{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:JGMFSZ2ENEYBG7TDWNDQ5URE5R","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":"a08b21a258ac688f0c9614277c4cf488222c7b64dd782cee59d31e93f9441d67","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-03-05T15:22:20Z","title_canon_sha256":"f5998366bfae89eed471f5998c1c906436d38f5bad18632fb38db67f329cb1a1"},"schema_version":"1.0","source":{"id":"1003.1289","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.1289","created_at":"2026-05-18T04:34:01Z"},{"alias_kind":"arxiv_version","alias_value":"1003.1289v2","created_at":"2026-05-18T04:34:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.1289","created_at":"2026-05-18T04:34:01Z"},{"alias_kind":"pith_short_12","alias_value":"JGMFSZ2ENEYB","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JGMFSZ2ENEYBG7TD","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JGMFSZ2E","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:08669667b28d06ff7004a8c0d88b5c1dbc4c4cbca7edc46f7e561c6ea6eb20c3","target":"graph","created_at":"2026-05-18T04:34:01Z","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":"The vacant set of random interlacements on ${\\mathbb{Z}}^d$, $d\\ge3$, has nontrivial percolative properties. It is known from Sznitman [Ann. Math. 171 (2010) 2039--2087], Sidoravicius and Sznitman [Comm. Pure Appl. Math. 62 (2009) 831--858] that there is a nondegenerate critical value $u_*$ such that the vacant set at level $u$ percolates when $u<u_*$ and does not percolate when $u>u_*$. We derive here an asymptotic upper bound on $u_*$, as $d$ goes to infinity, which complements the lower bound from Sznitman [Probab. Theory Related Fields, to appear]. Our main result shows that $u_*$ is equiv","authors_text":"Alain-Sol Sznitman","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-03-05T15:22:20Z","title":"On the critical parameter of interlacement percolation in high dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.1289","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:be58e01bcaf5d6f08bf42f99855e33daae796fc1d77a9cc36e02526631ea36ed","target":"record","created_at":"2026-05-18T04:34:01Z","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":"a08b21a258ac688f0c9614277c4cf488222c7b64dd782cee59d31e93f9441d67","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-03-05T15:22:20Z","title_canon_sha256":"f5998366bfae89eed471f5998c1c906436d38f5bad18632fb38db67f329cb1a1"},"schema_version":"1.0","source":{"id":"1003.1289","kind":"arxiv","version":2}},"canonical_sha256":"49985967446930137e63b3470ed224ec46e280551c0a0de2b97dcb1700da06ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49985967446930137e63b3470ed224ec46e280551c0a0de2b97dcb1700da06ff","first_computed_at":"2026-05-18T04:34:01.420166Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:01.420166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eTmoaX0x71b4FtcOF9HFdsq9LpEpd7XkEP6/kr6NSM6uzstgFqCJfaSbTPii+3jt5BJRK5BAsp17LkLXXcLLBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:01.420646Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.1289","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be58e01bcaf5d6f08bf42f99855e33daae796fc1d77a9cc36e02526631ea36ed","sha256:08669667b28d06ff7004a8c0d88b5c1dbc4c4cbca7edc46f7e561c6ea6eb20c3"],"state_sha256":"c254e927cc45635cfb4b5e7641c9685b2a71ee1f5834346b7719f3bbf59328e1"}