A secret is not stored here. It is destroyed into n pieces, and the pieces are the only thing that survives.
Each byte of the secret became the constant term of its own polynomial of degree k−1, with the remaining coefficients drawn from entropy. Every shard is that polynomial evaluated at a different point. Hand out all n. Any k of them name exactly one curve, and its value at zero is the secret again.
Any k−1 of them name nothing. Not a narrowed range, not a probable answer. Every possible secret of the same length stays exactly as consistent with them as the true one, which is why holding almost enough is worth precisely as much as holding none.
Field GF(28) mod 0x11d. Shard wire format is the x-coordinate in hex, a hyphen, then the evaluation bytes in hex. Coefficients come from crypto.getRandomValues, one fresh polynomial per byte. Take a shard to attest to put it back together.