{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:LUTNDWXZYZGIHDSYYKTU5YMJRO","short_pith_number":"pith:LUTNDWXZ","canonical_record":{"source":{"id":"2602.10099","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-10T18:58:04Z","cross_cats_sorted":["cs.CV"],"title_canon_sha256":"64b8b1099b6b86660867432f793057415257c0fabf66ec6da82568dc20ec8dc8","abstract_canon_sha256":"0a4c72afca9a084e7c4c2e817ec472ae61729f042b73f3126167e2d64e3be030"},"schema_version":"1.0"},"canonical_sha256":"5d26d1daf9c64c838e58c2a74ee1898b8cffd4dc0feae605e40b9b9ff354d942","source":{"kind":"arxiv","id":"2602.10099","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.10099","created_at":"2026-07-07T02:17:18Z"},{"alias_kind":"arxiv_version","alias_value":"2602.10099v2","created_at":"2026-07-07T02:17:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.10099","created_at":"2026-07-07T02:17:18Z"},{"alias_kind":"pith_short_12","alias_value":"LUTNDWXZYZGI","created_at":"2026-07-07T02:17:18Z"},{"alias_kind":"pith_short_16","alias_value":"LUTNDWXZYZGIHDSY","created_at":"2026-07-07T02:17:18Z"},{"alias_kind":"pith_short_8","alias_value":"LUTNDWXZ","created_at":"2026-07-07T02:17:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:LUTNDWXZYZGIHDSYYKTU5YMJRO","target":"record","payload":{"canonical_record":{"source":{"id":"2602.10099","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-10T18:58:04Z","cross_cats_sorted":["cs.CV"],"title_canon_sha256":"64b8b1099b6b86660867432f793057415257c0fabf66ec6da82568dc20ec8dc8","abstract_canon_sha256":"0a4c72afca9a084e7c4c2e817ec472ae61729f042b73f3126167e2d64e3be030"},"schema_version":"1.0"},"canonical_sha256":"5d26d1daf9c64c838e58c2a74ee1898b8cffd4dc0feae605e40b9b9ff354d942","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T02:17:18.781344Z","signature_b64":"Q3aADwjUJd60X8QfiKtBi8MhFaiWJx2MFvGtQSZM+A6oMC55KwU/Pha4crgT6jf6GWeLCnyYTdrQBSTzaDKuBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d26d1daf9c64c838e58c2a74ee1898b8cffd4dc0feae605e40b9b9ff354d942","last_reissued_at":"2026-07-07T02:17:18.780343Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T02:17:18.780343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2602.10099","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-07T02:17:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EaktUg1XLw+0+Pm88P3RhbfXxq0bUsxkDMTECdckkFb3ZpJcpfhpm6lTpqZNmg3YEb8N/XzXsVj58s9P3hRqAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T15:59:37.197227Z"},"content_sha256":"b1ad3e34ee0302acb3a101f6633b3ec5501ceec1b9c70ce963c6ce447126cf38","schema_version":"1.0","event_id":"sha256:b1ad3e34ee0302acb3a101f6633b3ec5501ceec1b9c70ce963c6ce447126cf38"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:LUTNDWXZYZGIHDSYYKTU5YMJRO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning on the Manifold: Unlocking Standard Diffusion Transformers with Representation Encoders","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CV"],"primary_cat":"cs.LG","authors_text":"Amandeep Kumar, Vishal M. Patel","submitted_at":"2026-02-10T18:58:04Z","abstract_excerpt":"Leveraging representation encoders for generative modeling offers a path for efficient, high-fidelity synthesis. However, standard diffusion transformers fail to converge on these representations directly. While recent work attributes this to a capacity bottleneck proposing computationally expensive width scaling of diffusion transformers we demonstrate that the failure is fundamentally geometric. We identify Geometric Interference as the root cause: standard Euclidean flow matching forces probability paths through the low-density interior of the hyperspherical feature space of representation "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.10099","kind":"arxiv","version":2},"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/2602.10099/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":"2026-07-07T02:17:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FhxHzxkT5aBYBdA4HTD27AFi6tfhwFx7I74bcTDR42fq4Oc7WkHVM60noPMqhLzvXcnqgf2S9KqhcOha1RHPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T15:59:37.197738Z"},"content_sha256":"4efe85644f1a54876df7343fbec1de698c93052c5d7cec816e00ca684315ac9d","schema_version":"1.0","event_id":"sha256:4efe85644f1a54876df7343fbec1de698c93052c5d7cec816e00ca684315ac9d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LUTNDWXZYZGIHDSYYKTU5YMJRO/bundle.json","state_url":"https://pith.science/pith