{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:64URIVCVTXLXJPCDMTXMCNC3DL","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":"0286ecb6be27d95bf8bca61825b41733fb6059021e42525a37e4ef87ff8b27f1","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2009-11-17T17:50:12Z","title_canon_sha256":"92178e6526d89cc86272d7099d37b6afdb6e047cb916a773690a9ca8e63b10ed"},"schema_version":"1.0","source":{"id":"0911.3357","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.3357","created_at":"2026-05-18T00:58:47Z"},{"alias_kind":"arxiv_version","alias_value":"0911.3357v1","created_at":"2026-05-18T00:58:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.3357","created_at":"2026-05-18T00:58:47Z"},{"alias_kind":"pith_short_12","alias_value":"64URIVCVTXLX","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"64URIVCVTXLXJPCD","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"64URIVCV","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:a2942ba2a49692fe6cc355de5c4b24065eae5e13304c343259266aceed0a71fa","target":"graph","created_at":"2026-05-18T00:58:47Z","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":"Sensor networks potentially feature large numbers of nodes that can sense their environment over time, communicate with each other over a wireless network, and process information. They differ from data networks in that the network as a whole may be designed for a specific application. We study the theoretical foundations of such large scale sensor networks, addressing four fundamental issues- connectivity, capacity, clocks and function computation.\n  To begin with, a sensor network must be connected so that information can indeed be exchanged between nodes. The connectivity graph of an ad-hoc","authors_text":"Hemant Kowshik, Nikolaos M. Freris, P. R. Kumar","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2009-11-17T17:50:12Z","title":"Fundamentals of Large Sensor Networks: Connectivity, Capacity, Clocks and Computation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.3357","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":"sha256:1be55912be84a2ef1782079c72f1e25175f3ef6e4f2871c4cf8c414b512b665e","target":"record","created_at":"2026-05-18T00:58:47Z","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":"0286ecb6be27d95bf8bca61825b41733fb6059021e42525a37e4ef87ff8b27f1","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2009-11-17T17:50:12Z","title_canon_sha256":"92178e6526d89cc86272d7099d37b6afdb6e047cb916a773690a9ca8e63b10ed"},"schema_version":"1.0","source":{"id":"0911.3357","kind":"arxiv","version":1}},"canonical_sha256":"f7291454559dd774bc4364eec1345b1af42fa4ca75f1f0aa79dd7fb3e3c23ad4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7291454559dd774bc4364eec1345b1af42fa4ca75f1f0aa79dd7fb3e3c23ad4","first_computed_at":"2026-05-18T00:58:47.860997Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:47.860997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s3YbYP2f+DWkTdDovjGFP+cGqUaFF/uvuiBe05EAPJqF2Q3/kPMytHFyBLchIir9Ni/loTjZ1cc6mahCp65WAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:47.861546Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.3357","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1be55912be84a2ef1782079c72f1e25175f3ef6e4f2871c4cf8c414b512b665e","sha256:a2942ba2a49692fe6cc355de5c4b24065eae5e13304c343259266aceed0a71fa"],"state_sha256":"8051cf7fdc3b6fe03cd3bcde88487c11da3e3f9a4ab683af8d21e77f5ba3a01b"}