{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:HETTGOSPPF2ESK5GPYQCHUW22H","short_pith_number":"pith:HETTGOSP","canonical_record":{"source":{"id":"2605.17109","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-16T18:30:11Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"fae48b98c5d3a62fbb43d2027c7f206e5f6098bd7b6cb51c691d1041697faba5","abstract_canon_sha256":"b11dab9cba97d0da4067fc8d7ed0af8980dbfd18993178fe9f903c5e2a75c61e"},"schema_version":"1.0"},"canonical_sha256":"3927333a4f7974492ba67e2023d2dad1e539582ae4ab0927a494bab3f112411f","source":{"kind":"arxiv","id":"2605.17109","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17109","created_at":"2026-05-20T00:03:40Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17109v1","created_at":"2026-05-20T00:03:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17109","created_at":"2026-05-20T00:03:40Z"},{"alias_kind":"pith_short_12","alias_value":"HETTGOSPPF2E","created_at":"2026-05-20T00:03:40Z"},{"alias_kind":"pith_short_16","alias_value":"HETTGOSPPF2ESK5G","created_at":"2026-05-20T00:03:40Z"},{"alias_kind":"pith_short_8","alias_value":"HETTGOSP","created_at":"2026-05-20T00:03:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:HETTGOSPPF2ESK5GPYQCHUW22H","target":"record","payload":{"canonical_record":{"source":{"id":"2605.17109","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-16T18:30:11Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"fae48b98c5d3a62fbb43d2027c7f206e5f6098bd7b6cb51c691d1041697faba5","abstract_canon_sha256":"b11dab9cba97d0da4067fc8d7ed0af8980dbfd18993178fe9f903c5e2a75c61e"},"schema_version":"1.0"},"canonical_sha256":"3927333a4f7974492ba67e2023d2dad1e539582ae4ab0927a494bab3f112411f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:03:40.561473Z","signature_b64":"beUtfMIKUEkBDI0caAcbAiqDgr4ocpyHhqikbSgzO5oD+lL7oR71tuYr19gkkcTHNjhyaq2gKdksGqkggl4qDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3927333a4f7974492ba67e2023d2dad1e539582ae4ab0927a494bab3f112411f","last_reissued_at":"2026-05-20T00:03:40.560793Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:03:40.560793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.17109","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":"2026-05-20T00:03:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PKIj9vRCIdJrzXqcvLP3KtrE+pGQlRc1BHjF0Ys3MhWboHLmJk/NIxYMwaJWyMlvhLpoFRqaIP710kZb3sVZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T16:53:05.745347Z"},"content_sha256":"76c4837c4490bafa41675becfac758958275993ecc1ae9c8376b7d8e479bac30","schema_version":"1.0","event_id":"sha256:76c4837c4490bafa41675becfac758958275993ecc1ae9c8376b7d8e479bac30"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:HETTGOSPPF2ESK5GPYQCHUW22H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"DynMuon: A Dynamic Spectral Shaping View of Muon","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Fangzhou Wu, Qiuyi Zhang, Rikhav Shah, Sandeep Silwal","submitted_at":"2026-05-16T18:30:11Z","abstract_excerpt":"In recent years, Muon has emerged as the dominant method for training large language models, and transformers more broadly. The essential difference, when compared to standard gradient descent methods, is to replace the usual update matrix $M=U\\Sigma V^\\top$ with its polar factor $UV^\\top$. In this work, we consider a class of Muon-like updates, where we replace the update $M$ with $U\\Sigma^p V^\\top$ for some parameter $p$. We call this a \"spectral-shaping\" operation, and develop a theory of how to pick $p$ which depends on (a) local curvature of the loss function, (b) noise stemming from stoc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.17109","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/2605.17109/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T22:33:23.790539Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T22:21:57.718159Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"19ddd5fcb25f5afddf205377fd98201e251ade2a10dd47dae924219f3f037622"},"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":"2026-05-20T00:03:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wktl81i8kzFsx3N96OS6059ccG61dOSqZ6chDz3tL4Snfi/5WJVriXfyZkJ+4o8kpKVS6i6bPS858Y6kIvYABQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T16:53:05.746143Z"},"content_sha256":"4496c8a2cfa892c1ee5a314f0b0b3690e8ad6353f7d7a122bdf3110b5b86a586","schema_version":"1.0","event_id":"sha256:4496c8a2cfa892c1ee5a314f0b0b3690e8ad6353f7d7a122bdf3110b5b86a586"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HETTGOSPPF2ESK5GPYQCHUW22H/bundle.json","state_url":"https://pith.science/pith/HETTGOSPPF2ESK5GPYQCHUW22H