{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:6EJC3GMZO4AKSKIP7YEUUTX3SQ","short_pith_number":"pith:6EJC3GMZ","canonical_record":{"source":{"id":"0912.2820","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-12-15T08:51:53Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"4f23da0a78ba450d561a8074cd50e19580fe7d5f4e2f761fd472f34585c3e60c","abstract_canon_sha256":"8152cb6a47cfd3ec9ca0297b096ca73aa1316409581548fc8382d473f37428a8"},"schema_version":"1.0"},"canonical_sha256":"f1122d99997700a9290ffe094a4efb9405b284fd07ecd4122eab91ce0506d9f4","source":{"kind":"arxiv","id":"0912.2820","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.2820","created_at":"2026-05-18T00:57:57Z"},{"alias_kind":"arxiv_version","alias_value":"0912.2820v3","created_at":"2026-05-18T00:57:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.2820","created_at":"2026-05-18T00:57:57Z"},{"alias_kind":"pith_short_12","alias_value":"6EJC3GMZO4AK","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"6EJC3GMZO4AKSKIP","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"6EJC3GMZ","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:6EJC3GMZO4AKSKIP7YEUUTX3SQ","target":"record","payload":{"canonical_record":{"source":{"id":"0912.2820","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-12-15T08:51:53Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"4f23da0a78ba450d561a8074cd50e19580fe7d5f4e2f761fd472f34585c3e60c","abstract_canon_sha256":"8152cb6a47cfd3ec9ca0297b096ca73aa1316409581548fc8382d473f37428a8"},"schema_version":"1.0"},"canonical_sha256":"f1122d99997700a9290ffe094a4efb9405b284fd07ecd4122eab91ce0506d9f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:57.978619Z","signature_b64":"iW7nIRrsDbSyqsgN5e+ED21kbDRbXz21mtuBiScQ0/YvrSAguQ6JqpUMU2BNQbVPKDjV7AaHcX1PHdj6I6fSCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1122d99997700a9290ffe094a4efb9405b284fd07ecd4122eab91ce0506d9f4","last_reissued_at":"2026-05-18T00:57:57.978120Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:57.978120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0912.2820","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:57:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6wK4uYH03QIqgrvS7ocD3WTLB0rcu+t2bpe+a3qDTj9R8NnffdtkZcGeOhUdlYZvQasT0MqFgZ1JUXxVBqgSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:37:07.409848Z"},"content_sha256":"c4c9a1ba3cfa0e9e28b3863aa0c610b8568dbf8616fc211f67764c35de18d0d5","schema_version":"1.0","event_id":"sha256:c4c9a1ba3cfa0e9e28b3863aa0c610b8568dbf8616fc211f67764c35de18d0d5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:6EJC3GMZO4AKSKIP7YEUUTX3SQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Network Coding for Computing: Cut-Set Bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ken Zeger, Massimo Franceschetti, Nikhil Karamchandani, Rathinakumar Appuswamy","submitted_at":"2009-12-15T08:51:53Z","abstract_excerpt":"The following \\textit{network computing} problem is considered. Source nodes in a directed acyclic network generate independent messages and a single receiver node computes a target function $f$ of the messages. The objective is to maximize the average number of times $f$ can be computed per network usage, i.e., the ``computing capacity''. The \\textit{network coding} problem for a single-receiver network is a special case of the network computing problem in which all of the source messages must be reproduced at the receiver. For network coding with a single receiver, routing is known to achiev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.2820","kind":"arxiv","version":3},"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":"2026-05-18T00:57:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PBTZEJODElieHjlDGoU9I+R5Tyu6PwQUE5c248p+S+NPDQ21nB95jJnePjko7v5Hl4M2NdNdW3HkD8tTgKSgCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:37:07.410188Z"},"content_sha256":"474d754fe7bcf386918337d394fcd8d088e830c6ecd109202e3d645460339c09","schema_version":"1.0","event_id":"sha256:474d754fe7bcf386918337d394fcd8d088e830c6ecd109202e3d645460339c09"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6EJC3GMZO4AKSKIP7YEUUTX3SQ/bundle.json","state_url":"https://pith.science