{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:UZGPHSG5G6ASYQXOOU32YGXNMX","short_pith_number":"pith:UZGPHSG5","canonical_record":{"source":{"id":"0704.2353","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cs.IT","submitted_at":"2007-04-18T15:57:37Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"fa6028d4c9df50111f688cb2cc701af461c794b15eba8cb5cf68e258bc312f7f","abstract_canon_sha256":"a8e39ee6cc6aed00ef5a58aa834aad5381e0d1f9b6e8910eacf299738d2c91d5"},"schema_version":"1.0"},"canonical_sha256":"a64cf3c8dd37812c42ee7537ac1aed65ff9ff28216b42b284caaf0f72cf747ae","source":{"kind":"arxiv","id":"0704.2353","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0704.2353","created_at":"2026-05-18T00:58:02Z"},{"alias_kind":"arxiv_version","alias_value":"0704.2353v2","created_at":"2026-05-18T00:58:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.2353","created_at":"2026-05-18T00:58:02Z"},{"alias_kind":"pith_short_12","alias_value":"UZGPHSG5G6AS","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"UZGPHSG5G6ASYQXO","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"UZGPHSG5","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:UZGPHSG5G6ASYQXOOU32YGXNMX","target":"record","payload":{"canonical_record":{"source":{"id":"0704.2353","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cs.IT","submitted_at":"2007-04-18T15:57:37Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"fa6028d4c9df50111f688cb2cc701af461c794b15eba8cb5cf68e258bc312f7f","abstract_canon_sha256":"a8e39ee6cc6aed00ef5a58aa834aad5381e0d1f9b6e8910eacf299738d2c91d5"},"schema_version":"1.0"},"canonical_sha256":"a64cf3c8dd37812c42ee7537ac1aed65ff9ff28216b42b284caaf0f72cf747ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:02.419927Z","signature_b64":"6MHsJNmAMpgdf5SfJmDn7//YiZsA+doKqz87jwon7t5AqEY7eob8Ub5cyfPw4M+uK9Wt8SWIhOWiU9yqImCzDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a64cf3c8dd37812c42ee7537ac1aed65ff9ff28216b42b284caaf0f72cf747ae","last_reissued_at":"2026-05-18T00:58:02.419247Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:02.419247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0704.2353","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:58:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pqnHd5jLWn7tDuYyPAsb4ZVlbL+37izs5mSkUeVarvDX1uMbhFAh6BKQgDUyz12aGoDRKQKJQf3jnP5m7sBcAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:08:09.107186Z"},"content_sha256":"4951591c45fde827809ed28639539433359d256ccf49837f2f3c9711e36a0564","schema_version":"1.0","event_id":"sha256:4951591c45fde827809ed28639539433359d256ccf49837f2f3c9711e36a0564"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:UZGPHSG5G6ASYQXOOU32YGXNMX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Scaling Laws of Cognitive Networks","license":"","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Mai Vu, Masoud Sharif, Natasha Devroye, Vahid Tarokh","submitted_at":"2007-04-18T15:57:37Z","abstract_excerpt":"We consider a cognitive network consisting of n random pairs of cognitive transmitters and receivers communicating simultaneously in the presence of multiple primary users. Of interest is how the maximum throughput achieved by the cognitive users scales with n. Furthermore, how far these users must be from a primary user to guarantee a given primary outage. Two scenarios are considered for the network scaling law: (i) when each cognitive transmitter uses constant power to communicate with a cognitive receiver at a bounded distance away, and (ii) when each cognitive transmitter scales its power"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.2353","kind":"arxiv","version":2},"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":"2026-05-18T00:58:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HDhEp5T3DSKIyzNOzOZeEGQIz879Z1XRZ8ze7u3y8FFbRy7M7rV9+YPA7BeQ4Q1sdF+s1RBPCMu8VaQyWmilDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:08:09.107891Z"},"content_sha256":"9a1caa483838074eb2d5bebfa4bbe36dd95f94304e7b4a882dedd9c2a66023df","schema_version":"1.0","event_id":"sha256:9a1caa483838074eb2d5bebfa4bbe36dd95f94304e7b4a882dedd9c2a66023df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UZGPHSG5G6ASYQXOOU32YGXNMX/bundle.json","state_url":"https://pith.science/pith/UZGPHSG5G6