{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:RGRTYJTXKRPJBMC4THT2LQGH7I","short_pith_number":"pith:RGRTYJTX","schema_version":"1.0","canonical_sha256":"89a33c2677545e90b05c99e7a5c0c7fa2f978806244b9989a9fe92550c379507","source":{"kind":"arxiv","id":"2606.04307","version":1},"attestation_state":"computed","paper":{"title":"Folded Transport MCMC: Certifiable Quotient Posterior Computation for Symmetric Bayesian Models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.CO","stat.ME"],"primary_cat":"cs.LG","authors_text":"Jun Hu","submitted_at":"2026-06-03T00:26:46Z","abstract_excerpt":"Bayesian models with finite symmetry - mixture models with exchangeable components, structural identification with closely-spaced modes - define posteriors that are invariant under a group of label permutations, creating redundant multimodality that degrades MCMC convergence diagnostics. We introduce Folded Transport MCMC (FolT-MCMC), which performs inference directly on the quotient posterior by constructing an independence sampler on the fundamental domain of the symmetry group. The quotient proposal is formed by symmetrising a learned normalising flow over the group orbits. We prove that th"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.04307","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-03T00:26:46Z","cross_cats_sorted":["stat.CO","stat.ME"],"title_canon_sha256":"27ce11c138db1fbf0efc0314d9d44b2ec391cc41defabe2ffdbe2b2fa5bbd59e","abstract_canon_sha256":"eb1d83e0e86b324ad2bec30022d6e9cc6d6017e5f7b12d55e23c1b31a6895b7e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T01:09:03.048407Z","signature_b64":"cJBaZrSVVXeLhmkKaCaCYT1DqvgRbp82HAYg0Syo0Vr/pYhY8Qg0m38wrkjCwbHd0bam1C6byiCA0q0dDthcCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89a33c2677545e90b05c99e7a5c0c7fa2f978806244b9989a9fe92550c379507","last_reissued_at":"2026-06-04T01:09:03.047919Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T01:09:03.047919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Folded Transport MCMC: Certifiable Quotient Posterior Computation for Symmetric Bayesian Models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.CO","stat.ME"],"primary_cat":"cs.LG","authors_text":"Jun Hu","submitted_at":"2026-06-03T00:26:46Z","abstract_excerpt":"Bayesian models with finite symmetry - mixture models with exchangeable components, structural identification with closely-spaced modes - define posteriors that are invariant under a group of label permutations, creating redundant multimodality that degrades MCMC convergence diagnostics. We introduce Folded Transport MCMC (FolT-MCMC), which performs inference directly on the quotient posterior by constructing an independence sampler on the fundamental domain of the symmetry group. The quotient proposal is formed by symmetrising a learned normalising flow over the group orbits. We prove that th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04307","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/2606.04307/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.04307","created_at":"2026-06-04T01:09:03.047992+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.04307v1","created_at":"2026-06-04T01:09:03.047992+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04307","created_at":"2026-06-04T01:09:03.047992+00:00"},{"alias_kind":"pith_short_12","alias_value":"RGRTYJTXKRPJ","created_at":"2026-06-04T01:09:03.047992+00:00"},{"alias_kind":"pith_short_16","alias_value":"RGRTYJTXKRPJBMC4","created_at":"2026-06-04T01:09:03.047992+00:00"},{"alias_kind":"pith_short_8","alias_value":"RGRTYJTX","created_at":"2026-06-04T01:09:03.047992+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RGRTYJTXKRPJBMC4THT2LQGH7I","json":"https://pith.science/pith/RGRTYJTXKRPJBMC4THT2LQGH7I.json","graph_json":"https://pith.science/api/pith-number/RGRTYJTXKRPJBMC4THT2LQGH7I/graph.json","events_json":"https://pith.science/api/pith-number/RGRTYJTXKRPJBMC4THT2LQGH7I/events.json","paper":"https://pith.science/paper/RGRTYJTX"},"agent_actions":{"view_html":"https://pith.science/pith/RGRTYJTXKRPJBMC4THT2LQGH7I","download_json":"https://pith.science/pith/RGRTYJTXKRPJBMC4THT2LQGH7I.json","view_paper":"https://pith.science/paper/RGRTYJTX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.04307&json=true","fetch_graph":"https://pith.science/api/pith-number/RGRTYJTXKRPJBMC4THT2LQGH7I/graph.json","fetch_events":"https://pith.science/api/pith-number/RGRTYJTXKRPJBMC4THT2LQGH7I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RGRTYJTXKRPJBMC4THT2LQGH7I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RGRTYJTXKRPJBMC4THT2LQGH7I/action/storage_attestation","attest_author":"https://pith.science/pith/RGRTYJTXKRPJBMC4THT2LQGH7I/action/author_attestation","sign_citation":"https://pith.science/pith/RGRTYJTXKRPJBMC4THT2LQGH7I/action/citation_signature","submit_replication":"https://pith.science/pith/RGRTYJTXKRPJBMC4THT2LQGH7I/action/replication_record"}},"created_at":"2026-06-04T01:09:03.047992+00:00","updated_at":"2026-06-04T01:09:03.047992+00:00"}