{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:U73LE6RZFUQ2IRQMLUDMGM5THJ","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":"a5347a4ce4d72b92f107139dd7fd7038590ed7fb52dc0752339dcdf81da0f995","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-29T13:15:11Z","title_canon_sha256":"cabef891d77a0d7f8e8779d98debeda51a43be6222536807ed7758facf7e20c1"},"schema_version":"1.0","source":{"id":"1611.09616","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.09616","created_at":"2026-05-18T00:32:31Z"},{"alias_kind":"arxiv_version","alias_value":"1611.09616v2","created_at":"2026-05-18T00:32:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.09616","created_at":"2026-05-18T00:32:31Z"},{"alias_kind":"pith_short_12","alias_value":"U73LE6RZFUQ2","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"U73LE6RZFUQ2IRQM","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"U73LE6RZ","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:5548f4617d8c42c05edecc5d84f225c9aa52933fd6a525b49bbc1ccf7dd29214","target":"graph","created_at":"2026-05-18T00:32:31Z","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 consider distance functions on a quotient module $M/K$ induced by distance functions on a module $M$. We define error-correction for codes in $M/K$ with respect to induced distance functions. For the case that the metric is induced by a homogeneous weight, we derive analogues of the Plotkin and Elias-Bassalygo bounds and give their asymptotic versions. These results have applications to coherent network error-correction in the presence of adversarial errors. We outline this connection, extending the linear network coding scheme introduced by Yang et al.","authors_text":"Eimear Byrne","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-29T13:15:11Z","title":"Induced Weights on Quotient Modules and an Application to Error Correction in Coherent Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09616","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":"sha256:92c0cce6136055cd91351e5de940c7cb04135834a37d5158ad7990bc28fbbaef","target":"record","created_at":"2026-05-18T00:32:31Z","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":"a5347a4ce4d72b92f107139dd7fd7038590ed7fb52dc0752339dcdf81da0f995","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-29T13:15:11Z","title_canon_sha256":"cabef891d77a0d7f8e8779d98debeda51a43be6222536807ed7758facf7e20c1"},"schema_version":"1.0","source":{"id":"1611.09616","kind":"arxiv","version":2}},"canonical_sha256":"a7f6b27a392d21a4460c5d06c333b33a66902999830fcdba827e23f5366acbd5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7f6b27a392d21a4460c5d06c333b33a66902999830fcdba827e23f5366acbd5","first_computed_at":"2026-05-18T00:32:31.209927Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:31.209927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VHYH+cBpg5RHtySjaEPy2eDgQg066Q4hBun0ZeDVWPpiNBCXIJMAIbFI7duJQWEScKPEuwv2pt7FuVHhNielAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:31.211724Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.09616","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92c0cce6136055cd91351e5de940c7cb04135834a37d5158ad7990bc28fbbaef","sha256:5548f4617d8c42c05edecc5d84f225c9aa52933fd6a525b49bbc1ccf7dd29214"],"state_sha256":"cbf83f40dcdcf13240142e4a257d43bfff5bd2c44f3b8185de938411c71eb1f8"}