{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CVPPAVEHTNFGXSZKYKMEAW5VMK","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":"300114ace2fe67c6fd13c6f892850519f8dd28ef1ab6cb532af4a0d3473da853","cross_cats_sorted":["cs.FL","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-02-06T15:24:52Z","title_canon_sha256":"00791941df305dc00862d662e30020e4a9b34b9c8195582040cdc4d4b3e7c130"},"schema_version":"1.0","source":{"id":"1502.01920","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.01920","created_at":"2026-05-18T02:27:50Z"},{"alias_kind":"arxiv_version","alias_value":"1502.01920v1","created_at":"2026-05-18T02:27:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01920","created_at":"2026-05-18T02:27:50Z"},{"alias_kind":"pith_short_12","alias_value":"CVPPAVEHTNFG","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CVPPAVEHTNFGXSZK","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CVPPAVEH","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:5f9fe558cec4094b17e585cd682f8458bdea92e4bf051006ded0c4242a772791","target":"graph","created_at":"2026-05-18T02:27:50Z","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":"Given an automaton (a letter-to-letter transducer, a dynamical 1-Lipschitz system on the space $\\mathbb Z_p$ of $p$-adic integers) $\\mathfrak A$ whose input and output alphabets are $\\mathbb F_p=\\{0,1,\\ldots,p-1\\}$, one visualizes word transformations performed by $\\mathfrak A$ by a point set $\\mathbf P(\\mathfrak A)$ in real plane $\\mathbb R^2$.\n  For a finite-state automaton $\\mathfrak A$, it is shown that once some points of $\\mathbf P(\\mathfrak A)$ constitute a smooth (of a class $C^2$) curve in $\\mathbb R^2$, the curve is a segment of a straight line with a rational slope; and there are on","authors_text":"Vladimir Anashin","cross_cats":["cs.FL","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-02-06T15:24:52Z","title":"Quantization causes waves:Smooth finitely computable functions are affine"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01920","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:d6e0b2acfd7f64ed601bf20bdb62cc348f3d26c3e2db877acdd5925789c53219","target":"record","created_at":"2026-05-18T02:27:50Z","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":"300114ace2fe67c6fd13c6f892850519f8dd28ef1ab6cb532af4a0d3473da853","cross_cats_sorted":["cs.FL","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-02-06T15:24:52Z","title_canon_sha256":"00791941df305dc00862d662e30020e4a9b34b9c8195582040cdc4d4b3e7c130"},"schema_version":"1.0","source":{"id":"1502.01920","kind":"arxiv","version":1}},"canonical_sha256":"155ef054879b4a6bcb2ac298405bb562ba8d210395d14813df04056bcb49481f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"155ef054879b4a6bcb2ac298405bb562ba8d210395d14813df04056bcb49481f","first_computed_at":"2026-05-18T02:27:50.436614Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:50.436614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qUTOWxe9rby8K3ZmNUSBUNDNdxSyI3ZszuDBCYY1sXmRDDfxRVagdbZRsOFm27oZGtyTAWWopyY79rbVsWXxAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:50.437028Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.01920","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6e0b2acfd7f64ed601bf20bdb62cc348f3d26c3e2db877acdd5925789c53219","sha256:5f9fe558cec4094b17e585cd682f8458bdea92e4bf051006ded0c4242a772791"],"state_sha256":"eccfa058e34537557a8ef375494f168baf2a107f57588fb8ef6d1e3ed22cad0b"}