{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:F6WQR77DLTAKDJFMBKYO4LVUHH","short_pith_number":"pith:F6WQR77D","canonical_record":{"source":{"id":"1010.0781","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-10-05T07:16:52Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"3f531bcfdd887d50710b3f3768073096ae5c4df69ac19a6564cdfd2b902c2b98","abstract_canon_sha256":"4ad74a112c6c84c7614d7dc7d093f494778fcd17188afc9bb03014519803928b"},"schema_version":"1.0"},"canonical_sha256":"2fad08ffe35cc0a1a4ac0ab0ee2eb439e463237be751736ba83c9b67dee113de","source":{"kind":"arxiv","id":"1010.0781","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0781","created_at":"2026-05-18T02:23:46Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0781v1","created_at":"2026-05-18T02:23:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0781","created_at":"2026-05-18T02:23:46Z"},{"alias_kind":"pith_short_12","alias_value":"F6WQR77DLTAK","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"F6WQR77DLTAKDJFM","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"F6WQR77D","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:F6WQR77DLTAKDJFMBKYO4LVUHH","target":"record","payload":{"canonical_record":{"source":{"id":"1010.0781","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-10-05T07:16:52Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"3f531bcfdd887d50710b3f3768073096ae5c4df69ac19a6564cdfd2b902c2b98","abstract_canon_sha256":"4ad74a112c6c84c7614d7dc7d093f494778fcd17188afc9bb03014519803928b"},"schema_version":"1.0"},"canonical_sha256":"2fad08ffe35cc0a1a4ac0ab0ee2eb439e463237be751736ba83c9b67dee113de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:23:46.912950Z","signature_b64":"4jQaZM6MQk2Uc5io7c0XHFnmV2a9FhRoWVSyUUmz3y05zAMcaZlyYPk9wmQQ86nGe01qBb6IHOG6tbdvogLuAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2fad08ffe35cc0a1a4ac0ab0ee2eb439e463237be751736ba83c9b67dee113de","last_reissued_at":"2026-05-18T02:23:46.912347Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:23:46.912347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.0781","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:23:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9XvyZHvCxmkxHj8jss4SV54TLnskpIA8psvs8QyN4vYZHf/tlWwW9ciUZbV5x3ZxqxSufk/xeDqHrOztFF/6Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T21:37:10.018626Z"},"content_sha256":"eeecfa51d3f6dc0760f5f5ad73c1cf4210971de1e5d07118123647d16334b023","schema_version":"1.0","event_id":"sha256:eeecfa51d3f6dc0760f5f5ad73c1cf4210971de1e5d07118123647d16334b023"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:F6WQR77DLTAKDJFMBKYO4LVUHH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transmission Capacity of Spectrum Sharing Ad-hoc Networks with Multiple Antennas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Rahul Vaze","submitted_at":"2010-10-05T07:16:52Z","abstract_excerpt":"Two coexisting ad-hoc networks, primary and secondary, are considered, where each node of the primary network has a single antenna, while each node of the secondary network is equipped with multiple antennas. Using multiple antennas, each secondary transmitter uses some of its spatial transmit degrees of freedom (STDOF) to null its interference towards the primary receivers, while each secondary receiver employs interference cancelation using some of its spatial receive degrees of freedom (SRDOF). This paper derives the optimal STDOF for nulling and SRDOF for interference cancelation that maxi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0781","kind":"arxiv","version":1},"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":"2026-05-18T02:23:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DX8MoCLLhwrJlM53888y2PRPEukQk99ur+2d/cWuTu2BBdiKivKk/fIR989/X/Wnp+cH8Nta4hoUe+TXN5mOAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T21:37:10.019095Z"},"content_sha256":"601200bad33cb9210225b4468e1c2ee1cc474ee80cf794422521a2eaaf68a856","schema_version":"1.0","event_id":"sha256:601200bad33cb9210225b4468e1c2ee1cc474ee80cf794422521a2eaaf68a856"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F6WQR77DLTAKDJFMBKYO4LVUHH/bundle.json","state_url":"https