{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WDRXKU3H5LGIBEJB3CIR4FOK6L","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":"21729a52908b35ad032aac4efe3d44c949e334a006f13fc460037eca71b3026d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-15T15:49:49Z","title_canon_sha256":"769839b0625e58623644655b5203d333ad2d377401dc0385d41b41a5340cb89a"},"schema_version":"1.0","source":{"id":"1810.06479","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.06479","created_at":"2026-05-18T00:03:20Z"},{"alias_kind":"arxiv_version","alias_value":"1810.06479v1","created_at":"2026-05-18T00:03:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.06479","created_at":"2026-05-18T00:03:20Z"},{"alias_kind":"pith_short_12","alias_value":"WDRXKU3H5LGI","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WDRXKU3H5LGIBEJB","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WDRXKU3H","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:2d3d85ac023eabde5956010ecb5cae70a817b9552c88d945198311c23b8f49ce","target":"graph","created_at":"2026-05-18T00:03:20Z","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":"Consider a dynamic random geometric social network identified by $s_t$ independent points $x_t^1,\\ldots,x_t^{s_t}$ in the unit square $[0,1]^2$ that interact in continuous time $t\\geq 0$. The generative model of the random points is a Poisson point measures. Each point $x_t^i$ can be active or not in the network with a Bernoulli probability $p$. Each pair being connected by affinity thanks to a step connection function if the interpoint distance $\\|x_t^i-x_t^j\\|\\leq a_\\mathsf{f}^\\star$ for any $i\\neq j$. We prove that when $a_\\mathsf{f}^\\star=\\sqrt{\\frac{(s_t)^{l-1}}{p\\pi}}$ for $l\\in(0,1)$, t","authors_text":"Ahmed Sid-Ali, Khader Khadraoui","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-15T15:49:49Z","title":"Asymptotic adaptive threshold for connectivity in a random geometric social network"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06479","kind":"arxiv","version":1},"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":"sha256:7867ecbab01b3373f445dcd14332a8b980e6127ae4a3b425926d53ff5127e0d9","target":"record","created_at":"2026-05-18T00:03:20Z","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":"21729a52908b35ad032aac4efe3d44c949e334a006f13fc460037eca71b3026d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-15T15:49:49Z","title_canon_sha256":"769839b0625e58623644655b5203d333ad2d377401dc0385d41b41a5340cb89a"},"schema_version":"1.0","source":{"id":"1810.06479","kind":"arxiv","version":1}},"canonical_sha256":"b0e3755367eacc809121d8911e15caf2e0c87437c3088d378c520a708af99f5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0e3755367eacc809121d8911e15caf2e0c87437c3088d378c520a708af99f5b","first_computed_at":"2026-05-18T00:03:20.383517Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:20.383517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xfZMhEAjKOlksmH0rJLkVWzp0sR4t+8m3QGbMHMapwNcO5Y9qruJ0Lyceh+BUj8Pv+7A34jwVnjSTPqI4EQ2Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:20.383957Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.06479","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7867ecbab01b3373f445dcd14332a8b980e6127ae4a3b425926d53ff5127e0d9","sha256:2d3d85ac023eabde5956010ecb5cae70a817b9552c88d945198311c23b8f49ce"],"state_sha256":"2a40da09d60ff315ddd24cae4c1b2e95acb1cd7c1c14b5b68c66e8f38df579ff"}