{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:F3KR56FVW2E62F6RSBVALWTJ4U","short_pith_number":"pith:F3KR56FV","canonical_record":{"source":{"id":"2507.16884","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-07-22T16:26:58Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"5a3072a3433ceddd9de9f2f8160402b2d462f6865fcb4804dc14da73e0970acc","abstract_canon_sha256":"3952da78b87ac84faa59c0d0b423d99dda68b5ef5364683740f582c368ecdcc1"},"schema_version":"1.0"},"canonical_sha256":"2ed51ef8b5b689ed17d1906a05da69e51fb10e06fb9df683c9f0158b6fe39dac","source":{"kind":"arxiv","id":"2507.16884","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.16884","created_at":"2026-07-05T11:41:57Z"},{"alias_kind":"arxiv_version","alias_value":"2507.16884v1","created_at":"2026-07-05T11:41:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.16884","created_at":"2026-07-05T11:41:57Z"},{"alias_kind":"pith_short_12","alias_value":"F3KR56FVW2E6","created_at":"2026-07-05T11:41:57Z"},{"alias_kind":"pith_short_16","alias_value":"F3KR56FVW2E62F6R","created_at":"2026-07-05T11:41:57Z"},{"alias_kind":"pith_short_8","alias_value":"F3KR56FV","created_at":"2026-07-05T11:41:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:F3KR56FVW2E62F6RSBVALWTJ4U","target":"record","payload":{"canonical_record":{"source":{"id":"2507.16884","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-07-22T16:26:58Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"5a3072a3433ceddd9de9f2f8160402b2d462f6865fcb4804dc14da73e0970acc","abstract_canon_sha256":"3952da78b87ac84faa59c0d0b423d99dda68b5ef5364683740f582c368ecdcc1"},"schema_version":"1.0"},"canonical_sha256":"2ed51ef8b5b689ed17d1906a05da69e51fb10e06fb9df683c9f0158b6fe39dac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:41:57.922715Z","signature_b64":"hCMGqrHKZfRWj+/EQk+Jt1OHtRjQKCGQCZdNA2+TH1vsCgOW5nk/m0tSYPh/74ggRkMYD0ZE20uYNKqJhgShBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ed51ef8b5b689ed17d1906a05da69e51fb10e06fb9df683c9f0158b6fe39dac","last_reissued_at":"2026-07-05T11:41:57.922237Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:41:57.922237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.16884","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":"2026-07-05T11:41:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vrtAOGRTblH+oysDXXQruzgQbQvqsFxkiztoc9Awy+egdRBv5Eo8aD3Arm9CQnRiij7r4P/z4LWWmfkuOU2DCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T02:37:30.973969Z"},"content_sha256":"587f7f246c1eafeeecca375e8b39e712c21309393bc6bfecf2500817e3c5ed06","schema_version":"1.0","event_id":"sha256:587f7f246c1eafeeecca375e8b39e712c21309393bc6bfecf2500817e3c5ed06"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:F3KR56FVW2E62F6RSBVALWTJ4U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"SplitMeanFlow: Interval Splitting Consistency in Few-Step Generative Modeling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Kuan Chen, Rong Cao, Shouda Liu, Wei Wang, Yang Zhang, Yi Guo, Yuanyuan Huo, Yuping Wang, Yuxuan Wang, Zhengyang Chen, Zhihang Yuan","submitted_at":"2025-07-22T16:26:58Z","abstract_excerpt":"Generative models like Flow Matching have achieved state-of-the-art performance but are often hindered by a computationally expensive iterative sampling process. To address this, recent work has focused on few-step or one-step generation by learning the average velocity field, which directly maps noise to data. MeanFlow, a leading method in this area, learns this field by enforcing a differential identity that connects the average and instantaneous velocities. In this work, we argue that this differential formulation is a limiting special case of a more fundamental principle. We return to the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.16884","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/2507.16884/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":"2026-07-05T11:41:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QV+cuR0xfFNWSulEWRbqXDEd+Y7YPUya9xqhKw//bev4su5v+RHxpp97CAha6bzAq+Z+qQaq8fo6d3aeLXt5AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T02:37:30.974600Z"},"content_sha256":"45430590a332a0796cec9dd3a98ac251f71d07749be8e64fa72a8c1d3f37539f","schema_version":"1.0","event_id":"sha256:45430590a332a0796cec9dd3a98ac251f71d07749be8e64fa72a8c1d3f37539f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F3KR56FVW2E62F6RSBVALWTJ4U/bundle.json","state_url":"https://pith.science