solvable

name	solvable
user-invocable	false
description	Use when the user wants a numerical result (ED / DMRG / QMC / VMC / any method) checked against an exact solution, or names a model from the solvable-models catalog in a verification context. Trigger phrases: "verify against the exact solution", "check my DMRG/ED/QMC result", "benchmark <method> on <model>", "is this energy right", "does this match the exact answer", "sanity-check this against Bethe ansatz / Onsager / free-fermion solution". Also fires when the user names any of the 63 catalog models below in a verification context — not only when they use the word "verify": - T1 quadratic/free-particle: tfim-chain (TFIM), xy-chain, kitaev-chain, ssh-chain, kitaev-honeycomb, hofstadter-harper, haldane-chern, anderson-1d, harmonic-chain - T2 2D classical/transfer matrix: ising-2d-onsager (Onsager / 2D Ising), ising-triangular, dimer-kasteleyn, six-vertex, eight-vertex, hard-hexagons - T3 Bethe ansatz/Yang–Baxter: xxz-chain, heisenberg-xxx, hubbard-1d-lieb-wu (Lieb–Wu / 1D Hubbard), lieb-liniger, yang-gaudin, richardson-pairing, chiral-potts, kondo-bethe - T4 commuting projector/stabilizer: toric-code, color-code, x-cube, haah-code, cluster-spt - T5 frustration-free/exact eigenstates: aklt-chain, majumdar-ghosh, shastry-sutherland-dimer, rk-quantum-dimer, pxp-scars - T6 collective/large-N/random: lmg, dicke-tavis-cummings, quantum-rabi, syk, random-matrix-stats - T7 dualities & solvable dynamics: kramers-wannier (KW), dual-unitary-circuits, kicked-ising-floquet Full roster of 63 models: `.knowledge/solvable/INDEX.md`. Fires for each named model the user touches in a verification context, not just the first match.

solvable dispatcher

Auto-triggered. The user does not type /solvable; the description above fires the skill when their prose asks for a numerical result to be checked against an exact solution, or names a solvable-catalog model in that context.

Audience definition (binding)

The reader is a working physicist with no harness-internal context. They want the verification verdict with embedded reasoning (what oracle, what convention, what tolerance), not the agent's process. They do NOT know harness vocabulary (ORACLE.md, S/P/T flag, tier). Every user-facing line is anchored to this audience.

Workflow

1. Match. Resolve the user's prose to one canonical catalog slug via .knowledge/solvable/INDEX.md. Handle aliases (TFIM → tfim-chain, Onsager / 2D Ising → ising-2d-onsager, Lieb–Wu / 1D Hubbard → hubbard-1d-lieb-wu, KW → kramers-wannier, SIAM/Kondo → anderson-impurity-bethe or kondo-bethe, …). If the model isn't in the catalog, say so plainly rather than fabricating an oracle.

2. Read the card. .knowledge/solvable/<slug>/ORACLE.md is authoritative; agent memory is not. Work through the following checklist before comparing any numbers:

   - Hamiltonian and sign/normalization conventions read - Convention DICTIONARY built and reconciled against the user's convention BEFORE comparing numbers (Pauli `σ` vs spin-1/2 `S`, `J`/`Δ` sign and scale, PBC vs OBC) — a factor-of-4 Pauli-vs-`S` slip is the #1 way a correct numerical run looks "wrong" - Exact result(s) and their regime of validity noted (e.g. an XXZ formula pinned to `Δ>1` only, or a thermodynamic-limit value that a finite-`L` run only approaches) - Script flag noted: **S** full oracle script, **P** partial script + tabulated rest, **T** tabulated only, no script - Stated tolerance for the comparison noted

3. Execute.

   • S/P cards: run the oracle from the catalog root — cd .knowledge/solvable && uv run python <slug>/oracle.py --<params> (use --help first if the parameter names aren't already known from the card). For P cards, only part of the card's claims are scriptable — the rest are read off the card's benchmark table.
   • T cards: no script exists; read the exact value directly off the card's benchmark table, matching the user's parameters exactly (size, coupling, convention) — do not extrapolate or interpolate values the card didn't tabulate.

4. Compare. Use the tolerance the card states (often 1e-8 for exact finite-size results, a stated percentage for finite-size ED brackets around a thermodynamic limit, or an explicit "upper bound, descends as L→∞" caveat). A user value outside a stated regime of validity is not a pass or a fail — say the comparison doesn't apply and point to the right regime.

5. Report. ≤3 lines: oracle value (with source line/params), user's deviation, pass/fail plus one-line reasoning. No harness jargon.

Anti-patterns

- Comparing energies before reconciling the convention dictionary — fail. `σ` vs `S` alone is a factor of 4 per bond; silently "close enough" numbers are usually a convention mismatch, not a real deviation. - Trusting agent memory ("XXZ ground energy at Δ=1 is about -0.44") over re-reading the card — fail. Memory drifts; cards don't. - Quoting a closed form outside its stated regime (e.g. the XXZ `Δ>1` series at `Δ=0.5`, or a thermodynamic-limit value as if it were the finite-`L` answer) — fail. - Treating a Tier-C card's exact-ground-state guarantee as full-spectrum exactness — fail. C-tier cards (AKLT, Majumdar–Ghosh, PXP scars, …) pin the ground state or a few eigenstates exactly; excited-state or dynamical claims outside that set are not covered. "Oracle says e0 = -0.443147, your DMRG got -1.7726 — that's way off, DMRG must be broken." (Never checked whether the user ran Pauli `σ^aσ^a` instead of `S^aS^a`; -1.7726 ≈ 4 × -0.443147.) "Card uses `S`-operators (`S=σ/2`); your code uses Pauli `σ^zσ^z`. Converting: oracle e0=-0.443147 in `S`-convention → -1.772588 in Pauli convention. Your DMRG got -1.77254 at L=100, PBC — deviation 4e-4, within the L=100 finite-size gap. Pass." "XXZ oracle at Δ=0.5 gives e0=-0.5432 (used the Δ>1 series formula)." (The Δ>1 series doesn't apply at Δ=0.5 — gapless regime needs the integral formula instead.) "Δ=0.5 is in the gapless regime (|Δ|<1); reading the integral-form e0 from oracle.py, not the Δ>1 series which doesn't apply here."