{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WRQOZV4QBZ5Y7U2TXRU4AZYKRQ","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":"868bbe8ef5e92ade0e3ae508df7c02059b5392f1d036eccded441f175c66e2cb","cross_cats_sorted":["math.OA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2026-06-10T10:26:19Z","title_canon_sha256":"4c1ea90925ad9b08e67e36487b6a541997f8287f68449f0fa02cc184a577c8a4"},"schema_version":"1.0","source":{"id":"2606.11899","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.11899","created_at":"2026-06-11T01:10:14Z"},{"alias_kind":"arxiv_version","alias_value":"2606.11899v1","created_at":"2026-06-11T01:10:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.11899","created_at":"2026-06-11T01:10:14Z"},{"alias_kind":"pith_short_12","alias_value":"WRQOZV4QBZ5Y","created_at":"2026-06-11T01:10:14Z"},{"alias_kind":"pith_short_16","alias_value":"WRQOZV4QBZ5Y7U2T","created_at":"2026-06-11T01:10:14Z"},{"alias_kind":"pith_short_8","alias_value":"WRQOZV4Q","created_at":"2026-06-11T01:10:14Z"}],"graph_snapshots":[{"event_id":"sha256:b2e9a432ea05d9679d43adce24b60925737bfbb70c8fcd161686edeae2e71f1b","target":"graph","created_at":"2026-06-11T01:10:14Z","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/2606.11899/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"To a full $m\\times n$ Mealy automaton $A$ we associate a bijection $\\theta_A$, a one-vertex rank-two graph $F_{\\theta_A}$, and a one-vertex $VH$-square complex $Y_A$ tiled by $mn$ Wang tiles. We prove that $Y_A$ contains an anti-torus if and only if $A$ is bi-reversible and $F_{\\theta_A}$ is aperiodic. The two hypotheses are independent and play disjoint roles: bi-reversibility is exactly what makes $Y_A$ a complete square complex, so that its universal cover splits as a product of two trees and anti-tori can be discussed at all; and, within that setting, an anti-torus is precisely a period-fr","authors_text":"David Pask","cross_cats":["math.OA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2026-06-10T10:26:19Z","title":"Full Mealy automata, complete square complexes, and anti-tori"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11899","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":"sha256:2778ec5d3d11983acdb52261f6fb6fd6bc3aab0b19fc7481d37f573bf41a6d62","target":"record","created_at":"2026-06-11T01:10:14Z","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":"868bbe8ef5e92ade0e3ae508df7c02059b5392f1d036eccded441f175c66e2cb","cross_cats_sorted":["math.OA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2026-06-10T10:26:19Z","title_canon_sha256":"4c1ea90925ad9b08e67e36487b6a541997f8287f68449f0fa02cc184a577c8a4"},"schema_version":"1.0","source":{"id":"2606.11899","kind":"arxiv","version":1}},"canonical_sha256":"b460ecd7900e7b8fd353bc69c0670a8c3ac70b52b018ec2a104054ac33200ac4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b460ecd7900e7b8fd353bc69c0670a8c3ac70b52b018ec2a104054ac33200ac4","first_computed_at":"2026-06-11T01:10:14.461288Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-11T01:10:14.461288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vsYti0kjdB/+DrbLgqkYg7hOCl+Stm6dKGr0gE7cFz/Vcy47lIrQY3rtWx9yX0tIMpjAUhgKGBT7qeMp/xdCAw==","signature_status":"signed_v1","signed_at":"2026-06-11T01:10:14.462233Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.11899","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2778ec5d3d11983acdb52261f6fb6fd6bc3aab0b19fc7481d37f573bf41a6d62","sha256:b2e9a432ea05d9679d43adce24b60925737bfbb70c8fcd161686edeae2e71f1b"],"state_sha256":"a7785d89eea9c883521ddc7e8a9c1c9b56dd0e1d19413e53d3d47183680fc1e7"}