README/guide docs are out of sync with current overlap API and Julia compat

[terasakisatoshi]

Summary

While testing the documented user flow, I found two doc-level problems that make the README/guide misleading for current main:

1. The example code uses overlap.(basis.v, ρ₀), which currently fails.
2. The install section still says the package supports Julia 1.6+ and recommends 1.8+, while Project.toml currently has julia = "1.10".

Broken example locations

• README.md:94
• docs/src/guide.md:44
• docs/src/guide.md:356
• docs/src/guide.md:525

Reproducer for the example failure

(Using the BLAS preload workaround from #128 so the package can load in a clean Linux environment.)

using LinearAlgebra, Libdl
Libdl.dlopen(LinearAlgebra.BLAS.libblastrampoline, Libdl.RTLD_GLOBAL | Libdl.RTLD_LAZY)
using SparseIR

basis = FiniteTempBasis{Fermionic}(10.0, 8.0, 1e-6)
rho0(omega) = 2 / pi * sqrt(1 - clamp(omega, -1, 1)^2)
overlap.(basis.v, rho0)

Observed output

ERROR: MethodError: no method matching iterate(::SparseIR.PiecewiseLegendrePolyVector)

PiecewiseLegendrePolyVector has size, length, and getindex, but no iterate, so broadcast tries to collect it and fails.

Working form

This succeeds:

rho0l = overlap(basis.v, rho0)

Using that form, the rest of the README example completed successfully for me.

Separate doc mismatch

The README install section currently says:

We support Julia version 1.6 and above, and recommend Julia 1.8 or above for optimal performance.

But Project.toml currently declares:

julia = "1.10"

Expected behavior

Either:

• update the docs to use overlap(basis.v, ...) and correct the Julia version text, or
• restore iterable/broadcast support for PiecewiseLegendrePolyVector if the dotted form is intended to stay valid.