{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:AYQUINCFCAXUCQILNUWTBBQZ6P","short_pith_number":"pith:AYQUINCF","canonical_record":{"source":{"id":"1012.3364","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-15T15:42:28Z","cross_cats_sorted":["cs.NI"],"title_canon_sha256":"c928920c675ac2f8f48079e8bc0c43322dffd69698ddbc6fbf466b9fe14518b1","abstract_canon_sha256":"227bd5c5beefec960c70c9382c9e890cf9c561ef1fa086b41e9ba47912425a20"},"schema_version":"1.0"},"canonical_sha256":"0621443445102f41410b6d2d308619f3c41fa914b7870a59724d59a72e745a34","source":{"kind":"arxiv","id":"1012.3364","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.3364","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"1012.3364v2","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3364","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"AYQUINCFCAXU","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AYQUINCFCAXUCQIL","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AYQUINCF","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:AYQUINCFCAXUCQILNUWTBBQZ6P","target":"record","payload":{"canonical_record":{"source":{"id":"1012.3364","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-15T15:42:28Z","cross_cats_sorted":["cs.NI"],"title_canon_sha256":"c928920c675ac2f8f48079e8bc0c43322dffd69698ddbc6fbf466b9fe14518b1","abstract_canon_sha256":"227bd5c5beefec960c70c9382c9e890cf9c561ef1fa086b41e9ba47912425a20"},"schema_version":"1.0"},"canonical_sha256":"0621443445102f41410b6d2d308619f3c41fa914b7870a59724d59a72e745a34","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:17.834777Z","signature_b64":"6b5RLwJ1hVU0jwIxP9rsQDb6sWhpPPdx6BLIPK23SfjzsAvHmsmgOh3GgVuJ+GE3FsXtRq2/JGoe9mughHRbAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0621443445102f41410b6d2d308619f3c41fa914b7870a59724d59a72e745a34","last_reissued_at":"2026-05-18T03:14:17.834118Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:17.834118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.3364","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:14:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/OIC8uQ7U0oEgxjApyO5QmP+oy0aYm6CGxApgA33/lx5UGNvSqqEoEQ2tsrB5LRSztxHYAtuLvFnJnycGWSpCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:18:03.652983Z"},"content_sha256":"3df073bd37e94f6f04d409b143439d0091929c7e113fb0eea5a99dea45b3451d","schema_version":"1.0","event_id":"sha256:3df073bd37e94f6f04d409b143439d0091929c7e113fb0eea5a99dea45b3451d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:AYQUINCFCAXUCQILNUWTBBQZ6P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability of Random Admissible-Set Scheduling in Spatially Continuous Wireless Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NI"],"primary_cat":"math.PR","authors_text":"Johan van Leeuwaarden, Niek Bouman, Sem Borst","submitted_at":"2010-12-15T15:42:28Z","abstract_excerpt":"We examine the stability of wireless networks whose users are distributed over a compact space. A subset of users is called {\\it admissible} when their simultaneous activity obeys the prevailing interference constraints and, in each time slot, an admissible subset of users is selected uniformly at random to transmit one packet. We show that, under a mild condition, this random admissible-set scheduling mechanism achieves maximum stability in a broad set of scenarios, and in particular in symmetric cases. The proof relies on a description of the system as a measure-valued process and the identi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3364","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:14:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2IYWnmA+xcL5F0BCptI/uSMDg2cJ9ik3gFOyrrdolJg/tCElfmCaITeln/IvdWkFYE7V77Rq+JlG7mfXXvMfBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:18:03.653448Z"},"content_sha256":"703f1efe1536fdb512aa2890c47b0f3b8dfda75175ed99e0f6cede6235c651e1","schema_version":"1.0","event_id":"sha256:703f1efe1536fdb512aa2890c47b0f3b8dfda75175ed99e0f6cede6235c651e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AYQUINCFCAXUCQILNUWTBBQZ6P/bundle.json","state_url":"https://pith.science/pith/AYQUINCFCAXUCQILNUWTBBQZ6P