ASYQXOOU32YGXNMX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UZGPHSG5G6ASYQXOOU32YGXNMX/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":"2026-05-26T04:08:09Z","links":{"resolver":"https://pith.science/pith/UZGPHSG5G6ASYQXOOU32YGXNMX","bundle":"https://pith.science/pith/UZGPHSG5G6ASYQXOOU32YGXNMX/bundle.json","state":"https://pith.science/pith/UZGPHSG5G6ASYQXOOU32YGXNMX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UZGPHSG5G6ASYQXOOU32YGXNMX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:UZGPHSG5G6ASYQXOOU32YGXNMX","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":"a8e39ee6cc6aed00ef5a58aa834aad5381e0d1f9b6e8910eacf299738d2c91d5","cross_cats_sorted":["math.IT"],"license":"","primary_cat":"cs.IT","submitted_at":"2007-04-18T15:57:37Z","title_canon_sha256":"fa6028d4c9df50111f688cb2cc701af461c794b15eba8cb5cf68e258bc312f7f"},"schema_version":"1.0","source":{"id":"0704.2353","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0704.2353","created_at":"2026-05-18T00:58:02Z"},{"alias_kind":"arxiv_version","alias_value":"0704.2353v2","created_at":"2026-05-18T00:58:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.2353","created_at":"2026-05-18T00:58:02Z"},{"alias_kind":"pith_short_12","alias_value":"UZGPHSG5G6AS","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"UZGPHSG5G6ASYQXO","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"UZGPHSG5","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:9a1caa483838074eb2d5bebfa4bbe36dd95f94304e7b4a882dedd9c2a66023df","target":"graph","created_at":"2026-05-18T00:58:02Z","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 a cognitive network consisting of n random pairs of cognitive transmitters and receivers communicating simultaneously in the presence of multiple primary users. Of interest is how the maximum throughput achieved by the cognitive users scales with n. Furthermore, how far these users must be from a primary user to guarantee a given primary outage. Two scenarios are considered for the network scaling law: (i) when each cognitive transmitter uses constant power to communicate with a cognitive receiver at a bounded distance away, and (ii) when each cognitive transmitter scales its power","authors_text":"Mai Vu, Masoud Sharif, Natasha Devroye, Vahid Tarokh","cross_cats":["math.IT"],"headline":"","license":"","primary_cat":"cs.IT","submitted_at":"2007-04-18T15:57:37Z","title":"Scaling Laws of Cognitive Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.2353","kind":"arxiv","version":2},"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":"sha256:4951591c45fde827809ed28639539433359d256ccf49837f2f3c9711e36a0564","target":"record","created_at":"2026-05-18T00:58:02Z","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":"a8e39ee6cc6aed00ef5a58aa834aad5381e0d1f9b6e8910eacf299738d2c91d5","cross_cats_sorted":["math.IT"],"license":"","primary_cat":"cs.IT","submitted_at":"2007-04-18T15:57:37Z","title_canon_sha256":"fa6028d4c9df50111f688cb2cc701af461c794b15eba8cb5cf68e258bc312f7f"},"schema_version":"1.0","source":{"id":"0704.2353","kind":"arxiv","version":2}},"canonical_sha256":"a64cf3c8dd37812c42ee7537ac1aed65ff9ff28216b42b284caaf0f72cf747ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a64cf3c8dd37812c42ee7537ac1aed65ff9ff28216b42b284caaf0f72cf747ae","first_computed_at":"2026-05-18T00:58:02.419247Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:02.419247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6MHsJNmAMpgdf5SfJmDn7//YiZsA+doKqz87jwon7t5AqEY7eob8Ub5cyfPw4M+uK9Wt8SWIhOWiU9yqImCzDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:02.419927Z","signed_message":"canonical_sha256_bytes"},"source_id":"0704.2353","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4951591c45fde827809ed28639539433359d256ccf49837f2f3c9711e36a0564","sha256:9a1caa483838074eb2d5bebfa4bbe36dd95f94304e7b4a882dedd9c2a66023df"],"state_sha256":"b65f6a29ea54308a0c62608046311627d5cae88a74342046654b22ad583a96f8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jlYL/PPo1mmJ7vFaMoq3sW1/TQf8v0gKaskVsB2npCY6LveJYBclJcra90XWwHO/ESLTH+I0xjzemtlB84j9DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T04:08:09.111931Z","bundle_sha256":"1da925219918dbd033cd1eb15f72d00c84938fb4797d31949b8bafb727421db8"}}