{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JRLTI5AJTVKRI5UO2HJEFGBNPB","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":"0f1c0ac5403b3bbf76402a5b285bbd3c64895a2e8453053e62dc149bb8cd79b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-08-06T11:13:43Z","title_canon_sha256":"b7d8d6851a381f627b73f328c5c335a7992e628a25339bbc708ccba11270bb35"},"schema_version":"1.0","source":{"id":"1208.1132","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1132","created_at":"2026-05-18T03:28:42Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1132v2","created_at":"2026-05-18T03:28:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1132","created_at":"2026-05-18T03:28:42Z"},{"alias_kind":"pith_short_12","alias_value":"JRLTI5AJTVKR","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JRLTI5AJTVKRI5UO","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JRLTI5AJ","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:c817aa020223984403b7d7eade8a672973f9fd7ff02fd14d5bfd091787a4941e","target":"graph","created_at":"2026-05-18T03:28:42Z","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 a one-parameter family of invertible maps of a two-dimensional lattice, obtained by discretising the space of planar rotations. We let the angle of rotation approach $\\pi/2$, and show that the limit of vanishing discretisation is described by an integrable piecewise-smooth Hamiltonian flow, whereby the plane foliates into families of invariant polygons with an increasing number of sides. Considered as perturbations of the flow, the lattice maps assume a different character, described in terms of strip maps, a variant of those found in outer billiards of polygons. The perturbation i","authors_text":"Franco Vivaldi, Heather Reeve-Black","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-08-06T11:13:43Z","title":"Near-integrable behaviour in a family of discretised rotations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1132","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":"sha256:1349fb6f9301d91c38fed5abb2e8f196de61ab0fef436d8e423c1ff2b2f3a31f","target":"record","created_at":"2026-05-18T03:28:42Z","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":"0f1c0ac5403b3bbf76402a5b285bbd3c64895a2e8453053e62dc149bb8cd79b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-08-06T11:13:43Z","title_canon_sha256":"b7d8d6851a381f627b73f328c5c335a7992e628a25339bbc708ccba11270bb35"},"schema_version":"1.0","source":{"id":"1208.1132","kind":"arxiv","version":2}},"canonical_sha256":"4c573474099d5514768ed1d242982d787c2be336e8600d398f718b7d8954c633","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c573474099d5514768ed1d242982d787c2be336e8600d398f718b7d8954c633","first_computed_at":"2026-05-18T03:28:42.708230Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:42.708230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PdvH8plgsNN5S4TJrqcPPJZowo9XL1uvM6seT8sLTlgYYeNsKi8XL/o8qEPHL3GTaK89a+oaMtwd6miKxbLtDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:42.709311Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.1132","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1349fb6f9301d91c38fed5abb2e8f196de61ab0fef436d8e423c1ff2b2f3a31f","sha256:c817aa020223984403b7d7eade8a672973f9fd7ff02fd14d5bfd091787a4941e"],"state_sha256":"5b8b590ffee5aadf6ff9a53164fd7d73d29deea946aa085e6e890def446cecb0"}