{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HJAJNPMI4HYASACFJAGY3ULG3A","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":"9f12a9230e5a9a7e1469e317490000b28f73a9e76883603da33d7a0d6de379db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-04T02:44:01Z","title_canon_sha256":"fbe66eb90efcbc764255a8eaf5cca6bc229b62bb21a39af455c1f39f883c729a"},"schema_version":"1.0","source":{"id":"1611.01250","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.01250","created_at":"2026-05-18T00:51:33Z"},{"alias_kind":"arxiv_version","alias_value":"1611.01250v2","created_at":"2026-05-18T00:51:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01250","created_at":"2026-05-18T00:51:33Z"},{"alias_kind":"pith_short_12","alias_value":"HJAJNPMI4HYA","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HJAJNPMI4HYASACF","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HJAJNPMI","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:c890f939e38bb64b5f39cef98939ee95467289af93f41aaf957e37ef832d9ac4","target":"graph","created_at":"2026-05-18T00:51:33Z","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":"In this paper, we consider the non-spectral problem for the planar self-affine measures $\\mu_{M,D}$ generated by an expanding integer matrix $M\\in M_2(\\mathbb{Z})$ and a finite digit set $D\\subset\\mathbb{Z}^2$. Let $p\\geq2$ be a positive integer, $E_p^2:=\\frac{1}{p}\\{(i,j)^t:0\\leq i,j\\leq p-1\\}$ and $\\mathcal{Z}_{D}^2:=\\{x\\in[0, 1)^2:\\sum_{d\\in D}{e^{2\\pi i\\langle d,x\\rangle}}=0\\}$. We show that if $\\emptyset\\neq\\mathcal{Z}_{D}^2\\subset E_p^2\\setminus\\{0\\}$ and $\\gcd(\\det(M),p)=1$, then there exist at most $p^2$ mutually orthogonal exponential functions in $L^2(\\mu_{M,D})$. In particular, if $","authors_text":"Jian-lin Li, Jing-Cheng Liu, Xin-han Dong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-04T02:44:01Z","title":"Non-spectral problem for the planar self-affine measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01250","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:d2cdef59fdcaeb9d9736ad889305140a1a8f32eb76e25cd6aeb70c467b4a0fe5","target":"record","created_at":"2026-05-18T00:51:33Z","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":"9f12a9230e5a9a7e1469e317490000b28f73a9e76883603da33d7a0d6de379db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-04T02:44:01Z","title_canon_sha256":"fbe66eb90efcbc764255a8eaf5cca6bc229b62bb21a39af455c1f39f883c729a"},"schema_version":"1.0","source":{"id":"1611.01250","kind":"arxiv","version":2}},"canonical_sha256":"3a4096bd88e1f0090045480d8dd166d82235b28c97f23f8d21eddba566a71c25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a4096bd88e1f0090045480d8dd166d82235b28c97f23f8d21eddba566a71c25","first_computed_at":"2026-05-18T00:51:33.823190Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:33.823190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UqdZ8T7efUKN4Ryk8Qt7Jn0T1H1hjPUNcZrpmwMHXROWLdOCAPQ/mQli0ITQLtEIoxGqj1asX0ZzC56X0CSYBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:33.823715Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.01250","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2cdef59fdcaeb9d9736ad889305140a1a8f32eb76e25cd6aeb70c467b4a0fe5","sha256:c890f939e38bb64b5f39cef98939ee95467289af93f41aaf957e37ef832d9ac4"],"state_sha256":"77ef4ec0028477cbeb7cbfa642e497501d2cf0bd7b81554a65a231fabf16676e"}