{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:H7TWUZHDOOAL57FDZ5T54RULDI","short_pith_number":"pith:H7TWUZHD","canonical_record":{"source":{"id":"1808.09857","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-29T14:44:54Z","cross_cats_sorted":[],"title_canon_sha256":"fa6915306d9c68935e1ecfca507b8400b507c42af7fb54ab5e44de7761a92f27","abstract_canon_sha256":"09550c8be4a713afba04d72395f06d3a686248fc6ae2d0eb488362bacf9be2e1"},"schema_version":"1.0"},"canonical_sha256":"3fe76a64e37380befca3cf67de468b1a128355917b9ff3a5053633fa5ac3f9a1","source":{"kind":"arxiv","id":"1808.09857","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.09857","created_at":"2026-07-05T00:40:11Z"},{"alias_kind":"arxiv_version","alias_value":"1808.09857v4","created_at":"2026-07-05T00:40:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.09857","created_at":"2026-07-05T00:40:11Z"},{"alias_kind":"pith_short_12","alias_value":"H7TWUZHDOOAL","created_at":"2026-07-05T00:40:11Z"},{"alias_kind":"pith_short_16","alias_value":"H7TWUZHDOOAL57FD","created_at":"2026-07-05T00:40:11Z"},{"alias_kind":"pith_short_8","alias_value":"H7TWUZHD","created_at":"2026-07-05T00:40:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:H7TWUZHDOOAL57FDZ5T54RULDI","target":"record","payload":{"canonical_record":{"source":{"id":"1808.09857","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-29T14:44:54Z","cross_cats_sorted":[],"title_canon_sha256":"fa6915306d9c68935e1ecfca507b8400b507c42af7fb54ab5e44de7761a92f27","abstract_canon_sha256":"09550c8be4a713afba04d72395f06d3a686248fc6ae2d0eb488362bacf9be2e1"},"schema_version":"1.0"},"canonical_sha256":"3fe76a64e37380befca3cf67de468b1a128355917b9ff3a5053633fa5ac3f9a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:40:11.585762Z","signature_b64":"sZff8Gd2UD09zEFFi3gDNoUJF1WsRy4UgItVMq71NOfh07kK7g/IHhz3CmaSiIRw1ZXXCsp9CD0RuJM3Fpj1AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3fe76a64e37380befca3cf67de468b1a128355917b9ff3a5053633fa5ac3f9a1","last_reissued_at":"2026-07-05T00:40:11.585353Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:40:11.585353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.09857","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:40:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I7wFjTcbbvVAMASa1SBt7O3wYKI6O2OA4nQfGrghWlA2+DuXsse7gg4vrMPg2gVXJriTfOPbE5a1NOj5XJWnBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T01:24:37.749828Z"},"content_sha256":"cd18e8c8e2da2ed245cb652c33389d8877cb6040568da9e5b7926b038d11e25c","schema_version":"1.0","event_id":"sha256:cd18e8c8e2da2ed245cb652c33389d8877cb6040568da9e5b7926b038d11e25c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:H7TWUZHDOOAL57FDZ5T54RULDI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Signal to interference ratio percolation for Cox point processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andr\\'as T\\'obi\\'as","submitted_at":"2018-08-29T14:44:54Z","abstract_excerpt":"We study the signal-to-interference ratio (SINR) percolation model for a stationary Cox point process in two or higher dimensions, in case of a bounded and integrable path-loss function. We show that if this function has compact support or if the stationary intensity measure evaluated at a unit box has some exponential moments, then the SINR graph has an infinite connected component in case the spatial density of points is large enough and the interferences are sufficiently reduced (without vanishing). This holds under suitable stabilization and connectivity assumptions on the intensity measur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09857","kind":"arxiv","version":4},"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/1808.09857/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:40:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qjdegUb/32s0+5lkGGuEgUd4gIGZ8ft/p6ODjpuzoi6VBOXdgc1rG60tD84OB2G1daeI5oTnk4pV+gJvxTuODg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T01:24:37.750363Z"},"content_sha256":"1a198aac411aeb7cb92cacde95f5024ca3871ffed1eb204ab40e5f3a9d5ccbb6","schema_version":"1.0","event_id":"sha256:1a198aac411aeb7cb92cacde95f5024ca3871ffed1eb204ab40e5f3a9d5ccbb6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H7TWUZHDOOAL57FDZ5T54RULDI/bundle.json","state_url":"https://pith