{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:O32Z4VB3BJC7OJCKX2FC7MSMZ5","short_pith_number":"pith:O32Z4VB3","schema_version":"1.0","canonical_sha256":"76f59e543b0a45f7244abe8a2fb24ccf6f5ee534517340f6a50707e73c3c1e67","source":{"kind":"arxiv","id":"1705.00101","version":1},"attestation_state":"computed","paper":{"title":"Uniformity of hitting times of the contact process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christian Hirsch, Daniel Valesin, Markus Heydenreich","submitted_at":"2017-04-29T00:27:57Z","abstract_excerpt":"For the supercritical contact process on the hyper-cubic lattice started from a single infection at the origin and conditioned on survival, we establish two uniformity results for the hitting times $t(x)$, defined for each site $x$ as the first time at which it becomes infected. First, the family of random variables $(t(x)-t(y))/|x-y|$, indexed by $x \\neq y$ in $\\mathbb{Z}^d$, is stochastically tight. Second, for each $\\varepsilon >0$ there exists $x$ such that, for infinitely many integers $n$, $t(nx) < t((n+1)x)$ with probability larger than $1-\\varepsilon$. A key ingredient in our proofs is"},"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":"1705.00101","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-29T00:27:57Z","cross_cats_sorted":[],"title_canon_sha256":"b097e59034fff1b2d499d6ba6aeb84d67d2b1a584e369d7f98875dc3ee40bd0a","abstract_canon_sha256":"2436dcd0239570ed7dc288f2ac6642ca57b5ebddb236c4d3d30c47008d4611a2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:21.481103Z","signature_b64":"zy9I8VgRoxi6xgusYG+UG5+fq9uK6xkza6hca+6t5EBsLWIhjV+sWVOu8l0Z787egMfJTe0IqTk0dUL+BG6oCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76f59e543b0a45f7244abe8a2fb24ccf6f5ee534517340f6a50707e73c3c1e67","last_reissued_at":"2026-05-18T00:45:21.480407Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:21.480407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniformity of hitting times of the contact process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christian Hirsch, Daniel Valesin, Markus Heydenreich","submitted_at":"2017-04-29T00:27:57Z","abstract_excerpt":"For the supercritical contact process on the hyper-cubic lattice started from a single infection at the origin and conditioned on survival, we establish two uniformity results for the hitting times $t(x)$, defined for each site $x$ as the first time at which it becomes infected. First, the family of random variables $(t(x)-t(y))/|x-y|$, indexed by $x \\neq y$ in $\\mathbb{Z}^d$, is stochastically tight. Second, for each $\\varepsilon >0$ there exists $x$ such that, for infinitely many integers $n$, $t(nx) < t((n+1)x)$ with probability larger than $1-\\varepsilon$. A key ingredient in our proofs is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00101","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":""},"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":"1705.00101","created_at":"2026-05-18T00:45:21.480511+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.00101v1","created_at":"2026-05-18T00:45:21.480511+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00101","created_at":"2026-05-18T00:45:21.480511+00:00"},{"alias_kind":"pith_short_12","alias_value":"O32Z4VB3BJC7","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"O32Z4VB3BJC7OJCK","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"O32Z4VB3","created_at":"2026-05-18T12:31:34.259226+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/O32Z4VB3BJC7OJCKX2FC7MSMZ5","json":"https://pith.science/pith/O32Z4VB3BJC7OJCKX2FC7MSMZ5.json","graph_json":"https://pith.science/api/pith-number/O32Z4VB3BJC7OJCKX2FC7MSMZ5/graph.json","events_json":"https://pith.science/api/pith-number/O32Z4VB3BJC7OJCKX2FC7MSMZ5/events.json","paper":"https://pith.science/paper/O32Z4VB3"},"agent_actions":{"view_html":"https://pith.science/pith/O32Z4VB3BJC7OJCKX2FC7MSMZ5","download_json":"https://pith.science/pith/O32Z4VB3BJC7OJCKX2FC7MSMZ5.json","view_paper":"https://pith.science/paper/O32Z4VB3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.00101&json=true","fetch_graph":"https://pith.science/api/pith-number/O32Z4VB3BJC7OJCKX2FC7MSMZ5/graph.json","fetch_events":"https://pith.science/api/pith-number/O32Z4VB3BJC7OJCKX2FC7MSMZ5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O32Z4VB3BJC7OJCKX2FC7MSMZ5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O32Z4VB3BJC7OJCKX2FC7MSMZ5/action/storage_attestation","attest_author":"https://pith.science/pith/O32Z4VB3BJC7OJCKX2FC7MSMZ5/action/author_attestation","sign_citation":"https://pith.science/pith/O32Z4VB3BJC7OJCKX2FC7MSMZ5/action/citation_signature","submit_replication":"https://pith.science/pith/O32Z4VB3BJC7OJCKX2FC7MSMZ5/action/replication_record"}},"created_at":"2026-05-18T00:45:21.480511+00:00","updated_at":"2026-05-18T00:45:21.480511+00:00"}