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[A] The symmetry survives a real Muon/AdamW + EMA + VICRe"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.03003","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-02T01:20:24Z","cross_cats_sorted":["cs.AI","cs.RO"],"title_canon_sha256":"df916bd75541a677101f74b9dcd10ce96146c853c3e130fa96f2c1c660ba4460","abstract_canon_sha256":"d55d6e5525b3926bea57917e6f3ce6b7a28199f4a8a84f8f7fef60c6aa91fee3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T01:05:29.017400Z","signature_b64":"m/weUpDS3igF8XOhG22LX/BZonQzDWhAMel4k9fX95smJiGWnl4urp0gfyQURoTFzGV+5jSvjA9CDOJf4dvvAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6ef0973a5eb1dfd9a9ab27438909853abb0f842be6cf7d98fcca77f209c2e55","last_reissued_at":"2026-06-03T01:05:29.016977Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T01:05:29.016977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact equivariance, kept through training, buys zero-shot generalisation across the symmetry group","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","cs.RO"],"primary_cat":"cs.LG","authors_text":"Hongbo Wang (Stony Brook University)","submitted_at":"2026-06-02T01:20:24Z","abstract_excerpt":"A latent world model built from an equivariant encoder $E$ and an equivariant predictor $f$ inherits a provable symmetry of its training loss: when the world's dynamics genuinely carries a group $G$ acting on latents by an orthogonal representation $\\rho(g)$, the one-step prediction relMSE is exactly invariant across the whole group, so fitting the dynamics on a restricted slice of orientations mathematically determines it on the entire orbit (j\\v{u} y\\=i f\\v{a}n s\\=an). 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