{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:KF557GCP4KOWXUBC65HWQNHSE3","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":"f856f52441b5b23ebfe2e75517a6d53c7ff5b9dedbd9921d39c6704cf9389f22","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-07-21T08:22:37Z","title_canon_sha256":"c6a352f1800409c88ff3f791af6c21cd4b107534cb5bca40012c32764a656b9a"},"schema_version":"1.0","source":{"id":"2507.15372","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.15372","created_at":"2026-07-05T11:40:23Z"},{"alias_kind":"arxiv_version","alias_value":"2507.15372v1","created_at":"2026-07-05T11:40:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.15372","created_at":"2026-07-05T11:40:23Z"},{"alias_kind":"pith_short_12","alias_value":"KF557GCP4KOW","created_at":"2026-07-05T11:40:23Z"},{"alias_kind":"pith_short_16","alias_value":"KF557GCP4KOWXUBC","created_at":"2026-07-05T11:40:23Z"},{"alias_kind":"pith_short_8","alias_value":"KF557GCP","created_at":"2026-07-05T11:40:23Z"}],"graph_snapshots":[{"event_id":"sha256:a92c576d303f246cdeffc9814aa0f600eb85f302c9925236668f66d6824dae3a","target":"graph","created_at":"2026-07-05T11:40:23Z","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":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2507.15372/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Mutual information (MI) is a useful information-theoretic measure to quantify the statistical dependence between two random variables: $X$ and $Y$. Often, we are interested in understanding how the dependence between $X$ and $Y$ in one set of samples compares to another. Although the dependence between $X$ and $Y$ in each set of samples can be measured separately using MI, these estimates cannot be compared directly if they are based on samples from a non-stationary distribution. Here, we propose an alternative measure for characterising how the dependence between $X$ and $Y$ as defined by one","authors_text":"Ben D. Fulcher, Chetan Gohil, James M. Shine, Joseph T. Lizier, Oliver M Cliff","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-07-21T08:22:37Z","title":"Cross Mutual Information"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.15372","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":"sha256:106ef8ce75398b993c9ce030a7ccddf907db72484555610fd5e7550e0cf53f89","target":"record","created_at":"2026-07-05T11:40:23Z","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":"f856f52441b5b23ebfe2e75517a6d53c7ff5b9dedbd9921d39c6704cf9389f22","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-07-21T08:22:37Z","title_canon_sha256":"c6a352f1800409c88ff3f791af6c21cd4b107534cb5bca40012c32764a656b9a"},"schema_version":"1.0","source":{"id":"2507.15372","kind":"arxiv","version":1}},"canonical_sha256":"517bdf984fe29d6bd022f74f6834f226efbe6504ac4f39d6383e9a3373dc9933","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"517bdf984fe29d6bd022f74f6834f226efbe6504ac4f39d6383e9a3373dc9933","first_computed_at":"2026-07-05T11:40:23.752539Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:40:23.752539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wEAy+FoBWUtJ5bTX0A0Chmfon/ToU/wT2wYFVxCjz+9RdwdJ2OWqqmfr33rOeKExigoaJtygz4XgvTubOGoTDw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:40:23.753032Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.15372","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:106ef8ce75398b993c9ce030a7ccddf907db72484555610fd5e7550e0cf53f89","sha256:a92c576d303f246cdeffc9814aa0f600eb85f302c9925236668f66d6824dae3a"],"state_sha256":"2e1add962de4baca98c64b23c30b13b0b29db974437982ee0f8e5d9d342e5854"}