{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:GPGD3YFMJAVXF3TTTP25A4FDOA","short_pith_number":"pith:GPGD3YFM","canonical_record":{"source":{"id":"0711.2745","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2007-11-19T19:59:52Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"1d5bc1ab50c5bbf54bc7b35b39547cc2d17432ec7bec278db9aa261553399521","abstract_canon_sha256":"d9591fc51ce28ae2d807020e24d08f0dbeaa07726595027eaafcd3f2690f9c3d"},"schema_version":"1.0"},"canonical_sha256":"33cc3de0ac482b72ee739bf5d070a37017d07e628e14ea5c9f7e798d98679551","source":{"kind":"arxiv","id":"0711.2745","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0711.2745","created_at":"2026-05-18T00:58:48Z"},{"alias_kind":"arxiv_version","alias_value":"0711.2745v3","created_at":"2026-05-18T00:58:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.2745","created_at":"2026-05-18T00:58:48Z"},{"alias_kind":"pith_short_12","alias_value":"GPGD3YFMJAVX","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"GPGD3YFMJAVXF3TT","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"GPGD3YFM","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:GPGD3YFMJAVXF3TTTP25A4FDOA","target":"record","payload":{"canonical_record":{"source":{"id":"0711.2745","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2007-11-19T19:59:52Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"1d5bc1ab50c5bbf54bc7b35b39547cc2d17432ec7bec278db9aa261553399521","abstract_canon_sha256":"d9591fc51ce28ae2d807020e24d08f0dbeaa07726595027eaafcd3f2690f9c3d"},"schema_version":"1.0"},"canonical_sha256":"33cc3de0ac482b72ee739bf5d070a37017d07e628e14ea5c9f7e798d98679551","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:48.800045Z","signature_b64":"msVVMEC/iue1wi9OOVmS8jZ6hAKV8pCBIro8cUgGzUhGt4v73nuMlOhmQlnqwlgFJhCog06hekgO8/3l214IBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33cc3de0ac482b72ee739bf5d070a37017d07e628e14ea5c9f7e798d98679551","last_reissued_at":"2026-05-18T00:58:48.799406Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:48.799406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0711.2745","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:58:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4/tlUhaJjP9Yp4kK/d42gwVWDAY8QFbW7Y/x3e16QKA+dAOjMf+hU/1e3Y9lMkYJmHYh2yyHIRWxKz6gqI77Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:50:14.374372Z"},"content_sha256":"43c839781d3d73442180a7dc656d656d3b843eb23c08a0fcd1a7aad0f681a643","schema_version":"1.0","event_id":"sha256:43c839781d3d73442180a7dc656d656d3b843eb23c08a0fcd1a7aad0f681a643"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:GPGD3YFMJAVXF3TTTP25A4FDOA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Capacity Scaling in Arbitrary Wireless Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Devavrat Shah, Piyush Gupta, Urs Niesen","submitted_at":"2007-11-19T19:59:52Z","abstract_excerpt":"In recent work, Ozgur, Leveque, and Tse (2007) obtained a complete scaling characterization of throughput scaling for random extended wireless networks (i.e., $n$ nodes are placed uniformly at random in a square region of area $n$). They showed that for small path-loss exponents $\\alpha\\in(2,3]$ cooperative communication is order optimal, and for large path-loss exponents $\\alpha > 3$ multi-hop communication is order optimal. However, their results (both the communication scheme and the proof technique) are strongly dependent on the regularity induced with high probability by the random node p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.2745","kind":"arxiv","version":3},"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":"2026-05-18T00:58:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kDCF8XTOw+XfYzarvN66MwAYs+8c2lDnemuNfpSXHLjO6Bvsa+SHtqB7heg7IS+VeJ6MaGYv90e/uy/9ReGhDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:50:14.374987Z"},"content_sha256":"455dc48da614b5b1874214a9279b082bcc8a83ec8f99a79ebd6b15ef831be20c","schema_version":"1.0","event_id":"sha256:455dc48da614b5b1874214a9279b082bcc8a83ec8f99a79ebd6b15ef831be20c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GPGD3YFMJAVXF3TTTP25A4FDOA/bundle.json","state_url":"https://pith.science