{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:JA5XQIMZDOA5NUTEBPIH5EM2S3","short_pith_number":"pith:JA5XQIMZ","canonical_record":{"source":{"id":"2607.13841","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-15T13:48:05Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"bc51302d520c4d9f7ad9c90b1abaeb0b60fbc987300b18773008f2170d9060be","abstract_canon_sha256":"370840802bceeddd5f4e013bce4d3ffa8b3eda15d9a9cb07a32505beb24ebacb"},"schema_version":"1.0"},"canonical_sha256":"483b7821991b81d6d2640bd07e919a96c856177951a4f745d2f5995d2f3b83d7","source":{"kind":"arxiv","id":"2607.13841","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.13841","created_at":"2026-07-16T01:23:09Z"},{"alias_kind":"arxiv_version","alias_value":"2607.13841v1","created_at":"2026-07-16T01:23:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.13841","created_at":"2026-07-16T01:23:09Z"},{"alias_kind":"pith_short_12","alias_value":"JA5XQIMZDOA5","created_at":"2026-07-16T01:23:09Z"},{"alias_kind":"pith_short_16","alias_value":"JA5XQIMZDOA5NUTE","created_at":"2026-07-16T01:23:09Z"},{"alias_kind":"pith_short_8","alias_value":"JA5XQIMZ","created_at":"2026-07-16T01:23:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:JA5XQIMZDOA5NUTEBPIH5EM2S3","target":"record","payload":{"canonical_record":{"source":{"id":"2607.13841","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-15T13:48:05Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"bc51302d520c4d9f7ad9c90b1abaeb0b60fbc987300b18773008f2170d9060be","abstract_canon_sha256":"370840802bceeddd5f4e013bce4d3ffa8b3eda15d9a9cb07a32505beb24ebacb"},"schema_version":"1.0"},"canonical_sha256":"483b7821991b81d6d2640bd07e919a96c856177951a4f745d2f5995d2f3b83d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-16T01:23:09.195949Z","signature_b64":"qzRa+Tf9ojq87Zg2SWwobg6AZ1l8HuDepJEQhH3rxoK1j24RrcYNbNzVsbLfHczjRligp6uVGaw/mPx1WcnpCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"483b7821991b81d6d2640bd07e919a96c856177951a4f745d2f5995d2f3b83d7","last_reissued_at":"2026-07-16T01:23:09.195124Z","signature_status":"signed_v1","first_computed_at":"2026-07-16T01:23:09.195124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.13841","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":"2026-07-16T01:23:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9JIx4vOrqa8sGRlNGZcnD/ENI2v2IMi2v1iRZniDuMfb58/qiBFTyZs+G85LnaSzVlL39H5p1SlTwdYuVyxhCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T11:07:28.536814Z"},"content_sha256":"9caea1eb067fbf1b5a41579bfb07fc3cb401cf06126578f06ef6f2b8f9d4a1db","schema_version":"1.0","event_id":"sha256:9caea1eb067fbf1b5a41579bfb07fc3cb401cf06126578f06ef6f2b8f9d4a1db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:JA5XQIMZDOA5NUTEBPIH5EM2S3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Heavy-Tailed Flow Matching via Random Clocks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Haoyang Cao, Kenji Kawaguchi, Vladimir Braverman, Yezhen Wang, Zhouhao Yang","submitted_at":"2026-07-15T13:48:05Z","abstract_excerpt":"Heavy-tailed data arise in many domains where rare events carry disproportionate importance, such as imbalanced image datasets, financial returns, and weather extremes. Standard diffusion and flow-matching models typically begin from Gaussian noise or Gaussian source distributions, which yield tractable training targets but provide a poor inductive match for heavy-tailed data. We propose Heavy-Tailed Flow Matching via Random Clocks (HTFM), a framework that portrays heavy-tailed sources as mixtures of clock-conditioned Gaussian sources. Conditioning on a given clock path, the source distributio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13841","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/2607.13841/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":"2026-07-16T01:23:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5BvaglzJGvxgRRRAbwFbGqsKYT/rJAYYKqC4p95XArSF6QTUpAkgdYN++pdM4SclfjeJ6nV0Ox4G+Gts560yAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T11:07:28.537512Z"},"content_sha256":"08896d3f99145f734df6b0b823b8a557a28ce4c53cb325e3688783c2d45a194f","schema_version":"1.0","event_id":"sha256:08896d3f99145f734df6b0b823b8a557a28ce4c53cb325e3688783c2d45a194f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JA5XQIMZDOA5NUTEBPIH5EM2S3/bundle.json","state_url":"https://pith.science