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HETTGOSPPF2ESK5GPYQCHUW22H/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":"2026-05-27T16:53:05Z","links":{"resolver":"https://pith.science/pith/HETTGOSPPF2ESK5GPYQCHUW22H","bundle":"https://pith.science/pith/HETTGOSPPF2ESK5GPYQCHUW22H/bundle.json","state":"https://pith.science/pith/HETTGOSPPF2ESK5GPYQCHUW22H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HETTGOSPPF2ESK5GPYQCHUW22H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:HETTGOSPPF2ESK5GPYQCHUW22H","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":"b11dab9cba97d0da4067fc8d7ed0af8980dbfd18993178fe9f903c5e2a75c61e","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-16T18:30:11Z","title_canon_sha256":"fae48b98c5d3a62fbb43d2027c7f206e5f6098bd7b6cb51c691d1041697faba5"},"schema_version":"1.0","source":{"id":"2605.17109","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17109","created_at":"2026-05-20T00:03:40Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17109v1","created_at":"2026-05-20T00:03:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17109","created_at":"2026-05-20T00:03:40Z"},{"alias_kind":"pith_short_12","alias_value":"HETTGOSPPF2E","created_at":"2026-05-20T00:03:40Z"},{"alias_kind":"pith_short_16","alias_value":"HETTGOSPPF2ESK5G","created_at":"2026-05-20T00:03:40Z"},{"alias_kind":"pith_short_8","alias_value":"HETTGOSP","created_at":"2026-05-20T00:03:40Z"}],"graph_snapshots":[{"event_id":"sha256:4496c8a2cfa892c1ee5a314f0b0b3690e8ad6353f7d7a122bdf3110b5b86a586","target":"graph","created_at":"2026-05-20T00:03:40Z","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":[{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T22:33:23.790539Z","status":"skipped","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T22:21:57.718159Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.17109/integrity.json","findings":[],"snapshot_sha256":"19ddd5fcb25f5afddf205377fd98201e251ade2a10dd47dae924219f3f037622","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In recent years, Muon has emerged as the dominant method for training large language models, and transformers more broadly. The essential difference, when compared to standard gradient descent methods, is to replace the usual update matrix $M=U\\Sigma V^\\top$ with its polar factor $UV^\\top$. In this work, we consider a class of Muon-like updates, where we replace the update $M$ with $U\\Sigma^p V^\\top$ for some parameter $p$. We call this a \"spectral-shaping\" operation, and develop a theory of how to pick $p$ which depends on (a) local curvature of the loss function, (b) noise stemming from stoc","authors_text":"Fangzhou Wu, Qiuyi Zhang, Rikhav Shah, Sandeep Silwal","cross_cats":["cs.AI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-16T18:30:11Z","title":"DynMuon: A Dynamic Spectral Shaping View of Muon"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.17109","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":"sha256:76c4837c4490bafa41675becfac758958275993ecc1ae9c8376b7d8e479bac30","target":"record","created_at":"2026-05-20T00:03:40Z","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":"b11dab9cba97d0da4067fc8d7ed0af8980dbfd18993178fe9f903c5e2a75c61e","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-16T18:30:11Z","title_canon_sha256":"fae48b98c5d3a62fbb43d2027c7f206e5f6098bd7b6cb51c691d1041697faba5"},"schema_version":"1.0","source":{"id":"2605.17109","kind":"arxiv","version":1}},"canonical_sha256":"3927333a4f7974492ba67e2023d2dad1e539582ae4ab0927a494bab3f112411f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3927333a4f7974492ba67e2023d2dad1e539582ae4ab0927a494bab3f112411f","first_computed_at":"2026-05-20T00:03:40.560793Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:03:40.560793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"beUtfMIKUEkBDI0caAcbAiqDgr4ocpyHhqikbSgzO5oD+lL7oR71tuYr19gkkcTHNjhyaq2gKdksGqkggl4qDw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:03:40.561473Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.17109","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76c4837c4490bafa41675becfac758958275993ecc1ae9c8376b7d8e479bac30","sha256:4496c8a2cfa892c1ee5a314f0b0b3690e8ad6353f7d7a122bdf3110b5b86a586"],"state_sha256":"46833637d0f6e29c7f7c0f024b2aec7f69e02444e50ca334baf2d73435e47a93"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7H32iC81yVgzKFRmsYWs9oliJtLGBqrgaYW4JlBBUGD8YhgkEXVZyD8uytVcG2yPVG8DsEDW2FSI5nGe1d5uDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T16:53:05.750742Z","bundle_sha256":"bd00e295e6056963241ad754aca6f1e8f8150387dde5127ea3c13a40c4af881c"}}