/pith/GPGD3YFMJAVXF3TTTP25A4FDOA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GPGD3YFMJAVXF3TTTP25A4FDOA/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":"2026-05-28T21:50:14Z","links":{"resolver":"https://pith.science/pith/GPGD3YFMJAVXF3TTTP25A4FDOA","bundle":"https://pith.science/pith/GPGD3YFMJAVXF3TTTP25A4FDOA/bundle.json","state":"https://pith.science/pith/GPGD3YFMJAVXF3TTTP25A4FDOA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GPGD3YFMJAVXF3TTTP25A4FDOA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:GPGD3YFMJAVXF3TTTP25A4FDOA","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":"d9591fc51ce28ae2d807020e24d08f0dbeaa07726595027eaafcd3f2690f9c3d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2007-11-19T19:59:52Z","title_canon_sha256":"1d5bc1ab50c5bbf54bc7b35b39547cc2d17432ec7bec278db9aa261553399521"},"schema_version":"1.0","source":{"id":"0711.2745","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0711.2745","created_at":"2026-05-18T00:58:48Z"},{"alias_kind":"arxiv_version","alias_value":"0711.2745v3","created_at":"2026-05-18T00:58:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.2745","created_at":"2026-05-18T00:58:48Z"},{"alias_kind":"pith_short_12","alias_value":"GPGD3YFMJAVX","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"GPGD3YFMJAVXF3TT","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"GPGD3YFM","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:455dc48da614b5b1874214a9279b082bcc8a83ec8f99a79ebd6b15ef831be20c","target":"graph","created_at":"2026-05-18T00:58:48Z","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":"In recent work, Ozgur, Leveque, and Tse (2007) obtained a complete scaling characterization of throughput scaling for random extended wireless networks (i.e., $n$ nodes are placed uniformly at random in a square region of area $n$). They showed that for small path-loss exponents $\\alpha\\in(2,3]$ cooperative communication is order optimal, and for large path-loss exponents $\\alpha > 3$ multi-hop communication is order optimal. However, their results (both the communication scheme and the proof technique) are strongly dependent on the regularity induced with high probability by the random node p","authors_text":"Devavrat Shah, Piyush Gupta, Urs Niesen","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2007-11-19T19:59:52Z","title":"On Capacity Scaling in Arbitrary Wireless Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.2745","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":"sha256:43c839781d3d73442180a7dc656d656d3b843eb23c08a0fcd1a7aad0f681a643","target":"record","created_at":"2026-05-18T00:58:48Z","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":"d9591fc51ce28ae2d807020e24d08f0dbeaa07726595027eaafcd3f2690f9c3d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2007-11-19T19:59:52Z","title_canon_sha256":"1d5bc1ab50c5bbf54bc7b35b39547cc2d17432ec7bec278db9aa261553399521"},"schema_version":"1.0","source":{"id":"0711.2745","kind":"arxiv","version":3}},"canonical_sha256":"33cc3de0ac482b72ee739bf5d070a37017d07e628e14ea5c9f7e798d98679551","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33cc3de0ac482b72ee739bf5d070a37017d07e628e14ea5c9f7e798d98679551","first_computed_at":"2026-05-18T00:58:48.799406Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:48.799406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"msVVMEC/iue1wi9OOVmS8jZ6hAKV8pCBIro8cUgGzUhGt4v73nuMlOhmQlnqwlgFJhCog06hekgO8/3l214IBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:48.800045Z","signed_message":"canonical_sha256_bytes"},"source_id":"0711.2745","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43c839781d3d73442180a7dc656d656d3b843eb23c08a0fcd1a7aad0f681a643","sha256:455dc48da614b5b1874214a9279b082bcc8a83ec8f99a79ebd6b15ef831be20c"],"state_sha256":"3974b5a469e9e7c23c03ab95a1ed4e336fd23d1b474453d3f390c00755516078"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tYY2A86g6dsMZ2IG7WLfza4Cx9VlChSn/w29Bwmaaz9BG/e3+5kFqLOxSB0MeHqnuSgDPspFGmPPDIVy4s7hAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T21:50:14.378117Z","bundle_sha256":"760322c289c3545e9e97abcf0c6acb164797e46778eeb7f059c595561203ba47"}}