{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:FXQTNM27OIAAVOEV6VDZ6RA5PE","short_pith_number":"pith:FXQTNM27","canonical_record":{"source":{"id":"1108.3780","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-08-18T15:36:07Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"69e5fdfe166a1870b63e4b3d129514eb7fae5a75bd499d8b67cd681995d3d74b","abstract_canon_sha256":"fe584d6d0195ba5163c1424f94260cea19b58ad82ad07e5eaedbde58c1045669"},"schema_version":"1.0"},"canonical_sha256":"2de136b35f72000ab895f5479f441d79349ce8f9a4a1d2c07369ab7fad4c2e00","source":{"kind":"arxiv","id":"1108.3780","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.3780","created_at":"2026-05-18T04:04:44Z"},{"alias_kind":"arxiv_version","alias_value":"1108.3780v3","created_at":"2026-05-18T04:04:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3780","created_at":"2026-05-18T04:04:44Z"},{"alias_kind":"pith_short_12","alias_value":"FXQTNM27OIAA","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FXQTNM27OIAAVOEV","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FXQTNM27","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:FXQTNM27OIAAVOEV6VDZ6RA5PE","target":"record","payload":{"canonical_record":{"source":{"id":"1108.3780","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-08-18T15:36:07Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"69e5fdfe166a1870b63e4b3d129514eb7fae5a75bd499d8b67cd681995d3d74b","abstract_canon_sha256":"fe584d6d0195ba5163c1424f94260cea19b58ad82ad07e5eaedbde58c1045669"},"schema_version":"1.0"},"canonical_sha256":"2de136b35f72000ab895f5479f441d79349ce8f9a4a1d2c07369ab7fad4c2e00","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:44.739862Z","signature_b64":"E9UiB8Mq4djk0+RCmVawz74L4RYbkJrVqirfQDUIqI3fKmcx6Kwod7l1E6TEfcpTOUHtOpxlX2mVENcZtg8/BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2de136b35f72000ab895f5479f441d79349ce8f9a4a1d2c07369ab7fad4c2e00","last_reissued_at":"2026-05-18T04:04:44.739333Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:44.739333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.3780","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":"2026-05-18T04:04:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"McRtWNk52RAmK6OPEJM3j2jBmL8FI1coTUHNHMemEPDjqcEsUR8qKvkc5Nd/A3gPGHVzulnj69dCN7k7PRKmDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:13:54.450729Z"},"content_sha256":"7c06c6005eaba50da29e2c3b76459ddcca34433e30427ffa9a615f9dba442310","schema_version":"1.0","event_id":"sha256:7c06c6005eaba50da29e2c3b76459ddcca34433e30427ffa9a615f9dba442310"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:FXQTNM27OIAAVOEV6VDZ6RA5PE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Performance Bounds and Associated Design Principles for Multi-Cellular Wireless OFDMA Systems (with Detailed Proofs)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"C. Emre Koksal, Philip Schniter, Rohit Aggarwal","submitted_at":"2011-08-18T15:36:07Z","abstract_excerpt":"In this paper, we consider the downlink of large-scale multi-cellular OFDMA-based networks and study performance bounds of the system as a function of the number of users $K$, the number of base-stations $B$, and the number of resource-blocks $N$. Here, a resource block is a collection of subcarriers such that all such collections, that are disjoint have associated independently fading channels. We derive novel upper and lower bounds on the sum-utility for a general spatial geometry of base stations, a truncated path loss model, and a variety of fading models (Rayleigh, Nakagami-$m$, Weibull, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3780","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":"2026-05-18T04:04:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ll1Rax/m+2Gt3xgLM247YHe3IgyMH3OBIdzex6tIod2zhnnh4oeUwDiPJFlRfS8qkyn+X8aoDaBOnAv3V6yxAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:13:54.451162Z"},"content_sha256":"935b5d0e051656a67cf163def2382a8b3444ddfda696bd797abb03e8eb979039","schema_version":"1.0","event_id":"sha256:935b5d0e051656a67cf163def2382a8b3444ddfda696bd797abb03e8eb979039"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FXQTNM27OIAAVOEV6VDZ6RA5PE/bundle.json","state_url":"https://pith.science