{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZZB4OTRCD5DDGE5W4ZW5NALKMI","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":"1887fee6fc1a7cfc2b59604fee4bef0692e235835dfbac0f372d08276fb40385","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-28T15:43:08Z","title_canon_sha256":"906ff9831966109da87558f30e95ed9afca3b0620347f81539435f2984fd6ad5"},"schema_version":"1.0","source":{"id":"1410.7667","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7667","created_at":"2026-05-18T02:39:09Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7667v1","created_at":"2026-05-18T02:39:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7667","created_at":"2026-05-18T02:39:09Z"},{"alias_kind":"pith_short_12","alias_value":"ZZB4OTRCD5DD","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZZB4OTRCD5DDGE5W","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZZB4OTRC","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:f36f8f06312a761b8417f96eb8ebb3a2d5a33148fdd0c50f6804fbc3054b4fdc","target":"graph","created_at":"2026-05-18T02:39:09Z","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":"For $d \\in \\mathbb{N}$ and $\\mathbf{r} \\in \\mathbb{C}^d$ let $\\gamma_\\mathbf{r}: \\mathbb{Z}[\\mathrm{i}]^d \\to \\mathbb{Z}[\\mathrm{i}]^d$, where $\\gamma_\\mathbf{r}(\\mathbf{a})=(a_2,...,a_d,$ $-\\lfloor\\mathbf{r}\\mathbf{a}\\rfloor)$ for $\\mathbf{a}=(a_1,...,a_d)$, denote the (d-dimensional) Gaussian shift radix system associated with $\\mathbf{r}$. $\\gamma_\\mathbf{r}$ is said to have the finiteness property iff all orbits of $\\gamma_\\mathbf{r}$ end up in $(0,...,0)$; the set of all corresponding $\\mathbf{r} \\in \\mathbb{C}^d$ is denoted by $\\mathcal{G}_{d}^{(0)}$. It has a very complicated structure ","authors_text":"Mario Weitzer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-28T15:43:08Z","title":"On the characterization of Peth\\H{o}'s Loudspeaker"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7667","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":"sha256:38c5b6d67d23aa02b0a9228c14d1f2dc707523ade22ad5dbde738bd6528576b1","target":"record","created_at":"2026-05-18T02:39:09Z","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":"1887fee6fc1a7cfc2b59604fee4bef0692e235835dfbac0f372d08276fb40385","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-28T15:43:08Z","title_canon_sha256":"906ff9831966109da87558f30e95ed9afca3b0620347f81539435f2984fd6ad5"},"schema_version":"1.0","source":{"id":"1410.7667","kind":"arxiv","version":1}},"canonical_sha256":"ce43c74e221f463313b6e66dd6816a62296b62a0c3b0919aaffc683b85654a9f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce43c74e221f463313b6e66dd6816a62296b62a0c3b0919aaffc683b85654a9f","first_computed_at":"2026-05-18T02:39:09.735431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:09.735431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gsT3+gTZO29P3cjF1Bg1x3YJNjrMIQb6r2MW7xsvPhD62Xa5qCuM49lkqmjTQPV5+Mx5vExga9KB/Mt3CjzwBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:09.736037Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.7667","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38c5b6d67d23aa02b0a9228c14d1f2dc707523ade22ad5dbde738bd6528576b1","sha256:f36f8f06312a761b8417f96eb8ebb3a2d5a33148fdd0c50f6804fbc3054b4fdc"],"state_sha256":"92a08c9e44627a01a1cd3f77b748584488ece2e785a92e2b461fe487fa5f5660"}