{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:YTABGUIP5UVFJJS7NJQZN2UARN","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":"2968f82109206f06be3a1a644a0c5c9354acff22303c15ae3daa0be27051fc32","cross_cats_sorted":["cs.DM","cs.FL"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-05-04T09:28:05Z","title_canon_sha256":"27f9f2ff677920b6b3aedfc0c0f1d95df265d0bac7a28b200cd2dfbd6d7bd49e"},"schema_version":"1.0","source":{"id":"2305.02672","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.02672","created_at":"2026-05-20T14:03:16Z"},{"alias_kind":"arxiv_version","alias_value":"2305.02672v6","created_at":"2026-05-20T14:03:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.02672","created_at":"2026-05-20T14:03:16Z"},{"alias_kind":"pith_short_12","alias_value":"YTABGUIP5UVF","created_at":"2026-05-20T14:03:16Z"},{"alias_kind":"pith_short_16","alias_value":"YTABGUIP5UVFJJS7","created_at":"2026-05-20T14:03:16Z"},{"alias_kind":"pith_short_8","alias_value":"YTABGUIP","created_at":"2026-05-20T14:03:16Z"}],"graph_snapshots":[{"event_id":"sha256:6aa9e04805a1d5dde14cd2893a40b60a8e6b579a294185fd2bde8ccf537546bf","target":"graph","created_at":"2026-05-20T14:03:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2305.02672/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We revisit a classic theorem of Frougny and Sakarovitch concerning automata for $\\varphi$-representations, and show how to obtain it in a different and more computationally direct way. Using it, we can find simple, induction-free proofs of existing results in the literature about these representations, in a uniform and straightforward manner. In particular, we can easily and \"automatically'' recover many of the results of recent papers of Dekking and Van Loon. We also obtain a number of new results on $\\varphi$-representations.","authors_text":"Jeffrey Shallit","cross_cats":["cs.DM","cs.FL"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-05-04T09:28:05Z","title":"Proving Properties of $\\varphi$-Representations with the Walnut Theorem-Prover"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.02672","kind":"arxiv","version":6},"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":"sha256:982ac31dbe93447377a811ece306155e93a3016e6c5ee3bae7e415986fa66165","target":"record","created_at":"2026-05-20T14:03:16Z","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":"2968f82109206f06be3a1a644a0c5c9354acff22303c15ae3daa0be27051fc32","cross_cats_sorted":["cs.DM","cs.FL"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-05-04T09:28:05Z","title_canon_sha256":"27f9f2ff677920b6b3aedfc0c0f1d95df265d0bac7a28b200cd2dfbd6d7bd49e"},"schema_version":"1.0","source":{"id":"2305.02672","kind":"arxiv","version":6}},"canonical_sha256":"c4c013510fed2a54a65f6a6196ea808b77b0d91d441a9fb8b6874724785e6a52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4c013510fed2a54a65f6a6196ea808b77b0d91d441a9fb8b6874724785e6a52","first_computed_at":"2026-05-20T14:03:16.552894Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T14:03:16.552894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bWnb5Q3mxeTmj2RuGuBq0tymQguC40SwstsChRS667EFY+lXY7JfRTQYMZiM/onImJoZhNZW4VNFZKpUJHOMCw==","signature_status":"signed_v1","signed_at":"2026-05-20T14:03:16.553407Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.02672","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:982ac31dbe93447377a811ece306155e93a3016e6c5ee3bae7e415986fa66165","sha256:6aa9e04805a1d5dde14cd2893a40b60a8e6b579a294185fd2bde8ccf537546bf"],"state_sha256":"6c3f2a7dce2bfd09ca4463c880f6d915c7e97367100973111930f3125acf6ecf"}