{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:LBDOGSOUTO3JDKJ6FS3NXQTRAT","short_pith_number":"pith:LBDOGSOU","canonical_record":{"source":{"id":"2606.19366","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-11T03:42:57Z","cross_cats_sorted":["cs.AI","eess.SP"],"title_canon_sha256":"aba10a38397849a4cf15117b9e04685fcc978bbe01022de5a6d7199630e4df3f","abstract_canon_sha256":"4863cfb9945ab09f2235157067b2765431c91e0914577b04a54bdccc033074bf"},"schema_version":"1.0"},"canonical_sha256":"5846e349d49bb691a93e2cb6dbc27104d432df03cd66d23c3e17d393a2a00667","source":{"kind":"arxiv","id":"2606.19366","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.19366","created_at":"2026-06-19T16:12:23Z"},{"alias_kind":"arxiv_version","alias_value":"2606.19366v1","created_at":"2026-06-19T16:12:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19366","created_at":"2026-06-19T16:12:23Z"},{"alias_kind":"pith_short_12","alias_value":"LBDOGSOUTO3J","created_at":"2026-06-19T16:12:23Z"},{"alias_kind":"pith_short_16","alias_value":"LBDOGSOUTO3JDKJ6","created_at":"2026-06-19T16:12:23Z"},{"alias_kind":"pith_short_8","alias_value":"LBDOGSOU","created_at":"2026-06-19T16:12:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:LBDOGSOUTO3JDKJ6FS3NXQTRAT","target":"record","payload":{"canonical_record":{"source":{"id":"2606.19366","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-11T03:42:57Z","cross_cats_sorted":["cs.AI","eess.SP"],"title_canon_sha256":"aba10a38397849a4cf15117b9e04685fcc978bbe01022de5a6d7199630e4df3f","abstract_canon_sha256":"4863cfb9945ab09f2235157067b2765431c91e0914577b04a54bdccc033074bf"},"schema_version":"1.0"},"canonical_sha256":"5846e349d49bb691a93e2cb6dbc27104d432df03cd66d23c3e17d393a2a00667","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:12:23.290254Z","signature_b64":"figgIgfQG/ARneBDqD6LatQ8Tz9JN0rZ7BsQnkjS5FAMq6vhKFvpWjsoCYbj5nJH9DDV7xsI7BA7Wxg2+2kKDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5846e349d49bb691a93e2cb6dbc27104d432df03cd66d23c3e17d393a2a00667","last_reissued_at":"2026-06-19T16:12:23.289911Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:12:23.289911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.19366","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":"2026-06-19T16:12:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mzFWfvMF96By687HxIM5K3KFZx7KBHBSUG9jd5X9WArhrRhdepB/qelovX6GXncmGfHvqjLjs3LbRncqD8SLBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T08:27:02.432401Z"},"content_sha256":"511adf3e69f55bfb6753a475440ea57cae6c19761f6f3cbbc20b6a568cee8f29","schema_version":"1.0","event_id":"sha256:511adf3e69f55bfb6753a475440ea57cae6c19761f6f3cbbc20b6a568cee8f29"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:LBDOGSOUTO3JDKJ6FS3NXQTRAT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Information Lattice Learning as Probabilistic Graphical Model Structure Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","eess.SP"],"primary_cat":"cs.LG","authors_text":"Haizi Yu, Lav R. Varshney","submitted_at":"2026-06-11T03:42:57Z","abstract_excerpt":"Information lattice learning (ILL) learns interpretable rules of a signal by alternately projecting the signal onto a partition lattice that encodes a hierarchy of abstractions and lifting selected rules back to the signal domain. When the signal is a probability mass function, we show the probabilistic rules learned by ILL admit a natural probabilistic graphical model (PGM) interpretation and develop this interpretation in detail. A partition in ILL induces a deterministic quotient variable, and a rule is the marginal law of that quotient variable. A rule set is therefore a collection of marg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19366","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/2606.19366/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":"2026-06-19T16:12:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UTgZ5Atnqv5jeI5Pgd9IfvMOJxWLT37csDVYESS3WcZvRxQtA/VMFwR7QGEWQ/2RNcRINJECG1M1LpGWW1B0Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T08:27:02.432781Z"},"content_sha256":"8cc76d328b2105b8b140f63a1b4db67bb1d44da130544d826e691cf531efe909","schema_version":"1.0","event_id":"sha256:8cc76d328b2105b8b140f63a1b4db67bb1d44da130544d826e691cf531efe909"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LBDOGSOUTO3JDKJ6FS3NXQTRAT/bundle.json","state_url":"https://pith.science/pith