{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:CZ4PQQ4D2G5EAGIURYKJJGTEO7","short_pith_number":"pith:CZ4PQQ4D","canonical_record":{"source":{"id":"0809.1344","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2008-09-08T14:26:17Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"543954469d3315849bd073c9c1229996b74563b974ae7b902feb20fe701382c2","abstract_canon_sha256":"2f6d5ad50b609426c479558b5240172d47ba951a753bcfc98c46a74d2d010f22"},"schema_version":"1.0"},"canonical_sha256":"1678f84383d1ba4019148e14949a6477de14df86ab15a700af6a1b5448d207dd","source":{"kind":"arxiv","id":"0809.1344","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.1344","created_at":"2026-05-18T00:57:58Z"},{"alias_kind":"arxiv_version","alias_value":"0809.1344v5","created_at":"2026-05-18T00:57:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.1344","created_at":"2026-05-18T00:57:58Z"},{"alias_kind":"pith_short_12","alias_value":"CZ4PQQ4D2G5E","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"CZ4PQQ4D2G5EAGIU","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"CZ4PQQ4D","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:CZ4PQQ4D2G5EAGIURYKJJGTEO7","target":"record","payload":{"canonical_record":{"source":{"id":"0809.1344","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2008-09-08T14:26:17Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"543954469d3315849bd073c9c1229996b74563b974ae7b902feb20fe701382c2","abstract_canon_sha256":"2f6d5ad50b609426c479558b5240172d47ba951a753bcfc98c46a74d2d010f22"},"schema_version":"1.0"},"canonical_sha256":"1678f84383d1ba4019148e14949a6477de14df86ab15a700af6a1b5448d207dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:58.473242Z","signature_b64":"WK7dDcmjer8qsdMzxGPTn3WFgp/pz1kbY0B7kdzH7G2kUHRawSLdD42qgm2nXwZ0qD79sGU1AE2PSrfg0pN+Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1678f84383d1ba4019148e14949a6477de14df86ab15a700af6a1b5448d207dd","last_reissued_at":"2026-05-18T00:57:58.472466Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:58.472466Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0809.1344","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:57:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u2cpyp4s8u32bFGn5P0hUcwepiT5O/Fj8flD3dwSuBA4DyC/Odl5ES3zuNTPm+A1hdMkPcICtQAct1JEN6p/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:27:24.232712Z"},"content_sha256":"357ce7d8aba5bcf3c688283a3f65aaf99ab4dd2db6fa134f389f0b3ee1cad924","schema_version":"1.0","event_id":"sha256:357ce7d8aba5bcf3c688283a3f65aaf99ab4dd2db6fa134f389f0b3ee1cad924"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:CZ4PQQ4D2G5EAGIURYKJJGTEO7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Balanced Unicast and Multicast Capacity Regions of Large 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":"2008-09-08T14:26:17Z","abstract_excerpt":"We consider the question of determining the scaling of the $n^2$-dimensional balanced unicast and the $n 2^n$-dimensional balanced multicast capacity regions of a wireless network with $n$ nodes placed uniformly at random in a square region of area $n$ and communicating over Gaussian fading channels. We identify this scaling of both the balanced unicast and multicast capacity regions in terms of $\\Theta(n)$, out of $2^n$ total possible, cuts. These cuts only depend on the geometry of the locations of the source nodes and their destination nodes and the traffic demands between them, and thus ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.1344","kind":"arxiv","version":5},"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":"2026-05-18T00:57:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HkD7TKc2QRxRbb2reztTucKltWj0ocxHREOhMGDjMJZ3ZMlRo59SDAPK/eZf14vPg3piqa5AV1CBoXX7xJc5Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:27:24.233398Z"},"content_sha256":"0dcc17e658ede5c5dec540ff3763109c0a76ca848b1401c6e32c9e4d099d62f9","schema_version":"1.0","event_id":"sha256:0dcc17e658ede5c5dec540ff3763109c0a76ca848b1401c6e32c9e4d099d62f9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CZ4PQQ4D2G5EAGIURYKJJGTEO7/bundle.json","state_url":"https://pith.science/pith/CZ4PQQ4D2G5EAGIURYKJJGTEO7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CZ4PQQ4D2G5EAGIURYKJJGTEO7/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":"2026-06-04T22:27:24Z","links":{"resolver":"https://pith.science/pith/CZ4PQQ4D2G5EAGIURYKJJGTEO7","bundle":"https://pith.science/pith/CZ4PQQ4D2G5EAGIURYKJJGTEO7/bundle.json","state":"https://pith.science/pith/CZ4PQQ4D2G5EAGIURYKJJGTEO7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CZ4PQQ4D2G5EAGIURYKJJGTEO7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:CZ4PQQ4D2G5EAGIURYKJJGTEO7","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":"2f6d5ad50b609426c479558b5240172d47ba951a753bcfc98c46a74d2d010f22","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2008-09-08T14:26:17Z","title_canon_sha256":"543954469d3315849bd073c9c1229996b74563b974ae7b902feb20fe701382c2"},"schema_version":"1.0","source":{"id":"0809.1344","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.1344","created_at":"2026-05-18T00:57:58Z"},{"alias_kind":"arxiv_version","alias_value":"0809.1344v5","created_at":"2026-05-18T00:57:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.1344","created_at":"2026-05-18T00:57:58Z"},{"alias_kind":"pith_short_12","alias_value":"CZ4PQQ4D2G5E","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"CZ4PQQ4D2G5EAGIU","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"CZ4PQQ4D","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:0dcc17e658ede5c5dec540ff3763109c0a76ca848b1401c6e32c9e4d099d62f9","target":"graph","created_at":"2026-05-18T00:57:58Z","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 consider the question of determining the scaling of the $n^2$-dimensional balanced unicast and the $n 2^n$-dimensional balanced multicast capacity regions of a wireless network with $n$ nodes placed uniformly at random in a square region of area $n$ and communicating over Gaussian fading channels. We identify this scaling of both the balanced unicast and multicast capacity regions in terms of $\\Theta(n)$, out of $2^n$ total possible, cuts. These cuts only depend on the geometry of the locations of the source nodes and their destination nodes and the traffic demands between them, and thus ca","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":"2008-09-08T14:26:17Z","title":"The Balanced Unicast and Multicast Capacity Regions of Large Wireless Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.1344","kind":"arxiv","version":5},"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":"sha256:357ce7d8aba5bcf3c688283a3f65aaf99ab4dd2db6fa134f389f0b3ee1cad924","target":"record","created_at":"2026-05-18T00:57:58Z","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":"2f6d5ad50b609426c479558b5240172d47ba951a753bcfc98c46a74d2d010f22","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2008-09-08T14:26:17Z","title_canon_sha256":"543954469d3315849bd073c9c1229996b74563b974ae7b902feb20fe701382c2"},"schema_version":"1.0","source":{"id":"0809.1344","kind":"arxiv","version":5}},"canonical_sha256":"1678f84383d1ba4019148e14949a6477de14df86ab15a700af6a1b5448d207dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1678f84383d1ba4019148e14949a6477de14df86ab15a700af6a1b5448d207dd","first_computed_at":"2026-05-18T00:57:58.472466Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:58.472466Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WK7dDcmjer8qsdMzxGPTn3WFgp/pz1kbY0B7kdzH7G2kUHRawSLdD42qgm2nXwZ0qD79sGU1AE2PSrfg0pN+Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:58.473242Z","signed_message":"canonical_sha256_bytes"},"source_id":"0809.1344","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:357ce7d8aba5bcf3c688283a3f65aaf99ab4dd2db6fa134f389f0b3ee1cad924","sha256:0dcc17e658ede5c5dec540ff3763109c0a76ca848b1401c6e32c9e4d099d62f9"],"state_sha256":"d061536754aa99bef346e5caea78704300132ef38cd11913e12e407ce0c3de1d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ac1sA91oGTyQcCXNBPP3X/1XUdrDcsLOGeRwAxDO0OkOaV2HeitUVrYfTVQJ8KYTUPJKbWACnGsKDKkxCV6aBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T22:27:24.236991Z","bundle_sha256":"d482b441baacd61457ee5cb20295ec92bcd697606be39d18ba9c3486f13f1220"}}