://pith.science/pith/F6WQR77DLTAKDJFMBKYO4LVUHH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F6WQR77DLTAKDJFMBKYO4LVUHH/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":"2026-06-25T21:37:10Z","links":{"resolver":"https://pith.science/pith/F6WQR77DLTAKDJFMBKYO4LVUHH","bundle":"https://pith.science/pith/F6WQR77DLTAKDJFMBKYO4LVUHH/bundle.json","state":"https://pith.science/pith/F6WQR77DLTAKDJFMBKYO4LVUHH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F6WQR77DLTAKDJFMBKYO4LVUHH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:F6WQR77DLTAKDJFMBKYO4LVUHH","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":"4ad74a112c6c84c7614d7dc7d093f494778fcd17188afc9bb03014519803928b","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-10-05T07:16:52Z","title_canon_sha256":"3f531bcfdd887d50710b3f3768073096ae5c4df69ac19a6564cdfd2b902c2b98"},"schema_version":"1.0","source":{"id":"1010.0781","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0781","created_at":"2026-05-18T02:23:46Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0781v1","created_at":"2026-05-18T02:23:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0781","created_at":"2026-05-18T02:23:46Z"},{"alias_kind":"pith_short_12","alias_value":"F6WQR77DLTAK","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"F6WQR77DLTAKDJFM","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"F6WQR77D","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:601200bad33cb9210225b4468e1c2ee1cc474ee80cf794422521a2eaaf68a856","target":"graph","created_at":"2026-05-18T02:23:46Z","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":"Two coexisting ad-hoc networks, primary and secondary, are considered, where each node of the primary network has a single antenna, while each node of the secondary network is equipped with multiple antennas. Using multiple antennas, each secondary transmitter uses some of its spatial transmit degrees of freedom (STDOF) to null its interference towards the primary receivers, while each secondary receiver employs interference cancelation using some of its spatial receive degrees of freedom (SRDOF). This paper derives the optimal STDOF for nulling and SRDOF for interference cancelation that maxi","authors_text":"Rahul Vaze","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-10-05T07:16:52Z","title":"Transmission Capacity of Spectrum Sharing Ad-hoc Networks with Multiple Antennas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0781","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:eeecfa51d3f6dc0760f5f5ad73c1cf4210971de1e5d07118123647d16334b023","target":"record","created_at":"2026-05-18T02:23:46Z","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":"4ad74a112c6c84c7614d7dc7d093f494778fcd17188afc9bb03014519803928b","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-10-05T07:16:52Z","title_canon_sha256":"3f531bcfdd887d50710b3f3768073096ae5c4df69ac19a6564cdfd2b902c2b98"},"schema_version":"1.0","source":{"id":"1010.0781","kind":"arxiv","version":1}},"canonical_sha256":"2fad08ffe35cc0a1a4ac0ab0ee2eb439e463237be751736ba83c9b67dee113de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fad08ffe35cc0a1a4ac0ab0ee2eb439e463237be751736ba83c9b67dee113de","first_computed_at":"2026-05-18T02:23:46.912347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:46.912347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4jQaZM6MQk2Uc5io7c0XHFnmV2a9FhRoWVSyUUmz3y05zAMcaZlyYPk9wmQQ86nGe01qBb6IHOG6tbdvogLuAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:46.912950Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.0781","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eeecfa51d3f6dc0760f5f5ad73c1cf4210971de1e5d07118123647d16334b023","sha256:601200bad33cb9210225b4468e1c2ee1cc474ee80cf794422521a2eaaf68a856"],"state_sha256":"ec0ea84f3dd3d097a414e15a6a10cf1102aa19427c9699773b3d70baa86fd73f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VJIiXLOVmfB7Bpc6pdIzuFre4vv/Svm1Gt/mMmvMEfRCEK8E1wFDGln4qcCG2Q2L4k738mD2oy/VCmZIQe2kBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T21:37:10.021709Z","bundle_sha256":"849acb682dd1fc8b90d3ab3ff9885f71b0ca4d8c31fd52569959eac998e8c823"}}