{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:7GD3BQ37QG7NP52A2PJPXLCDEK","short_pith_number":"pith:7GD3BQ37","schema_version":"1.0","canonical_sha256":"f987b0c37f81bed7f740d3d2fbac4322a62a9bf66abb50e0536e43b6ea6ec559","source":{"kind":"arxiv","id":"1301.0873","version":3},"attestation_state":"computed","paper":{"title":"Infinite reduced words and the Tits boundary of a Coxeter group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GT","math.RT"],"primary_cat":"math.GR","authors_text":"Anne Thomas, Thomas Lam","submitted_at":"2013-01-05T05:34:50Z","abstract_excerpt":"Let (W,S) be a finite rank Coxeter system with W infinite. We prove that the limit weak order on the blocks of infinite reduced words of W is encoded by the topology of the Tits boundary of the Davis complex X of W. We consider many special cases, including W word hyperbolic, and X with isolated flats. We establish that when W is word hyperbolic, the limit weak order is the disjoint union of weak orders of finite Coxeter groups. We also establish, for each boundary point \\xi, a natural order-preserving correspondence between infinite reduced words which \"point towards\" \\xi, and elements of the"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1301.0873","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-01-05T05:34:50Z","cross_cats_sorted":["math.CO","math.GT","math.RT"],"title_canon_sha256":"83ae8d8e4af3d0918b98f612fa2855936118fbeeb1ad104b6cfc563fdd6ab4f3","abstract_canon_sha256":"12c38f2f7f5336c1760f7b65559de73dcd97871f288daee5b7e237d26ba826a2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:37.494480Z","signature_b64":"8BQI2KfsZdb5vnRmt9P0nejRkEit0Yw/KuPXAl4FTEs6iKS+ZZlIsLGth9MMeLteBeQGq5L0RZ9eNyFQc+kkCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f987b0c37f81bed7f740d3d2fbac4322a62a9bf66abb50e0536e43b6ea6ec559","last_reissued_at":"2026-05-18T02:42:37.493936Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:37.493936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Infinite reduced words and the Tits boundary of a Coxeter group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GT","math.RT"],"primary_cat":"math.GR","authors_text":"Anne Thomas, Thomas Lam","submitted_at":"2013-01-05T05:34:50Z","abstract_excerpt":"Let (W,S) be a finite rank Coxeter system with W infinite. We prove that the limit weak order on the blocks of infinite reduced words of W is encoded by the topology of the Tits boundary of the Davis complex X of W. We consider many special cases, including W word hyperbolic, and X with isolated flats. We establish that when W is word hyperbolic, the limit weak order is the disjoint union of weak orders of finite Coxeter groups. We also establish, for each boundary point \\xi, a natural order-preserving correspondence between infinite reduced words which \"point towards\" \\xi, and elements of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0873","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1301.0873","created_at":"2026-05-18T02:42:37.494025+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.0873v3","created_at":"2026-05-18T02:42:37.494025+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0873","created_at":"2026-05-18T02:42:37.494025+00:00"},{"alias_kind":"pith_short_12","alias_value":"7GD3BQ37QG7N","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"7GD3BQ37QG7NP52A","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"7GD3BQ37","created_at":"2026-05-18T12:27:36.564083+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7GD3BQ37QG7NP52A2PJPXLCDEK","json":"https://pith.science/pith/7GD3BQ37QG7NP52A2PJPXLCDEK.json","graph_json":"https://pith.science/api/pith-number/7GD3BQ37QG7NP52A2PJPXLCDEK/graph.json","events_json":"https://pith.science/api/pith-number/7GD3BQ37QG7NP52A2PJPXLCDEK/events.json","paper":"https://pith.science/paper/7GD3BQ37"},"agent_actions":{"view_html":"https://pith.science/pith/7GD3BQ37QG7NP52A2PJPXLCDEK","download_json":"https://pith.science/pith/7GD3BQ37QG7NP52A2PJPXLCDEK.json","view_paper":"https://pith.science/paper/7GD3BQ37","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.0873&json=true","fetch_graph":"https://pith.science/api/pith-number/7GD3BQ37QG7NP52A2PJPXLCDEK/graph.json","fetch_events":"https://pith.science/api/pith-number/7GD3BQ37QG7NP52A2PJPXLCDEK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7GD3BQ37QG7NP52A2PJPXLCDEK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7GD3BQ37QG7NP52A2PJPXLCDEK/action/storage_attestation","attest_author":"https://pith.science/pith/7GD3BQ37QG7NP52A2PJPXLCDEK/action/author_attestation","sign_citation":"https://pith.science/pith/7GD3BQ37QG7NP52A2PJPXLCDEK/action/citation_signature","submit_replication":"https://pith.science/pith/7GD3BQ37QG7NP52A2PJPXLCDEK/action/replication_record"}},"created_at":"2026-05-18T02:42:37.494025+00:00","updated_at":"2026-05-18T02:42:37.494025+00:00"}