{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6H75S54TXSBVVMB7N34NO7756L","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":"c72993b5495a3ebdf68079c457134a54f90358ddf329a602f8b10ea8aee6b925","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-03-03T10:02:34Z","title_canon_sha256":"f13bf56644cdb3fcc57e68088a46c9cbb918d83b845a2ba61d635364956c3cda"},"schema_version":"1.0","source":{"id":"1403.0362","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0362","created_at":"2026-05-18T02:40:10Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0362v3","created_at":"2026-05-18T02:40:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0362","created_at":"2026-05-18T02:40:10Z"},{"alias_kind":"pith_short_12","alias_value":"6H75S54TXSBV","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6H75S54TXSBVVMB7","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6H75S54T","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:ee2574cebc85873f5517ffc85fcd0effb6cd014e88e2d2089ea381a37e4c084d","target":"graph","created_at":"2026-05-18T02:40:10Z","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":"By the algorithm implemented in the paper [2] by Akiyama-Lee and some of its predecessors, we have examined the pure discreteness of the spectrum for all irreducible Pisot substitutions of trace less than or equal to $2$, and some cases of planar tilings generated by boundary substitutions due to the paper [17] by Kenyon.","authors_text":"Franz Gaehler, Jeong-Yup Lee, Shigeki Akiyama","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-03-03T10:02:34Z","title":"Determining pure discrete spectrum for some self-affine tilings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0362","kind":"arxiv","version":3},"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":"sha256:69539fb4a24a1799bbc2b33bd6ce1bdca4fed045de91161d0bc8f106af993cbf","target":"record","created_at":"2026-05-18T02:40:10Z","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":"c72993b5495a3ebdf68079c457134a54f90358ddf329a602f8b10ea8aee6b925","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-03-03T10:02:34Z","title_canon_sha256":"f13bf56644cdb3fcc57e68088a46c9cbb918d83b845a2ba61d635364956c3cda"},"schema_version":"1.0","source":{"id":"1403.0362","kind":"arxiv","version":3}},"canonical_sha256":"f1ffd97793bc835ab03f6ef8d77ffdf2dcfa7e2012cdf4c6131ab7dfe3d63d7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1ffd97793bc835ab03f6ef8d77ffdf2dcfa7e2012cdf4c6131ab7dfe3d63d7c","first_computed_at":"2026-05-18T02:40:10.703487Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:10.703487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nY2x0xM1NYlOSl4RVcyQCUGNzTF8wll1QbFC4x7bOfk1+qAHa4anH5IhwLkAOJfI0uc5WYnGNYC8ET1FixsRDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:10.703905Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.0362","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69539fb4a24a1799bbc2b33bd6ce1bdca4fed045de91161d0bc8f106af993cbf","sha256:ee2574cebc85873f5517ffc85fcd0effb6cd014e88e2d2089ea381a37e4c084d"],"state_sha256":"0708c1446e1ae2d63d4510e4d16743e294d709d4477ac0b2d1cd5b1c4484558c"}