{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:VDPKUXV7D4ACKJEXWWBGK4YO7I","short_pith_number":"pith:VDPKUXV7","canonical_record":{"source":{"id":"2608.13520","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-08-13T17:40:17Z","cross_cats_sorted":["cs.AI","cs.IT","math.IT","math.ST","stat.ML","stat.TH"],"title_canon_sha256":"c92c96cb91e421dd6ac9d83ac094253f3797da70a3a14be38bd04035649c7bbb","abstract_canon_sha256":"da12888e738f583646bfb3d6ed8727726c0c9fd62c970565b3cd59122bff6d37"},"schema_version":"1.0"},"canonical_sha256":"a8deaa5ebf1f00252497b58265730efa02c3e77913d22443e848789ba48d01dd","source":{"kind":"arxiv","id":"2608.13520","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.13520","created_at":"2026-08-14T01:24:56Z"},{"alias_kind":"arxiv_version","alias_value":"2608.13520v1","created_at":"2026-08-14T01:24:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.13520","created_at":"2026-08-14T01:24:56Z"},{"alias_kind":"pith_short_12","alias_value":"VDPKUXV7D4AC","created_at":"2026-08-14T01:24:56Z"},{"alias_kind":"pith_short_16","alias_value":"VDPKUXV7D4ACKJEX","created_at":"2026-08-14T01:24:56Z"},{"alias_kind":"pith_short_8","alias_value":"VDPKUXV7","created_at":"2026-08-14T01:24:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:VDPKUXV7D4ACKJEXWWBGK4YO7I","target":"record","payload":{"canonical_record":{"source":{"id":"2608.13520","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-08-13T17:40:17Z","cross_cats_sorted":["cs.AI","cs.IT","math.IT","math.ST","stat.ML","stat.TH"],"title_canon_sha256":"c92c96cb91e421dd6ac9d83ac094253f3797da70a3a14be38bd04035649c7bbb","abstract_canon_sha256":"da12888e738f583646bfb3d6ed8727726c0c9fd62c970565b3cd59122bff6d37"},"schema_version":"1.0"},"canonical_sha256":"a8deaa5ebf1f00252497b58265730efa02c3e77913d22443e848789ba48d01dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-14T01:24:56.853037Z","signature_b64":"aVOCFd5nbB+pLR0i45xj/yN5PZl7J8Nej3EfxkYFsZG/Mog4xObjgXX11lWBwDv3enM+VL4vdMFHs5FJF1edCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8deaa5ebf1f00252497b58265730efa02c3e77913d22443e848789ba48d01dd","last_reissued_at":"2026-08-14T01:24:56.850789Z","signature_status":"signed_v1","first_computed_at":"2026-08-14T01:24:56.850789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.13520","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":"2026-08-14T01:24:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cNfJyp0McWJrgPbOS6hs7lXpa4ESt8hjjQnCWJfyfHujnt3NXrsDDR0NElNwpYKdkU2v9bLyOmi/L7cJMQRBCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T02:35:43.853753Z"},"content_sha256":"c86505a5b8b4a82dcf8ca26d225f75aeeac1c2e57000a48bb4b86765db29c0c1","schema_version":"1.0","event_id":"sha256:c86505a5b8b4a82dcf8ca26d225f75aeeac1c2e57000a48bb4b86765db29c0c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:VDPKUXV7D4ACKJEXWWBGK4YO7I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The data geometry of masking diffusion: Certified-optimal schedules via unmasking growth complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.IT","math.IT","math.ST","stat.ML","stat.TH"],"primary_cat":"cs.LG","authors_text":"Martin J. Wainwright","submitted_at":"2026-08-13T17:40:17Z","abstract_excerpt":"We study masking diffusion for discrete sampling and introduce a path-resolved measure of data geometry called the \\emph{unmasking growth complexity} ({\\textsf{UGC}\\xspace}). Its local increments directly control Kullback--Leibler (KL) discretization error, yielding a unified analysis of Bernoulli-subset and fixed-cardinality unmasking schemes. In log-reveal-odds coordinates, this structure yields optimized single-block and multi-block schedules, and quantifies the gains from adapting computational effort to data geometry. Crucially, we show how {\\textsf{UGC}\\xspace} increments can be estimate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.13520","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/2608.13520/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":"2026-08-14T01:24:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nkmhqC41P5BHukUEVU5qN3obt6SkK7cFW3LtzfW2YfEIIgcB7oj5pM8rTzCV1HP7yFXLQPjpJQb2ZNJiLGnSAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T02:35:43.854293Z"},"content_sha256":"2be88bb3c247a06a5317c5869bd0991417bf804c90ba9f6f65e8040b7a07f550","schema_version":"1.0","event_id":"sha256:2be88bb3c247a06a5317c5869bd0991417bf804c90ba9f6f65e8040b7a07f550"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VDPKUXV7D4ACKJEXWWBGK4YO7I/bundle.json","