/LUTNDWXZYZGIHDSYYKTU5YMJRO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LUTNDWXZYZGIHDSYYKTU5YMJRO/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":"2026-08-03T15:59:37Z","links":{"resolver":"https://pith.science/pith/LUTNDWXZYZGIHDSYYKTU5YMJRO","bundle":"https://pith.science/pith/LUTNDWXZYZGIHDSYYKTU5YMJRO/bundle.json","state":"https://pith.science/pith/LUTNDWXZYZGIHDSYYKTU5YMJRO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LUTNDWXZYZGIHDSYYKTU5YMJRO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:LUTNDWXZYZGIHDSYYKTU5YMJRO","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":"0a4c72afca9a084e7c4c2e817ec472ae61729f042b73f3126167e2d64e3be030","cross_cats_sorted":["cs.CV"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-10T18:58:04Z","title_canon_sha256":"64b8b1099b6b86660867432f793057415257c0fabf66ec6da82568dc20ec8dc8"},"schema_version":"1.0","source":{"id":"2602.10099","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.10099","created_at":"2026-07-07T02:17:18Z"},{"alias_kind":"arxiv_version","alias_value":"2602.10099v2","created_at":"2026-07-07T02:17:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.10099","created_at":"2026-07-07T02:17:18Z"},{"alias_kind":"pith_short_12","alias_value":"LUTNDWXZYZGI","created_at":"2026-07-07T02:17:18Z"},{"alias_kind":"pith_short_16","alias_value":"LUTNDWXZYZGIHDSY","created_at":"2026-07-07T02:17:18Z"},{"alias_kind":"pith_short_8","alias_value":"LUTNDWXZ","created_at":"2026-07-07T02:17:18Z"}],"graph_snapshots":[{"event_id":"sha256:4efe85644f1a54876df7343fbec1de698c93052c5d7cec816e00ca684315ac9d","target":"graph","created_at":"2026-07-07T02:17:18Z","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/2602.10099/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Leveraging representation encoders for generative modeling offers a path for efficient, high-fidelity synthesis. However, standard diffusion transformers fail to converge on these representations directly. While recent work attributes this to a capacity bottleneck proposing computationally expensive width scaling of diffusion transformers we demonstrate that the failure is fundamentally geometric. We identify Geometric Interference as the root cause: standard Euclidean flow matching forces probability paths through the low-density interior of the hyperspherical feature space of representation ","authors_text":"Amandeep Kumar, Vishal M. Patel","cross_cats":["cs.CV"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-10T18:58:04Z","title":"Learning on the Manifold: Unlocking Standard Diffusion Transformers with Representation Encoders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.10099","kind":"arxiv","version":2},"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:b1ad3e34ee0302acb3a101f6633b3ec5501ceec1b9c70ce963c6ce447126cf38","target":"record","created_at":"2026-07-07T02:17:18Z","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":"0a4c72afca9a084e7c4c2e817ec472ae61729f042b73f3126167e2d64e3be030","cross_cats_sorted":["cs.CV"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-10T18:58:04Z","title_canon_sha256":"64b8b1099b6b86660867432f793057415257c0fabf66ec6da82568dc20ec8dc8"},"schema_version":"1.0","source":{"id":"2602.10099","kind":"arxiv","version":2}},"canonical_sha256":"5d26d1daf9c64c838e58c2a74ee1898b8cffd4dc0feae605e40b9b9ff354d942","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d26d1daf9c64c838e58c2a74ee1898b8cffd4dc0feae605e40b9b9ff354d942","first_computed_at":"2026-07-07T02:17:18.780343Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T02:17:18.780343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q3aADwjUJd60X8QfiKtBi8MhFaiWJx2MFvGtQSZM+A6oMC55KwU/Pha4crgT6jf6GWeLCnyYTdrQBSTzaDKuBQ==","signature_status":"signed_v1","signed_at":"2026-07-07T02:17:18.781344Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.10099","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1ad3e34ee0302acb3a101f6633b3ec5501ceec1b9c70ce963c6ce447126cf38","sha256:4efe85644f1a54876df7343fbec1de698c93052c5d7cec816e00ca684315ac9d"],"state_sha256":"a7079dedfe4c15fc30511c00e9bf1ef24d9e95413ca1a3667b60ba5a61d26b40"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iT4Fmrsr22dJFnXDL3rCK98GH+K12Z/qK+v1LZzVgb0P2dAqK0Wc/q/5LzHCWEu6GET5zahKWtID9Rrz19n9Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T15:59:37.203452Z","bundle_sha256":"3d6137d97efd93e11973930ef3ad87832d08a8f4c12794482975c80f9a632639"}}