{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PV6HFMVX2IXCLH7CDY5YPUMPYH","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":"bccfda210dede676caa94d24fbc4c163f2e814e7ce51d6b57beae69b08230642","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-01-22T19:28:08Z","title_canon_sha256":"1c1f9058c5ec3225244f1c60e585975c74dd01dde229127fe813439939f5ea2f"},"schema_version":"1.0","source":{"id":"1701.06211","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06211","created_at":"2026-05-18T00:52:18Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06211v1","created_at":"2026-05-18T00:52:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06211","created_at":"2026-05-18T00:52:18Z"},{"alias_kind":"pith_short_12","alias_value":"PV6HFMVX2IXC","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PV6HFMVX2IXCLH7C","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PV6HFMVX","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:604e135e04f74e72ee74d3cae6ac5c3ca1fc073c5f2df10965a2e487fd43596a","target":"graph","created_at":"2026-05-18T00:52:18Z","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":"We find new simple conditions for support of a discrete measure on Euclidean space to be a finite union of translated lattices. The arguments are based on a local analog of Wiener's Theorem on absolutely convergent trigonometric series and theory of almost periodic functions.","authors_text":"Sergey Favorov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-01-22T19:28:08Z","title":"Large Fourier Quasicrystals and Wiener's Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06211","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":"sha256:2bb76898efa1b75fdd27b102cc1151154c30efcc5851cb24d925268812f77288","target":"record","created_at":"2026-05-18T00:52:18Z","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":"bccfda210dede676caa94d24fbc4c163f2e814e7ce51d6b57beae69b08230642","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-01-22T19:28:08Z","title_canon_sha256":"1c1f9058c5ec3225244f1c60e585975c74dd01dde229127fe813439939f5ea2f"},"schema_version":"1.0","source":{"id":"1701.06211","kind":"arxiv","version":1}},"canonical_sha256":"7d7c72b2b7d22e259fe21e3b87d18fc1cac2ceebd56079d2a196174bf6a391f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d7c72b2b7d22e259fe21e3b87d18fc1cac2ceebd56079d2a196174bf6a391f7","first_computed_at":"2026-05-18T00:52:18.992308Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:18.992308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kBw90CNqAB7UgridUgEcui+73qdma1vDyTz89g1/MBRwysJ9VtHUosYhSgyfiQZUVO1bS0AwjWD3V/2WOKhrCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:18.993001Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.06211","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2bb76898efa1b75fdd27b102cc1151154c30efcc5851cb24d925268812f77288","sha256:604e135e04f74e72ee74d3cae6ac5c3ca1fc073c5f2df10965a2e487fd43596a"],"state_sha256":"229cc14936e20a7d747c7276031bcddca41618072c3e1d6612f1ff20c404e780"}