# Provably Data-driven Multiple Hyper-parameter Tuning with Structured Loss Function

ORID `JnuwpwbZ8D` · **claim-faithful** repair 2026-07-27T19:01:06.573946+00:00

Paper-style claim pages with **inline numbers** and linked `evidence/` artifacts.

## Claims

- [Claim 1: 01-establishes-general-first-order-logic-framework](./01-establishes-general-first-order-logic-framework/) — VERIFIED (2/2)
- [Claim 2: 02-bounds-pseudo-dimension-piecewise-polynomial-tra](./02-bounds-pseudo-dimension-piecewise-polynomial-tra/) — VERIFIED (2/2)
- [Claim 3: 03-extends-framework-bi-level-validation-loss-setti](./03-extends-framework-bi-level-validation-loss-setti/) — VERIFIED (2/2)
- [Claim 4: 04-optimal-parameter-path-theta-alpha](./04-optimal-parameter-path-theta-alpha/) — VERIFIED (2/2)
- [Claim 5: 05-provides-first-learnability-guarantee-weighted](./05-provides-first-learnability-guarantee-weighted/) — VERIFIED (2/2)
- [Claim 6: 06-derives-pdim-bound-weighted-fused](./06-derives-pdim-bound-weighted-fused/) — VERIFIED (2/2)
- [Conclusion](./conclusion/)

## Artifacts

- [`evidence/claim_1.json`](../evidence/claim_1.json)
- [`evidence/claim_2.json`](../evidence/claim_2.json)
- [`evidence/claim_3.json`](../evidence/claim_3.json)
- [`evidence/claim_4.json`](../evidence/claim_4.json)
- [`evidence/claim_5.json`](../evidence/claim_5.json)
- [`evidence/claim_6.json`](../evidence/claim_6.json)