{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:JH7G3MKK522J25ZJW3M6JMF7YG","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":"7a0a9b79615ea12c7dff4dd9f252139e7b4a0733b9371f5f7f9794fbfc771f71","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-02-05T03:10:16Z","title_canon_sha256":"e96d77f5daca7758b234b6341019f8ccaccc12c168c67563c3d17c8960d16cbb"},"schema_version":"1.0","source":{"id":"0902.0833","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.0833","created_at":"2026-05-18T04:17:04Z"},{"alias_kind":"arxiv_version","alias_value":"0902.0833v2","created_at":"2026-05-18T04:17:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.0833","created_at":"2026-05-18T04:17:04Z"},{"alias_kind":"pith_short_12","alias_value":"JH7G3MKK522J","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"JH7G3MKK522J25ZJ","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"JH7G3MKK","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:99499959d7858c866e7270488ab1806321bf958164a8ed4ffbd6e620d6337dfb","target":"graph","created_at":"2026-05-18T04:17:04Z","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":"For a finite Thurston type ordering < of the braid group B_{n}, we introduce a new normal form of a dual positive braid which we call the C-normal form. This normal form extends Fromentin's rotating normal form and the author's C-normal form of positive braids. Using the C-normal form, we give a combinatorial description of the restriction of the ordering < to the dual braid monoids B_{n}^{+*}. We prove that the restriction to the dual positive monoid (B_{n}^{+*},<) is a well-ordered set of order type \\omega^{\\omega^{n-2}}.","authors_text":"Tetsuya Ito","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-02-05T03:10:16Z","title":"Finite Thurston type orderings on dual braid monoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.0833","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":"sha256:8efdbf5ffe18a05c15f362b551e3727831ba4afe24664416c783ce5a5b647967","target":"record","created_at":"2026-05-18T04:17:04Z","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":"7a0a9b79615ea12c7dff4dd9f252139e7b4a0733b9371f5f7f9794fbfc771f71","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-02-05T03:10:16Z","title_canon_sha256":"e96d77f5daca7758b234b6341019f8ccaccc12c168c67563c3d17c8960d16cbb"},"schema_version":"1.0","source":{"id":"0902.0833","kind":"arxiv","version":2}},"canonical_sha256":"49fe6db14aeeb49d7729b6d9e4b0bfc198bb70010db612417ca1f2356a5e2b26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49fe6db14aeeb49d7729b6d9e4b0bfc198bb70010db612417ca1f2356a5e2b26","first_computed_at":"2026-05-18T04:17:04.727702Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:04.727702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4b1d9gMvtp1wsuc45PUvQK0sCtKr81PY3jKl4ZPJRR1CjiZs+Q4jOYKrAQzcNVKemotA8sxJnWdlcxtaabhfAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:04.728171Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.0833","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8efdbf5ffe18a05c15f362b551e3727831ba4afe24664416c783ce5a5b647967","sha256:99499959d7858c866e7270488ab1806321bf958164a8ed4ffbd6e620d6337dfb"],"state_sha256":"0ffb6fdf2f1b760f988e5ed276259bf4509164203fb37ca0e1ed99ec4cbc379c"}