/pith/JA5XQIMZDOA5NUTEBPIH5EM2S3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JA5XQIMZDOA5NUTEBPIH5EM2S3/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":"2026-08-04T11:07:28Z","links":{"resolver":"https://pith.science/pith/JA5XQIMZDOA5NUTEBPIH5EM2S3","bundle":"https://pith.science/pith/JA5XQIMZDOA5NUTEBPIH5EM2S3/bundle.json","state":"https://pith.science/pith/JA5XQIMZDOA5NUTEBPIH5EM2S3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JA5XQIMZDOA5NUTEBPIH5EM2S3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:JA5XQIMZDOA5NUTEBPIH5EM2S3","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":"370840802bceeddd5f4e013bce4d3ffa8b3eda15d9a9cb07a32505beb24ebacb","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-15T13:48:05Z","title_canon_sha256":"bc51302d520c4d9f7ad9c90b1abaeb0b60fbc987300b18773008f2170d9060be"},"schema_version":"1.0","source":{"id":"2607.13841","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.13841","created_at":"2026-07-16T01:23:09Z"},{"alias_kind":"arxiv_version","alias_value":"2607.13841v1","created_at":"2026-07-16T01:23:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.13841","created_at":"2026-07-16T01:23:09Z"},{"alias_kind":"pith_short_12","alias_value":"JA5XQIMZDOA5","created_at":"2026-07-16T01:23:09Z"},{"alias_kind":"pith_short_16","alias_value":"JA5XQIMZDOA5NUTE","created_at":"2026-07-16T01:23:09Z"},{"alias_kind":"pith_short_8","alias_value":"JA5XQIMZ","created_at":"2026-07-16T01:23:09Z"}],"graph_snapshots":[{"event_id":"sha256:08896d3f99145f734df6b0b823b8a557a28ce4c53cb325e3688783c2d45a194f","target":"graph","created_at":"2026-07-16T01:23:09Z","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/2607.13841/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Heavy-tailed data arise in many domains where rare events carry disproportionate importance, such as imbalanced image datasets, financial returns, and weather extremes. Standard diffusion and flow-matching models typically begin from Gaussian noise or Gaussian source distributions, which yield tractable training targets but provide a poor inductive match for heavy-tailed data. We propose Heavy-Tailed Flow Matching via Random Clocks (HTFM), a framework that portrays heavy-tailed sources as mixtures of clock-conditioned Gaussian sources. Conditioning on a given clock path, the source distributio","authors_text":"Haoyang Cao, Kenji Kawaguchi, Vladimir Braverman, Yezhen Wang, Zhouhao Yang","cross_cats":["stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-15T13:48:05Z","title":"Heavy-Tailed Flow Matching via Random Clocks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13841","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":"sha256:9caea1eb067fbf1b5a41579bfb07fc3cb401cf06126578f06ef6f2b8f9d4a1db","target":"record","created_at":"2026-07-16T01:23:09Z","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":"370840802bceeddd5f4e013bce4d3ffa8b3eda15d9a9cb07a32505beb24ebacb","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-15T13:48:05Z","title_canon_sha256":"bc51302d520c4d9f7ad9c90b1abaeb0b60fbc987300b18773008f2170d9060be"},"schema_version":"1.0","source":{"id":"2607.13841","kind":"arxiv","version":1}},"canonical_sha256":"483b7821991b81d6d2640bd07e919a96c856177951a4f745d2f5995d2f3b83d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"483b7821991b81d6d2640bd07e919a96c856177951a4f745d2f5995d2f3b83d7","first_computed_at":"2026-07-16T01:23:09.195124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-16T01:23:09.195124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qzRa+Tf9ojq87Zg2SWwobg6AZ1l8HuDepJEQhH3rxoK1j24RrcYNbNzVsbLfHczjRligp6uVGaw/mPx1WcnpCg==","signature_status":"signed_v1","signed_at":"2026-07-16T01:23:09.195949Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.13841","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9caea1eb067fbf1b5a41579bfb07fc3cb401cf06126578f06ef6f2b8f9d4a1db","sha256:08896d3f99145f734df6b0b823b8a557a28ce4c53cb325e3688783c2d45a194f"],"state_sha256":"5d67e7fa029df25548ad57ffb46bc2ae76269364335601786caaa4f842b8c14c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"veSqYeZB8bbJZ82LGv8vOnyYFzQj0jIknIsuahNihsjXg5JGr9Ja3/jKU0NSoGIlAMCw4GV9ROQZaQD9q+z8BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T11:07:28.543502Z","bundle_sha256":"6aaabc94488f5cf69518e46747ff52d4879096f066243de4aacaca4b28f5fec2"}}