{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GHCRMU7GVB6YOWTHUC4RXQI4RH","short_pith_number":"pith:GHCRMU7G","canonical_record":{"source":{"id":"1710.02252","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-10-06T01:31:19Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"4ad6b5644ad47f45c99728c24727dba7234738d15cf9deec752f4ba3290de77d","abstract_canon_sha256":"99039ae5a2e73a4f665fcd9a5f9d0d1604b4c0ecc9be1aaba79951dcffab98e0"},"schema_version":"1.0"},"canonical_sha256":"31c51653e6a87d875a67a0b91bc11c89da255d6046c602c999c4fbb23dd53093","source":{"kind":"arxiv","id":"1710.02252","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.02252","created_at":"2026-05-18T00:33:34Z"},{"alias_kind":"arxiv_version","alias_value":"1710.02252v1","created_at":"2026-05-18T00:33:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.02252","created_at":"2026-05-18T00:33:34Z"},{"alias_kind":"pith_short_12","alias_value":"GHCRMU7GVB6Y","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GHCRMU7GVB6YOWTH","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GHCRMU7G","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GHCRMU7GVB6YOWTHUC4RXQI4RH","target":"record","payload":{"canonical_record":{"source":{"id":"1710.02252","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-10-06T01:31:19Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"4ad6b5644ad47f45c99728c24727dba7234738d15cf9deec752f4ba3290de77d","abstract_canon_sha256":"99039ae5a2e73a4f665fcd9a5f9d0d1604b4c0ecc9be1aaba79951dcffab98e0"},"schema_version":"1.0"},"canonical_sha256":"31c51653e6a87d875a67a0b91bc11c89da255d6046c602c999c4fbb23dd53093","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:34.011739Z","signature_b64":"2Gtu0xmkgfEJjhHmPZplfobE7GW6YIrA8iU5HNy4ZCVYCGm+DXa4bbaZA9kI5x+7QOs8wfrJDc/0JwXAcLATAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31c51653e6a87d875a67a0b91bc11c89da255d6046c602c999c4fbb23dd53093","last_reissued_at":"2026-05-18T00:33:34.011041Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:34.011041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.02252","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":"2026-05-18T00:33:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F6b/eslX1HE4hpOxKhAzJ1qtvVVEGDgKYO+Cqpw1ddqeDkZcuEvOdLbpZvfV7DQhdDeosM5wUncW6PIHJ0sxCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T16:14:27.881653Z"},"content_sha256":"831fc84b450924045bee7f3b7e54c74e2c31c2e5b4f0ab33bd4f64da60507a15","schema_version":"1.0","event_id":"sha256:831fc84b450924045bee7f3b7e54c74e2c31c2e5b4f0ab33bd4f64da60507a15"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GHCRMU7GVB6YOWTHUC4RXQI4RH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Improved Upper Bound on the Network Function Computing Capacity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Congduan Li, Raymond W. Yeung, Shenghao Yang, Xuan Guang","submitted_at":"2017-10-06T01:31:19Z","abstract_excerpt":"The problem of network function computation over a directed acyclic network is investigated in this paper. In such a network, a sink node desires to compute with zero error a {\\em target function}, of which the inputs are generated at multiple source nodes. The edges in the network are assumed to be error-free and have limited capacity. The nodes in the network are assumed to have unbounded computing capability and be able to perform network coding. The {\\em computing rate} of a network code that can compute the target function over the network is the average number of times that the target fu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02252","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":"2026-05-18T00:33:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vggbJZxhBzCIgsbcOhHps9sVW5ZNXoxKQ2Ax8SiR9qLRwVzEs0X4XMsrgp3j1b7LItV1dmzfo9gI66gaIGs+AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T16:14:27.882031Z"},"content_sha256":"188f23aab0be0f6ecf631ca2e179bb970cff32f346b7f513b6a311fccd268843","schema_version":"1.0","event_id":"sha256:188f23aab0be0f6ecf631ca2e179bb970cff32f346b7f513b6a311fccd268843"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GHCRMU7GVB6YOWTHUC4RXQI4RH/bundle.json","state_url":"https://pith.science