{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:Z2UVJYQSQ7L7FGLD6C2KBND3NS","short_pith_number":"pith:Z2UVJYQS","canonical_record":{"source":{"id":"1901.02933","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-01-09T21:14:53Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"492082d6cc54703ee6b46479428e58b68fc58702a7112c4d26a1fd6b89b2fa41","abstract_canon_sha256":"f3913fc7a78f8d107b0f2728d1a2c8e3d8263085fed50f9f7ca24a9835ee6b47"},"schema_version":"1.0"},"canonical_sha256":"cea954e21287d7f29963f0b4a0b47b6c8ac0374b4b9a540e14bb7dcaea05a14b","source":{"kind":"arxiv","id":"1901.02933","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.02933","created_at":"2026-05-17T23:56:35Z"},{"alias_kind":"arxiv_version","alias_value":"1901.02933v1","created_at":"2026-05-17T23:56:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.02933","created_at":"2026-05-17T23:56:35Z"},{"alias_kind":"pith_short_12","alias_value":"Z2UVJYQSQ7L7","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"Z2UVJYQSQ7L7FGLD","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"Z2UVJYQS","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:Z2UVJYQSQ7L7FGLD6C2KBND3NS","target":"record","payload":{"canonical_record":{"source":{"id":"1901.02933","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-01-09T21:14:53Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"492082d6cc54703ee6b46479428e58b68fc58702a7112c4d26a1fd6b89b2fa41","abstract_canon_sha256":"f3913fc7a78f8d107b0f2728d1a2c8e3d8263085fed50f9f7ca24a9835ee6b47"},"schema_version":"1.0"},"canonical_sha256":"cea954e21287d7f29963f0b4a0b47b6c8ac0374b4b9a540e14bb7dcaea05a14b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:35.989348Z","signature_b64":"ZCJHfAEgFe47RyHNKX0mHiAn3Jvn3UsA/587gf5K1XkGNwASMgW9ONIpHBlzZej8r11l75AUqX88BtpSC3djBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cea954e21287d7f29963f0b4a0b47b6c8ac0374b4b9a540e14bb7dcaea05a14b","last_reissued_at":"2026-05-17T23:56:35.988852Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:35.988852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.02933","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":"2026-05-17T23:56:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q36gJzQ/LDKDL09EC4A4ozE4EHXDAH2WHVV6d00wUD3NKKlU+UgCkAh8/VPblxs2u3Pm3kJXROTEbt55Lqc5Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:57:47.852898Z"},"content_sha256":"ddcc640aa84927d84324dc57e35bddf9c12731d5723cfa8b6490af1188c894f4","schema_version":"1.0","event_id":"sha256:ddcc640aa84927d84324dc57e35bddf9c12731d5723cfa8b6490af1188c894f4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:Z2UVJYQSQ7L7FGLD6C2KBND3NS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial-time Capacity Calculation and Scheduling for Half-Duplex 1-2-1 Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Christina Fragouli, Giuseppe Caire, Martina Cardone, Yahya H. Ezzeldin","submitted_at":"2019-01-09T21:14:53Z","abstract_excerpt":"This paper studies the 1-2-1 half-duplex network model, where two half-duplex nodes can communicate only if they point `beams' at each other; otherwise, no signal can be exchanged or interference can be generated. The main result of this paper is the design of two polynomial-time algorithms that: (i) compute the approximate capacity of the 1-2-1 half-duplex network and, (ii) find the network schedule optimal for the approximate capacity. The paper starts by expressing the approximate capacity as a linear program with an exponential number of constraints. A core technical component consists of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02933","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":"2026-05-17T23:56:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wMVEjyfr0+fD8jzPy8t3OXsj3jjq4SuIuCT9NVd7NDiYyLk9rvnl6+qO6Sso4104el4FgMZYu/aTvTcLz/vBAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:57:47.853244Z"},"content_sha256":"ed802da81c90ec75047ce8f249493b9a6297195c96c0f86b0dddc31ece1fefaf","schema_version":"1.0","event_id":"sha256:ed802da81c90ec75047ce8f249493b9a6297195c96c0f86b0dddc31ece1fefaf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z2UVJYQSQ7L7FGLD6C2KBND3NS/bundle.json","state_url":"https://pith.science