{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:OLA5JGR2X477C5BQBG7D6SI5OL","short_pith_number":"pith:OLA5JGR2","canonical_record":{"source":{"id":"1501.04867","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-20T16:28:01Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"14c088a278c1638cabbc6d1f05bd4299e19991c4c4d61396f66ae62bff8dcb0b","abstract_canon_sha256":"11bc0a5e7832bb0609cb07ec044f2b42cc28304531ab807c19aed4148f7bdf99"},"schema_version":"1.0"},"canonical_sha256":"72c1d49a3abf3ff1743009be3f491d72ee8004121ed7904dc4fefb276d246add","source":{"kind":"arxiv","id":"1501.04867","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04867","created_at":"2026-05-18T00:35:18Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04867v4","created_at":"2026-05-18T00:35:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04867","created_at":"2026-05-18T00:35:18Z"},{"alias_kind":"pith_short_12","alias_value":"OLA5JGR2X477","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OLA5JGR2X477C5BQ","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OLA5JGR2","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:OLA5JGR2X477C5BQBG7D6SI5OL","target":"record","payload":{"canonical_record":{"source":{"id":"1501.04867","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-20T16:28:01Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"14c088a278c1638cabbc6d1f05bd4299e19991c4c4d61396f66ae62bff8dcb0b","abstract_canon_sha256":"11bc0a5e7832bb0609cb07ec044f2b42cc28304531ab807c19aed4148f7bdf99"},"schema_version":"1.0"},"canonical_sha256":"72c1d49a3abf3ff1743009be3f491d72ee8004121ed7904dc4fefb276d246add","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:18.830892Z","signature_b64":"dE4mOm6Xg1lqjYWKzpLsXSb2qpNCSOXvWSuJDG+LXnVR5U10u7A4YO3aZpcXwTtG+Z9oKUfTSAJiPbpaJZd/AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72c1d49a3abf3ff1743009be3f491d72ee8004121ed7904dc4fefb276d246add","last_reissued_at":"2026-05-18T00:35:18.830473Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:18.830473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.04867","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:35:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L8ZmGD3E3HzzH10qg4L5f28Q0l9XrF3Vhi3LtKUwR5hH4xAD66INjGvFu1nVtC1Q/e42AsFGpy7rUJ1mdrywAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:12:16.401535Z"},"content_sha256":"f6a2d7a2e6d6ff7cb4b0100d95f7294f22f162975915c1027259a45615b87acb","schema_version":"1.0","event_id":"sha256:f6a2d7a2e6d6ff7cb4b0100d95f7294f22f162975915c1027259a45615b87acb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:OLA5JGR2X477C5BQBG7D6SI5OL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conditional Information Inequalities and Combinatorial Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Andrei Romashchenko, Nikolay Vereshchagin, Tarik Kaced","submitted_at":"2015-01-20T16:28:01Z","abstract_excerpt":"We show that the inequality $H(A \\mid B,X) + H(A \\mid B,Y) \\le H(A\\mid B)$ for jointly distributed random variables $A,B,X,Y$, which does not hold in general case, holds under some natural condition on the support of the probability distribution of $A,B,X,Y$. This result generalizes a version of the conditional Ingleton inequality: if for some distribution $I(X: Y \\mid A) = H(A\\mid X,Y)=0$, then $I(A : B) \\le I(A : B \\mid X) + I(A: B \\mid Y) + I(X : Y)$.\n  We present two applications of our result. The first one is the following easy-to-formulate combinatorial theorem: assume that the edges of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04867","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:35:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yX6MSD8SdhU+cqxKCrJwNQXQCc5VI7GAOcw1tGVhW4USufNe+zBsc49JbVUJXvyxn/bKwV8pXjysiizEFJwPBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:12:16.402231Z"},"content_sha256":"ca0cab74aea936b205c76de014e15f52b58511f8104a92dd838396e3244ccd7b","schema_version":"1.0","event_id":"sha256:ca0cab74aea936b205c76de014e15f52b58511f8104a92dd838396e3244ccd7b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OLA5JGR2X477C5BQBG7D6SI5OL/bundle.json","state_url":"https://pith.science/pith/OLA5JGR2X477C5BQBG7D6SI5OL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OLA5JGR2X477C5BQBG7D6SI5OL/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":"2026-05-26T19:12:16Z","links":{"resolver":"https://pith.science/pith/OLA5JGR2X477C5BQBG7D6SI5OL","bundle":"https://pith.science/pith/OLA5JGR2X477C5BQBG7D6SI5OL/bundle.json","state":"https://pith.science/pith/OLA5JGR2X477C5BQBG7D6SI5OL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OLA5JGR2X477C5BQBG7D6SI5OL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OLA5JGR2X477C5BQBG7D6SI5OL","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":"11bc0a5e7832bb0609cb07ec044f2b42cc28304531ab807c19aed4148f7bdf99","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-20T16:28:01Z","title_canon_sha256":"14c088a278c1638cabbc6d1f05bd4299e19991c4c4d61396f66ae62bff8dcb0b"},"schema_version":"1.0","source":{"id":"1501.04867","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04867","created_at":"2026-05-18T00:35:18Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04867v4","created_at":"2026-05-18T00:35:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04867","created_at":"2026-05-18T00:35:18Z"},{"alias_kind":"pith_short_12","alias_value":"OLA5JGR2X477","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OLA5JGR2X477C5BQ","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OLA5JGR2","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:ca0cab74aea936b205c76de014e15f52b58511f8104a92dd838396e3244ccd7b","target":"graph","created_at":"2026-05-18T00:35:18Z","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 show that the inequality $H(A \\mid B,X) + H(A \\mid B,Y) \\le H(A\\mid B)$ for jointly distributed random variables $A,B,X,Y$, which does not hold in general case, holds under some natural condition on the support of the probability distribution of $A,B,X,Y$. This result generalizes a version of the conditional Ingleton inequality: if for some distribution $I(X: Y \\mid A) = H(A\\mid X,Y)=0$, then $I(A : B) \\le I(A : B \\mid X) + I(A: B \\mid Y) + I(X : Y)$.\n  We present two applications of our result. The first one is the following easy-to-formulate combinatorial theorem: assume that the edges of","authors_text":"Andrei Romashchenko, Nikolay Vereshchagin, Tarik Kaced","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-20T16:28:01Z","title":"Conditional Information Inequalities and Combinatorial Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04867","kind":"arxiv","version":4},"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:f6a2d7a2e6d6ff7cb4b0100d95f7294f22f162975915c1027259a45615b87acb","target":"record","created_at":"2026-05-18T00:35:18Z","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":"11bc0a5e7832bb0609cb07ec044f2b42cc28304531ab807c19aed4148f7bdf99","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-20T16:28:01Z","title_canon_sha256":"14c088a278c1638cabbc6d1f05bd4299e19991c4c4d61396f66ae62bff8dcb0b"},"schema_version":"1.0","source":{"id":"1501.04867","kind":"arxiv","version":4}},"canonical_sha256":"72c1d49a3abf3ff1743009be3f491d72ee8004121ed7904dc4fefb276d246add","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72c1d49a3abf3ff1743009be3f491d72ee8004121ed7904dc4fefb276d246add","first_computed_at":"2026-05-18T00:35:18.830473Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:18.830473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dE4mOm6Xg1lqjYWKzpLsXSb2qpNCSOXvWSuJDG+LXnVR5U10u7A4YO3aZpcXwTtG+Z9oKUfTSAJiPbpaJZd/AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:18.830892Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.04867","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6a2d7a2e6d6ff7cb4b0100d95f7294f22f162975915c1027259a45615b87acb","sha256:ca0cab74aea936b205c76de014e15f52b58511f8104a92dd838396e3244ccd7b"],"state_sha256":"73023ac5b08212a99df736f093df1242e9af7ec92d52990d03acd01d0ce3ea43"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EDse2ZiEzXMV4tG060Ze/ARDa/EyjpOYQxfRR7IGDgIoSUNOgEMLwnDGCXSRU0+mz2IVLTEG+mOvCFBTM8PkDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T19:12:16.406155Z","bundle_sha256":"99c5bf11fa25530cc45c2d39a61b5c1f473e2d0f62336dad249c6967d4e773fe"}}