/pith/GHCRMU7GVB6YOWTHUC4RXQI4RH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GHCRMU7GVB6YOWTHUC4RXQI4RH/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":"2026-06-08T16:14:27Z","links":{"resolver":"https://pith.science/pith/GHCRMU7GVB6YOWTHUC4RXQI4RH","bundle":"https://pith.science/pith/GHCRMU7GVB6YOWTHUC4RXQI4RH/bundle.json","state":"https://pith.science/pith/GHCRMU7GVB6YOWTHUC4RXQI4RH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GHCRMU7GVB6YOWTHUC4RXQI4RH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GHCRMU7GVB6YOWTHUC4RXQI4RH","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":"99039ae5a2e73a4f665fcd9a5f9d0d1604b4c0ecc9be1aaba79951dcffab98e0","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-10-06T01:31:19Z","title_canon_sha256":"4ad6b5644ad47f45c99728c24727dba7234738d15cf9deec752f4ba3290de77d"},"schema_version":"1.0","source":{"id":"1710.02252","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.02252","created_at":"2026-05-18T00:33:34Z"},{"alias_kind":"arxiv_version","alias_value":"1710.02252v1","created_at":"2026-05-18T00:33:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.02252","created_at":"2026-05-18T00:33:34Z"},{"alias_kind":"pith_short_12","alias_value":"GHCRMU7GVB6Y","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GHCRMU7GVB6YOWTH","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GHCRMU7G","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:188f23aab0be0f6ecf631ca2e179bb970cff32f346b7f513b6a311fccd268843","target":"graph","created_at":"2026-05-18T00:33:34Z","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":"The problem of network function computation over a directed acyclic network is investigated in this paper. In such a network, a sink node desires to compute with zero error a {\\em target function}, of which the inputs are generated at multiple source nodes. The edges in the network are assumed to be error-free and have limited capacity. The nodes in the network are assumed to have unbounded computing capability and be able to perform network coding. The {\\em computing rate} of a network code that can compute the target function over the network is the average number of times that the target fu","authors_text":"Congduan Li, Raymond W. Yeung, Shenghao Yang, Xuan Guang","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-10-06T01:31:19Z","title":"Improved Upper Bound on the Network Function Computing Capacity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02252","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":"sha256:831fc84b450924045bee7f3b7e54c74e2c31c2e5b4f0ab33bd4f64da60507a15","target":"record","created_at":"2026-05-18T00:33:34Z","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":"99039ae5a2e73a4f665fcd9a5f9d0d1604b4c0ecc9be1aaba79951dcffab98e0","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-10-06T01:31:19Z","title_canon_sha256":"4ad6b5644ad47f45c99728c24727dba7234738d15cf9deec752f4ba3290de77d"},"schema_version":"1.0","source":{"id":"1710.02252","kind":"arxiv","version":1}},"canonical_sha256":"31c51653e6a87d875a67a0b91bc11c89da255d6046c602c999c4fbb23dd53093","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31c51653e6a87d875a67a0b91bc11c89da255d6046c602c999c4fbb23dd53093","first_computed_at":"2026-05-18T00:33:34.011041Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:34.011041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2Gtu0xmkgfEJjhHmPZplfobE7GW6YIrA8iU5HNy4ZCVYCGm+DXa4bbaZA9kI5x+7QOs8wfrJDc/0JwXAcLATAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:34.011739Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.02252","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:831fc84b450924045bee7f3b7e54c74e2c31c2e5b4f0ab33bd4f64da60507a15","sha256:188f23aab0be0f6ecf631ca2e179bb970cff32f346b7f513b6a311fccd268843"],"state_sha256":"dc093cd8f191d6f821da7a32b08b7e2790838d12e96d15496e89d5f48f9b163a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"daTNkpHO3BP93bztvcS38QJXseaKgkLouqKJNMzW0gw2xvKdFykg8kaq461BV9zr1CmITL2BC3QKZJZm5/6WBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T16:14:27.885463Z","bundle_sha256":"107882b8516340026734c4e827a222069e695916d2b8f30166cc015651fb13ca"}}