{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RBTCTU2JV5VTS7J2Q3JS6ZGSD6","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":"32830e406168c1018797088739ee446dc6669a8daf33933dbf1e5c64f13a3bb5","cross_cats_sorted":["physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-05-10T19:07:51Z","title_canon_sha256":"c3073f9985e7a8feddb243d218a33e8564e6290f3a8e9ed27242fa9c172466b2"},"schema_version":"1.0","source":{"id":"1705.03927","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.03927","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"arxiv_version","alias_value":"1705.03927v2","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.03927","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"pith_short_12","alias_value":"RBTCTU2JV5VT","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RBTCTU2JV5VTS7J2","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RBTCTU2J","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:bfc766b48bc7e27d1c514ae569671792d9a356546159feea84fb08bbae2709bb","target":"graph","created_at":"2026-05-18T00:42:23Z","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"},"paper":{"abstract_excerpt":"In earlier work, my colleagues and I developed a formalism for using information theory to understand scales of organization and structure in multi-component systems. One prominent theme of that work was that the structure of a system cannot always be decomposed into pairwise relationships. In this brief communication, I refine that formalism to address recent examples which bring out that theme in a novel and subtle way. After summarizing key points of earlier papers, I introduce the crucial new concept of an ancilla component, and I apply this refinement of our formalism to illustrative exam","authors_text":"Blake C. Stacey","cross_cats":["physics.data-an"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-05-10T19:07:51Z","title":"Multiscale Structure of More-than-Binary Variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03927","kind":"arxiv","version":2},"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:f46e0068fdea209af2e78edeef83b5365159cffd4f6b6a754543c550c3e46f5f","target":"record","created_at":"2026-05-18T00:42:23Z","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":"32830e406168c1018797088739ee446dc6669a8daf33933dbf1e5c64f13a3bb5","cross_cats_sorted":["physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-05-10T19:07:51Z","title_canon_sha256":"c3073f9985e7a8feddb243d218a33e8564e6290f3a8e9ed27242fa9c172466b2"},"schema_version":"1.0","source":{"id":"1705.03927","kind":"arxiv","version":2}},"canonical_sha256":"886629d349af6b397d3a86d32f64d21f913d9d4c95fccc1fb7332345a957c66d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"886629d349af6b397d3a86d32f64d21f913d9d4c95fccc1fb7332345a957c66d","first_computed_at":"2026-05-18T00:42:23.370639Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:23.370639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KjShWfnjLAIKum0S1Lt6/cwbeNtv51rKzuvAGwwJQQWTQtjIvlPiGBao95BTCqRhm4cJb9KRYcqcVwu1AeCSDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:23.371050Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.03927","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f46e0068fdea209af2e78edeef83b5365159cffd4f6b6a754543c550c3e46f5f","sha256:bfc766b48bc7e27d1c514ae569671792d9a356546159feea84fb08bbae2709bb"],"state_sha256":"180b0f5913d3a0b5bcee8612966af20a77f09a80322217c5ecbcebea19f1cde7"}