/pith/6EJC3GMZO4AKSKIP7YEUUTX3SQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6EJC3GMZO4AKSKIP7YEUUTX3SQ/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":"2026-05-28T12:37:07Z","links":{"resolver":"https://pith.science/pith/6EJC3GMZO4AKSKIP7YEUUTX3SQ","bundle":"https://pith.science/pith/6EJC3GMZO4AKSKIP7YEUUTX3SQ/bundle.json","state":"https://pith.science/pith/6EJC3GMZO4AKSKIP7YEUUTX3SQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6EJC3GMZO4AKSKIP7YEUUTX3SQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:6EJC3GMZO4AKSKIP7YEUUTX3SQ","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":"8152cb6a47cfd3ec9ca0297b096ca73aa1316409581548fc8382d473f37428a8","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-12-15T08:51:53Z","title_canon_sha256":"4f23da0a78ba450d561a8074cd50e19580fe7d5f4e2f761fd472f34585c3e60c"},"schema_version":"1.0","source":{"id":"0912.2820","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.2820","created_at":"2026-05-18T00:57:57Z"},{"alias_kind":"arxiv_version","alias_value":"0912.2820v3","created_at":"2026-05-18T00:57:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.2820","created_at":"2026-05-18T00:57:57Z"},{"alias_kind":"pith_short_12","alias_value":"6EJC3GMZO4AK","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"6EJC3GMZO4AKSKIP","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"6EJC3GMZ","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:474d754fe7bcf386918337d394fcd8d088e830c6ecd109202e3d645460339c09","target":"graph","created_at":"2026-05-18T00:57:57Z","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 following \\textit{network computing} problem is considered. Source nodes in a directed acyclic network generate independent messages and a single receiver node computes a target function $f$ of the messages. The objective is to maximize the average number of times $f$ can be computed per network usage, i.e., the ``computing capacity''. The \\textit{network coding} problem for a single-receiver network is a special case of the network computing problem in which all of the source messages must be reproduced at the receiver. For network coding with a single receiver, routing is known to achiev","authors_text":"Ken Zeger, Massimo Franceschetti, Nikhil Karamchandani, Rathinakumar Appuswamy","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-12-15T08:51:53Z","title":"Network Coding for Computing: Cut-Set Bounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.2820","kind":"arxiv","version":3},"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:c4c9a1ba3cfa0e9e28b3863aa0c610b8568dbf8616fc211f67764c35de18d0d5","target":"record","created_at":"2026-05-18T00:57:57Z","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":"8152cb6a47cfd3ec9ca0297b096ca73aa1316409581548fc8382d473f37428a8","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-12-15T08:51:53Z","title_canon_sha256":"4f23da0a78ba450d561a8074cd50e19580fe7d5f4e2f761fd472f34585c3e60c"},"schema_version":"1.0","source":{"id":"0912.2820","kind":"arxiv","version":3}},"canonical_sha256":"f1122d99997700a9290ffe094a4efb9405b284fd07ecd4122eab91ce0506d9f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1122d99997700a9290ffe094a4efb9405b284fd07ecd4122eab91ce0506d9f4","first_computed_at":"2026-05-18T00:57:57.978120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:57.978120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iW7nIRrsDbSyqsgN5e+ED21kbDRbXz21mtuBiScQ0/YvrSAguQ6JqpUMU2BNQbVPKDjV7AaHcX1PHdj6I6fSCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:57.978619Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.2820","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4c9a1ba3cfa0e9e28b3863aa0c610b8568dbf8616fc211f67764c35de18d0d5","sha256:474d754fe7bcf386918337d394fcd8d088e830c6ecd109202e3d645460339c09"],"state_sha256":"192513912c26017a0afbb3ac38a56a7e810c49ad56d1b1d495ef5a6bd6233275"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b+AX3NX2jyMn3iTNpcre+W4JZKbKzXYOI1FyBCOR4KUQTL0wRZj7Kmi97wViB9eMEEde7DeL/Vyyz9ftT1mtCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T12:37:07.412112Z","bundle_sha256":"794e99e6a6c3bc8688f7ecab637c19d5e2a2501519caff49d9a5c8dc9b0ad3ef"}}