{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LGNLN6NR2NPBBCUDG7IAURJUY5","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":"f1836220b1f2da8d867c6f87fda13e82684b490040a96e9532923341fe050805","cross_cats_sorted":["math.MP","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-12T23:55:27Z","title_canon_sha256":"72fd094c40ae5f303daad402dd098b0c0f86e16d3fab0b5e85c508bd8ed33f62"},"schema_version":"1.0","source":{"id":"1602.06330","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.06330","created_at":"2026-05-18T01:20:15Z"},{"alias_kind":"arxiv_version","alias_value":"1602.06330v1","created_at":"2026-05-18T01:20:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.06330","created_at":"2026-05-18T01:20:15Z"},{"alias_kind":"pith_short_12","alias_value":"LGNLN6NR2NPB","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LGNLN6NR2NPBBCUD","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LGNLN6NR","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:18b30db8e053d05df0c8b3e147f09bc5c0f1c4d2f6c6afbb366a72c23ffbf703","target":"graph","created_at":"2026-05-18T01:20:15Z","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":"The location of zeros of the basic double sum over the square lattice is studied. This sum can be represented in terms of the product of the Riemann zeta function and the Dirichlet beta function, so that the assertion that all its non-trivial zeros lie on the critical line is a particular case of the Generalised Riemann Hypothesis (GRH). It is shown that a new necessary and sufficient condition for this special case of the GRH to hold is that a particular set of equimodular and equiargument contours of a ratio of MacDonald function double sums intersect only on the critical line. It is further","authors_text":"R. C. McPhedran","cross_cats":["math.MP","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-12T23:55:27Z","title":"Zeros of Lattice Sums: 2. A Geometry for the Generalised Riemann Hypothesis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06330","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:f8fd3986b9819627700b108abb1a11d0ce18fc1dd9309f4b4d073060b2e2caee","target":"record","created_at":"2026-05-18T01:20:15Z","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":"f1836220b1f2da8d867c6f87fda13e82684b490040a96e9532923341fe050805","cross_cats_sorted":["math.MP","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-12T23:55:27Z","title_canon_sha256":"72fd094c40ae5f303daad402dd098b0c0f86e16d3fab0b5e85c508bd8ed33f62"},"schema_version":"1.0","source":{"id":"1602.06330","kind":"arxiv","version":1}},"canonical_sha256":"599ab6f9b1d35e108a8337d00a4534c77c222a38f4cf04a2dd0bddbfa9801b2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"599ab6f9b1d35e108a8337d00a4534c77c222a38f4cf04a2dd0bddbfa9801b2b","first_computed_at":"2026-05-18T01:20:15.941482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:15.941482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yLYnLtVBZlmOFJL7RhW1R4PTuJn+DXtruNvCOAAHO4TFp6HV87rRcn0B17G0A6HjaB1B7ljpcWkn4KwLHrSrCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:15.942199Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.06330","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8fd3986b9819627700b108abb1a11d0ce18fc1dd9309f4b4d073060b2e2caee","sha256:18b30db8e053d05df0c8b3e147f09bc5c0f1c4d2f6c6afbb366a72c23ffbf703"],"state_sha256":"93168fb488754f289fec352d2053497d328f4a44746c91c63f0872aa5b2da5c4"}