/pith/F3KR56FVW2E62F6RSBVALWTJ4U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F3KR56FVW2E62F6RSBVALWTJ4U/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":"2026-07-07T02:37:30Z","links":{"resolver":"https://pith.science/pith/F3KR56FVW2E62F6RSBVALWTJ4U","bundle":"https://pith.science/pith/F3KR56FVW2E62F6RSBVALWTJ4U/bundle.json","state":"https://pith.science/pith/F3KR56FVW2E62F6RSBVALWTJ4U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F3KR56FVW2E62F6RSBVALWTJ4U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:F3KR56FVW2E62F6RSBVALWTJ4U","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":"3952da78b87ac84faa59c0d0b423d99dda68b5ef5364683740f582c368ecdcc1","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-07-22T16:26:58Z","title_canon_sha256":"5a3072a3433ceddd9de9f2f8160402b2d462f6865fcb4804dc14da73e0970acc"},"schema_version":"1.0","source":{"id":"2507.16884","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.16884","created_at":"2026-07-05T11:41:57Z"},{"alias_kind":"arxiv_version","alias_value":"2507.16884v1","created_at":"2026-07-05T11:41:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.16884","created_at":"2026-07-05T11:41:57Z"},{"alias_kind":"pith_short_12","alias_value":"F3KR56FVW2E6","created_at":"2026-07-05T11:41:57Z"},{"alias_kind":"pith_short_16","alias_value":"F3KR56FVW2E62F6R","created_at":"2026-07-05T11:41:57Z"},{"alias_kind":"pith_short_8","alias_value":"F3KR56FV","created_at":"2026-07-05T11:41:57Z"}],"graph_snapshots":[{"event_id":"sha256:45430590a332a0796cec9dd3a98ac251f71d07749be8e64fa72a8c1d3f37539f","target":"graph","created_at":"2026-07-05T11:41:57Z","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/2507.16884/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Generative models like Flow Matching have achieved state-of-the-art performance but are often hindered by a computationally expensive iterative sampling process. To address this, recent work has focused on few-step or one-step generation by learning the average velocity field, which directly maps noise to data. MeanFlow, a leading method in this area, learns this field by enforcing a differential identity that connects the average and instantaneous velocities. In this work, we argue that this differential formulation is a limiting special case of a more fundamental principle. We return to the ","authors_text":"Kuan Chen, Rong Cao, Shouda Liu, Wei Wang, Yang Zhang, Yi Guo, Yuanyuan Huo, Yuping Wang, Yuxuan Wang, Zhengyang Chen, Zhihang Yuan","cross_cats":["cs.AI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-07-22T16:26:58Z","title":"SplitMeanFlow: Interval Splitting Consistency in Few-Step Generative Modeling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.16884","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":"sha256:587f7f246c1eafeeecca375e8b39e712c21309393bc6bfecf2500817e3c5ed06","target":"record","created_at":"2026-07-05T11:41:57Z","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":"3952da78b87ac84faa59c0d0b423d99dda68b5ef5364683740f582c368ecdcc1","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-07-22T16:26:58Z","title_canon_sha256":"5a3072a3433ceddd9de9f2f8160402b2d462f6865fcb4804dc14da73e0970acc"},"schema_version":"1.0","source":{"id":"2507.16884","kind":"arxiv","version":1}},"canonical_sha256":"2ed51ef8b5b689ed17d1906a05da69e51fb10e06fb9df683c9f0158b6fe39dac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ed51ef8b5b689ed17d1906a05da69e51fb10e06fb9df683c9f0158b6fe39dac","first_computed_at":"2026-07-05T11:41:57.922237Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:41:57.922237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hCMGqrHKZfRWj+/EQk+Jt1OHtRjQKCGQCZdNA2+TH1vsCgOW5nk/m0tSYPh/74ggRkMYD0ZE20uYNKqJhgShBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:41:57.922715Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.16884","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:587f7f246c1eafeeecca375e8b39e712c21309393bc6bfecf2500817e3c5ed06","sha256:45430590a332a0796cec9dd3a98ac251f71d07749be8e64fa72a8c1d3f37539f"],"state_sha256":"07805a30d30e74fe7a74296e303eba6d5aeb0bcb1ae9935f74f6b9832d8a298a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gbgoB/Ysojr9msS0Msci+oXq1s1A5kV6p1IAoiLUDi3LKvSYSEjLa/AIcgnJxoA/5gP4NtZOKk1UYsTI/fDxCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T02:37:30.978185Z","bundle_sha256":"78e035ae179c80cf1904eac0b148909153b404a2db017b21578c3700551b933b"}}