{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YM6MASQWY6EJLM4LWIAXU2XGRD","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":"5346712475a75f76741de53d139e7afb18c03e16f9449cb5c5f6c13c27c67075","cross_cats_sorted":["cs.DM","math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-12-29T23:13:25Z","title_canon_sha256":"8dc8261fb93af23a45a03828b916ee7e348948abffce6535e393bb7c5b382a21"},"schema_version":"1.0","source":{"id":"1612.09343","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.09343","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"arxiv_version","alias_value":"1612.09343v2","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09343","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"pith_short_12","alias_value":"YM6MASQWY6EJ","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YM6MASQWY6EJLM4L","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YM6MASQW","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:44325a95f0a2a32db5631bd1527146ccdc92eb050cafd10292d58a3410c6786a","target":"graph","created_at":"2026-05-18T00:33:59Z","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 introduce the notion of information ratio $\\text{Ir}(H/G)$ between two (simple, undirected) graphs $G$ and $H$, defined as the supremum of ratios $k/n$ such that there exists a mapping between the strong products $G^k$ to $H^n$ that preserves non-adjacency. Operationally speaking, the information ratio is the maximal number of source symbols per channel use that can be reliably sent over a channel with a confusion graph $H$, where reliability is measured w.r.t. a source confusion graph $G$. Various results are provided, including in particular lower and upper bounds on $\\text{Ir}(H/G)$ in t","authors_text":"Lele Wang, Ofer Shayevitz","cross_cats":["cs.DM","math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-12-29T23:13:25Z","title":"Graph Information Ratio"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09343","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":"sha256:0557893c77cf396d7d1ae2786acc3a6717aecc5216188e3844763085c80ae445","target":"record","created_at":"2026-05-18T00:33:59Z","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":"5346712475a75f76741de53d139e7afb18c03e16f9449cb5c5f6c13c27c67075","cross_cats_sorted":["cs.DM","math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-12-29T23:13:25Z","title_canon_sha256":"8dc8261fb93af23a45a03828b916ee7e348948abffce6535e393bb7c5b382a21"},"schema_version":"1.0","source":{"id":"1612.09343","kind":"arxiv","version":2}},"canonical_sha256":"c33cc04a16c78895b38bb2017a6ae688fc39d58978f07f260cdc812fe8a119a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c33cc04a16c78895b38bb2017a6ae688fc39d58978f07f260cdc812fe8a119a2","first_computed_at":"2026-05-18T00:33:59.575923Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:59.575923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W+Rl6krWkA1WlVPnWLEaGy5iK6RPmWWIVZZPLxzUZA97k73cCpm5oBXCxVluGUqX3gGyHlJUaITUT4VPqSLbDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:59.576539Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.09343","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0557893c77cf396d7d1ae2786acc3a6717aecc5216188e3844763085c80ae445","sha256:44325a95f0a2a32db5631bd1527146ccdc92eb050cafd10292d58a3410c6786a"],"state_sha256":"4ae82007e60a45e931ab60c73bee3deb37625f1c51f8aac200f105a0608e7e1b"}