{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XMJ3YR556XTRQUOREDPOAL6GWE","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":"124109ffcf4dc2dafaf4ff0b97c44a6b0115a790e252a8073d0ecc1aedbcfe23","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-06T18:13:06Z","title_canon_sha256":"87169de6f8b6002b7bddf2432dc00af031c99414b431b92a9c5cdcad733ba0db"},"schema_version":"1.0","source":{"id":"1312.1948","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1948","created_at":"2026-05-18T01:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1948v3","created_at":"2026-05-18T01:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1948","created_at":"2026-05-18T01:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"XMJ3YR556XTR","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XMJ3YR556XTRQUOR","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XMJ3YR55","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:f61e75f953df01ef44fa390606fdd1eaf8257cf2926a69224f3ad393a707a606","target":"graph","created_at":"2026-05-18T01:03:44Z","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 study of real-life network modeling has become very popular in recent years. An attractive model is the scale-free percolation model on the lattice $\\mathbb{Z}^d$, $d\\ge1$, because it fulfills several stylized facts observed in large real-life networks. We adopt this model to continuum space which leads to a heterogeneous random-connection model on $\\mathbb{R}^d$: particles are generated by a homogeneous marked Poisson point process on $\\mathbb{R}^d$, and the probability of an edge between two particles is determined by their marks and their distance. In this model we study several propert","authors_text":"Mario V. W\\\"uthrich, Philippe Deprez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-06T18:13:06Z","title":"Scale-Free Percolation in Continuum Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1948","kind":"arxiv","version":3},"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":"sha256:5f95f1fcfee49400cc20ba864144da3ca7bf693e0ab6f96f0de09f336b8a3be7","target":"record","created_at":"2026-05-18T01:03:44Z","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":"124109ffcf4dc2dafaf4ff0b97c44a6b0115a790e252a8073d0ecc1aedbcfe23","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-06T18:13:06Z","title_canon_sha256":"87169de6f8b6002b7bddf2432dc00af031c99414b431b92a9c5cdcad733ba0db"},"schema_version":"1.0","source":{"id":"1312.1948","kind":"arxiv","version":3}},"canonical_sha256":"bb13bc47bdf5e71851d120dee02fc6b12f6e4a997fbf55505c1d93726a46102c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb13bc47bdf5e71851d120dee02fc6b12f6e4a997fbf55505c1d93726a46102c","first_computed_at":"2026-05-18T01:03:44.695229Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:44.695229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9qwdF5lSzRC+4hWtNnC65MgupPKgwcquhKj+GlqOpGmxJPIr9gHBXV/07JAGlpcUNionCqE98MlinuvXUeF1BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:44.695698Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1948","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f95f1fcfee49400cc20ba864144da3ca7bf693e0ab6f96f0de09f336b8a3be7","sha256:f61e75f953df01ef44fa390606fdd1eaf8257cf2926a69224f3ad393a707a606"],"state_sha256":"fdc634d4f5bff167b6261724ea8802292c3baf4429eb1e823cf333a06884ab31"}