{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:A7H44ODGVAANXQF5Y7I7JJQ7TW","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":"79c628e4416d4006b8e2d71d752c196b50a5d1f76d4b3579e653623b585b9eed","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-29T17:50:06Z","title_canon_sha256":"586181778c905357662b53c751ac0f159d49cba484e203ca799587d761d0d7d5"},"schema_version":"1.0","source":{"id":"1709.10515","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.10515","created_at":"2026-05-18T00:00:43Z"},{"alias_kind":"arxiv_version","alias_value":"1709.10515v2","created_at":"2026-05-18T00:00:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.10515","created_at":"2026-05-18T00:00:43Z"},{"alias_kind":"pith_short_12","alias_value":"A7H44ODGVAAN","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"A7H44ODGVAANXQF5","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"A7H44ODG","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:3f1448726eda3082ca5a231121e1af2d49253c538de6beee939f1d9b79e3a0c6","target":"graph","created_at":"2026-05-18T00:00:43Z","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":"We study self-avoiding walk on graphs whose automorphism group has a transitive nonunimodular subgroup. We prove that self-avoiding walk is ballistic, that the bubble diagram converges at criticality, and that the critical two-point function decays exponentially in the distance from the origin. This implies that the critical exponent governing the susceptibility takes its mean-field value, and hence that the number of self-avoiding walks of length $n$ is comparable to the $n$th power of the connective constant. We also prove that the same results hold for a large class of repulsive walk models","authors_text":"Tom Hutchcroft","cross_cats":["math-ph","math.CO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-29T17:50:06Z","title":"Self-avoiding walk on nonunimodular transitive graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.10515","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":"sha256:9de5bad80b97f363622e67397803d8ca981f6067bdd5c5e35ef9b33d20eb38b7","target":"record","created_at":"2026-05-18T00:00:43Z","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":"79c628e4416d4006b8e2d71d752c196b50a5d1f76d4b3579e653623b585b9eed","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-29T17:50:06Z","title_canon_sha256":"586181778c905357662b53c751ac0f159d49cba484e203ca799587d761d0d7d5"},"schema_version":"1.0","source":{"id":"1709.10515","kind":"arxiv","version":2}},"canonical_sha256":"07cfce3866a800dbc0bdc7d1f4a61f9dae68fe9b24071d3120cd0a40ed2b0e5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07cfce3866a800dbc0bdc7d1f4a61f9dae68fe9b24071d3120cd0a40ed2b0e5c","first_computed_at":"2026-05-18T00:00:43.675957Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:43.675957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5OGlclRuBClVOoSg9V/X9I/2RlqUbX7be1Amxhx9uw8LncsC0J1+R3Hm5RwbtQu65OIPWBzdRurR1Ltb4AM+Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:43.676308Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.10515","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9de5bad80b97f363622e67397803d8ca981f6067bdd5c5e35ef9b33d20eb38b7","sha256:3f1448726eda3082ca5a231121e1af2d49253c538de6beee939f1d9b79e3a0c6"],"state_sha256":"73eb8ca79ad8240159dab2bff287d40d018532005117ebab89a4ff7bfed80175"}