/pith/FXQTNM27OIAAVOEV6VDZ6RA5PE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FXQTNM27OIAAVOEV6VDZ6RA5PE/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":"2026-06-06T20:13:54Z","links":{"resolver":"https://pith.science/pith/FXQTNM27OIAAVOEV6VDZ6RA5PE","bundle":"https://pith.science/pith/FXQTNM27OIAAVOEV6VDZ6RA5PE/bundle.json","state":"https://pith.science/pith/FXQTNM27OIAAVOEV6VDZ6RA5PE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FXQTNM27OIAAVOEV6VDZ6RA5PE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:FXQTNM27OIAAVOEV6VDZ6RA5PE","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":"fe584d6d0195ba5163c1424f94260cea19b58ad82ad07e5eaedbde58c1045669","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-08-18T15:36:07Z","title_canon_sha256":"69e5fdfe166a1870b63e4b3d129514eb7fae5a75bd499d8b67cd681995d3d74b"},"schema_version":"1.0","source":{"id":"1108.3780","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.3780","created_at":"2026-05-18T04:04:44Z"},{"alias_kind":"arxiv_version","alias_value":"1108.3780v3","created_at":"2026-05-18T04:04:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3780","created_at":"2026-05-18T04:04:44Z"},{"alias_kind":"pith_short_12","alias_value":"FXQTNM27OIAA","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FXQTNM27OIAAVOEV","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FXQTNM27","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:935b5d0e051656a67cf163def2382a8b3444ddfda696bd797abb03e8eb979039","target":"graph","created_at":"2026-05-18T04:04:44Z","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 this paper, we consider the downlink of large-scale multi-cellular OFDMA-based networks and study performance bounds of the system as a function of the number of users $K$, the number of base-stations $B$, and the number of resource-blocks $N$. Here, a resource block is a collection of subcarriers such that all such collections, that are disjoint have associated independently fading channels. We derive novel upper and lower bounds on the sum-utility for a general spatial geometry of base stations, a truncated path loss model, and a variety of fading models (Rayleigh, Nakagami-$m$, Weibull, ","authors_text":"C. Emre Koksal, Philip Schniter, Rohit Aggarwal","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-08-18T15:36:07Z","title":"Performance Bounds and Associated Design Principles for Multi-Cellular Wireless OFDMA Systems (with Detailed Proofs)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3780","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":"sha256:7c06c6005eaba50da29e2c3b76459ddcca34433e30427ffa9a615f9dba442310","target":"record","created_at":"2026-05-18T04:04:44Z","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":"fe584d6d0195ba5163c1424f94260cea19b58ad82ad07e5eaedbde58c1045669","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-08-18T15:36:07Z","title_canon_sha256":"69e5fdfe166a1870b63e4b3d129514eb7fae5a75bd499d8b67cd681995d3d74b"},"schema_version":"1.0","source":{"id":"1108.3780","kind":"arxiv","version":3}},"canonical_sha256":"2de136b35f72000ab895f5479f441d79349ce8f9a4a1d2c07369ab7fad4c2e00","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2de136b35f72000ab895f5479f441d79349ce8f9a4a1d2c07369ab7fad4c2e00","first_computed_at":"2026-05-18T04:04:44.739333Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:44.739333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E9UiB8Mq4djk0+RCmVawz74L4RYbkJrVqirfQDUIqI3fKmcx6Kwod7l1E6TEfcpTOUHtOpxlX2mVENcZtg8/BA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:44.739862Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.3780","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c06c6005eaba50da29e2c3b76459ddcca34433e30427ffa9a615f9dba442310","sha256:935b5d0e051656a67cf163def2382a8b3444ddfda696bd797abb03e8eb979039"],"state_sha256":"848846a779a5f19d4f06c7f75ad087ca878f640843eb8d089f52e5f954e06257"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K5aYABAvxJ1s/zqw4OUhwW/nNuzDSHk4gV4qrFbNbGihJ4xsQlZryAtrLgTWFZg4tifGnJNAg4qvT66ijllYDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T20:13:54.454452Z","bundle_sha256":"44a517904954a53aaacd7af957619918ed6c2efd46e7ffd92cb49ab1946ec942"}}