{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:VKZBUJ4RW3SXKHC3J6MJZGHWPZ","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":"191225b27234d036367899432a975d7907c8e61b7e81911c1159a99d5909f485","cross_cats_sorted":["cs.DM","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-05-28T14:51:19Z","title_canon_sha256":"ecaef3c06112e626961fcf68f0951b28d57235825d2e566e36602c16a69db81c"},"schema_version":"1.0","source":{"id":"2305.17743","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.17743","created_at":"2026-07-05T09:12:53Z"},{"alias_kind":"arxiv_version","alias_value":"2305.17743v2","created_at":"2026-07-05T09:12:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.17743","created_at":"2026-07-05T09:12:53Z"},{"alias_kind":"pith_short_12","alias_value":"VKZBUJ4RW3SX","created_at":"2026-07-05T09:12:53Z"},{"alias_kind":"pith_short_16","alias_value":"VKZBUJ4RW3SXKHC3","created_at":"2026-07-05T09:12:53Z"},{"alias_kind":"pith_short_8","alias_value":"VKZBUJ4R","created_at":"2026-07-05T09:12:53Z"}],"graph_snapshots":[{"event_id":"sha256:34cc2c7b32decb765e56ee43de9aa337afbcfacd0ffd6c6069a1b6a1660d7d17","target":"graph","created_at":"2026-07-05T09:12:53Z","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/2305.17743/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The recently discovered \"hat\" aperiodic monotile mixes unreflected and reflected tiles in every tiling it admits, leaving open the question of whether a single shape can tile aperiodically using translations and rotations alone. We show that a close relative of the hat -- the equilateral member of the continuum to which it belongs -- is a weakly chiral aperiodic monotile: it admits only non-periodic tilings if we forbid reflections by fiat. Furthermore, by modifying this polygon's edges we obtain a family of shapes called Spectres that are strictly chiral aperiodic monotiles: they admit only c","authors_text":"Chaim Goodman-Strauss, Craig S. Kaplan, David Smith, Joseph Samuel Myers","cross_cats":["cs.DM","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-05-28T14:51:19Z","title":"A chiral aperiodic monotile"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.17743","kind":"arxiv","version":2},"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":"sha256:06d7a055886fc0e232789070a9dcf761d07f0c1e4356eb49244359aeadb8d453","target":"record","created_at":"2026-07-05T09:12:53Z","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":"191225b27234d036367899432a975d7907c8e61b7e81911c1159a99d5909f485","cross_cats_sorted":["cs.DM","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-05-28T14:51:19Z","title_canon_sha256":"ecaef3c06112e626961fcf68f0951b28d57235825d2e566e36602c16a69db81c"},"schema_version":"1.0","source":{"id":"2305.17743","kind":"arxiv","version":2}},"canonical_sha256":"aab21a2791b6e5751c5b4f989c98f67e49c3682c7c78b65bdca6d8080746a548","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aab21a2791b6e5751c5b4f989c98f67e49c3682c7c78b65bdca6d8080746a548","first_computed_at":"2026-07-05T09:12:53.271163Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:12:53.271163Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bJLfM0Y0nh0GFqOsSqW6tAyx2vUvUkEFEkmg26uBNHUn5JXFGKJrBy103PXb5tptbnReYzJwU2degHmjaScQBA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:12:53.271654Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.17743","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06d7a055886fc0e232789070a9dcf761d07f0c1e4356eb49244359aeadb8d453","sha256:34cc2c7b32decb765e56ee43de9aa337afbcfacd0ffd6c6069a1b6a1660d7d17"],"state_sha256":"46e4c25519d862c55bca6e54b01e53562131875612281df5c5a9ad69cd081949"}