{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:T47X4UDER5UTX3RLQSC2GZRA3P","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":"89c86ca9b7a938da70b5ca7944ce1f33f4e9246e0fd9f0924fb917f10c77501d","cross_cats_sorted":["cs.PL","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-02-26T21:47:11Z","title_canon_sha256":"6518c37e04b17766e90456ca5060f9a3575c2f26ca7a29e03e2c48a4c172b8ff"},"schema_version":"1.0","source":{"id":"2602.23520","kind":"arxiv","version":9}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.23520","created_at":"2026-05-21T01:04:23Z"},{"alias_kind":"arxiv_version","alias_value":"2602.23520v9","created_at":"2026-05-21T01:04:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.23520","created_at":"2026-05-21T01:04:23Z"},{"alias_kind":"pith_short_12","alias_value":"T47X4UDER5UT","created_at":"2026-05-21T01:04:23Z"},{"alias_kind":"pith_short_16","alias_value":"T47X4UDER5UTX3RL","created_at":"2026-05-21T01:04:23Z"},{"alias_kind":"pith_short_8","alias_value":"T47X4UDE","created_at":"2026-05-21T01:04:23Z"}],"graph_snapshots":[{"event_id":"sha256:1dfddae58ff023993354d9677157603528168c604aba667a9e75236fa055ce64","target":"graph","created_at":"2026-05-21T01:04:23Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"For affine realized state families with explicit linear presentations, restricted coordinate ranks form a representable matroid certificate giving polynomial-time upper bounds on one-shot confusability and asymptotic capacity, with rank additivity matching direct-sum block composition."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The latent state family must be affine realized with explicit linear presentations for the matroid certificate and rank-additivity claims to apply; the abstract does not state how restrictive this class is."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Zero-error recovery under partial views reduces to graph T-colorability and Shannon capacity, with representable matroid certificates providing bounds for affine families and Lean-verified conditions for host realizability."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"For affine realized state families, restricted coordinate ranks form a representable matroid that certifies polynomial-time upper bounds on zero-error confusability and asymptotic capacity."}],"snapshot_sha256":"2bc76bad49c9dbbda371abc6149ecb29f5b046dbda09c367fef3153cb04735d6"},"formal_canon":{"evidence_count":1,"snapshot_sha256":"4c69fce0fbb54f98b468d5186aebd0dee7174a41e0ac285dd176d2294cf45e68"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2602.23520/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Zero-error recovery under deterministic partial views is graph recovery for the induced confusability relation. A finite family of coordinate-subset observations determines a graph on latent states; $T$-ary exact recovery is graph $T$-colorability, block composition is strong powering, and asymptotic recoverability is Shannon capacity.\n  Coordinate structure gives tractable certificates inside the graph semantics. For affine realized state families with explicit linear presentations, restricted coordinate ranks form a representable matroid certificate giving polynomial-time upper bounds on one","authors_text":"Tristan Simas","cross_cats":["cs.PL","math.IT"],"headline":"For affine realized state families, restricted coordinate ranks form a representable matroid that certifies polynomial-time upper bounds on zero-error confusability and asymptotic capacity.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-02-26T21:47:11Z","title":"Zero-Error Recovery under Deterministic Partial Views: Matroid Bounds and Verifiable Realizability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.23520","kind":"arxiv","version":9},"verdict":{"created_at":"2026-05-15T18:32:02.954534Z","id":"53128576-ae94-47a8-b1ca-736730a59479","model_set":{"reader":"grok-4.3"},"one_line_summary":"Zero-error recovery under partial views reduces to graph T-colorability and Shannon capacity, with representable matroid certificates providing bounds for affine families and Lean-verified conditions for host realizability.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"For affine realized state families, restricted coordinate ranks form a representable matroid that certifies polynomial-time upper bounds on zero-error confusability and asymptotic capacity.","strongest_claim":"For affine realized state families with explicit linear presentations, restricted coordinate ranks form a representable matroid certificate giving polynomial-time upper bounds on one-shot confusability and asymptotic capacity, with rank additivity matching direct-sum block composition.","weakest_assumption":"The latent state family must be affine realized with explicit linear presentations for the matroid certificate and rank-additivity claims to apply; the abstract does not state how restrictive this class is."}},"verdict_id":"53128576-ae94-47a8-b1ca-736730a59479"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a1d1cc7172e0a8c7cb44f87b3f17bef906d0bf0aa6c20a4a472c5ece0698b886","target":"record","created_at":"2026-05-21T01:04:23Z","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":"89c86ca9b7a938da70b5ca7944ce1f33f4e9246e0fd9f0924fb917f10c77501d","cross_cats_sorted":["cs.PL","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-02-26T21:47:11Z","title_canon_sha256":"6518c37e04b17766e90456ca5060f9a3575c2f26ca7a29e03e2c48a4c172b8ff"},"schema_version":"1.0","source":{"id":"2602.23520","kind":"arxiv","version":9}},"canonical_sha256":"9f3f7e50648f693bee2b8485a36620dbdb04bdcea8fbb7abe35a2636bcd6d145","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f3f7e50648f693bee2b8485a36620dbdb04bdcea8fbb7abe35a2636bcd6d145","first_computed_at":"2026-05-21T01:04:23.787556Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:04:23.787556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0Ew7ri83N9Tl4N48d8DBkpRk1i+OFq1A4b79/Q3NOZdt45ivmRHMJTkaKIHtd57A/4Wmz6XAQIqg/zfmNECaBQ==","signature_status":"signed_v1","signed_at":"2026-05-21T01:04:23.788158Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.23520","source_kind":"arxiv","source_version":9}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1d1cc7172e0a8c7cb44f87b3f17bef906d0bf0aa6c20a4a472c5ece0698b886","sha256:1dfddae58ff023993354d9677157603528168c604aba667a9e75236fa055ce64"],"state_sha256":"96dc118962e6b3148b12c0b79c422d3cab469c86178d88e621d565fc1903d26b"}