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AYQUINCFCAXUCQILNUWTBBQZ6P/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":"2026-05-27T23:18:03Z","links":{"resolver":"https://pith.science/pith/AYQUINCFCAXUCQILNUWTBBQZ6P","bundle":"https://pith.science/pith/AYQUINCFCAXUCQILNUWTBBQZ6P/bundle.json","state":"https://pith.science/pith/AYQUINCFCAXUCQILNUWTBBQZ6P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AYQUINCFCAXUCQILNUWTBBQZ6P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:AYQUINCFCAXUCQILNUWTBBQZ6P","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":"227bd5c5beefec960c70c9382c9e890cf9c561ef1fa086b41e9ba47912425a20","cross_cats_sorted":["cs.NI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-15T15:42:28Z","title_canon_sha256":"c928920c675ac2f8f48079e8bc0c43322dffd69698ddbc6fbf466b9fe14518b1"},"schema_version":"1.0","source":{"id":"1012.3364","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.3364","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"1012.3364v2","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3364","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"AYQUINCFCAXU","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AYQUINCFCAXUCQIL","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AYQUINCF","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:703f1efe1536fdb512aa2890c47b0f3b8dfda75175ed99e0f6cede6235c651e1","target":"graph","created_at":"2026-05-18T03:14:17Z","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":"We examine the stability of wireless networks whose users are distributed over a compact space. A subset of users is called {\\it admissible} when their simultaneous activity obeys the prevailing interference constraints and, in each time slot, an admissible subset of users is selected uniformly at random to transmit one packet. We show that, under a mild condition, this random admissible-set scheduling mechanism achieves maximum stability in a broad set of scenarios, and in particular in symmetric cases. The proof relies on a description of the system as a measure-valued process and the identi","authors_text":"Johan van Leeuwaarden, Niek Bouman, Sem Borst","cross_cats":["cs.NI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-15T15:42:28Z","title":"Stability of Random Admissible-Set Scheduling in Spatially Continuous Wireless Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3364","kind":"arxiv","version":2},"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":"sha256:3df073bd37e94f6f04d409b143439d0091929c7e113fb0eea5a99dea45b3451d","target":"record","created_at":"2026-05-18T03:14:17Z","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":"227bd5c5beefec960c70c9382c9e890cf9c561ef1fa086b41e9ba47912425a20","cross_cats_sorted":["cs.NI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-15T15:42:28Z","title_canon_sha256":"c928920c675ac2f8f48079e8bc0c43322dffd69698ddbc6fbf466b9fe14518b1"},"schema_version":"1.0","source":{"id":"1012.3364","kind":"arxiv","version":2}},"canonical_sha256":"0621443445102f41410b6d2d308619f3c41fa914b7870a59724d59a72e745a34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0621443445102f41410b6d2d308619f3c41fa914b7870a59724d59a72e745a34","first_computed_at":"2026-05-18T03:14:17.834118Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:17.834118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6b5RLwJ1hVU0jwIxP9rsQDb6sWhpPPdx6BLIPK23SfjzsAvHmsmgOh3GgVuJ+GE3FsXtRq2/JGoe9mughHRbAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:17.834777Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.3364","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3df073bd37e94f6f04d409b143439d0091929c7e113fb0eea5a99dea45b3451d","sha256:703f1efe1536fdb512aa2890c47b0f3b8dfda75175ed99e0f6cede6235c651e1"],"state_sha256":"6002a3440d09ec64c46359e27e81ec38eaab967a35b2be129e2a5affcfcf9b4d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gaamdRyNaIwFw4lbtpdQcKUrYoeH79i/NhbNVWFev/VZEOsTnn7wkhgPWSTvkS7wbwp0a0c2G2qPC7flvEhADw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T23:18:03.656854Z","bundle_sha256":"5721aad07a049dd39172bf3a6f7540b1b5c2d3c2ff22ce775515368564cd1bef"}}