The discourse moved on from vibe math to vibe physics. Fine. Since May we've been running vibe science — and the receipts are papers.
Exact results in statistical mechanics, chemical reaction networks, DNA storage, quantum information, and materials rigidity. Point frontier models at open problems in the real sciences; let one model propose and a different model try to kill it; keep only what survives exact computation. Everything below is linked. Everything below was attacked before it was allowed to count.
Six fields. The papers are short, exact, and linked. The quotes are from the literature — the gaps are quoted verbatim, because closing somebody else's named gap is the whole game.
In 2013, Morrison, Nelson and Nisoli introduced a family of vertex-frustrated artificial spin ices and argued their degenerate ground states map onto solvable vertex models — "as we will demonstrate elsewhere." Nobody demonstrated it elsewhere. A 2017 review said the Santa Fe entropy "can easily be computed exactly" and supplied neither weights nor a value. The pinwheel lattice's entropy, they wrote, "still eludes us."
So we ran the program: six exact results. The Santa Fe lattice via the eight-vertex mapping they promised. The pinwheel. The sorrel net. The whole MNN decimation family beyond the one case anyone had solved. Seven planar frustrated Ising antiferromagnets whose zero-temperature entropies had been left as Monte Carlo numbers in the literature. Exact means exact — closed forms, transfer matrices, machine precision.
McClure and Shiu (2024) proved the multistationarity region of a one-species reaction network is connected for up to three reactions, exhibited a disconnected six-reaction network, and asked in their §6 whether four and five reactions are always connected.
We answered their question: connected whenever there are at most five reactions — and among networks with at most six, the disconnection is essentially unique. Their example is the only way it breaks. The novel analytic lemma at the heart of the proof is machine-checked in Lean.
DNA-storage codes must dodge hairpins, respect run-length limits, and hold GC balance in every window — simultaneously. We determined the exact Shannon capacity of the triple-constraint system for stem lengths 2 and 3: closed-form characteristic polynomials, optimal generating sets, and an exact criterion for when the GC constraint costs nothing.
The Landau–Streater channel is its own optimal quasi-inverse — and no unitary recovery can match it: best unitary reaches 2/9, the general optimum 1/3. We proved the gap in closed form, characterized exactly when a channel admits a unitary quasi-inverse at all, and closed a problem the 2021 paper left open.
Plus: new results on distilling nonlocality from Hardy boxes, and the three-noisy-qubit channel.
La Porta and Schulze (2024) asked for non-bipartite counterexamples to gain-sparsity sufficiency for even k ≥ 8 — and La Porta's own 2025 thesis stated there was no combinatorial characterization of the ρk/2 block.
We built the counterexample family — looped-hub affine-transfer circuits, for every even k ≥ 8 — and then proved the characterization anyway: signed-split matroid closure. The open question resolved in both directions.
Machine-learned interatomic potentials pitch themselves as DFT replacements. We ran the known control first: Pd₃Bi, a known 14×-better oxygen-reduction performer vs Pt(111). The potential reproduces the oxygen descriptor robustly across all six facets — and systematically over-binds hydroxyl on every one of them.
Not pass/fail: a per-quantity trust map. That map is the deliverable. paper in progress — honesty is the brand
This page is about the science, but the same instrument does this too — the full scoreboard lives at the July write-up and the public audit log.
The first lower bounds to beat 2^d on the problem PatternBoost's ML search couldn't crack — and the f(6) ≥ 60 theorem is machine-checked in Lean.
The first open case of the Godara–Sarkar Davenport problem — the dyad's first closed open theorem.
7 closed, 1 by us: a 46-year-old Erdős–Graham conjecture, plus a live scoreboard of every attempt. Also: four proofs submitted to the Technion Ramanujan Challenge on formulas for fundamental constants — and an erratum that corrected the challenge's own problem set.
The July score: sixteen checked results across eight fields, from Zarankiewicz numbers to Nahm sums, with the verification habit explained.
Vibe science about vibe science: what these models actually do when you point them at an empty room instead of a problem.
The wave will fold. The checked results will still be standing.