{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:WEDH5LXFFMDILWXW2Y5POGMJDL","short_pith_number":"pith:WEDH5LXF","canonical_record":{"source":{"id":"2605.30722","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-29T01:31:56Z","cross_cats_sorted":["stat.CO","stat.ME"],"title_canon_sha256":"7573c193b3dea37269ed50ddc813725912854571c7ba556c0e2fbbdc5c87f176","abstract_canon_sha256":"288cdc899a23f6ba80110380cfcacc595aad001e243ca2f36f4fd3bf92bd0d47"},"schema_version":"1.0"},"canonical_sha256":"b1067eaee52b0685daf6d63af719891adb9fd9c0315ca90800d58313f5b7446b","source":{"kind":"arxiv","id":"2605.30722","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.30722","created_at":"2026-06-01T01:03:12Z"},{"alias_kind":"arxiv_version","alias_value":"2605.30722v1","created_at":"2026-06-01T01:03:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.30722","created_at":"2026-06-01T01:03:12Z"},{"alias_kind":"pith_short_12","alias_value":"WEDH5LXFFMDI","created_at":"2026-06-01T01:03:12Z"},{"alias_kind":"pith_short_16","alias_value":"WEDH5LXFFMDILWXW","created_at":"2026-06-01T01:03:12Z"},{"alias_kind":"pith_short_8","alias_value":"WEDH5LXF","created_at":"2026-06-01T01:03:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:WEDH5LXFFMDILWXW2Y5POGMJDL","target":"record","payload":{"canonical_record":{"source":{"id":"2605.30722","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-29T01:31:56Z","cross_cats_sorted":["stat.CO","stat.ME"],"title_canon_sha256":"7573c193b3dea37269ed50ddc813725912854571c7ba556c0e2fbbdc5c87f176","abstract_canon_sha256":"288cdc899a23f6ba80110380cfcacc595aad001e243ca2f36f4fd3bf92bd0d47"},"schema_version":"1.0"},"canonical_sha256":"b1067eaee52b0685daf6d63af719891adb9fd9c0315ca90800d58313f5b7446b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-01T01:03:12.274650Z","signature_b64":"lROPYaEiq2t8uRRdqDJPIOavMCHKrKfgEcudym7xMJlapF8psoav6bhkPq/UXR5uZDCD8WNZtIWJBg+NxwoMBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1067eaee52b0685daf6d63af719891adb9fd9c0315ca90800d58313f5b7446b","last_reissued_at":"2026-06-01T01:03:12.273914Z","signature_status":"signed_v1","first_computed_at":"2026-06-01T01:03:12.273914Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.30722","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":"2026-06-01T01:03:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uRqm1iP8I/TP+WTky3QybGhfwyf1UHD2/v01MUGnAxIN91EeT2uD5jTkUSJBWHOI6d7BLZP2dpkFO4Z9jPuNCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:14:09.965681Z"},"content_sha256":"2bc881ca1b46369be50da801bc92c8e455a856b0b69f3fd382d89fce252ca4bc","schema_version":"1.0","event_id":"sha256:2bc881ca1b46369be50da801bc92c8e455a856b0b69f3fd382d89fce252ca4bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:WEDH5LXFFMDILWXW2Y5POGMJDL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Self-Certifying Transport MCMC via Dual Spectral-Gap Certificates","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":"2026-05-29T01:31:56Z","abstract_excerpt":"We propose CerT-MCMC, a framework that equips learned-transport Markov chain Monte Carlo with automatic, rigorous convergence certificates. A normalising flow maps a Gaussian reference to an approximation of the target posterior; the same flow then serves as both the independence Metropolis-Hastings proposal and the basis for a computable spectral-gap bound. We develop two complementary certificates. The covering certificate bounds the weight-ratio oscillation over the full proposal support via finite-sample covering arguments, yielding full-support spectral-gap bounds when a conservative grad"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30722","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/2605.30722/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":"2026-06-01T01:03:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IwxVEmuA6i+iZ+bSYjkeXRaxiLQcLCWVd7Fas8esnJt0YluDF4xaOkodxEqytk9+LPUWhO1FvmhOUqcDEdDuDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:14:09.966078Z"},"content_sha256":"7642a10276b19a68929aa2adf2edb905b76b19a024368d1a624889646cbc6450","schema_version":"1.0","event_id":"sha256:7642a10276b19a68929aa2adf2edb905b76b19a024368d1a624889646cbc6450"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WEDH5LXFFMDILWXW2Y5POGMJDL/bundle.json","state_url":"https://pith.science/pith/WEDH5LXFFMDILWXW2Y5POGMJDL