{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:5E4LGLF73OVICCJ7ANEV37YPG7","short_pith_number":"pith:5E4LGLF7","canonical_record":{"source":{"id":"1406.5860","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-06-23T10:34:44Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"85b76140453ccdbceb1dd852ed7f2ec44c2498a39357d7f823369ee632330fee","abstract_canon_sha256":"6addc8bfca02b087acde52e682cf2d2172fdaca6a88f510111d3554d7d91d3c4"},"schema_version":"1.0"},"canonical_sha256":"e938b32cbfdbaa81093f03495dff0f37ea745547807b09a76aab26ec94083576","source":{"kind":"arxiv","id":"1406.5860","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5860","created_at":"2026-05-18T01:58:27Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5860v2","created_at":"2026-05-18T01:58:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5860","created_at":"2026-05-18T01:58:27Z"},{"alias_kind":"pith_short_12","alias_value":"5E4LGLF73OVI","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5E4LGLF73OVICCJ7","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5E4LGLF7","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:5E4LGLF73OVICCJ7ANEV37YPG7","target":"record","payload":{"canonical_record":{"source":{"id":"1406.5860","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-06-23T10:34:44Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"85b76140453ccdbceb1dd852ed7f2ec44c2498a39357d7f823369ee632330fee","abstract_canon_sha256":"6addc8bfca02b087acde52e682cf2d2172fdaca6a88f510111d3554d7d91d3c4"},"schema_version":"1.0"},"canonical_sha256":"e938b32cbfdbaa81093f03495dff0f37ea745547807b09a76aab26ec94083576","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:58:27.291099Z","signature_b64":"QyeGIJBe1sl5otXE3tQbVUd1qPI1GxoIa8NI8jIzn27NTIBf3VkNtkBhwjIK4YM2e1/3HH/rEUMPMWZD4TU1Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e938b32cbfdbaa81093f03495dff0f37ea745547807b09a76aab26ec94083576","last_reissued_at":"2026-05-18T01:58:27.290642Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:58:27.290642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.5860","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":"2026-05-18T01:58:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0lPtnn9gDMeDsOn+Uw3xz934IFIAYGYFS0xFPh499q6qKOJUU3kS7WGyVFejeLWGq0GrYBkh+BmDlOvq+vsPAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:55:58.375340Z"},"content_sha256":"9df2c386b2b59fc6cc420ac9c251e6a383491f57de34f41ea9b14c917726342a","schema_version":"1.0","event_id":"sha256:9df2c386b2b59fc6cc420ac9c251e6a383491f57de34f41ea9b14c917726342a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:5E4LGLF73OVICCJ7ANEV37YPG7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Deterministic Linear Network Coded Broadcast and Its Relation to Matroid Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Mingchao Yu, Neda Aboutorab, Parastoo Sadeghi","submitted_at":"2014-06-23T10:34:44Z","abstract_excerpt":"Deterministic linear network coding (DLNC) is an important family of network coding techniques for wireless packet broadcast. In this paper, we show that DLNC is strongly related to and can be effectively studied using matroid theory without bridging index coding. We prove the equivalence between the DLNC solution and matrix matroid. We use this equivalence to study the performance limits of DLNC in terms of the number of transmissions and its dependence on the finite field size. Specifically, we derive the sufficient and necessary condition for the existence of perfect DLNC solutions and prov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5860","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":"2026-05-18T01:58:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vhhIFWKeY4+tM+m4ESdWTrNiQ8kwb5u4d+evl2ZGx5zS4E/d9+l4NCDLBl4xMMwi++hL59+c05Q0+m0h9w/MBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:55:58.375992Z"},"content_sha256":"c8dd6671e166fae722b09e11121834ba25bf681ea8a5fd65df34bdb97b808212","schema_version":"1.0","event_id":"sha256:c8dd6671e166fae722b09e11121834ba25bf681ea8a5fd65df34bdb97b808212"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5E4LGLF73OVICCJ7ANEV37YPG7/bundle.json","state_url":"https://pith.science