{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:7YTF6FUT665DOKM5LJ7RL5NKCS","short_pith_number":"pith:7YTF6FUT","canonical_record":{"source":{"id":"1201.6459","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-01-31T07:19:09Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"36b5c5e2dbcc244e69326d391b2f07a85bb6c6b7a3424d89dd491246a1411195","abstract_canon_sha256":"6c26d23f520b3a32ca51043a1cd1de0a96cdb6bfaf02a92658e93e8f63e192d3"},"schema_version":"1.0"},"canonical_sha256":"fe265f1693f7ba37299d5a7f15f5aa14aa276773e5e0646b766d913be380c28c","source":{"kind":"arxiv","id":"1201.6459","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.6459","created_at":"2026-05-18T03:19:11Z"},{"alias_kind":"arxiv_version","alias_value":"1201.6459v3","created_at":"2026-05-18T03:19:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.6459","created_at":"2026-05-18T03:19:11Z"},{"alias_kind":"pith_short_12","alias_value":"7YTF6FUT665D","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7YTF6FUT665DOKM5","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7YTF6FUT","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:7YTF6FUT665DOKM5LJ7RL5NKCS","target":"record","payload":{"canonical_record":{"source":{"id":"1201.6459","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-01-31T07:19:09Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"36b5c5e2dbcc244e69326d391b2f07a85bb6c6b7a3424d89dd491246a1411195","abstract_canon_sha256":"6c26d23f520b3a32ca51043a1cd1de0a96cdb6bfaf02a92658e93e8f63e192d3"},"schema_version":"1.0"},"canonical_sha256":"fe265f1693f7ba37299d5a7f15f5aa14aa276773e5e0646b766d913be380c28c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:11.787437Z","signature_b64":"2PzUwUkhjAQ5vVpsw6mytO7oKc8Kw61+b+WBa7ep8xqSUQ2FHI9SGYk3etMhQpYwjurByfVR7IUHMS+JauHJAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe265f1693f7ba37299d5a7f15f5aa14aa276773e5e0646b766d913be380c28c","last_reissued_at":"2026-05-18T03:19:11.786796Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:11.786796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.6459","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":"2026-05-18T03:19:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tc5RMPB+L7B0oveZgqZAWNMcleR9gZkg9S+29EXXakK+9LBAgFC13y2vRnjZ41UxnkjaVi7KOBuFcRk6cVZlDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:41:03.834392Z"},"content_sha256":"0b020f53fae202fc0d738f4ae8bc1a404fb3d4f7663d5a14b5db1522c4868751","schema_version":"1.0","event_id":"sha256:0b020f53fae202fc0d738f4ae8bc1a404fb3d4f7663d5a14b5db1522c4868751"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:7YTF6FUT665DOKM5LJ7RL5NKCS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Matroidal Framework for Network-Error Correcting Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"B. Sundar Rajan, K. Prasad","submitted_at":"2012-01-31T07:19:09Z","abstract_excerpt":"We abstract the essential aspects of network-error detecting and correcting codes to arrive at the definitions of matroidal error detecting networks and matroidal error correcting networks. An acyclic network (with arbitrary sink demands) is then shown to possess a scalar linear error detecting (correcting) network code if and only if it is a matroidal error detecting (correcting) network associated with a representable matroid. Therefore, constructing such network-error correcting and detecting codes implies the construction of certain representable matroids that satisfy some special conditio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6459","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":"2026-05-18T03:19:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YQksUWtBDso7Gt2OQ6ejWnJ7RConrpkhnZeSn70bzYJXbja48gNk7ADckiwGDU1mV6EyS4p3n6qYArVu0k5KDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:41:03.834762Z"},"content_sha256":"c8a8d35d37509733b53bd344a367a547c906b2c4f33ad3c127150dfea6483492","schema_version":"1.0","event_id":"sha256:c8a8d35d37509733b53bd344a367a547c906b2c4f33ad3c127150dfea6483492"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7YTF6FUT665DOKM5LJ7RL5NKCS/bundle.json","state_url":"https://pith.science