{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:GOJQEIIPSUIYDXWZGCNT5KIPIU","short_pith_number":"pith:GOJQEIIP","canonical_record":{"source":{"id":"2606.10374","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IT","submitted_at":"2026-06-09T03:35:33Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"cf8e73d97b8fc6d38c3737178205ea0ae067b1fe94de929d7719f69520901459","abstract_canon_sha256":"d28eea4791b0bbc1973dfceaaf6600a42efd103cee2709774f57fd5ab438f5b4"},"schema_version":"1.0"},"canonical_sha256":"339302210f951181ded9309b3ea90f45136b788195e7f21865ae4d5ed0850798","source":{"kind":"arxiv","id":"2606.10374","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.10374","created_at":"2026-06-10T01:10:14Z"},{"alias_kind":"arxiv_version","alias_value":"2606.10374v1","created_at":"2026-06-10T01:10:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.10374","created_at":"2026-06-10T01:10:14Z"},{"alias_kind":"pith_short_12","alias_value":"GOJQEIIPSUIY","created_at":"2026-06-10T01:10:14Z"},{"alias_kind":"pith_short_16","alias_value":"GOJQEIIPSUIYDXWZ","created_at":"2026-06-10T01:10:14Z"},{"alias_kind":"pith_short_8","alias_value":"GOJQEIIP","created_at":"2026-06-10T01:10:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:GOJQEIIPSUIYDXWZGCNT5KIPIU","target":"record","payload":{"canonical_record":{"source":{"id":"2606.10374","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IT","submitted_at":"2026-06-09T03:35:33Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"cf8e73d97b8fc6d38c3737178205ea0ae067b1fe94de929d7719f69520901459","abstract_canon_sha256":"d28eea4791b0bbc1973dfceaaf6600a42efd103cee2709774f57fd5ab438f5b4"},"schema_version":"1.0"},"canonical_sha256":"339302210f951181ded9309b3ea90f45136b788195e7f21865ae4d5ed0850798","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-10T01:10:14.513187Z","signature_b64":"RUSM7hdRGeuLPkqbCLi7FdJek/CDzOD6vx5MD5Hbc9mFDjUMcAWsvFkmlvTjotngkbdcXOakz9dUQPKLNMuJAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"339302210f951181ded9309b3ea90f45136b788195e7f21865ae4d5ed0850798","last_reissued_at":"2026-06-10T01:10:14.512280Z","signature_status":"signed_v1","first_computed_at":"2026-06-10T01:10:14.512280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.10374","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-10T01:10:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A4Nvtl048Vu8iFqicm8l4BXiorkp+xGXqrqHvKDCTADV41fTIjISuWaumjszy7+pX8smwMVsCyM4cMzIUUMTDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:53:12.800546Z"},"content_sha256":"0abe93196c8c4db70931f0fd6868ed14a1295fcb830afb45b80b34bed30af6d3","schema_version":"1.0","event_id":"sha256:0abe93196c8c4db70931f0fd6868ed14a1295fcb830afb45b80b34bed30af6d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:GOJQEIIPSUIYDXWZGCNT5KIPIU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equation Asymmetry: An Algebraic Framework for Unifying Secrecy and Covertness in Information-Theoretic Security","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Wang Hao, Zhang Kuang","submitted_at":"2026-06-09T03:35:33Z","abstract_excerpt":"This paper studies the algebraic structure underlying a broad class of information-theoretic security problems. We define the equation asymmetry degree (EAD) as $\\Phi = (n - r)/n$, where $n$ is the signal embedding dimension and $r$ is the effective rank of the adversary's observation matrix. This single parameter is shown to simultaneously govern both secrecy (measured by equivocation $H(M|Y_E)$) and covertness (measured by detection error probability $P_e$). On finite fields $\\mathbb{F}_q$, we establish the equivocation lower bound $H(M|Y_E) = \\min(k, n - r_E) \\log q$ with exact probabilisti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10374","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.10374/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-10T01:10:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wq1hdZCSYY2Lw20e4zKbTIG7noLTECytcCe16652RIKMs+t9tRYo+l2TvJLYd/p1Dpysq6PyOs6VNTwioUuUDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:53:12.801309Z"},"content_sha256":"3ff1efa0413912d905fafaf07d745c143e5e3bccf23af58db086cfb36489cead","schema_version":"1.0","event_id":"sha256:3ff1efa0413912d905fafaf07d745c143e5e3bccf23af58db086cfb36489cead"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GOJQEIIPSUIYDXWZGCNT5KIPIU/bundle.json","state_url":"https://pith.science/pith/GOJQEIIPSUIYDXWZGCNT5KIPIU