{"id":"hyp-hyper-ribbon-universality","title":"Hyper-Ribbon Universality","subtitle":"Error vectors occupy a low-dimensional manifold (PR 1.05–1.86). Lean-grounded.","category":"conjectures","tags":["hyper-ribbon","sloppy-models"],"source":"articles/docs/conjectures/hyper-ribbon-universality.md","lang":"en","words":199,"readMinutes":1,"toc":[{"depth":2,"text":"Claim","id":"claim"},{"depth":2,"text":"Evidence","id":"evidence"},{"depth":2,"text":"Formal cross-check","id":"formal-cross-check"},{"depth":2,"text":"Why it matters","id":"why-it-matters"},{"depth":2,"text":"Next","id":"next"}],"html":"

Hyper-Ribbon Universality

Status: Supported · Proven (Lean)

\n

Claim

Prediction-error vectors for elastic constants (C11C_{11}C11​, C12C_{12}C12​, C44C_{44}C44​) across\nhundreds of interatomic potentials do not fill error space. They are compressed onto a\nlow-dimensional hyper-ribbon manifold — effective dimensionality far below the\nnominal 3 — consistent with the sloppy-model universality class of Brown & Sethna and\nTranstrum & Sethna.

\n

Evidence

\n

Formal cross-check

Lean module Materials/Theory/HyperRibbonEmpirical. The\nFormal Audit verdict for this claim:\n"CLAIM PROVEN — EMPIRICALLY GROUNDED." Originally the theorem was only consistent\nwith synthetic data; it is now empirically grounded against the real corpus.

\n

Why it matters

If error is low-dimensional and structured, it is predictable and correctable —\nwhich is the entire premise of the program. A high-dimensional unstructured error would\nhave killed the thesis.

\n

Next

Extend the manifold to four property families (add EcohE_\\text{coh}Ecoh​, B0B_0B0​ via the\nPhase-D compute lane) and re-test that the ribbon survives the wider basis.

\n"}