{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3ZQMW62LTKAJDI2F5PEBCPRUFE","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":"e781ac5e9118c03e63a5373c31ba6ee08bae8f2d18cd91751b15dee9f23973bf","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-09-13T11:59:31Z","title_canon_sha256":"acb8b1e76346b91ddb43cec7dc760679a3951e65e241c8826d47bec332ab40c1"},"schema_version":"1.0","source":{"id":"1809.04899","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.04899","created_at":"2026-05-18T00:05:47Z"},{"alias_kind":"arxiv_version","alias_value":"1809.04899v1","created_at":"2026-05-18T00:05:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.04899","created_at":"2026-05-18T00:05:47Z"},{"alias_kind":"pith_short_12","alias_value":"3ZQMW62LTKAJ","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"3ZQMW62LTKAJDI2F","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"3ZQMW62L","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:5125837810150049adff51c4322dc3299dad0fbfad01ecffabfb5f3cb1244443","target":"graph","created_at":"2026-05-18T00:05:47Z","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":"Define the augmented square twist origami crease pattern to be the classic square twist crease pattern with one crease added along a diagonal of the twisted square. In this paper we fully describe the rigid foldability of this new crease pattern. Specifically, the extra crease allows the square twist to rigidly fold in ways the original cannot. We prove that there are exactly four non-degenerate rigid foldings of this crease pattern from the unfolded state.","authors_text":"Michael T. Urbanski, Thomas C. Hull","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-09-13T11:59:31Z","title":"Rigid foldability of the augmented square twist"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.04899","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:d756da1be74b780ccbf0098056a3a736897088b584a273834c7ff1ec01547639","target":"record","created_at":"2026-05-18T00:05:47Z","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":"e781ac5e9118c03e63a5373c31ba6ee08bae8f2d18cd91751b15dee9f23973bf","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-09-13T11:59:31Z","title_canon_sha256":"acb8b1e76346b91ddb43cec7dc760679a3951e65e241c8826d47bec332ab40c1"},"schema_version":"1.0","source":{"id":"1809.04899","kind":"arxiv","version":1}},"canonical_sha256":"de60cb7b4b9a8091a345ebc8113e34290402c23f2a8a5245047fd5c9336a6f2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de60cb7b4b9a8091a345ebc8113e34290402c23f2a8a5245047fd5c9336a6f2d","first_computed_at":"2026-05-18T00:05:47.158273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:47.158273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wrqUYpfxi0j0rccvA5/MRxy5NAtjXITbDNcr4VFJBd0ugHw70nSx2maT3/9PfbpMkhK/WtWXrhaZ7h+t4CFDDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:47.158946Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.04899","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d756da1be74b780ccbf0098056a3a736897088b584a273834c7ff1ec01547639","sha256:5125837810150049adff51c4322dc3299dad0fbfad01ecffabfb5f3cb1244443"],"state_sha256":"14cf1a36d2d8bd5d4a0aa69729b587a3d0f3b811c4c71ff809cfb6407abc8104"}