{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:ZJ6Y7ANXG72YBDTSIIODCLJ4W3","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":"14033af0bef8dca1280d9aa9c5af36e09fac9d3aa786661126678e6ca2398b2c","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2021-07-14T01:44:04Z","title_canon_sha256":"4682ea54dacc0c5ec7d129456c37a874da0a2c338acff75136b21939aa18a8df"},"schema_version":"1.0","source":{"id":"2107.06447","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.06447","created_at":"2026-07-05T04:46:32Z"},{"alias_kind":"arxiv_version","alias_value":"2107.06447v2","created_at":"2026-07-05T04:46:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.06447","created_at":"2026-07-05T04:46:32Z"},{"alias_kind":"pith_short_12","alias_value":"ZJ6Y7ANXG72Y","created_at":"2026-07-05T04:46:32Z"},{"alias_kind":"pith_short_16","alias_value":"ZJ6Y7ANXG72YBDTS","created_at":"2026-07-05T04:46:32Z"},{"alias_kind":"pith_short_8","alias_value":"ZJ6Y7ANX","created_at":"2026-07-05T04:46:32Z"}],"graph_snapshots":[{"event_id":"sha256:ab7ae92b1a55e2c0041445319cd65bf6a785ed089c5c38cb2e5a7219d9ee1133","target":"graph","created_at":"2026-07-05T04:46:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2107.06447/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the Bloch variety of discrete Schr\\\"odinger operators associated with a complex periodic potential and a general finite-range interaction, showing that the Bloch variety is irreducible for a wide class of lattice geometries in arbitrary dimension. Examples include the triangular lattice and the extended Harper lattice.","authors_text":"Jake Fillman, Rodrigo Matos, Wencai Liu","cross_cats":["math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2021-07-14T01:44:04Z","title":"Irreducibility of the Bloch Variety for Finite-Range Schr\\\"odinger Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.06447","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":"sha256:1ba926623333dc05af4667a0907abf263aaf024f4e541940b0356c077af55914","target":"record","created_at":"2026-07-05T04:46:32Z","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":"14033af0bef8dca1280d9aa9c5af36e09fac9d3aa786661126678e6ca2398b2c","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2021-07-14T01:44:04Z","title_canon_sha256":"4682ea54dacc0c5ec7d129456c37a874da0a2c338acff75136b21939aa18a8df"},"schema_version":"1.0","source":{"id":"2107.06447","kind":"arxiv","version":2}},"canonical_sha256":"ca7d8f81b737f5808e72421c312d3cb6c92188077a4afa6d479550a6a87cb56a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca7d8f81b737f5808e72421c312d3cb6c92188077a4afa6d479550a6a87cb56a","first_computed_at":"2026-07-05T04:46:32.147782Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:46:32.147782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tSNUNmTmoYp6H0Tks3nw0Xm7XQD13CHgJh+E0p8eb1TVHpNPqW4GmUaZYYCL0fMSU99mfaSlhxbObjp0JBUwDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:46:32.148204Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.06447","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ba926623333dc05af4667a0907abf263aaf024f4e541940b0356c077af55914","sha256:ab7ae92b1a55e2c0041445319cd65bf6a785ed089c5c38cb2e5a7219d9ee1133"],"state_sha256":"ca700ba43041aa667c30fc2d8db4d47b4ae121d08625d45903f5e937e5b3cfc8"}