{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2SEV3VPTFFZLKLCSAOGYJWRNJS","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":"b3fe52a38e9d30df06b18f31f7554e0439f6a11d1aa93a3ef0a5691f013886ae","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-24T18:45:03Z","title_canon_sha256":"ece7178e07125188e478d316fbbeb4687a6a13ca4fc1029536bb7ed7d2a92fdc"},"schema_version":"1.0","source":{"id":"1403.6079","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6079","created_at":"2026-05-18T02:43:54Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6079v2","created_at":"2026-05-18T02:43:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6079","created_at":"2026-05-18T02:43:54Z"},{"alias_kind":"pith_short_12","alias_value":"2SEV3VPTFFZL","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2SEV3VPTFFZLKLCS","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2SEV3VPT","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:16d26d3f7dcf30b01070d82a5616e5a0450289b2bea0589bb914dca1e3442a53","target":"graph","created_at":"2026-05-18T02:43:54Z","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 show transience of the edge-reinforced random walk (ERRW) for small reinforcement in dimension d greater than 2. This proves the existence of a phase transition between recurrent and transient behavior, thus solving an open problem stated by Diaconis in 1986. The argument adapts the proof of quasi-diffusive behavior of the SuSy hyperbolic model for fixed conductances by Disertori, Spencer and Zirnbauer [CMP 2010], using the representation of ERRW as a mixture of vertex-reinforced jump processes (VRJP) with independent gamma conductances, and the interpretation of the limit law of VRJP as a ","authors_text":"Christophe Sabot, Margherita Disertori, Pierre Tarr\\`es","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-24T18:45:03Z","title":"Transience of Edge-Reinforced Random Walk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6079","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:dd092b6f7ec9a4066856a0783fd739b87a3b7c6e05fb143d547840d770be7ac9","target":"record","created_at":"2026-05-18T02:43:54Z","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":"b3fe52a38e9d30df06b18f31f7554e0439f6a11d1aa93a3ef0a5691f013886ae","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-24T18:45:03Z","title_canon_sha256":"ece7178e07125188e478d316fbbeb4687a6a13ca4fc1029536bb7ed7d2a92fdc"},"schema_version":"1.0","source":{"id":"1403.6079","kind":"arxiv","version":2}},"canonical_sha256":"d4895dd5f32972b52c52038d84da2d4cb439bb273caac1d0847636bd7c5cc94d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4895dd5f32972b52c52038d84da2d4cb439bb273caac1d0847636bd7c5cc94d","first_computed_at":"2026-05-18T02:43:54.005037Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:54.005037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8C+LORykIM9UzeWSGIFG/ddXhqzKscb60e9BT5K3CCt+3tNmWVd2WBFvI+NiP25Mfq38kIhfmoUXaVHSe8i1Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:54.005463Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.6079","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd092b6f7ec9a4066856a0783fd739b87a3b7c6e05fb143d547840d770be7ac9","sha256:16d26d3f7dcf30b01070d82a5616e5a0450289b2bea0589bb914dca1e3442a53"],"state_sha256":"bf40df41a0a11d33e528189112cc2f38da4fd65383cd66b6763e61b1d6a54f6a"}