{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:UCU3YWLFMEFGUGAIV66OPYZBOZ","short_pith_number":"pith:UCU3YWLF","schema_version":"1.0","canonical_sha256":"a0a9bc5965610a6a1808afbce7e32176499a6a393dda968a0883ae6bd37e88c0","source":{"kind":"arxiv","id":"1501.00476","version":5},"attestation_state":"computed","paper":{"title":"Connective constants and height functions for Cayley graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.GR","math.MP","math.PR"],"primary_cat":"math.CO","authors_text":"Geoffrey R. Grimmett, Zhongyang Li","submitted_at":"2015-01-02T20:34:06Z","abstract_excerpt":"The connective constant $\\mu(G)$ of an infinite transitive graph $G$ is the exponential growth rate of the number of self-avoiding walks from a given origin. In earlier work of Grimmett and Li, a locality theorem was proved for connective constants, namely, that the connective constants of two graphs are close in value whenever the graphs agree on a large ball around the origin. A condition of the theorem was that the graphs support so-called 'unimodular graph height functions'. When the graphs are Cayley graphs of infinite, finitely generated groups, there is a special type of unimodular grap"},"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":"1501.00476","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-02T20:34:06Z","cross_cats_sorted":["math-ph","math.GR","math.MP","math.PR"],"title_canon_sha256":"a1bd960f57b2b59ae6ed5e26a6a1e48718692bc9165c9a7d507535100fbed4a4","abstract_canon_sha256":"9a68ccc2d121df62658ae07479fcbacc9ac4efb4a6e0a5917ea0c91b02519f4a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:26.732186Z","signature_b64":"Fr9PiGV4J0zrzBc6F2I8G+S8s902KJDRc11xb1bLJT4AxWJ0AJ/97XVE6G2tMWgN8FA800vIWrSbNg9wVaV0AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0a9bc5965610a6a1808afbce7e32176499a6a393dda968a0883ae6bd37e88c0","last_reissued_at":"2026-05-18T01:08:26.731501Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:26.731501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Connective constants and height functions for Cayley graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.GR","math.MP","math.PR"],"primary_cat":"math.CO","authors_text":"Geoffrey R. Grimmett, Zhongyang Li","submitted_at":"2015-01-02T20:34:06Z","abstract_excerpt":"The connective constant $\\mu(G)$ of an infinite transitive graph $G$ is the exponential growth rate of the number of self-avoiding walks from a given origin. In earlier work of Grimmett and Li, a locality theorem was proved for connective constants, namely, that the connective constants of two graphs are close in value whenever the graphs agree on a large ball around the origin. A condition of the theorem was that the graphs support so-called 'unimodular graph height functions'. When the graphs are Cayley graphs of infinite, finitely generated groups, there is a special type of unimodular grap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00476","kind":"arxiv","version":5},"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":"1501.00476","created_at":"2026-05-18T01:08:26.731611+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.00476v5","created_at":"2026-05-18T01:08:26.731611+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00476","created_at":"2026-05-18T01:08:26.731611+00:00"},{"alias_kind":"pith_short_12","alias_value":"UCU3YWLFMEFG","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"UCU3YWLFMEFGUGAI","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"UCU3YWLF","created_at":"2026-05-18T12:29:44.643036+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/UCU3YWLFMEFGUGAIV66OPYZBOZ","json":"https://pith.science/pith/UCU3YWLFMEFGUGAIV66OPYZBOZ.json","graph_json":"https://pith.science/api/pith-number/UCU3YWLFMEFGUGAIV66OPYZBOZ/graph.json","events_json":"https://pith.science/api/pith-number/UCU3YWLFMEFGUGAIV66OPYZBOZ/events.json","paper":"https://pith.science/paper/UCU3YWLF"},"agent_actions":{"view_html":"https://pith.science/pith/UCU3YWLFMEFGUGAIV66OPYZBOZ","download_json":"https://pith.science/pith/UCU3YWLFMEFGUGAIV66OPYZBOZ.json","view_paper":"https://pith.science/paper/UCU3YWLF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.00476&json=true","fetch_graph":"https://pith.science/api/pith-number/UCU3YWLFMEFGUGAIV66OPYZBOZ/graph.json","fetch_events":"https://pith.science/api/pith-number/UCU3YWLFMEFGUGAIV66OPYZBOZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UCU3YWLFMEFGUGAIV66OPYZBOZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UCU3YWLFMEFGUGAIV66OPYZBOZ/action/storage_attestation","attest_author":"https://pith.science/pith/UCU3YWLFMEFGUGAIV66OPYZBOZ/action/author_attestation","sign_citation":"https://pith.science/pith/UCU3YWLFMEFGUGAIV66OPYZBOZ/action/citation_signature","submit_replication":"https://pith.science/pith/UCU3YWLFMEFGUGAIV66OPYZBOZ/action/replication_record"}},"created_at":"2026-05-18T01:08:26.731611+00:00","updated_at":"2026-05-18T01:08:26.731611+00:00"}