{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:VB3X23B6VGQ3GXFSP7ZWZ4E2HQ","short_pith_number":"pith:VB3X23B6","canonical_record":{"source":{"id":"1512.01738","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-11-03T11:50:01Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c5dc33edbae5e9db9be3b578922e83e0020f9c309ee30791da53814cf8b9792b","abstract_canon_sha256":"8da0f8202f586fa15a109f08c44ce7833331370c6511983a7aa14461c9f1c871"},"schema_version":"1.0"},"canonical_sha256":"a8777d6c3ea9a1b35cb27ff36cf09a3c3e16b9ef1fcc89f1f90a147675d44d70","source":{"kind":"arxiv","id":"1512.01738","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01738","created_at":"2026-05-18T00:58:09Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01738v2","created_at":"2026-05-18T00:58:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01738","created_at":"2026-05-18T00:58:09Z"},{"alias_kind":"pith_short_12","alias_value":"VB3X23B6VGQ3","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"VB3X23B6VGQ3GXFS","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"VB3X23B6","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:VB3X23B6VGQ3GXFSP7ZWZ4E2HQ","target":"record","payload":{"canonical_record":{"source":{"id":"1512.01738","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-11-03T11:50:01Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c5dc33edbae5e9db9be3b578922e83e0020f9c309ee30791da53814cf8b9792b","abstract_canon_sha256":"8da0f8202f586fa15a109f08c44ce7833331370c6511983a7aa14461c9f1c871"},"schema_version":"1.0"},"canonical_sha256":"a8777d6c3ea9a1b35cb27ff36cf09a3c3e16b9ef1fcc89f1f90a147675d44d70","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:09.945662Z","signature_b64":"Ux2w0YXVP0ZjbbWZuHhVWTmuyWeeVF+RkIkmDkPOPYg2cIwewNhf95uVKUpZ6Orao1O0QwC/YBinIAGvyhRaDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8777d6c3ea9a1b35cb27ff36cf09a3c3e16b9ef1fcc89f1f90a147675d44d70","last_reissued_at":"2026-05-18T00:58:09.944892Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:09.944892Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.01738","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":"2026-05-18T00:58:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ro3jdO+FfsBkNmsvJ3rIbsbgHsYsve92b/jveXq/WzMX7cEaf7y+ors5j8tDaOVnT4G+P7cRzxd/PCOezo4sAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T13:45:36.273828Z"},"content_sha256":"286910812b76f574a4734fc1dafc6ee32a30e863e79ad597c38ef2acc378a95a","schema_version":"1.0","event_id":"sha256:286910812b76f574a4734fc1dafc6ee32a30e863e79ad597c38ef2acc378a95a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:VB3X23B6VGQ3GXFSP7ZWZ4E2HQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Network Coding: Connections Between Information Theory And Estimation Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Samah A. M. Ghanem","submitted_at":"2015-11-03T11:50:01Z","abstract_excerpt":"In this paper, we prove the existence of fundamental relations between information theory and estimation theory for network-coded flows. When the network is represented by a directed graph G=(V, E) and under the assumption of uncorrelated noise over information flows between the directed links connecting transmitters, switches (relays), and receivers. We unveil that there yet exist closed-form relations for the gradient of the mutual information with respect to different components of the system matrix M. On the one hand, this result opens a new class of problems casting further insights into "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01738","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":"2026-05-18T00:58:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Emas4dBcMRUZCEJpu3Bt1EaGE73OhV12pQcCX1mHf2N8mjNf3EWijMjrAgFwt7qYyL5wsHHTzL/OhT+FrPpFDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T13:45:36.274173Z"},"content_sha256":"c0807dc49090c0a095513b44307d5ceceb164951aa64885d7e207709d6804ac8","schema_version":"1.0","event_id":"sha256:c0807dc49090c0a095513b44307d5ceceb164951aa64885d7e207709d6804ac8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VB3X23B6VGQ3GXFSP7ZWZ4E2HQ/bundle.json","state_url":"https://pith.