{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:YSGLNLKGLGCWXLIUDNN4D5YB2I","short_pith_number":"pith:YSGLNLKG","canonical_record":{"source":{"id":"2606.08202","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-06-06T14:40:32Z","cross_cats_sorted":["cs.LG","physics.data-an","q-bio.NC"],"title_canon_sha256":"b3c2f98f1b5725e08f3c4d2367c3a48e9b764d682832f97d4e58db092e19a0cd","abstract_canon_sha256":"afe124b910ba7c8961a65a3caa28b3c7c86979f130d574b8a1b734bdd05e2fd3"},"schema_version":"1.0"},"canonical_sha256":"c48cb6ad4659856bad141b5bc1f701d204cf20caf9eaaebbe4cf7a4fee46b4ca","source":{"kind":"arxiv","id":"2606.08202","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08202","created_at":"2026-06-09T01:05:29Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08202v1","created_at":"2026-06-09T01:05:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08202","created_at":"2026-06-09T01:05:29Z"},{"alias_kind":"pith_short_12","alias_value":"YSGLNLKGLGCW","created_at":"2026-06-09T01:05:29Z"},{"alias_kind":"pith_short_16","alias_value":"YSGLNLKGLGCWXLIU","created_at":"2026-06-09T01:05:29Z"},{"alias_kind":"pith_short_8","alias_value":"YSGLNLKG","created_at":"2026-06-09T01:05:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:YSGLNLKGLGCWXLIUDNN4D5YB2I","target":"record","payload":{"canonical_record":{"source":{"id":"2606.08202","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-06-06T14:40:32Z","cross_cats_sorted":["cs.LG","physics.data-an","q-bio.NC"],"title_canon_sha256":"b3c2f98f1b5725e08f3c4d2367c3a48e9b764d682832f97d4e58db092e19a0cd","abstract_canon_sha256":"afe124b910ba7c8961a65a3caa28b3c7c86979f130d574b8a1b734bdd05e2fd3"},"schema_version":"1.0"},"canonical_sha256":"c48cb6ad4659856bad141b5bc1f701d204cf20caf9eaaebbe4cf7a4fee46b4ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:05:29.910121Z","signature_b64":"q/7AgjD+ofGSrePYaqoxoENPhnZydnKZ1MCok0fTSgJsoreyMlqWQma5og5TCK2Qb4KvxfifwryAgfFGCji5Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c48cb6ad4659856bad141b5bc1f701d204cf20caf9eaaebbe4cf7a4fee46b4ca","last_reissued_at":"2026-06-09T01:05:29.909505Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:05:29.909505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.08202","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":"2026-06-09T01:05:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tq1qazoy93CJCqXU+LOrEBjgGswaOCKn7EUnZVjzJuAWkiB/5Oh2zTUbHmP1mNQhqY8uJ/nTOLApKDANZe1QAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T21:56:17.468428Z"},"content_sha256":"2198e584283a4b09816e639a1ba86012f387fcfc7282af7fc2364bbf1a4ae407","schema_version":"1.0","event_id":"sha256:2198e584283a4b09816e639a1ba86012f387fcfc7282af7fc2364bbf1a4ae407"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:YSGLNLKGLGCWXLIUDNN4D5YB2I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vector Space of Cycles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","physics.data-an","q-bio.NC"],"primary_cat":"stat.ML","authors_text":"Anass B. El-Yaagoubi, Hernando Ombao, Moo K. Chung","submitted_at":"2026-06-06T14:40:32Z","abstract_excerpt":"Most statistical and machine learning methods for directed interactions focus on pairwise effects among variables. Even existing cyclic models represent feedback primarily through node-level dependencies, making large-scale recurrent organization difficult to estimate and compare. This limitation is particularly acute in biological and neural systems, where interactions are highly recurrent and involve many overlapping cycles. We introduce a variational framework for statistical inference on cyclic interactions. Directed interactions are represented as edge flows on a simplicial complex and ev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08202","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/2606.08202/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":"2026-06-09T01:05:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3fjHNJa/Pbpiv2dbX0ODXFnBoR6VVSqSt+vjDyoLOmvrybt2IoXQ6acjcwhp0PheZsXeqYnyMDvKxG0AHTMsBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T21:56:17.468795Z"},"content_sha256":"b1056ad0823e7ea1507301d317beeae73e28ff0d9226090e7d03b2756bcf5c8d","schema_version":"1.0","event_id":"sha256:b1056ad0823e7ea1507301d317beeae73e28ff0d9226090e7d03b2756bcf5c8d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YSGLNLKGLGCWXLIUDNN4D5YB2I/bundle.json","state_url":"https://pith.science/pith/