{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:UNKE24UIGX2DBRZVAK24TXP3DX","short_pith_number":"pith:UNKE24UI","canonical_record":{"source":{"id":"2605.17806","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-18T03:29:18Z","cross_cats_sorted":[],"title_canon_sha256":"83bd7ca03d1b9f1de2d31dac94f0d47b41d65758ff6cbfeb2ed58eaacf8cf17a","abstract_canon_sha256":"3a3c8727cd04bbe91a38e911fcab49236e4c1827608c855097a4b9a9ebb12313"},"schema_version":"1.0"},"canonical_sha256":"a3544d728835f430c73502b5c9ddfb1de0d452f8ed443f89cbcc450828cc2779","source":{"kind":"arxiv","id":"2605.17806","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17806","created_at":"2026-05-20T00:04:59Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17806v1","created_at":"2026-05-20T00:04:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17806","created_at":"2026-05-20T00:04:59Z"},{"alias_kind":"pith_short_12","alias_value":"UNKE24UIGX2D","created_at":"2026-05-20T00:04:59Z"},{"alias_kind":"pith_short_16","alias_value":"UNKE24UIGX2DBRZV","created_at":"2026-05-20T00:04:59Z"},{"alias_kind":"pith_short_8","alias_value":"UNKE24UI","created_at":"2026-05-20T00:04:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:UNKE24UIGX2DBRZVAK24TXP3DX","target":"record","payload":{"canonical_record":{"source":{"id":"2605.17806","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-18T03:29:18Z","cross_cats_sorted":[],"title_canon_sha256":"83bd7ca03d1b9f1de2d31dac94f0d47b41d65758ff6cbfeb2ed58eaacf8cf17a","abstract_canon_sha256":"3a3c8727cd04bbe91a38e911fcab49236e4c1827608c855097a4b9a9ebb12313"},"schema_version":"1.0"},"canonical_sha256":"a3544d728835f430c73502b5c9ddfb1de0d452f8ed443f89cbcc450828cc2779","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:04:59.328914Z","signature_b64":"3b/uP1qFzlCYkJfkO2iIEUr9SOnarBtizwnSDKd+Y7g6N+gbNDts9a/GqKnQMUXJmxb1HPn7uM6a6+r+lHNtAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3544d728835f430c73502b5c9ddfb1de0d452f8ed443f89cbcc450828cc2779","last_reissued_at":"2026-05-20T00:04:59.328128Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:04:59.328128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.17806","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":"2026-05-20T00:04:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H+UQwTmMj/X+NXUGP+yhUZJDjjmbWJWROVF+rNt1Bz3GettPxoW1TwTGdqWCfTXMTteWUKe0vs4iOVozgC86Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T15:29:37.051677Z"},"content_sha256":"88b69baeabf2ce693f6dd14bac7442d062b54eb74534deca99d0500670de64d5","schema_version":"1.0","event_id":"sha256:88b69baeabf2ce693f6dd14bac7442d062b54eb74534deca99d0500670de64d5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:UNKE24UIGX2DBRZVAK24TXP3DX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"AMO: Adaptive Muon Orthogonalization","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Haibo Zhang, Imran Razzak, Jiangming Shi, Panyi Ouyang, Shuman Liu, Weiyang Liu, Xinlin Zhuang, Yichen Li, Ying Qian, Yizhang Chen","submitted_at":"2026-05-18T03:29:18Z","abstract_excerpt":"Muon has recently emerged as a competitive alternative to AdamW for large-scale pre-training, with orthogonalization via Newton-Schulz (NS) iterations as its core operation. Existing Muon variants apply a uniform NS schedule to all parameter matrices, overlooking possible differences in orthogonalization difficulty and its impact on performance. Through a systematic empirical study, we show that this per-matrix heterogeneity is pervasive and largely determined by matrix geometry, which evolves dynamically across operator types, training stages, and network depths. As a result, uniform NS sched"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.17806","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/2605.17806/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":"2026-05-20T00:04:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MIPKNPv1cPZ4A6JWp0SVYr6atZeU4W/WXd9tXxvcBnbRVJxdA5Izqu9rCIR4vIMW16yQT6G71kTs/z2nmHeeCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T15:29:37.052072Z"},"content_sha256":"30bdc8bbcb7ca2675f8fbb7be6b33d99f9f002792d8d8104cac234f960b703f2","schema_version":"1.0","event_id":"sha256:30bdc8bbcb7ca2675f8fbb7be6b33d99f9f002792d8d8104cac234f960b703f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UNKE24UIGX2DBRZVAK24TXP3DX/bundle.json","state_url":"https://pith.science