groups. We prove","authors_text":"Leonardo Manuel Cabrer","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-05-28T05:39:33Z","title":"Rational Simplicial geometry and projective unital lattice-ordered abelian groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7118","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:d7955c80e239f43e1079f8275f4ba9ebc77939581e4a543e3cd6161ba7c6e689","target":"record","created_at":"2026-05-18T02:50:59Z","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":"63c09bbbe8a7c157d524eb17c40aae0b13139d738e7df73c60cbf0652f21f5dd","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-05-28T05:39:33Z","title_canon_sha256":"6e9d4b3fbf43fedb11065bd7c0850709c2d16b350e44bfb2c2b2563da782cd35"},"schema_version":"1.0","source":{"id":"1405.7118","kind":"arxiv","version":1}},"canonical_sha256":"1afa7b700c51e5f147713de08d2abfb8109cbfc53805a2b21d56b979f7bd9124","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1afa7b700c51e5f147713de08d2abfb8109cbfc53805a2b21d56b979f7bd9124","first_computed_at":"2026-05-18T02:50:59.157495Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:59.157495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SDdVMc/rHMPlr1DDAWppt79zsVcIfKQSHX3coTatfOJPGQn2djvnxGybiJ1Ek6GHPJetTkNcXs5AEODMPFOBCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:59.158107Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.7118","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7955c80e239f43e1079f8275f4ba9ebc77939581e4a543e3cd6161ba7c6e689","sha256:18fede67796e56978809339c5b406f2a5eca23e07ea0418c6fc8a31f796b83aa"],"state_sha256":"57b26c84163b9d44349cd0e60b755739ccfcbabcd0fd143d5eaf224afb664f34"}