science/pith/VB3X23B6VGQ3GXFSP7ZWZ4E2HQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VB3X23B6VGQ3GXFSP7ZWZ4E2HQ/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":"2026-07-01T13:45:36Z","links":{"resolver":"https://pith.science/pith/VB3X23B6VGQ3GXFSP7ZWZ4E2HQ","bundle":"https://pith.science/pith/VB3X23B6VGQ3GXFSP7ZWZ4E2HQ/bundle.json","state":"https://pith.science/pith/VB3X23B6VGQ3GXFSP7ZWZ4E2HQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VB3X23B6VGQ3GXFSP7ZWZ4E2HQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VB3X23B6VGQ3GXFSP7ZWZ4E2HQ","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":"8da0f8202f586fa15a109f08c44ce7833331370c6511983a7aa14461c9f1c871","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-11-03T11:50:01Z","title_canon_sha256":"c5dc33edbae5e9db9be3b578922e83e0020f9c309ee30791da53814cf8b9792b"},"schema_version":"1.0","source":{"id":"1512.01738","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01738","created_at":"2026-05-18T00:58:09Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01738v2","created_at":"2026-05-18T00:58:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01738","created_at":"2026-05-18T00:58:09Z"},{"alias_kind":"pith_short_12","alias_value":"VB3X23B6VGQ3","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"VB3X23B6VGQ3GXFS","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"VB3X23B6","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:c0807dc49090c0a095513b44307d5ceceb164951aa64885d7e207709d6804ac8","target":"graph","created_at":"2026-05-18T00:58:09Z","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 this paper, we prove the existence of fundamental relations between information theory and estimation theory for network-coded flows. When the network is represented by a directed graph G=(V, E) and under the assumption of uncorrelated noise over information flows between the directed links connecting transmitters, switches (relays), and receivers. We unveil that there yet exist closed-form relations for the gradient of the mutual information with respect to different components of the system matrix M. On the one hand, this result opens a new class of problems casting further insights into ","authors_text":"Samah A. M. Ghanem","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-11-03T11:50:01Z","title":"Network Coding: Connections Between Information Theory And Estimation Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01738","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":"sha256:286910812b76f574a4734fc1dafc6ee32a30e863e79ad597c38ef2acc378a95a","target":"record","created_at":"2026-05-18T00:58:09Z","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":"8da0f8202f586fa15a109f08c44ce7833331370c6511983a7aa14461c9f1c871","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-11-03T11:50:01Z","title_canon_sha256":"c5dc33edbae5e9db9be3b578922e83e0020f9c309ee30791da53814cf8b9792b"},"schema_version":"1.0","source":{"id":"1512.01738","kind":"arxiv","version":2}},"canonical_sha256":"a8777d6c3ea9a1b35cb27ff36cf09a3c3e16b9ef1fcc89f1f90a147675d44d70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8777d6c3ea9a1b35cb27ff36cf09a3c3e16b9ef1fcc89f1f90a147675d44d70","first_computed_at":"2026-05-18T00:58:09.944892Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:09.944892Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ux2w0YXVP0ZjbbWZuHhVWTmuyWeeVF+RkIkmDkPOPYg2cIwewNhf95uVKUpZ6Orao1O0QwC/YBinIAGvyhRaDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:09.945662Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.01738","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:286910812b76f574a4734fc1dafc6ee32a30e863e79ad597c38ef2acc378a95a","sha256:c0807dc49090c0a095513b44307d5ceceb164951aa64885d7e207709d6804ac8"],"state_sha256":"95e2892b8e3ab0712e250445c7354cfc303bdd9c35a863db20da12ccc8c83aef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+wYZIQNb+80JY6KQiO/EujsSKJgkvZPy3g/PpRe6zk4cfBrj4yYAU8mDPTvsutHOf/nWDxFtha6PmrimBPNZDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T13:45:36.276205Z","bundle_sha256":"e677fde3885be0ef6efa7388a313523dd738109b4941ff852360c7671b656d13"}}