YSGLNLKGLGCWXLIUDNN4D5YB2I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YSGLNLKGLGCWXLIUDNN4D5YB2I/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":"2026-06-29T21:56:17Z","links":{"resolver":"https://pith.science/pith/YSGLNLKGLGCWXLIUDNN4D5YB2I","bundle":"https://pith.science/pith/YSGLNLKGLGCWXLIUDNN4D5YB2I/bundle.json","state":"https://pith.science/pith/YSGLNLKGLGCWXLIUDNN4D5YB2I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YSGLNLKGLGCWXLIUDNN4D5YB2I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YSGLNLKGLGCWXLIUDNN4D5YB2I","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":"afe124b910ba7c8961a65a3caa28b3c7c86979f130d574b8a1b734bdd05e2fd3","cross_cats_sorted":["cs.LG","physics.data-an","q-bio.NC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-06-06T14:40:32Z","title_canon_sha256":"b3c2f98f1b5725e08f3c4d2367c3a48e9b764d682832f97d4e58db092e19a0cd"},"schema_version":"1.0","source":{"id":"2606.08202","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08202","created_at":"2026-06-09T01:05:29Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08202v1","created_at":"2026-06-09T01:05:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08202","created_at":"2026-06-09T01:05:29Z"},{"alias_kind":"pith_short_12","alias_value":"YSGLNLKGLGCW","created_at":"2026-06-09T01:05:29Z"},{"alias_kind":"pith_short_16","alias_value":"YSGLNLKGLGCWXLIU","created_at":"2026-06-09T01:05:29Z"},{"alias_kind":"pith_short_8","alias_value":"YSGLNLKG","created_at":"2026-06-09T01:05:29Z"}],"graph_snapshots":[{"event_id":"sha256:b1056ad0823e7ea1507301d317beeae73e28ff0d9226090e7d03b2756bcf5c8d","target":"graph","created_at":"2026-06-09T01:05:29Z","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/2606.08202/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Most statistical and machine learning methods for directed interactions focus on pairwise effects among variables. Even existing cyclic models represent feedback primarily through node-level dependencies, making large-scale recurrent organization difficult to estimate and compare. This limitation is particularly acute in biological and neural systems, where interactions are highly recurrent and involve many overlapping cycles. We introduce a variational framework for statistical inference on cyclic interactions. Directed interactions are represented as edge flows on a simplicial complex and ev","authors_text":"Anass B. El-Yaagoubi, Hernando Ombao, Moo K. Chung","cross_cats":["cs.LG","physics.data-an","q-bio.NC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-06-06T14:40:32Z","title":"Vector Space of Cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08202","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":"sha256:2198e584283a4b09816e639a1ba86012f387fcfc7282af7fc2364bbf1a4ae407","target":"record","created_at":"2026-06-09T01:05:29Z","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":"afe124b910ba7c8961a65a3caa28b3c7c86979f130d574b8a1b734bdd05e2fd3","cross_cats_sorted":["cs.LG","physics.data-an","q-bio.NC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-06-06T14:40:32Z","title_canon_sha256":"b3c2f98f1b5725e08f3c4d2367c3a48e9b764d682832f97d4e58db092e19a0cd"},"schema_version":"1.0","source":{"id":"2606.08202","kind":"arxiv","version":1}},"canonical_sha256":"c48cb6ad4659856bad141b5bc1f701d204cf20caf9eaaebbe4cf7a4fee46b4ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c48cb6ad4659856bad141b5bc1f701d204cf20caf9eaaebbe4cf7a4fee46b4ca","first_computed_at":"2026-06-09T01:05:29.909505Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:05:29.909505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q/7AgjD+ofGSrePYaqoxoENPhnZydnKZ1MCok0fTSgJsoreyMlqWQma5og5TCK2Qb4KvxfifwryAgfFGCji5Aw==","signature_status":"signed_v1","signed_at":"2026-06-09T01:05:29.910121Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.08202","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2198e584283a4b09816e639a1ba86012f387fcfc7282af7fc2364bbf1a4ae407","sha256:b1056ad0823e7ea1507301d317beeae73e28ff0d9226090e7d03b2756bcf5c8d"],"state_sha256":"fe219894aa9cc2f2f38ad08e5365d56b495435402d78eadf50d56e460832e2be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lRMZv0smNztKyMFjIzROuGjvI4bJd1JteiifynwRoXyMXN82aY01kZwSUMOICp+B/d4U3sSdeLYDBUBtO1VwBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T21:56:17.470696Z","bundle_sha256":"9236b0854c4927fb1adcf806e2858c54a4b2e157307c341c7f8fc6824275d5d6"}}