{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:PERJBTYWEXHP3NWNA76R3EV5UL","short_pith_number":"pith:PERJBTYW","schema_version":"1.0","canonical_sha256":"792290cf1625cefdb6cd07fd1d92bda2c37617ba551318f484a9c982babb17e1","source":{"kind":"arxiv","id":"1908.07872","version":3},"attestation_state":"computed","paper":{"title":"Functional CLT for the range of stable random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Nikola Sandri\\'c, Stjepan \\v{S}ebek, Wojciech Cygan","submitted_at":"2019-08-21T13:52:27Z","abstract_excerpt":"In this note, we establish a functional central limit theorem for the capacity of the range for a class of $\\alpha$-stable random walks on the integer lattice $\\mathbb{Z}^d$ with $d > 5\\alpha/2$. Using similar methods, we also prove an analogous result for the cardinality of the range when $d > 3\\alpha / 2$."},"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":"1908.07872","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-08-21T13:52:27Z","cross_cats_sorted":[],"title_canon_sha256":"9539e1b01bbe301b7d45a2400a2f8dadf4faf6f33d6f3774c124925432655573","abstract_canon_sha256":"4963028f71d62ec0b006a92b60e6747c31c27668c0736efdfdcb716547fbbb1e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:35:25.190305Z","signature_b64":"EgvdiPtjm31zDH9jTOaakMLfs7Ifn2V+k0UlglO69k83jm5hNfshsI0NKs56zbqeUgrwceOIQ39CUlf1ikugBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"792290cf1625cefdb6cd07fd1d92bda2c37617ba551318f484a9c982babb17e1","last_reissued_at":"2026-07-05T01:35:25.189898Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:35:25.189898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Functional CLT for the range of stable random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Nikola Sandri\\'c, Stjepan \\v{S}ebek, Wojciech Cygan","submitted_at":"2019-08-21T13:52:27Z","abstract_excerpt":"In this note, we establish a functional central limit theorem for the capacity of the range for a class of $\\alpha$-stable random walks on the integer lattice $\\mathbb{Z}^d$ with $d > 5\\alpha/2$. Using similar methods, we also prove an analogous result for the cardinality of the range when $d > 3\\alpha / 2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07872","kind":"arxiv","version":3},"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/1908.07872/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":"1908.07872","created_at":"2026-07-05T01:35:25.189956+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.07872v3","created_at":"2026-07-05T01:35:25.189956+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07872","created_at":"2026-07-05T01:35:25.189956+00:00"},{"alias_kind":"pith_short_12","alias_value":"PERJBTYWEXHP","created_at":"2026-07-05T01:35:25.189956+00:00"},{"alias_kind":"pith_short_16","alias_value":"PERJBTYWEXHP3NWN","created_at":"2026-07-05T01:35:25.189956+00:00"},{"alias_kind":"pith_short_8","alias_value":"PERJBTYW","created_at":"2026-07-05T01:35:25.189956+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.03343","citing_title":"Functional Limit Theorems for the range of stable random walks","ref_index":8,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PERJBTYWEXHP3NWNA76R3EV5UL","json":"https://pith.science/pith/PERJBTYWEXHP3NWNA76R3EV5UL.json","graph_json":"https://pith.science/api/pith-number/PERJBTYWEXHP3NWNA76R3EV5UL/graph.json","events_json":"https://pith.science/api/pith-number/PERJBTYWEXHP3NWNA76R3EV5UL/events.json","paper":"https://pith.science/paper/PERJBTYW"},"agent_actions":{"view_html":"https://pith.science/pith/PERJBTYWEXHP3NWNA76R3EV5UL","download_json":"https://pith.science/pith/PERJBTYWEXHP3NWNA76R3EV5UL.json","view_paper":"https://pith.science/paper/PERJBTYW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.07872&json=true","fetch_graph":"https://pith.science/api/pith-number/PERJBTYWEXHP3NWNA76R3EV5UL/graph.json","fetch_events":"https://pith.science/api/pith-number/PERJBTYWEXHP3NWNA76R3EV5UL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PERJBTYWEXHP3NWNA76R3EV5UL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PERJBTYWEXHP3NWNA76R3EV5UL/action/storage_attestation","attest_author":"https://pith.science/pith/PERJBTYWEXHP3NWNA76R3EV5UL/action/author_attestation","sign_citation":"https://pith.science/pith/PERJBTYWEXHP3NWNA76R3EV5UL/action/citation_signature","submit_replication":"https://pith.science/pith/PERJBTYWEXHP3NWNA76R3EV5UL/action/replication_record"}},"created_at":"2026-07-05T01:35:25.189956+00:00","updated_at":"2026-07-05T01:35:25.189956+00:00"}