{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:OW5PIABXKH4NILYTNELBESNJCR","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":"e87484554402ade293840341634ab5d3d634ebe5d1422b80f3726692db3529a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-07-17T07:11:54Z","title_canon_sha256":"bcbe0c52c6595a3cf9e4cd2f78ffdc6831ef6c648c558b9036d3d95a0f010847"},"schema_version":"1.0","source":{"id":"1907.08675","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.08675","created_at":"2026-05-17T23:40:08Z"},{"alias_kind":"arxiv_version","alias_value":"1907.08675v1","created_at":"2026-05-17T23:40:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.08675","created_at":"2026-05-17T23:40:08Z"},{"alias_kind":"pith_short_12","alias_value":"OW5PIABXKH4N","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"OW5PIABXKH4NILYT","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"OW5PIABX","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:bafa3f7efac47fbded6c55d540a09aff20356a8097c84c809b9a9a60733891f0","target":"graph","created_at":"2026-05-17T23:40:08Z","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":"In this paper we study ideas which have proved useful in topological network theory in the context of lattices of numbers. A number lattice $L_S$ is a collection of row vectors, over $\\mathbb{Q}$ on a finite column set $S,$ generated by integral linear combination of a finite set of row vectors. A generalized number lattice $K_S$ is the sum of a number lattice $L_S$ and a vector space $V_S$ which has only the zero vector in common with it. The dual $K^d_S$ of a generalized number lattice is the collection of all vectors whose dot product with vectors in $K_S$ are integral and is another genera","authors_text":"Hariharan Narayanan, H. Narayanan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-07-17T07:11:54Z","title":"On the linking of number lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08675","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":"sha256:53fba43f0c1a3e1f69a13c142cfd61d15842eb136ab0af0219b4d97e0a0f70f2","target":"record","created_at":"2026-05-17T23:40:08Z","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":"e87484554402ade293840341634ab5d3d634ebe5d1422b80f3726692db3529a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-07-17T07:11:54Z","title_canon_sha256":"bcbe0c52c6595a3cf9e4cd2f78ffdc6831ef6c648c558b9036d3d95a0f010847"},"schema_version":"1.0","source":{"id":"1907.08675","kind":"arxiv","version":1}},"canonical_sha256":"75baf4003751f8d42f1369161249a9144f37d3df9c8ea22fd2bb83e726894807","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75baf4003751f8d42f1369161249a9144f37d3df9c8ea22fd2bb83e726894807","first_computed_at":"2026-05-17T23:40:08.174051Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:08.174051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7qdiPH5ubNqCpwnF7ld+8C8Kg8fYOMluoDH3ZVs0V/7AgqISvAVXwhR8rE/SB5GSkZ5tYSokocRM8vcLeUV/DQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:08.174840Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.08675","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:53fba43f0c1a3e1f69a13c142cfd61d15842eb136ab0af0219b4d97e0a0f70f2","sha256:bafa3f7efac47fbded6c55d540a09aff20356a8097c84c809b9a9a60733891f0"],"state_sha256":"675a02ef8151933de0ea9d370e1ec49b0010463d590a8bb2caf09a3cb77f245b"}