{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:BPTJUGJXZCJSNRALMCEXT3WRUD","short_pith_number":"pith:BPTJUGJX","schema_version":"1.0","canonical_sha256":"0be69a1937c89326c40b608979eed1a0e331a99761ccc6d7a12477ccb79dbe76","source":{"kind":"arxiv","id":"1309.7018","version":3},"attestation_state":"computed","paper":{"title":"Eulerian cube complexes and reciprocity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Richard Scott","submitted_at":"2013-09-26T19:12:32Z","abstract_excerpt":"Let $G$ be the fundamental group of a compact nonpositively curved cube complex $Y$. With respect to a basepoint $x$, one obtains an integer-valued length function on $G$ by counting the number of edges in a minimal length edge-path representing each group element. The growth series of $G$ with respect to $x$ is then defined to be the power series $G_x(t)=\\sum_g t^{|g|}$ where $|g|$ denotes the length of $g$. Using the fact that $G$ admits a suitable automatic structure, $G_x(t)$ can be shown to be a rational function. We prove that if $Y$ is a manifold of dimension $n$, then this rational fun"},"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":"1309.7018","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-09-26T19:12:32Z","cross_cats_sorted":[],"title_canon_sha256":"f0a4af4b8ad0ace8f5dfc408d5a793897c24bc34d52dfcc5bda4875278474688","abstract_canon_sha256":"cc895aa6aed6049ac8eb1f2572e8bc1ebb06a987c74b43074096c6ccfdfda03c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:24.875689Z","signature_b64":"vAeDSDZd3t3OMWt0qCCWjGyJuanTMt4xgIP+28TxB1SW+m/yfukXFT4GglT4+OfRZmoWZ2tfhGZL7TU2BWiDDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0be69a1937c89326c40b608979eed1a0e331a99761ccc6d7a12477ccb79dbe76","last_reissued_at":"2026-05-18T01:22:24.875115Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:24.875115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Eulerian cube complexes and reciprocity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Richard Scott","submitted_at":"2013-09-26T19:12:32Z","abstract_excerpt":"Let $G$ be the fundamental group of a compact nonpositively curved cube complex $Y$. With respect to a basepoint $x$, one obtains an integer-valued length function on $G$ by counting the number of edges in a minimal length edge-path representing each group element. The growth series of $G$ with respect to $x$ is then defined to be the power series $G_x(t)=\\sum_g t^{|g|}$ where $|g|$ denotes the length of $g$. Using the fact that $G$ admits a suitable automatic structure, $G_x(t)$ can be shown to be a rational function. We prove that if $Y$ is a manifold of dimension $n$, then this rational fun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7018","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":"1309.7018","created_at":"2026-05-18T01:22:24.875185+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.7018v3","created_at":"2026-05-18T01:22:24.875185+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7018","created_at":"2026-05-18T01:22:24.875185+00:00"},{"alias_kind":"pith_short_12","alias_value":"BPTJUGJXZCJS","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"BPTJUGJXZCJSNRAL","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"BPTJUGJX","created_at":"2026-05-18T12:27:40.988391+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/BPTJUGJXZCJSNRALMCEXT3WRUD","json":"https://pith.science/pith/BPTJUGJXZCJSNRALMCEXT3WRUD.json","graph_json":"https://pith.science/api/pith-number/BPTJUGJXZCJSNRALMCEXT3WRUD/graph.json","events_json":"https://pith.science/api/pith-number/BPTJUGJXZCJSNRALMCEXT3WRUD/events.json","paper":"https://pith.science/paper/BPTJUGJX"},"agent_actions":{"view_html":"https://pith.science/pith/BPTJUGJXZCJSNRALMCEXT3WRUD","download_json":"https://pith.science/pith/BPTJUGJXZCJSNRALMCEXT3WRUD.json","view_paper":"https://pith.science/paper/BPTJUGJX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.7018&json=true","fetch_graph":"https://pith.science/api/pith-number/BPTJUGJXZCJSNRALMCEXT3WRUD/graph.json","fetch_events":"https://pith.science/api/pith-number/BPTJUGJXZCJSNRALMCEXT3WRUD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BPTJUGJXZCJSNRALMCEXT3WRUD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BPTJUGJXZCJSNRALMCEXT3WRUD/action/storage_attestation","attest_author":"https://pith.science/pith/BPTJUGJXZCJSNRALMCEXT3WRUD/action/author_attestation","sign_citation":"https://pith.science/pith/BPTJUGJXZCJSNRALMCEXT3WRUD/action/citation_signature","submit_replication":"https://pith.science/pith/BPTJUGJXZCJSNRALMCEXT3WRUD/action/replication_record"}},"created_at":"2026-05-18T01:22:24.875185+00:00","updated_at":"2026-05-18T01:22:24.875185+00:00"}