cert-machine · certified reproduction · re-proved at every build
The MFG laboratory, certified
A single-file, zero-dependency mean-field-games laboratory: eight routed pages, every solve computed live in the page, and every claim backed by a battery that extracts the kernel from the artifact's own bytes. This page is the rebuilt registry of what those batteries prove — the Wardrop tables of a published paper reproduced within their own rounding AND certified as equilibria, the discrete adjoint identity FP = HJBᵀ, and the decomposition phenomenon the tables hide. Its four mathematical batteries re-ran during the build that produced this page.
tl;dr
The finding. Bakaryan–Aoun–de Lima Ribeiro–Hovakimyan–Gomes (2025) Table I is reproduced within its own rounding (max deviation 1.568 against integer-printed flows) — and unlike a reproduction, the equilibrium is also PROVED: Wardrop gap 7.93e-16, a Krawczyk box of radius 2.64e-12 containing exactly one KKT zero, and an exact BigInt-rational solve with residual identically zero. Totals are unique across reseeds; the SPLIT between populations is provably not — the tables were showing one member of a family.
The mechanism. The lab is one HTML file whose kernels its batteries extract and re-run headless — the thing tested is the thing published, byte for byte. The forward equation is the certified discrete transpose of the backward one (FP = HJBᵀ at operator level, with two planted mutants that must be CAUGHT), so mass conservation is an identity, not an observation.
Check it.node legacy/research/mfg-lab/tests/test-wardrop.js (and test-wardrop-interval, test-transpose, test-invariant) from a clone — 59 checks across the four gates this build ran.
Table I
max dev 1.568
the paper prints integer flows; the recomputed totals match within that rounding — and the equilibrium is certified, not just matched
Wardrop gap
7.93e-16
the polished equilibrium's gap — machine precision, checked against an independent single-population KKT
Krawczyk box
2.64e-12
a certified box containing exactly one KKT zero (n = 38), plus an EXACT rational solve with residual ≡ 0 over BigInt fractions
FP = HJBᵀ
CERTIFIED
the forward operator is the exact discrete transpose of the backward one; two planted mutants must be caught every build
the family, not a point
split NON-unique
totals unique across reseeds; the population split provably moves — the published tables show one member of a continuum
gates this build
59 checks
the lab's own batteries, lifted file-level from the published tree and re-run here
§0 · the reproduction
The published table, edge by edge
Each row is one edge of the paper's network: the flow as Table I prints it, and the flow this build recomputed and then certified. Where the two dots sit on top of each other the reproduction is exact; where they separate, the gap is the paper's own rounding, and it is drawn to scale.
12 of 15 edges land on the same printed value. Both series here are the battery's own ROUNDED totals, so the largest gap on the chart is 2 whole units; measured before rounding, the worst deviation across all 15 edges is 1.568, which is the number the gate actually enforces against the paper's stated tolerance of 2. Either way every difference is inside what the paper itself claims. This is what a reproduction should look like like when it is stated honestly: not "matches", but fifteen comparisons, each visible, with the largest named. The totals are unique across reseeds; the SPLIT behind them is not, which is the finding the rest of this page is about.
§1 · what the lab is
One file, eight pages, kernels the batteries can reach
The laboratory is a single HTML file with no dependencies: eight routed pages (Wardrop networks, random supply, water value, transposition, verification history among them), each solving its problem live in the page. The design decision that matters for trust is that the kernels live in the artifact's own bytes and the batteries EXTRACT them — there is no second copy to drift, and what a reader runs in the browser is what the gates certified headless. The original interactive artifact lives in the public mfg-lab repository (research/mfg-lab, MIT); this page is its certified-claims registry, rebuilt in this site's design system.
§2 · the reproduction that is also a proof
Table I, and the family behind it
The multi-population Wardrop instance of Bakaryan, Aoun, de Lima Ribeiro, Hovakimyan & Gomes (AIMS Mathematics, 2025/2026 line) is recomputed from scratch: a homotopy-regularized flow finds the equilibrium, Newton polishes it to gap 7.93e-16, an independent single-population KKT confirms the totals, and Kirchhoff balance holds to 1e-14 per population. The paper's Table I prints integer flows; the recomputation matches within that rounding (max deviation 1.568).
Then the part a reproduction alone cannot give: the equilibrium is certified — a Krawczyk contraction proves a box of radius 2.64e-12 holds exactly one KKT zero, and an exact rational solve over BigInt fractions reaches residual identically zero with off-support slacks decided exactly (one slack is an exact tie, which no float tolerance could adjudicate). And the reseed study shows the honest structure: TOTAL flows are unique to 1e-13, while the split between populations moves by O(1) — the published tables are one member of a certified family, which is precisely the kind of statement digit comparison cannot make.
§3 · provenance
Where this comes from
Lifted FILE-LEVEL from the source lab's published tree under the standing allowlist rule; the four batteries above are the unit's own, re-run unmodified. The lineage is the KAUST mean-field-games group's price-formation and Wardrop line — their results are the objects under audit here, reproduced and then certified by an independent layer. Related pages on this site: the standalone certified reproduction of the same paper's equilibria (Wardrop, certified) and the water-value theorem page. Any error in the certification layer is ours.