/pith/5E4LGLF73OVICCJ7ANEV37YPG7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5E4LGLF73OVICCJ7ANEV37YPG7/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":"2026-05-25T19:55:58Z","links":{"resolver":"https://pith.science/pith/5E4LGLF73OVICCJ7ANEV37YPG7","bundle":"https://pith.science/pith/5E4LGLF73OVICCJ7ANEV37YPG7/bundle.json","state":"https://pith.science/pith/5E4LGLF73OVICCJ7ANEV37YPG7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5E4LGLF73OVICCJ7ANEV37YPG7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5E4LGLF73OVICCJ7ANEV37YPG7","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":"6addc8bfca02b087acde52e682cf2d2172fdaca6a88f510111d3554d7d91d3c4","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-06-23T10:34:44Z","title_canon_sha256":"85b76140453ccdbceb1dd852ed7f2ec44c2498a39357d7f823369ee632330fee"},"schema_version":"1.0","source":{"id":"1406.5860","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5860","created_at":"2026-05-18T01:58:27Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5860v2","created_at":"2026-05-18T01:58:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5860","created_at":"2026-05-18T01:58:27Z"},{"alias_kind":"pith_short_12","alias_value":"5E4LGLF73OVI","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5E4LGLF73OVICCJ7","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5E4LGLF7","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:c8dd6671e166fae722b09e11121834ba25bf681ea8a5fd65df34bdb97b808212","target":"graph","created_at":"2026-05-18T01:58:27Z","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":"Deterministic linear network coding (DLNC) is an important family of network coding techniques for wireless packet broadcast. In this paper, we show that DLNC is strongly related to and can be effectively studied using matroid theory without bridging index coding. We prove the equivalence between the DLNC solution and matrix matroid. We use this equivalence to study the performance limits of DLNC in terms of the number of transmissions and its dependence on the finite field size. Specifically, we derive the sufficient and necessary condition for the existence of perfect DLNC solutions and prov","authors_text":"Mingchao Yu, Neda Aboutorab, Parastoo Sadeghi","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-06-23T10:34:44Z","title":"On Deterministic Linear Network Coded Broadcast and Its Relation to Matroid Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5860","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":"sha256:9df2c386b2b59fc6cc420ac9c251e6a383491f57de34f41ea9b14c917726342a","target":"record","created_at":"2026-05-18T01:58:27Z","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":"6addc8bfca02b087acde52e682cf2d2172fdaca6a88f510111d3554d7d91d3c4","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-06-23T10:34:44Z","title_canon_sha256":"85b76140453ccdbceb1dd852ed7f2ec44c2498a39357d7f823369ee632330fee"},"schema_version":"1.0","source":{"id":"1406.5860","kind":"arxiv","version":2}},"canonical_sha256":"e938b32cbfdbaa81093f03495dff0f37ea745547807b09a76aab26ec94083576","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e938b32cbfdbaa81093f03495dff0f37ea745547807b09a76aab26ec94083576","first_computed_at":"2026-05-18T01:58:27.290642Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:58:27.290642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QyeGIJBe1sl5otXE3tQbVUd1qPI1GxoIa8NI8jIzn27NTIBf3VkNtkBhwjIK4YM2e1/3HH/rEUMPMWZD4TU1Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:58:27.291099Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.5860","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9df2c386b2b59fc6cc420ac9c251e6a383491f57de34f41ea9b14c917726342a","sha256:c8dd6671e166fae722b09e11121834ba25bf681ea8a5fd65df34bdb97b808212"],"state_sha256":"9a0e60e6981666ab943c0f58b6412bfda6991cb31c722dde1fb1d554be89edc3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WqRPTdcTL7afat0YVUHmxiDfj8CkCLMfJhQkSjBQl6ZZhEwcpE3tSof4BSFKUMDsen0J8NTQQxFyf3zhsLlRDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T19:55:58.378465Z","bundle_sha256":"0d75ad130207345bb2046aa6ad0768e51dcf224482b2d2eedceb8852a12fb8b1"}}