.science/pith/H7TWUZHDOOAL57FDZ5T54RULDI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H7TWUZHDOOAL57FDZ5T54RULDI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-17T01:24:37Z","links":{"resolver":"https://pith.science/pith/H7TWUZHDOOAL57FDZ5T54RULDI","bundle":"https://pith.science/pith/H7TWUZHDOOAL57FDZ5T54RULDI/bundle.json","state":"https://pith.science/pith/H7TWUZHDOOAL57FDZ5T54RULDI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H7TWUZHDOOAL57FDZ5T54RULDI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:H7TWUZHDOOAL57FDZ5T54RULDI","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":"09550c8be4a713afba04d72395f06d3a686248fc6ae2d0eb488362bacf9be2e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-29T14:44:54Z","title_canon_sha256":"fa6915306d9c68935e1ecfca507b8400b507c42af7fb54ab5e44de7761a92f27"},"schema_version":"1.0","source":{"id":"1808.09857","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.09857","created_at":"2026-07-05T00:40:11Z"},{"alias_kind":"arxiv_version","alias_value":"1808.09857v4","created_at":"2026-07-05T00:40:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.09857","created_at":"2026-07-05T00:40:11Z"},{"alias_kind":"pith_short_12","alias_value":"H7TWUZHDOOAL","created_at":"2026-07-05T00:40:11Z"},{"alias_kind":"pith_short_16","alias_value":"H7TWUZHDOOAL57FD","created_at":"2026-07-05T00:40:11Z"},{"alias_kind":"pith_short_8","alias_value":"H7TWUZHD","created_at":"2026-07-05T00:40:11Z"}],"graph_snapshots":[{"event_id":"sha256:1a198aac411aeb7cb92cacde95f5024ca3871ffed1eb204ab40e5f3a9d5ccbb6","target":"graph","created_at":"2026-07-05T00:40:11Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1808.09857/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the signal-to-interference ratio (SINR) percolation model for a stationary Cox point process in two or higher dimensions, in case of a bounded and integrable path-loss function. We show that if this function has compact support or if the stationary intensity measure evaluated at a unit box has some exponential moments, then the SINR graph has an infinite connected component in case the spatial density of points is large enough and the interferences are sufficiently reduced (without vanishing). This holds under suitable stabilization and connectivity assumptions on the intensity measur","authors_text":"Andr\\'as T\\'obi\\'as","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-29T14:44:54Z","title":"Signal to interference ratio percolation for Cox point processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09857","kind":"arxiv","version":4},"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:cd18e8c8e2da2ed245cb652c33389d8877cb6040568da9e5b7926b038d11e25c","target":"record","created_at":"2026-07-05T00:40:11Z","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":"09550c8be4a713afba04d72395f06d3a686248fc6ae2d0eb488362bacf9be2e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-29T14:44:54Z","title_canon_sha256":"fa6915306d9c68935e1ecfca507b8400b507c42af7fb54ab5e44de7761a92f27"},"schema_version":"1.0","source":{"id":"1808.09857","kind":"arxiv","version":4}},"canonical_sha256":"3fe76a64e37380befca3cf67de468b1a128355917b9ff3a5053633fa5ac3f9a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3fe76a64e37380befca3cf67de468b1a128355917b9ff3a5053633fa5ac3f9a1","first_computed_at":"2026-07-05T00:40:11.585353Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:40:11.585353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sZff8Gd2UD09zEFFi3gDNoUJF1WsRy4UgItVMq71NOfh07kK7g/IHhz3CmaSiIRw1ZXXCsp9CD0RuJM3Fpj1AA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:40:11.585762Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.09857","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd18e8c8e2da2ed245cb652c33389d8877cb6040568da9e5b7926b038d11e25c","sha256:1a198aac411aeb7cb92cacde95f5024ca3871ffed1eb204ab40e5f3a9d5ccbb6"],"state_sha256":"21604ccf575c628213f7ea3f48e0e4c210d9aef88ea769a36fe34e75d2d95933"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r3nThI5r5SPkCxtJO4N0Gy1m4Lga+fPLf/va6mhkyyOi638uzPCijJRhK1U7M6KSUvjfMt4rQx3wkIIasJbJCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T01:24:37.755225Z","bundle_sha256":"80a1e4f36a3a86fc1801d32eeb25bf1add48816c861582d062bd4f78dbb972d4"}}