{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:BDPUJP7TKZBV2UR4BMFG4W2B7N","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":"b9e231e09b470a78d4b0ab5d1e21db5b5a0baffbae5a7bb316fd7c38b96f1b8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2010-11-15T19:49:41Z","title_canon_sha256":"71ce8d64c2d718df4c6846a6080fe406e685038268422a4b4b3ca9f76c39c428"},"schema_version":"1.0","source":{"id":"1011.3482","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.3482","created_at":"2026-05-18T04:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"1011.3482v1","created_at":"2026-05-18T04:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3482","created_at":"2026-05-18T04:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"BDPUJP7TKZBV","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BDPUJP7TKZBV2UR4","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BDPUJP7T","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:0adb09fc5d1bd4f71b1498593888c1bf378e513a4d37b8d89630c32d6698bc4d","target":"graph","created_at":"2026-05-18T04:35:55Z","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":"Wireless sensor networks are often modeled in terms of a dense deployment of smart sensor nodes in a two-dimensional region. Give a node deployment, the \\emph{critical geometric graph (CGG)} over these locations (i.e., the connected \\emph{geometric graph (GG)} with the smallest radius) is a useful structure since it provides the most accurate proportionality between hop-count and Euclidean distance. Hence, it can be used for GPS-free node localisation as well as minimum distance packet forwarding. It is also known to be asymptotically optimal for network transport capacity and power efficiency","authors_text":"Anurag Kumar, Malati Hegde, Navneet Sankara, Srivathsa Acharya, S.V.R. Anand, Vijay Dewangan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2010-11-15T19:49:41Z","title":"Distributed Construction of the Critical Geometric Graph in Dense Wireless Sensor Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3482","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:de92fe6e7e42cc5a000d775aeeae188c02696a56469eb09359e9a7467b59cbf8","target":"record","created_at":"2026-05-18T04:35:55Z","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":"b9e231e09b470a78d4b0ab5d1e21db5b5a0baffbae5a7bb316fd7c38b96f1b8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2010-11-15T19:49:41Z","title_canon_sha256":"71ce8d64c2d718df4c6846a6080fe406e685038268422a4b4b3ca9f76c39c428"},"schema_version":"1.0","source":{"id":"1011.3482","kind":"arxiv","version":1}},"canonical_sha256":"08df44bff356435d523c0b0a6e5b41fb7da5a0b39ef2683249b77abe0b688768","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08df44bff356435d523c0b0a6e5b41fb7da5a0b39ef2683249b77abe0b688768","first_computed_at":"2026-05-18T04:35:55.746817Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:55.746817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6A8xBQ2QoI8m7S4xtw24E6YjZiP/rN8JndA1r23m6ZODnuw/MfeZFxFhjdOVgo2i7JNxCwLwVV3HepkScVedCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:55.747547Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.3482","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de92fe6e7e42cc5a000d775aeeae188c02696a56469eb09359e9a7467b59cbf8","sha256:0adb09fc5d1bd4f71b1498593888c1bf378e513a4d37b8d89630c32d6698bc4d"],"state_sha256":"2e74b43dcf97986a863d7ad221d429189943903b1da53a19c80cc03089ec8cc7"}