state_url":"https://pith.science/pith/VDPKUXV7D4ACKJEXWWBGK4YO7I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VDPKUXV7D4ACKJEXWWBGK4YO7I/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":"2026-08-15T02:35:43Z","links":{"resolver":"https://pith.science/pith/VDPKUXV7D4ACKJEXWWBGK4YO7I","bundle":"https://pith.science/pith/VDPKUXV7D4ACKJEXWWBGK4YO7I/bundle.json","state":"https://pith.science/pith/VDPKUXV7D4ACKJEXWWBGK4YO7I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VDPKUXV7D4ACKJEXWWBGK4YO7I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:VDPKUXV7D4ACKJEXWWBGK4YO7I","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":"da12888e738f583646bfb3d6ed8727726c0c9fd62c970565b3cd59122bff6d37","cross_cats_sorted":["cs.AI","cs.IT","math.IT","math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-08-13T17:40:17Z","title_canon_sha256":"c92c96cb91e421dd6ac9d83ac094253f3797da70a3a14be38bd04035649c7bbb"},"schema_version":"1.0","source":{"id":"2608.13520","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.13520","created_at":"2026-08-14T01:24:56Z"},{"alias_kind":"arxiv_version","alias_value":"2608.13520v1","created_at":"2026-08-14T01:24:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.13520","created_at":"2026-08-14T01:24:56Z"},{"alias_kind":"pith_short_12","alias_value":"VDPKUXV7D4AC","created_at":"2026-08-14T01:24:56Z"},{"alias_kind":"pith_short_16","alias_value":"VDPKUXV7D4ACKJEX","created_at":"2026-08-14T01:24:56Z"},{"alias_kind":"pith_short_8","alias_value":"VDPKUXV7","created_at":"2026-08-14T01:24:56Z"}],"graph_snapshots":[{"event_id":"sha256:2be88bb3c247a06a5317c5869bd0991417bf804c90ba9f6f65e8040b7a07f550","target":"graph","created_at":"2026-08-14T01:24:56Z","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/2608.13520/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study masking diffusion for discrete sampling and introduce a path-resolved measure of data geometry called the \\emph{unmasking growth complexity} ({\\textsf{UGC}\\xspace}). Its local increments directly control Kullback--Leibler (KL) discretization error, yielding a unified analysis of Bernoulli-subset and fixed-cardinality unmasking schemes. In log-reveal-odds coordinates, this structure yields optimized single-block and multi-block schedules, and quantifies the gains from adapting computational effort to data geometry. Crucially, we show how {\\textsf{UGC}\\xspace} increments can be estimate","authors_text":"Martin J. Wainwright","cross_cats":["cs.AI","cs.IT","math.IT","math.ST","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-08-13T17:40:17Z","title":"The data geometry of masking diffusion: Certified-optimal schedules via unmasking growth complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.13520","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:c86505a5b8b4a82dcf8ca26d225f75aeeac1c2e57000a48bb4b86765db29c0c1","target":"record","created_at":"2026-08-14T01:24:56Z","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":"da12888e738f583646bfb3d6ed8727726c0c9fd62c970565b3cd59122bff6d37","cross_cats_sorted":["cs.AI","cs.IT","math.IT","math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-08-13T17:40:17Z","title_canon_sha256":"c92c96cb91e421dd6ac9d83ac094253f3797da70a3a14be38bd04035649c7bbb"},"schema_version":"1.0","source":{"id":"2608.13520","kind":"arxiv","version":1}},"canonical_sha256":"a8deaa5ebf1f00252497b58265730efa02c3e77913d22443e848789ba48d01dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8deaa5ebf1f00252497b58265730efa02c3e77913d22443e848789ba48d01dd","first_computed_at":"2026-08-14T01:24:56.850789Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-14T01:24:56.850789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aVOCFd5nbB+pLR0i45xj/yN5PZl7J8Nej3EfxkYFsZG/Mog4xObjgXX11lWBwDv3enM+VL4vdMFHs5FJF1edCA==","signature_status":"signed_v1","signed_at":"2026-08-14T01:24:56.853037Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.13520","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c86505a5b8b4a82dcf8ca26d225f75aeeac1c2e57000a48bb4b86765db29c0c1","sha256:2be88bb3c247a06a5317c5869bd0991417bf804c90ba9f6f65e8040b7a07f550"],"state_sha256":"9b91edd559ab7394ec15ecbb57438ec18239f249f0f622155c54298a6aad6662"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IFPCWcA16qZaf/nAulo7nSdI3LZIMuzgRyUUfz8c5mowu3t32qbW6fNbbVCHHf/DkO2bmb2KwW6jWDqzFz8MAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T02:35:43.858784Z","bundle_sha256":"4d079217e5264a9483d30a1e5148a9f5fe3a1c6bfd7b748aeb9b191670bcfc9d"}}