{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:R3FSH7IJCI7LUAMZG77ZYOM5DE","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":"bdfcb6a1369deda0f63c087d6c57b327b0ea00d4df36326006bab7ae1b9d249b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-11-05T19:38:09Z","title_canon_sha256":"ec71b20b836da140ee3bc3741c87426522365173ed96f6e21ba232d7fe273f83"},"schema_version":"1.0","source":{"id":"1711.02537","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02537","created_at":"2026-05-18T00:31:07Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02537v1","created_at":"2026-05-18T00:31:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02537","created_at":"2026-05-18T00:31:07Z"},{"alias_kind":"pith_short_12","alias_value":"R3FSH7IJCI7L","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"R3FSH7IJCI7LUAMZ","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"R3FSH7IJ","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:9c4da289a4e58fe1042b06721e0128cf5e28f7dd4f437468836fbf9c1384122f","target":"graph","created_at":"2026-05-18T00:31:07Z","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":"On any torus $\\mathbb{T}^d$, $d \\geq 2$, we prove the existence of a real-analytic diffeomorphism $T$ with a good approximation of type $\\left(h,h+1\\right)$, a maximal spectral type disjoint with its convolutions and a homogeneous spectrum of multiplicity two for the Cartesian square $T\\times T$. The proof is based on a real-analytic version of the Approximation by Conjugation-method.","authors_text":"Philipp Kunde, Shilpak Banerjee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-11-05T19:38:09Z","title":"Real-analytic diffeomorphisms with homogeneous spectrum and disjointness of convolutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02537","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":"sha256:33fa818ba2f4abe1ca1631ef449a80af46ef2e2b13430bd38e4aca2b0354504a","target":"record","created_at":"2026-05-18T00:31:07Z","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":"bdfcb6a1369deda0f63c087d6c57b327b0ea00d4df36326006bab7ae1b9d249b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-11-05T19:38:09Z","title_canon_sha256":"ec71b20b836da140ee3bc3741c87426522365173ed96f6e21ba232d7fe273f83"},"schema_version":"1.0","source":{"id":"1711.02537","kind":"arxiv","version":1}},"canonical_sha256":"8ecb23fd09123eba019937ff9c399d191bbf181fe25ba85d815bf3e0c4e5967f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ecb23fd09123eba019937ff9c399d191bbf181fe25ba85d815bf3e0c4e5967f","first_computed_at":"2026-05-18T00:31:07.659934Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:07.659934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pDfXybZa8FazADxkW+R4EmPhMtXntWkoUFBfUjKdaaxUaEK/JpG5WTvZkkY32dCMKTaB65EiYnbqvVR45VEqCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:07.660447Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.02537","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33fa818ba2f4abe1ca1631ef449a80af46ef2e2b13430bd38e4aca2b0354504a","sha256:9c4da289a4e58fe1042b06721e0128cf5e28f7dd4f437468836fbf9c1384122f"],"state_sha256":"0d2e4abeeb898b6522ba67450ca0a94659ed79fb40311357d788c40d39a5096e"}