{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:LUVIZRQNXM4S2UNQW35ZW47GIT","short_pith_number":"pith:LUVIZRQN","schema_version":"1.0","canonical_sha256":"5d2a8cc60dbb392d51b0b6fb9b73e644ed909d8098ef050a34451755e1b6c16e","source":{"kind":"arxiv","id":"2004.05927","version":2},"attestation_state":"computed","paper":{"title":"Vertex-reinforced jump process on the integers with nonlinear reinforcement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andrea Collevecchio, Stanislav Volkov, Tuan-Minh Nguyen","submitted_at":"2020-04-13T13:17:54Z","abstract_excerpt":"We consider a non-linear vertex-reinforced jump process (VRJP($w$)) on $\\mathbb{Z}$ with an increasing measurable weight function $w:[1,\\infty)\\to [1,\\infty)$ and initial weights equal to one. Our main goal is to study the asymptotic behaviour of VRJP($w$) depending on the integrability of the reciprocal of $w$. In particular, we prove that if $\\int_1^{\\infty} \\frac{\\text{d}u}{w(u)} =\\infty$ then the process is recurrent, i.e. it visits each vertex infinitely often and all local times are unbounded. On the other hand, if $\\int_1^{\\infty} \\frac{\\text{d} u}{w(u)} <\\infty$ and there exists a $\\rh"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2004.05927","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-04-13T13:17:54Z","cross_cats_sorted":[],"title_canon_sha256":"160791676dcb0aea3dd8e1c11c9a9732394ca7531a1abf35596298abde02f59c","abstract_canon_sha256":"3e8368d52c73a0eb9c80dc60a5ec4055e738a603722076d52ee1281ef9c2895b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:49:28.043972Z","signature_b64":"PBjVCN3xqmRbROgVFBgCJTO7x/MN9Wjuv/gkgar+it72TCW5gyWiiaSiO/QGfVN3WCqpufPpN1T/rAUi6LNMAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d2a8cc60dbb392d51b0b6fb9b73e644ed909d8098ef050a34451755e1b6c16e","last_reissued_at":"2026-07-05T04:49:28.043511Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:49:28.043511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vertex-reinforced jump process on the integers with nonlinear reinforcement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andrea Collevecchio, Stanislav Volkov, Tuan-Minh Nguyen","submitted_at":"2020-04-13T13:17:54Z","abstract_excerpt":"We consider a non-linear vertex-reinforced jump process (VRJP($w$)) on $\\mathbb{Z}$ with an increasing measurable weight function $w:[1,\\infty)\\to [1,\\infty)$ and initial weights equal to one. Our main goal is to study the asymptotic behaviour of VRJP($w$) depending on the integrability of the reciprocal of $w$. In particular, we prove that if $\\int_1^{\\infty} \\frac{\\text{d}u}{w(u)} =\\infty$ then the process is recurrent, i.e. it visits each vertex infinitely often and all local times are unbounded. On the other hand, if $\\int_1^{\\infty} \\frac{\\text{d} u}{w(u)} <\\infty$ and there exists a $\\rh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.05927","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2004.05927/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2004.05927","created_at":"2026-07-05T04:49:28.043565+00:00"},{"alias_kind":"arxiv_version","alias_value":"2004.05927v2","created_at":"2026-07-05T04:49:28.043565+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.05927","created_at":"2026-07-05T04:49:28.043565+00:00"},{"alias_kind":"pith_short_12","alias_value":"LUVIZRQNXM4S","created_at":"2026-07-05T04:49:28.043565+00:00"},{"alias_kind":"pith_short_16","alias_value":"LUVIZRQNXM4S2UNQ","created_at":"2026-07-05T04:49:28.043565+00:00"},{"alias_kind":"pith_short_8","alias_value":"LUVIZRQN","created_at":"2026-07-05T04:49:28.043565+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/LUVIZRQNXM4S2UNQW35ZW47GIT","json":"https://pith.science/pith/LUVIZRQNXM4S2UNQW35ZW47GIT.json","graph_json":"https://pith.science/api/pith-number/LUVIZRQNXM4S2UNQW35ZW47GIT/graph.json","events_json":"https://pith.science/api/pith-number/LUVIZRQNXM4S2UNQW35ZW47GIT/events.json","paper":"https://pith.science/paper/LUVIZRQN"},"agent_actions":{"view_html":"https://pith.science/pith/LUVIZRQNXM4S2UNQW35ZW47GIT","download_json":"https://pith.science/pith/LUVIZRQNXM4S2UNQW35ZW47GIT.json","view_paper":"https://pith.science/paper/LUVIZRQN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2004.05927&json=true","fetch_graph":"https://pith.science/api/pith-number/LUVIZRQNXM4S2UNQW35ZW47GIT/graph.json","fetch_events":"https://pith.science/api/pith-number/LUVIZRQNXM4S2UNQW35ZW47GIT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LUVIZRQNXM4S2UNQW35ZW47GIT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LUVIZRQNXM4S2UNQW35ZW47GIT/action/storage_attestation","attest_author":"https://pith.science/pith/LUVIZRQNXM4S2UNQW35ZW47GIT/action/author_attestation","sign_citation":"https://pith.science/pith/LUVIZRQNXM4S2UNQW35ZW47GIT/action/citation_signature","submit_replication":"https://pith.science/pith/LUVIZRQNXM4S2UNQW35ZW47GIT/action/replication_record"}},"created_at":"2026-07-05T04:49:28.043565+00:00","updated_at":"2026-07-05T04:49:28.043565+00:00"}