{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:GXYRYN72CHFNTVPWLFQ3NNZXC3","short_pith_number":"pith:GXYRYN72","schema_version":"1.0","canonical_sha256":"35f11c37fa11cad9d5f65961b6b73716ec56b2b584e3557474a6409ef762ef89","source":{"kind":"arxiv","id":"2308.07303","version":1},"attestation_state":"computed","paper":{"title":"Finite range interlacements and couplings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Augusto Teixeira, Franco Severo, Hugo Duminil-Copin, Pierre-Fran\\c{c}ois Rodriguez, Subhajit Goswami","submitted_at":"2023-08-14T17:42:52Z","abstract_excerpt":"In this article, we consider the interlacement set $\\mathcal{I}^u$ at level $u>0$ on $\\mathbb{Z}^d$, $d \\geq3$, and its finite range version $\\mathcal{I}^{u,L}$ for $L >0$, given by the union of the ranges of a Poisson cloud of random walks on $\\mathbb{Z}^d$ having intensity $u/L$ and killed after $L$ steps. As $L\\to \\infty$, the random set $\\mathcal{I}^{u,L}$ has a non-trivial (local) limit, which is precisely $\\mathcal{I}^u$. A natural question is to understand how the sets $\\mathcal{I}^{u,L}$ and $\\mathcal{I}^{{u}}$ can be related, if at all, in such a way that their intersections with a bo"},"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":"2308.07303","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-08-14T17:42:52Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"3c59ffd3d328a9b5d91a33173d0c52b3a7286ee132167692cdf2a47d694ff924","abstract_canon_sha256":"953357073c6ba8f585c16e8295e19ba213be5ce7f9ed44a555bcf814e7b51e9f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:40:58.971686Z","signature_b64":"C5JdhFK5n1eedaFDMWr01zK6FGb5hImKisZi7isIw5PesvVqb95BPmMsRY5Tp7lKXTfsfGLLF7aFgckNz2sJCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35f11c37fa11cad9d5f65961b6b73716ec56b2b584e3557474a6409ef762ef89","last_reissued_at":"2026-07-05T06:40:58.971249Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:40:58.971249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite range interlacements and couplings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Augusto Teixeira, Franco Severo, Hugo Duminil-Copin, Pierre-Fran\\c{c}ois Rodriguez, Subhajit Goswami","submitted_at":"2023-08-14T17:42:52Z","abstract_excerpt":"In this article, we consider the interlacement set $\\mathcal{I}^u$ at level $u>0$ on $\\mathbb{Z}^d$, $d \\geq3$, and its finite range version $\\mathcal{I}^{u,L}$ for $L >0$, given by the union of the ranges of a Poisson cloud of random walks on $\\mathbb{Z}^d$ having intensity $u/L$ and killed after $L$ steps. As $L\\to \\infty$, the random set $\\mathcal{I}^{u,L}$ has a non-trivial (local) limit, which is precisely $\\mathcal{I}^u$. A natural question is to understand how the sets $\\mathcal{I}^{u,L}$ and $\\mathcal{I}^{{u}}$ can be related, if at all, in such a way that their intersections with a bo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.07303","kind":"arxiv","version":1},"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/2308.07303/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":"2308.07303","created_at":"2026-07-05T06:40:58.971300+00:00"},{"alias_kind":"arxiv_version","alias_value":"2308.07303v1","created_at":"2026-07-05T06:40:58.971300+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.07303","created_at":"2026-07-05T06:40:58.971300+00:00"},{"alias_kind":"pith_short_12","alias_value":"GXYRYN72CHFN","created_at":"2026-07-05T06:40:58.971300+00:00"},{"alias_kind":"pith_short_16","alias_value":"GXYRYN72CHFNTVPW","created_at":"2026-07-05T06:40:58.971300+00:00"},{"alias_kind":"pith_short_8","alias_value":"GXYRYN72","created_at":"2026-07-05T06:40:58.971300+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.26869","citing_title":"Law of Large Numbers for a random walk on dynamic environments with drift","ref_index":15,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GXYRYN72CHFNTVPWLFQ3NNZXC3","json":"https://pith.science/pith/GXYRYN72CHFNTVPWLFQ3NNZXC3.json","graph_json":"https://pith.science/api/pith-number/GXYRYN72CHFNTVPWLFQ3NNZXC3/graph.json","events_json":"https://pith.science/api/pith-number/GXYRYN72CHFNTVPWLFQ3NNZXC3/events.json","paper":"https://pith.science/paper/GXYRYN72"},"agent_actions":{"view_html":"https://pith.science/pith/GXYRYN72CHFNTVPWLFQ3NNZXC3","download_json":"https://pith.science/pith/GXYRYN72CHFNTVPWLFQ3NNZXC3.json","view_paper":"https://pith.science/paper/GXYRYN72","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2308.07303&json=true","fetch_graph":"https://pith.science/api/pith-number/GXYRYN72CHFNTVPWLFQ3NNZXC3/graph.json","fetch_events":"https://pith.science/api/pith-number/GXYRYN72CHFNTVPWLFQ3NNZXC3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GXYRYN72CHFNTVPWLFQ3NNZXC3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GXYRYN72CHFNTVPWLFQ3NNZXC3/action/storage_attestation","attest_author":"https://pith.science/pith/GXYRYN72CHFNTVPWLFQ3NNZXC3/action/author_attestation","sign_citation":"https://pith.science/pith/GXYRYN72CHFNTVPWLFQ3NNZXC3/action/citation_signature","submit_replication":"https://pith.science/pith/GXYRYN72CHFNTVPWLFQ3NNZXC3/action/replication_record"}},"created_at":"2026-07-05T06:40:58.971300+00:00","updated_at":"2026-07-05T06:40:58.971300+00:00"}