/LBDOGSOUTO3JDKJ6FS3NXQTRAT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LBDOGSOUTO3JDKJ6FS3NXQTRAT/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":"2026-06-30T08:27:02Z","links":{"resolver":"https://pith.science/pith/LBDOGSOUTO3JDKJ6FS3NXQTRAT","bundle":"https://pith.science/pith/LBDOGSOUTO3JDKJ6FS3NXQTRAT/bundle.json","state":"https://pith.science/pith/LBDOGSOUTO3JDKJ6FS3NXQTRAT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LBDOGSOUTO3JDKJ6FS3NXQTRAT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:LBDOGSOUTO3JDKJ6FS3NXQTRAT","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":"4863cfb9945ab09f2235157067b2765431c91e0914577b04a54bdccc033074bf","cross_cats_sorted":["cs.AI","eess.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-11T03:42:57Z","title_canon_sha256":"aba10a38397849a4cf15117b9e04685fcc978bbe01022de5a6d7199630e4df3f"},"schema_version":"1.0","source":{"id":"2606.19366","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.19366","created_at":"2026-06-19T16:12:23Z"},{"alias_kind":"arxiv_version","alias_value":"2606.19366v1","created_at":"2026-06-19T16:12:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19366","created_at":"2026-06-19T16:12:23Z"},{"alias_kind":"pith_short_12","alias_value":"LBDOGSOUTO3J","created_at":"2026-06-19T16:12:23Z"},{"alias_kind":"pith_short_16","alias_value":"LBDOGSOUTO3JDKJ6","created_at":"2026-06-19T16:12:23Z"},{"alias_kind":"pith_short_8","alias_value":"LBDOGSOU","created_at":"2026-06-19T16:12:23Z"}],"graph_snapshots":[{"event_id":"sha256:8cc76d328b2105b8b140f63a1b4db67bb1d44da130544d826e691cf531efe909","target":"graph","created_at":"2026-06-19T16:12:23Z","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/2606.19366/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Information lattice learning (ILL) learns interpretable rules of a signal by alternately projecting the signal onto a partition lattice that encodes a hierarchy of abstractions and lifting selected rules back to the signal domain. When the signal is a probability mass function, we show the probabilistic rules learned by ILL admit a natural probabilistic graphical model (PGM) interpretation and develop this interpretation in detail. A partition in ILL induces a deterministic quotient variable, and a rule is the marginal law of that quotient variable. A rule set is therefore a collection of marg","authors_text":"Haizi Yu, Lav R. Varshney","cross_cats":["cs.AI","eess.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-11T03:42:57Z","title":"Information Lattice Learning as Probabilistic Graphical Model Structure Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19366","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":"sha256:511adf3e69f55bfb6753a475440ea57cae6c19761f6f3cbbc20b6a568cee8f29","target":"record","created_at":"2026-06-19T16:12:23Z","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":"4863cfb9945ab09f2235157067b2765431c91e0914577b04a54bdccc033074bf","cross_cats_sorted":["cs.AI","eess.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-11T03:42:57Z","title_canon_sha256":"aba10a38397849a4cf15117b9e04685fcc978bbe01022de5a6d7199630e4df3f"},"schema_version":"1.0","source":{"id":"2606.19366","kind":"arxiv","version":1}},"canonical_sha256":"5846e349d49bb691a93e2cb6dbc27104d432df03cd66d23c3e17d393a2a00667","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5846e349d49bb691a93e2cb6dbc27104d432df03cd66d23c3e17d393a2a00667","first_computed_at":"2026-06-19T16:12:23.289911Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:12:23.289911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"figgIgfQG/ARneBDqD6LatQ8Tz9JN0rZ7BsQnkjS5FAMq6vhKFvpWjsoCYbj5nJH9DDV7xsI7BA7Wxg2+2kKDg==","signature_status":"signed_v1","signed_at":"2026-06-19T16:12:23.290254Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.19366","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:511adf3e69f55bfb6753a475440ea57cae6c19761f6f3cbbc20b6a568cee8f29","sha256:8cc76d328b2105b8b140f63a1b4db67bb1d44da130544d826e691cf531efe909"],"state_sha256":"2da81ecadc985edee06d2f53a7ff4ff292f616f59ec81ac01527769afc9e3ca5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ISy27XMihF8zTnywnUsoNE9wr64bSHdFN2HcrBD6wckSCUOtoBaIIFZNe0i03hL4flhy1MNbmciy4vYcCXrqBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T08:27:02.434824Z","bundle_sha256":"2c6ba58fc4363f837bd8ec79c0ede2f124d8b89de78a19219ddf7c9d26de528e"}}