{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ZQF3AHUJWT3JMEYILGPXMF2KUE","short_pith_number":"pith:ZQF3AHUJ","canonical_record":{"source":{"id":"1207.3018","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-12T16:51:32Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"94bb9df84a98932cf2a73ab48666543ebb85128bff9e1ed11b6045019d7990c2","abstract_canon_sha256":"4ae253a0fc807bd0f229e8f554cc9867333275ea445f2b2032cf354cf52ccc7e"},"schema_version":"1.0"},"canonical_sha256":"cc0bb01e89b4f6961308599f76174aa13f20b4f7ea1b1674dafa3b2acfc430a1","source":{"kind":"arxiv","id":"1207.3018","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3018","created_at":"2026-05-18T03:33:37Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3018v2","created_at":"2026-05-18T03:33:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3018","created_at":"2026-05-18T03:33:37Z"},{"alias_kind":"pith_short_12","alias_value":"ZQF3AHUJWT3J","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZQF3AHUJWT3JMEYI","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZQF3AHUJ","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ZQF3AHUJWT3JMEYILGPXMF2KUE","target":"record","payload":{"canonical_record":{"source":{"id":"1207.3018","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-12T16:51:32Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"94bb9df84a98932cf2a73ab48666543ebb85128bff9e1ed11b6045019d7990c2","abstract_canon_sha256":"4ae253a0fc807bd0f229e8f554cc9867333275ea445f2b2032cf354cf52ccc7e"},"schema_version":"1.0"},"canonical_sha256":"cc0bb01e89b4f6961308599f76174aa13f20b4f7ea1b1674dafa3b2acfc430a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:37.701124Z","signature_b64":"zG8EFb5mAEws68WLB+j2t3FZlCFal51l7dfukVaxXAsf/qyF7rmgQN5f+yipW0z09iiXUjSxriMUHTQvAYDqCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc0bb01e89b4f6961308599f76174aa13f20b4f7ea1b1674dafa3b2acfc430a1","last_reissued_at":"2026-05-18T03:33:37.700385Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:37.700385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.3018","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":"2026-05-18T03:33:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I4Qarivym6k07GXAiVFACO9uLeS80aSiVe5wqUrO++1LSdGGgWTZNpn8iggbXC/2KN12SIj5tMKMciDA15a7AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T05:40:05.241025Z"},"content_sha256":"0f64018619e2addba33febc899563ae3cd7fb08b77368bdcb3ae436a1344c0d4","schema_version":"1.0","event_id":"sha256:0f64018619e2addba33febc899563ae3cd7fb08b77368bdcb3ae436a1344c0d4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ZQF3AHUJWT3JMEYILGPXMF2KUE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fundamental Limits of Communications in Interference Networks-Part I: Basic Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Reza K. Farsani","submitted_at":"2012-07-12T16:51:32Z","abstract_excerpt":"In these series of multi-part papers, a systematic study of fundamental limits of communications in interference networks is established. Here, interference network is referred to as a general single-hop communication scenario with arbitrary number of transmitters and receivers, and also arbitrary distribution of messages among transmitters and receivers. It is shown that the information flow in such networks follows similar derivations from many aspects. This systematic study is launched by considering the basic building blocks in Part I. The Multiple Access Channel (MAC), the Broadcast Chann"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3018","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":"2026-05-18T03:33:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cOCWkwcNCAZpXmAHAaqFK3fvRxnB1DjcfvwiCLjTAsLZeYueWjDEFYHEV3LmvsUK9wAb1TjBlt5xYs/1YtNcAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T05:40:05.241384Z"},"content_sha256":"4a78007b5a50048a498798b281b0190f495b2430cedb1b630381c3da640929c5","schema_version":"1.0","event_id":"sha256:4a78007b5a50048a498798b281b0190f495b2430cedb1b630381c3da640929c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZQF3AHUJWT3JMEYILGPXMF2KUE/bundle.json","state_url":"https://pith.science