{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LNZJKCSNXKRZEHYMRGKCILXTOR","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":"fa7dc3fcaa219821e6ea166be0abc812d4a388b191b5960f2a460951c02bf1fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-27T13:51:09Z","title_canon_sha256":"1c667d1fdf496ea8bf4e1c6cf7206a90d35c7e22a38940f31cfe630c3d833131"},"schema_version":"1.0","source":{"id":"1711.09687","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.09687","created_at":"2026-05-18T00:11:11Z"},{"alias_kind":"arxiv_version","alias_value":"1711.09687v2","created_at":"2026-05-18T00:11:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.09687","created_at":"2026-05-18T00:11:11Z"},{"alias_kind":"pith_short_12","alias_value":"LNZJKCSNXKRZ","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LNZJKCSNXKRZEHYM","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LNZJKCSN","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:0f5e7abad0015a26ffe6edba2022f510386a1147746f327c253ce792bf1d79e3","target":"graph","created_at":"2026-05-18T00:11:11Z","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":"Let $R$ be an arbitrary subset of a commutative ring. We introduce a combinatorial model for the set of tame frieze patterns with entries in $R$ based on a notion of irreducibility of frieze patterns. When $R$ is a ring, then a frieze pattern is reducible if and only if it contains an entry (not on the border) which is $1$ or $-1$. To my knowledge, this model generalizes simultaneously all previously presented models for tame frieze patterns bounded by $0$'s and $1$'s.","authors_text":"Michael Cuntz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-27T13:51:09Z","title":"A combinatorial model for tame frieze patterns"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09687","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":"sha256:006ebe97cbe5f4919a30889efc00c8d40a23f2adb6996d35f7d6df87d6f582c3","target":"record","created_at":"2026-05-18T00:11:11Z","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":"fa7dc3fcaa219821e6ea166be0abc812d4a388b191b5960f2a460951c02bf1fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-27T13:51:09Z","title_canon_sha256":"1c667d1fdf496ea8bf4e1c6cf7206a90d35c7e22a38940f31cfe630c3d833131"},"schema_version":"1.0","source":{"id":"1711.09687","kind":"arxiv","version":2}},"canonical_sha256":"5b72950a4dbaa3921f0c8994242ef374461e75835e71c09d385ce713b756e8a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b72950a4dbaa3921f0c8994242ef374461e75835e71c09d385ce713b756e8a1","first_computed_at":"2026-05-18T00:11:11.378419Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:11.378419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BF0XMawEv4qyoQde7dKUTyPCQiS9K1bh13D0k/OOSoHxkwae6BTpHh7sBZvGiSHs2k3ndIeiSMSI7g8D3H/+CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:11.379197Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.09687","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:006ebe97cbe5f4919a30889efc00c8d40a23f2adb6996d35f7d6df87d6f582c3","sha256:0f5e7abad0015a26ffe6edba2022f510386a1147746f327c253ce792bf1d79e3"],"state_sha256":"39417712fb62ed8a68d1513727953831475379b53c8ffca2f7a96556f2bd57db"}