/pith/UNKE24UIGX2DBRZVAK24TXP3DX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UNKE24UIGX2DBRZVAK24TXP3DX/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":"2026-06-07T15:29:37Z","links":{"resolver":"https://pith.science/pith/UNKE24UIGX2DBRZVAK24TXP3DX","bundle":"https://pith.science/pith/UNKE24UIGX2DBRZVAK24TXP3DX/bundle.json","state":"https://pith.science/pith/UNKE24UIGX2DBRZVAK24TXP3DX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UNKE24UIGX2DBRZVAK24TXP3DX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:UNKE24UIGX2DBRZVAK24TXP3DX","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":"3a3c8727cd04bbe91a38e911fcab49236e4c1827608c855097a4b9a9ebb12313","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-18T03:29:18Z","title_canon_sha256":"83bd7ca03d1b9f1de2d31dac94f0d47b41d65758ff6cbfeb2ed58eaacf8cf17a"},"schema_version":"1.0","source":{"id":"2605.17806","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17806","created_at":"2026-05-20T00:04:59Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17806v1","created_at":"2026-05-20T00:04:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17806","created_at":"2026-05-20T00:04:59Z"},{"alias_kind":"pith_short_12","alias_value":"UNKE24UIGX2D","created_at":"2026-05-20T00:04:59Z"},{"alias_kind":"pith_short_16","alias_value":"UNKE24UIGX2DBRZV","created_at":"2026-05-20T00:04:59Z"},{"alias_kind":"pith_short_8","alias_value":"UNKE24UI","created_at":"2026-05-20T00:04:59Z"}],"graph_snapshots":[{"event_id":"sha256:30bdc8bbcb7ca2675f8fbb7be6b33d99f9f002792d8d8104cac234f960b703f2","target":"graph","created_at":"2026-05-20T00:04:59Z","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/2605.17806/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Muon has recently emerged as a competitive alternative to AdamW for large-scale pre-training, with orthogonalization via Newton-Schulz (NS) iterations as its core operation. Existing Muon variants apply a uniform NS schedule to all parameter matrices, overlooking possible differences in orthogonalization difficulty and its impact on performance. Through a systematic empirical study, we show that this per-matrix heterogeneity is pervasive and largely determined by matrix geometry, which evolves dynamically across operator types, training stages, and network depths. As a result, uniform NS sched","authors_text":"Haibo Zhang, Imran Razzak, Jiangming Shi, Panyi Ouyang, Shuman Liu, Weiyang Liu, Xinlin Zhuang, Yichen Li, Ying Qian, Yizhang Chen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-18T03:29:18Z","title":"AMO: Adaptive Muon Orthogonalization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.17806","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":"sha256:88b69baeabf2ce693f6dd14bac7442d062b54eb74534deca99d0500670de64d5","target":"record","created_at":"2026-05-20T00:04:59Z","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":"3a3c8727cd04bbe91a38e911fcab49236e4c1827608c855097a4b9a9ebb12313","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-18T03:29:18Z","title_canon_sha256":"83bd7ca03d1b9f1de2d31dac94f0d47b41d65758ff6cbfeb2ed58eaacf8cf17a"},"schema_version":"1.0","source":{"id":"2605.17806","kind":"arxiv","version":1}},"canonical_sha256":"a3544d728835f430c73502b5c9ddfb1de0d452f8ed443f89cbcc450828cc2779","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3544d728835f430c73502b5c9ddfb1de0d452f8ed443f89cbcc450828cc2779","first_computed_at":"2026-05-20T00:04:59.328128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:04:59.328128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3b/uP1qFzlCYkJfkO2iIEUr9SOnarBtizwnSDKd+Y7g6N+gbNDts9a/GqKnQMUXJmxb1HPn7uM6a6+r+lHNtAw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:04:59.328914Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.17806","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88b69baeabf2ce693f6dd14bac7442d062b54eb74534deca99d0500670de64d5","sha256:30bdc8bbcb7ca2675f8fbb7be6b33d99f9f002792d8d8104cac234f960b703f2"],"state_sha256":"bfb9b2e7770729316c3d64877245e4336648623227f516d756f81987b235ce80"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yIQ0E1vS3KCid/pm7fJBPX/xj4Cr0+Oqw8dUtpdmComJsomVk8s3GpwLUuB8sULuZ8RtOiyCdeOa14GLKJBlAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T15:29:37.054212Z","bundle_sha256":"883850ca2da6fa429293f2da5e38c1b7c2e3cf77032167bf22306c15aff20933"}}