/pith/Z2UVJYQSQ7L7FGLD6C2KBND3NS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z2UVJYQSQ7L7FGLD6C2KBND3NS/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":"2026-05-30T08:57:47Z","links":{"resolver":"https://pith.science/pith/Z2UVJYQSQ7L7FGLD6C2KBND3NS","bundle":"https://pith.science/pith/Z2UVJYQSQ7L7FGLD6C2KBND3NS/bundle.json","state":"https://pith.science/pith/Z2UVJYQSQ7L7FGLD6C2KBND3NS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z2UVJYQSQ7L7FGLD6C2KBND3NS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:Z2UVJYQSQ7L7FGLD6C2KBND3NS","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":"f3913fc7a78f8d107b0f2728d1a2c8e3d8263085fed50f9f7ca24a9835ee6b47","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-01-09T21:14:53Z","title_canon_sha256":"492082d6cc54703ee6b46479428e58b68fc58702a7112c4d26a1fd6b89b2fa41"},"schema_version":"1.0","source":{"id":"1901.02933","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.02933","created_at":"2026-05-17T23:56:35Z"},{"alias_kind":"arxiv_version","alias_value":"1901.02933v1","created_at":"2026-05-17T23:56:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.02933","created_at":"2026-05-17T23:56:35Z"},{"alias_kind":"pith_short_12","alias_value":"Z2UVJYQSQ7L7","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"Z2UVJYQSQ7L7FGLD","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"Z2UVJYQS","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:ed802da81c90ec75047ce8f249493b9a6297195c96c0f86b0dddc31ece1fefaf","target":"graph","created_at":"2026-05-17T23:56:35Z","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":"This paper studies the 1-2-1 half-duplex network model, where two half-duplex nodes can communicate only if they point `beams' at each other; otherwise, no signal can be exchanged or interference can be generated. The main result of this paper is the design of two polynomial-time algorithms that: (i) compute the approximate capacity of the 1-2-1 half-duplex network and, (ii) find the network schedule optimal for the approximate capacity. The paper starts by expressing the approximate capacity as a linear program with an exponential number of constraints. A core technical component consists of ","authors_text":"Christina Fragouli, Giuseppe Caire, Martina Cardone, Yahya H. Ezzeldin","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-01-09T21:14:53Z","title":"Polynomial-time Capacity Calculation and Scheduling for Half-Duplex 1-2-1 Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02933","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:ddcc640aa84927d84324dc57e35bddf9c12731d5723cfa8b6490af1188c894f4","target":"record","created_at":"2026-05-17T23:56:35Z","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":"f3913fc7a78f8d107b0f2728d1a2c8e3d8263085fed50f9f7ca24a9835ee6b47","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-01-09T21:14:53Z","title_canon_sha256":"492082d6cc54703ee6b46479428e58b68fc58702a7112c4d26a1fd6b89b2fa41"},"schema_version":"1.0","source":{"id":"1901.02933","kind":"arxiv","version":1}},"canonical_sha256":"cea954e21287d7f29963f0b4a0b47b6c8ac0374b4b9a540e14bb7dcaea05a14b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cea954e21287d7f29963f0b4a0b47b6c8ac0374b4b9a540e14bb7dcaea05a14b","first_computed_at":"2026-05-17T23:56:35.988852Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:35.988852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZCJHfAEgFe47RyHNKX0mHiAn3Jvn3UsA/587gf5K1XkGNwASMgW9ONIpHBlzZej8r11l75AUqX88BtpSC3djBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:35.989348Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.02933","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ddcc640aa84927d84324dc57e35bddf9c12731d5723cfa8b6490af1188c894f4","sha256:ed802da81c90ec75047ce8f249493b9a6297195c96c0f86b0dddc31ece1fefaf"],"state_sha256":"dda4085529642d03bbc440d5da3f32d3a3e6726846a3f7e9dc15d2eb3a5c9bbf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LAczvNpvTS7BR6xgC61CA/1Q0q41pJOyJ5BvhMlkrdHgcgyf2kuAfB5Sqkq8MFvdKJ69TFGJQ/P8kP2aaDhEDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:57:47.855222Z","bundle_sha256":"16869faf738ed5566d68d764863ef885e091d197d4e09861c63038bb3f344fa2"}}