{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PWJ4GUUEGC2MV76DAKISYBOZDA","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":"a8bd2acff828aad58f6323afa9b17b874e1cbdde5678170df8631f32733e7f26","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-01-16T13:55:28Z","title_canon_sha256":"982dfb38d4d58f5a83f96778ecfba46b448a3b3a76fcead0d2e611289279bd44"},"schema_version":"1.0","source":{"id":"1301.3689","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.3689","created_at":"2026-05-18T00:25:12Z"},{"alias_kind":"arxiv_version","alias_value":"1301.3689v2","created_at":"2026-05-18T00:25:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3689","created_at":"2026-05-18T00:25:12Z"},{"alias_kind":"pith_short_12","alias_value":"PWJ4GUUEGC2M","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"PWJ4GUUEGC2MV76D","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"PWJ4GUUE","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:6d328d5492bce0d39e9eb66ffd2ea89f59ce96c212be631e2c1a30fd38c8b534","target":"graph","created_at":"2026-05-18T00:25:12Z","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 coincidence site lattice is a sublattice formed by the intersection of a lattice $\\Gamma$ in $\\mathbb{R}^d$ with the image of $\\Gamma$ under a linear isometry. Such a linear isometry is referred to as a linear coincidence isometry of $\\Gamma$. Here, we consider the more general case allowing any affine isometry. Consequently, general results on coincidence isometries of shifted copies of lattices, and of crystallographic point packings are obtained. In particular, we discuss the shifted square lattice and the diamond packing in detail.","authors_text":"Manuel Joseph C. Loquias, Peter Zeiner","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-01-16T13:55:28Z","title":"The coincidence problem for shifted lattices and crystallographic point packings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3689","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:ea155f4538ed5ef1909cdf5a9a520329d29f9a2df47b65f5e5c88aeec9eaac3f","target":"record","created_at":"2026-05-18T00:25:12Z","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":"a8bd2acff828aad58f6323afa9b17b874e1cbdde5678170df8631f32733e7f26","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-01-16T13:55:28Z","title_canon_sha256":"982dfb38d4d58f5a83f96778ecfba46b448a3b3a76fcead0d2e611289279bd44"},"schema_version":"1.0","source":{"id":"1301.3689","kind":"arxiv","version":2}},"canonical_sha256":"7d93c3528430b4caffc302912c05d91827c28a2e0bd7cca16604bd711931444d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d93c3528430b4caffc302912c05d91827c28a2e0bd7cca16604bd711931444d","first_computed_at":"2026-05-18T00:25:12.225168Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:12.225168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I5FDfCrx+ya9bozHZpRwYzBzwZKDizkq+TINb+rUnBEINDPU4QlvS5Au8G9i7hbTi3/lmcCUIbcv4G3Yg/IxCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:12.225763Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.3689","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea155f4538ed5ef1909cdf5a9a520329d29f9a2df47b65f5e5c88aeec9eaac3f","sha256:6d328d5492bce0d39e9eb66ffd2ea89f59ce96c212be631e2c1a30fd38c8b534"],"state_sha256":"873ded5cca2e53f3e487f2e9f7a71719216a5f95f4c94052f9d5f6fee302c02e"}