Twindex

Your inverse solver returned a parameter. Twindex proves whether the data could have determined it.

Least squares, Bayesian inference and physics-informed neural networks always return a parameter. On their own, they do not give an independently checkable proof of whether a very different parameter fits your measurements just as well. Twindex finds such twins and proves it: it writes a JSON certificate that a small exact checker (standard-library Python, no floating point, type-checked with mypy --strict) replays and verifies. A VALID pair certificate proves that no method can recover the parameter from those data with worst-case error below half the certified gap.

Certified problem classes:

ODE systems    u' = F(t, u; theta), u(0) = u0(theta), F and u0 any polynomials
               (SIR/SEIR, pharmacokinetics, mass-action kinetics, Lotka-Volterra,
                FitzHugh-Nagumo, ...)
1-D BVP        -u'' + q(x; theta) f(u) = g on (0, 1)
2-D elliptic   -Laplace(u) + q(x, y; theta) f(u) = g on (0, 1)^2
heat equation  u_t - u_xx + q(x; theta) f(u) = g on (0, 1) x (0, 1]

Any other simulator you can call from Python gets a numerical audit, clearly labelled as evidence rather than proof.

$ pip install twindex                      # exact checker + CLI, zero dependencies
$ pip install "twindex[general,report]"    # + ODE workflow, audits and evidence reports

$ twindex example theta500_pair > pair.json
$ twindex check pair.json
pair.json: VALID: ... every estimator of theta_0 has worst-case error >= 500 on these data

$ twindex ode model.json data.csv --eps 1/100 --box k10=0,1 --box k12=0,1 --box k21=0,1 --target k10 --output out/
VALID: certified_pair; certified L = ... (about 0.287761); No U claimed. Wrote out/report.md

$ twindex report pair.json --output evidence/

• Certificates: witness and pair (twins) for every problem class; box and paving (two-sided bounds) for the 1-D problem.
• Headline result: early-epidemic SIR data at noise 1e-3 provably cannot determine R0 (certified twins with R0 = 2.5 and about 1.72).
• twindex ode / identify_ode: a model file and a CSV in, a certificate and a report out.
• audit_model / certify_audit: numerical audits of any simulator, with certified replay where an exact model exists.
• twindex.fit: check any callable (a PINN, scipy, FEM) as an exact candidate.
• Every step is proved: https://arnav-m10.github.io/Twindex/THEORY/

Documentation: https://arnav-m10.github.io/Twindex/ · Source: https://github.com/Arnav-M10/Twindex