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GOJQEIIPSUIYDXWZGCNT5KIPIU/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":"2026-06-11T03:53:12Z","links":{"resolver":"https://pith.science/pith/GOJQEIIPSUIYDXWZGCNT5KIPIU","bundle":"https://pith.science/pith/GOJQEIIPSUIYDXWZGCNT5KIPIU/bundle.json","state":"https://pith.science/pith/GOJQEIIPSUIYDXWZGCNT5KIPIU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GOJQEIIPSUIYDXWZGCNT5KIPIU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:GOJQEIIPSUIYDXWZGCNT5KIPIU","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":"d28eea4791b0bbc1973dfceaaf6600a42efd103cee2709774f57fd5ab438f5b4","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IT","submitted_at":"2026-06-09T03:35:33Z","title_canon_sha256":"cf8e73d97b8fc6d38c3737178205ea0ae067b1fe94de929d7719f69520901459"},"schema_version":"1.0","source":{"id":"2606.10374","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.10374","created_at":"2026-06-10T01:10:14Z"},{"alias_kind":"arxiv_version","alias_value":"2606.10374v1","created_at":"2026-06-10T01:10:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.10374","created_at":"2026-06-10T01:10:14Z"},{"alias_kind":"pith_short_12","alias_value":"GOJQEIIPSUIY","created_at":"2026-06-10T01:10:14Z"},{"alias_kind":"pith_short_16","alias_value":"GOJQEIIPSUIYDXWZ","created_at":"2026-06-10T01:10:14Z"},{"alias_kind":"pith_short_8","alias_value":"GOJQEIIP","created_at":"2026-06-10T01:10:14Z"}],"graph_snapshots":[{"event_id":"sha256:3ff1efa0413912d905fafaf07d745c143e5e3bccf23af58db086cfb36489cead","target":"graph","created_at":"2026-06-10T01:10:14Z","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/2606.10374/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper studies the algebraic structure underlying a broad class of information-theoretic security problems. We define the equation asymmetry degree (EAD) as $\\Phi = (n - r)/n$, where $n$ is the signal embedding dimension and $r$ is the effective rank of the adversary's observation matrix. This single parameter is shown to simultaneously govern both secrecy (measured by equivocation $H(M|Y_E)$) and covertness (measured by detection error probability $P_e$). On finite fields $\\mathbb{F}_q$, we establish the equivocation lower bound $H(M|Y_E) = \\min(k, n - r_E) \\log q$ with exact probabilisti","authors_text":"Wang Hao, Zhang Kuang","cross_cats":["math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IT","submitted_at":"2026-06-09T03:35:33Z","title":"Equation Asymmetry: An Algebraic Framework for Unifying Secrecy and Covertness in Information-Theoretic Security"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10374","kind":"arxiv","version":1},"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":"sha256:0abe93196c8c4db70931f0fd6868ed14a1295fcb830afb45b80b34bed30af6d3","target":"record","created_at":"2026-06-10T01:10:14Z","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":"d28eea4791b0bbc1973dfceaaf6600a42efd103cee2709774f57fd5ab438f5b4","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IT","submitted_at":"2026-06-09T03:35:33Z","title_canon_sha256":"cf8e73d97b8fc6d38c3737178205ea0ae067b1fe94de929d7719f69520901459"},"schema_version":"1.0","source":{"id":"2606.10374","kind":"arxiv","version":1}},"canonical_sha256":"339302210f951181ded9309b3ea90f45136b788195e7f21865ae4d5ed0850798","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"339302210f951181ded9309b3ea90f45136b788195e7f21865ae4d5ed0850798","first_computed_at":"2026-06-10T01:10:14.512280Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-10T01:10:14.512280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RUSM7hdRGeuLPkqbCLi7FdJek/CDzOD6vx5MD5Hbc9mFDjUMcAWsvFkmlvTjotngkbdcXOakz9dUQPKLNMuJAA==","signature_status":"signed_v1","signed_at":"2026-06-10T01:10:14.513187Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.10374","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0abe93196c8c4db70931f0fd6868ed14a1295fcb830afb45b80b34bed30af6d3","sha256:3ff1efa0413912d905fafaf07d745c143e5e3bccf23af58db086cfb36489cead"],"state_sha256":"0b4c87b54d8e188ae40019ee9c06cd1c3de34d94c4ca399d5c0b3341d8ece41e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0PSijHcUW4sBy1WS6VJcbCxkPLHCmPnLn5NAnAepj13YhjJXpQ+eDBKoxXcS1ln/Urck2FO5sL8LZljyvNHuBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T03:53:12.805181Z","bundle_sha256":"dac807999e4d1b5bbbf96451f20332733c2fc67ffdd21b4964e62526ee2d9ac5"}}