{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6JWZTVEMRBZQAOUO3DPDKAZ5HT","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":"b5a0044abee9d10a01a4f8399facd9c5507dec653cff18286c49aa12b4721cab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-09-03T00:16:40Z","title_canon_sha256":"b13b634bb9b4b8d8833761f307f9fd8ca11a1c3b649a77b18e81caacad8eb818"},"schema_version":"1.0","source":{"id":"1609.00772","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.00772","created_at":"2026-05-18T00:10:13Z"},{"alias_kind":"arxiv_version","alias_value":"1609.00772v2","created_at":"2026-05-18T00:10:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00772","created_at":"2026-05-18T00:10:13Z"},{"alias_kind":"pith_short_12","alias_value":"6JWZTVEMRBZQ","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6JWZTVEMRBZQAOUO","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6JWZTVEM","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:7f60e6274ae5f288dba04c2fa5bfe0e90da26ddc85fbeb928c023e95d2b4f2f7","target":"graph","created_at":"2026-05-18T00:10:13Z","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":"We consider the dynamics of light rays in the trihexagonal tiling where triangles and hexagons are transparent and have equal but opposite indices of refraction. We find that almost every ray of light is dense in a region of a particular form: the regions have infinite area and consist of the plane with a periodic family of triangles removed. We also completely describe initial conditions for periodic and drift-periodic light rays.","authors_text":"Diana Davis, W. Patrick Hooper","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-09-03T00:16:40Z","title":"Periodicity and ergodicity in the trihexagonal tiling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00772","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:f65ef6a28c9be316ba58772a4b225a77147d13883449fd6aaf6140ebeb364598","target":"record","created_at":"2026-05-18T00:10:13Z","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":"b5a0044abee9d10a01a4f8399facd9c5507dec653cff18286c49aa12b4721cab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-09-03T00:16:40Z","title_canon_sha256":"b13b634bb9b4b8d8833761f307f9fd8ca11a1c3b649a77b18e81caacad8eb818"},"schema_version":"1.0","source":{"id":"1609.00772","kind":"arxiv","version":2}},"canonical_sha256":"f26d99d48c8873003a8ed8de35033d3cd0f0342cc8b73073864f4d9aaacc37ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f26d99d48c8873003a8ed8de35033d3cd0f0342cc8b73073864f4d9aaacc37ca","first_computed_at":"2026-05-18T00:10:13.943461Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:13.943461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0RzXdDZhoumocowX8MY7Y2z1IsC7FxfPCuP/l+H09jmMecIELZppMzBORaASxFmnu7tooAJ4OTLruFjXbythAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:13.944197Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.00772","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f65ef6a28c9be316ba58772a4b225a77147d13883449fd6aaf6140ebeb364598","sha256:7f60e6274ae5f288dba04c2fa5bfe0e90da26ddc85fbeb928c023e95d2b4f2f7"],"state_sha256":"1208647d0bd61c62153769d310bdc67f87e645fbea2245c8536307303c7cabb2"}