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WEDH5LXFFMDILWXW2Y5POGMJDL/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":"2026-06-20T05:14:09Z","links":{"resolver":"https://pith.science/pith/WEDH5LXFFMDILWXW2Y5POGMJDL","bundle":"https://pith.science/pith/WEDH5LXFFMDILWXW2Y5POGMJDL/bundle.json","state":"https://pith.science/pith/WEDH5LXFFMDILWXW2Y5POGMJDL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WEDH5LXFFMDILWXW2Y5POGMJDL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WEDH5LXFFMDILWXW2Y5POGMJDL","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":"288cdc899a23f6ba80110380cfcacc595aad001e243ca2f36f4fd3bf92bd0d47","cross_cats_sorted":["stat.CO","stat.ME"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-29T01:31:56Z","title_canon_sha256":"7573c193b3dea37269ed50ddc813725912854571c7ba556c0e2fbbdc5c87f176"},"schema_version":"1.0","source":{"id":"2605.30722","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.30722","created_at":"2026-06-01T01:03:12Z"},{"alias_kind":"arxiv_version","alias_value":"2605.30722v1","created_at":"2026-06-01T01:03:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.30722","created_at":"2026-06-01T01:03:12Z"},{"alias_kind":"pith_short_12","alias_value":"WEDH5LXFFMDI","created_at":"2026-06-01T01:03:12Z"},{"alias_kind":"pith_short_16","alias_value":"WEDH5LXFFMDILWXW","created_at":"2026-06-01T01:03:12Z"},{"alias_kind":"pith_short_8","alias_value":"WEDH5LXF","created_at":"2026-06-01T01:03:12Z"}],"graph_snapshots":[{"event_id":"sha256:7642a10276b19a68929aa2adf2edb905b76b19a024368d1a624889646cbc6450","target":"graph","created_at":"2026-06-01T01:03:12Z","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/2605.30722/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose CerT-MCMC, a framework that equips learned-transport Markov chain Monte Carlo with automatic, rigorous convergence certificates. A normalising flow maps a Gaussian reference to an approximation of the target posterior; the same flow then serves as both the independence Metropolis-Hastings proposal and the basis for a computable spectral-gap bound. We develop two complementary certificates. The covering certificate bounds the weight-ratio oscillation over the full proposal support via finite-sample covering arguments, yielding full-support spectral-gap bounds when a conservative grad","authors_text":"Jun Hu","cross_cats":["stat.CO","stat.ME"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-29T01:31:56Z","title":"Self-Certifying Transport MCMC via Dual Spectral-Gap Certificates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30722","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":"sha256:2bc881ca1b46369be50da801bc92c8e455a856b0b69f3fd382d89fce252ca4bc","target":"record","created_at":"2026-06-01T01:03:12Z","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":"288cdc899a23f6ba80110380cfcacc595aad001e243ca2f36f4fd3bf92bd0d47","cross_cats_sorted":["stat.CO","stat.ME"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-29T01:31:56Z","title_canon_sha256":"7573c193b3dea37269ed50ddc813725912854571c7ba556c0e2fbbdc5c87f176"},"schema_version":"1.0","source":{"id":"2605.30722","kind":"arxiv","version":1}},"canonical_sha256":"b1067eaee52b0685daf6d63af719891adb9fd9c0315ca90800d58313f5b7446b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1067eaee52b0685daf6d63af719891adb9fd9c0315ca90800d58313f5b7446b","first_computed_at":"2026-06-01T01:03:12.273914Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-01T01:03:12.273914Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lROPYaEiq2t8uRRdqDJPIOavMCHKrKfgEcudym7xMJlapF8psoav6bhkPq/UXR5uZDCD8WNZtIWJBg+NxwoMBQ==","signature_status":"signed_v1","signed_at":"2026-06-01T01:03:12.274650Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.30722","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2bc881ca1b46369be50da801bc92c8e455a856b0b69f3fd382d89fce252ca4bc","sha256:7642a10276b19a68929aa2adf2edb905b76b19a024368d1a624889646cbc6450"],"state_sha256":"d50b1a50dbd8267e24e27367139bfa90cdaa59d887a96642d4149eb00c4b0256"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PoXjur9uJkYih0KfSDzeCrySIKjsxlJD0kdXDcNLLJLDgf/L/KTCncOTFepZ0W/Ho297fwgVOrESmRV8kHF6Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T05:14:09.968194Z","bundle_sha256":"e213e95f14da242ee07e02b2099edf356a8b342819650c22d43518886e137ad1"}}