{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VASWN356G3GWIW43664HOA26AA","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":"63a87199ab1751bede3d4ab57db6722efd29e82f8972730314aa9ff5d80788ef","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-11-08T17:42:13Z","title_canon_sha256":"d0d84745684a2527bcf53a360fda7eea6490b6e97ef2879450ab9a961e2549fd"},"schema_version":"1.0","source":{"id":"1611.02627","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.02627","created_at":"2026-05-18T00:09:53Z"},{"alias_kind":"arxiv_version","alias_value":"1611.02627v2","created_at":"2026-05-18T00:09:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02627","created_at":"2026-05-18T00:09:53Z"},{"alias_kind":"pith_short_12","alias_value":"VASWN356G3GW","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VASWN356G3GWIW43","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VASWN356","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:ca9dda581fe3218447d48bf2b2235722c3a45b044bfb5abfdbf569166c938bc4","target":"graph","created_at":"2026-05-18T00:09:53Z","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 problem about how to transport profitably a group of cars leads us to study the set $T$ formed by the integers $n$ such that the system of inequalities, with non-negative integer coefficients,\n  $$a_1x_1 +\\cdots+ a_px_p + \\alpha \\leq n \\leq b_1x_1 +\\cdots+ b_px_p - \\beta$$ has at least one solution in ${\\mathbb N}^p$. We will see that $T\\cup\\{0\\}$ is a submonoid of $({\\mathbb N},+)$. Moreover, we show algorithmic processes to compute $T$.","authors_text":"Aureliano M. Robles-P\\'erez, Jos\\'e Carlos Rosales","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-11-08T17:42:13Z","title":"On a transport problem and monoids of non-negative integers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02627","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:fc81a176ab0aaed6ce17b4b28c2b15c84d53321f15b548804fb2d24a80d6d92f","target":"record","created_at":"2026-05-18T00:09:53Z","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":"63a87199ab1751bede3d4ab57db6722efd29e82f8972730314aa9ff5d80788ef","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-11-08T17:42:13Z","title_canon_sha256":"d0d84745684a2527bcf53a360fda7eea6490b6e97ef2879450ab9a961e2549fd"},"schema_version":"1.0","source":{"id":"1611.02627","kind":"arxiv","version":2}},"canonical_sha256":"a82566efbe36cd645b9bf7b877035e0020957f689c53fb6f79bb5fa30adc6f96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a82566efbe36cd645b9bf7b877035e0020957f689c53fb6f79bb5fa30adc6f96","first_computed_at":"2026-05-18T00:09:53.252246Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:53.252246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jV29DoBTHvDPV7RI67wUh23FuzTd9HdCW49DQJySMar9Misewrcgv2jYei+l/YJY2z+RYgHwp0ZHvKtAJ7XpAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:53.252843Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.02627","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc81a176ab0aaed6ce17b4b28c2b15c84d53321f15b548804fb2d24a80d6d92f","sha256:ca9dda581fe3218447d48bf2b2235722c3a45b044bfb5abfdbf569166c938bc4"],"state_sha256":"f053730b13a5b79ac0dda52136dfaa20278d5360f7a131303024b03dd3bb3673"}