/pith/ZQF3AHUJWT3JMEYILGPXMF2KUE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZQF3AHUJWT3JMEYILGPXMF2KUE/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":"2026-06-25T05:40:05Z","links":{"resolver":"https://pith.science/pith/ZQF3AHUJWT3JMEYILGPXMF2KUE","bundle":"https://pith.science/pith/ZQF3AHUJWT3JMEYILGPXMF2KUE/bundle.json","state":"https://pith.science/pith/ZQF3AHUJWT3JMEYILGPXMF2KUE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZQF3AHUJWT3JMEYILGPXMF2KUE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZQF3AHUJWT3JMEYILGPXMF2KUE","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":"4ae253a0fc807bd0f229e8f554cc9867333275ea445f2b2032cf354cf52ccc7e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-12T16:51:32Z","title_canon_sha256":"94bb9df84a98932cf2a73ab48666543ebb85128bff9e1ed11b6045019d7990c2"},"schema_version":"1.0","source":{"id":"1207.3018","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3018","created_at":"2026-05-18T03:33:37Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3018v2","created_at":"2026-05-18T03:33:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3018","created_at":"2026-05-18T03:33:37Z"},{"alias_kind":"pith_short_12","alias_value":"ZQF3AHUJWT3J","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZQF3AHUJWT3JMEYI","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZQF3AHUJ","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:4a78007b5a50048a498798b281b0190f495b2430cedb1b630381c3da640929c5","target":"graph","created_at":"2026-05-18T03:33:37Z","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 these series of multi-part papers, a systematic study of fundamental limits of communications in interference networks is established. Here, interference network is referred to as a general single-hop communication scenario with arbitrary number of transmitters and receivers, and also arbitrary distribution of messages among transmitters and receivers. It is shown that the information flow in such networks follows similar derivations from many aspects. This systematic study is launched by considering the basic building blocks in Part I. The Multiple Access Channel (MAC), the Broadcast Chann","authors_text":"Reza K. Farsani","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-12T16:51:32Z","title":"Fundamental Limits of Communications in Interference Networks-Part I: Basic Structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3018","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":"sha256:0f64018619e2addba33febc899563ae3cd7fb08b77368bdcb3ae436a1344c0d4","target":"record","created_at":"2026-05-18T03:33:37Z","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":"4ae253a0fc807bd0f229e8f554cc9867333275ea445f2b2032cf354cf52ccc7e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-12T16:51:32Z","title_canon_sha256":"94bb9df84a98932cf2a73ab48666543ebb85128bff9e1ed11b6045019d7990c2"},"schema_version":"1.0","source":{"id":"1207.3018","kind":"arxiv","version":2}},"canonical_sha256":"cc0bb01e89b4f6961308599f76174aa13f20b4f7ea1b1674dafa3b2acfc430a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc0bb01e89b4f6961308599f76174aa13f20b4f7ea1b1674dafa3b2acfc430a1","first_computed_at":"2026-05-18T03:33:37.700385Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:37.700385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zG8EFb5mAEws68WLB+j2t3FZlCFal51l7dfukVaxXAsf/qyF7rmgQN5f+yipW0z09iiXUjSxriMUHTQvAYDqCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:37.701124Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.3018","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f64018619e2addba33febc899563ae3cd7fb08b77368bdcb3ae436a1344c0d4","sha256:4a78007b5a50048a498798b281b0190f495b2430cedb1b630381c3da640929c5"],"state_sha256":"c7c75363e905132ca3702fbb8acb6f54738244f6840fd6d128b64ef8ef17232a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FENR9VLS4Icvl3NZgIKx/aoglbwIa++P01Yt0gDMdSVmE8twAajYCeQL4LBwRLOcRO+2P5YFTWQVSXZJl/IhDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T05:40:05.243359Z","bundle_sha256":"f9fe5fdaf29cc3135e46a8b634c2e7e8f14ad223b9a0db6fdce2d3d2ed844a26"}}