/pith/7YTF6FUT665DOKM5LJ7RL5NKCS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7YTF6FUT665DOKM5LJ7RL5NKCS/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":"2026-06-05T00:41:03Z","links":{"resolver":"https://pith.science/pith/7YTF6FUT665DOKM5LJ7RL5NKCS","bundle":"https://pith.science/pith/7YTF6FUT665DOKM5LJ7RL5NKCS/bundle.json","state":"https://pith.science/pith/7YTF6FUT665DOKM5LJ7RL5NKCS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7YTF6FUT665DOKM5LJ7RL5NKCS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7YTF6FUT665DOKM5LJ7RL5NKCS","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":"6c26d23f520b3a32ca51043a1cd1de0a96cdb6bfaf02a92658e93e8f63e192d3","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-01-31T07:19:09Z","title_canon_sha256":"36b5c5e2dbcc244e69326d391b2f07a85bb6c6b7a3424d89dd491246a1411195"},"schema_version":"1.0","source":{"id":"1201.6459","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.6459","created_at":"2026-05-18T03:19:11Z"},{"alias_kind":"arxiv_version","alias_value":"1201.6459v3","created_at":"2026-05-18T03:19:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.6459","created_at":"2026-05-18T03:19:11Z"},{"alias_kind":"pith_short_12","alias_value":"7YTF6FUT665D","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7YTF6FUT665DOKM5","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7YTF6FUT","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:c8a8d35d37509733b53bd344a367a547c906b2c4f33ad3c127150dfea6483492","target":"graph","created_at":"2026-05-18T03:19:11Z","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":"We abstract the essential aspects of network-error detecting and correcting codes to arrive at the definitions of matroidal error detecting networks and matroidal error correcting networks. An acyclic network (with arbitrary sink demands) is then shown to possess a scalar linear error detecting (correcting) network code if and only if it is a matroidal error detecting (correcting) network associated with a representable matroid. Therefore, constructing such network-error correcting and detecting codes implies the construction of certain representable matroids that satisfy some special conditio","authors_text":"B. Sundar Rajan, K. Prasad","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-01-31T07:19:09Z","title":"A Matroidal Framework for Network-Error Correcting Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6459","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":"sha256:0b020f53fae202fc0d738f4ae8bc1a404fb3d4f7663d5a14b5db1522c4868751","target":"record","created_at":"2026-05-18T03:19:11Z","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":"6c26d23f520b3a32ca51043a1cd1de0a96cdb6bfaf02a92658e93e8f63e192d3","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-01-31T07:19:09Z","title_canon_sha256":"36b5c5e2dbcc244e69326d391b2f07a85bb6c6b7a3424d89dd491246a1411195"},"schema_version":"1.0","source":{"id":"1201.6459","kind":"arxiv","version":3}},"canonical_sha256":"fe265f1693f7ba37299d5a7f15f5aa14aa276773e5e0646b766d913be380c28c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe265f1693f7ba37299d5a7f15f5aa14aa276773e5e0646b766d913be380c28c","first_computed_at":"2026-05-18T03:19:11.786796Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:11.786796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2PzUwUkhjAQ5vVpsw6mytO7oKc8Kw61+b+WBa7ep8xqSUQ2FHI9SGYk3etMhQpYwjurByfVR7IUHMS+JauHJAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:11.787437Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.6459","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b020f53fae202fc0d738f4ae8bc1a404fb3d4f7663d5a14b5db1522c4868751","sha256:c8a8d35d37509733b53bd344a367a547c906b2c4f33ad3c127150dfea6483492"],"state_sha256":"0361b5c134609be2dfc65df1a1cb5e58206a0e474da6a47a144f551d0ba50095"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ld9b58wsVvWuB6R4b2Cfkz01fCvTc7StOJA8kamPDmmBkdfbWSgq4nC7ZGsZo1vjfHtC8BH4GLijgthCa3RzCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T00:41:03.836759Z","bundle_sha256":"8b6ceccd2e66e08832b483a141f630f401d5f5e93d3914b6d4758d0cd6b98ad1"}}