{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:ZB5JU2LUTFEYLDBZ5BMOZDMD3F","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":"28354f57cd93fe02ee3720d2aefe068a17caeee82405a9ce745e0e5898a762c4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2005-07-08T19:07:04Z","title_canon_sha256":"885602547a6b45980bf1a76d4ddfe6bf4f3007ddc5f8f1b891c8b8bfb81f0535"},"schema_version":"1.0","source":{"id":"quant-ph/0507088","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0507088","created_at":"2026-07-05T01:55:26Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0507088v3","created_at":"2026-07-05T01:55:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0507088","created_at":"2026-07-05T01:55:26Z"},{"alias_kind":"pith_short_12","alias_value":"ZB5JU2LUTFEY","created_at":"2026-07-05T01:55:26Z"},{"alias_kind":"pith_short_16","alias_value":"ZB5JU2LUTFEYLDBZ","created_at":"2026-07-05T01:55:26Z"},{"alias_kind":"pith_short_8","alias_value":"ZB5JU2LU","created_at":"2026-07-05T01:55:26Z"}],"graph_snapshots":[{"event_id":"sha256:89a1fb62f355d808fa0e05333c15533637dcad16f4d2930abb3cd0bd7f591c7e","target":"graph","created_at":"2026-07-05T01:55:26Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/quant-ph/0507088/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show some chain-rules for the capacity of classical-quantum and quantum channels. We use the concept of Nash-Equilibrium in game-theory, and its existence in suitably defined games, to arrive at the chain-rules.","authors_text":"Rahul Jain","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2005-07-08T19:07:04Z","title":"Chain-rules for channel capacity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0507088","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":"sha256:54cd556cf358e72cbd0652ec3a3a388cb7114ea4b41df2985c1c2e978c208554","target":"record","created_at":"2026-07-05T01:55:26Z","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":"28354f57cd93fe02ee3720d2aefe068a17caeee82405a9ce745e0e5898a762c4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2005-07-08T19:07:04Z","title_canon_sha256":"885602547a6b45980bf1a76d4ddfe6bf4f3007ddc5f8f1b891c8b8bfb81f0535"},"schema_version":"1.0","source":{"id":"quant-ph/0507088","kind":"arxiv","version":3}},"canonical_sha256":"c87a9a69749949858c39e858ec8d83d9537ac66080c0eed324ef9db1564d218a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c87a9a69749949858c39e858ec8d83d9537ac66080c0eed324ef9db1564d218a","first_computed_at":"2026-07-05T01:55:26.917155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:55:26.917155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Dcsnbzd2ctv+2TwQSb8Aay0TIJ0cjyh6qpqs0M3yKFdi46/wfIbL/FpnN6qipGxBeEcuwiAKaiUpzcn+i9fkDg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:55:26.917638Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0507088","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54cd556cf358e72cbd0652ec3a3a388cb7114ea4b41df2985c1c2e978c208554","sha256:89a1fb62f355d808fa0e05333c15533637dcad16f4d2930abb3cd0bd7f591c7e"],"state_sha256":"f5a398650d1acedb5926bf6c2ea3100e51eb387cdc9a8b69dfe3f11528e4e4a3"}