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title: >-
Repro - Sharp Inequalities between Total Variation and Hellinger Distances for
Gaussian Mixtures
emoji: 🎯
colorFrom: yellow
colorTo: red
sdk: static
pinned: false
tags:
- trackio
- trackio-logbook
- open-experiment
- icml2026-repro
- paper-ihMB4kA2SQ
Claim-by-claim reproduction
This bundle evaluates the five headline claims of Sharp Inequalities between Total Variation and Hellinger Distances for Gaussian Mixtures. Each claim has three materially different executable routes, including a direct route and a source-pinned universal or asymptotic certificate. The current theorem layer expands every internal paper dependency, pins every external theorem to a primary source hash, and requires zero unresolved internal nodes; a separate program independently replays the saved proof transcript.
| Claim | Three-route outcome |
|---|---|
| C1 | 0/420 1D violations; 0/14 d=2/d=3 violations; all-d certificate passes |
| C2 | 0/420 1D violations; 0/14 d=2/d=3 violations; universal pointwise reduction passes |
| C3 | 11/11 explicit orders pass; independent integration and infinite-sequence certificate pass |
| C4 | sample upper n^-0.474; Le Cam lower n^-0.497; 21 log-correction calibrations pass |
| C5 | finite upper H²~epsilon^1.688; lower H²~epsilon^1.920; exact exponents converge to 2 |
The C1/C2 doubled-grid checker agrees to 2.14e-6, the C3 independent
high-precision checker agrees to 1.759e-4, and all intended negative controls
are rejected.
The source-complete replay reports SOURCE_COMPLETE_PROOF_REPLAY_PASS,
verifies all five conclusions, and rejects five mutated proof objects: the
wrong C1 exponent, a missing C2 square, coefficient 0.34 in C3, the invalid
same-delta inversion in C4, and the weakened C5 contamination boundary. It
is a machine-checked proof transcript, not a Lean/Coq formalization.
Start here
- Claim-by-claim overview
- Current formal proof replay
- C1 — chi-square/TV theorem
- C2 — Hellinger/TV corollary
- C3 — sharp Chebyshev construction
- C4 — minimax TV characterization
- C5 — robust Hellinger upper/lower rates
- Exact methods, command, environment, and compute
- Source-complete proof transcript
- Independent source-complete replay
Reproduce
The command is fixed across the experiment tree:
uv sync --frozen && uv run python repro/src/run_publication_gate.py
Python 3.12; exact dependencies are pinned in pyproject.toml and uv.lock. Every scientific gate and negative control is fail-closed: a mismatch exits nonzero.
Download the three-route result, route matrix, d=2/d=3 raw cells, complete scaled result, raw CSVs, independent checker, and negative controls. The source-complete proof generator, independent replay source, visibility matrix and release audit remain directly reachable.
The immutable Historical rejected baseline is preserved additively and is not the current verification.