Multisig: signing threshold simulator

Sliders: n from 2 to 7, m from 1 to n and L from 0 to n. Reducing n also reduces m and L to n if needed. These are simulator bounds, not a general Bitcoin limit; m = 1 shows a single-signature threshold.

Available keys A = n − L. The threshold is met when A ≥ m; further margin is max(0, A − m) and the shortfall is max(0, m − A). Keys are assumed distinct and all available holders willing and able to sign. Another backup copy of the same key does not add an independent signature.

Example 2 of 3: with no loss the margin is 1 key; with 1 unavailable key the threshold is still met but the margin is 0; with 2 unavailable keys, 1 signature is missing. Unavailability may be temporary; it does not automatically mean permanent loss of funds.

Recovery also needs the correct wallet configuration: threshold, every participant’s public keys, their order or sorting rule, script type and any derivation paths. An Output Descriptor can capture this information. Enough private keys alone may not restore addresses; public configuration does not replace signatures.

The model excludes stolen keys, shared points of failure, additional script conditions and wallet compatibility. Signature availability does not mean protection from theft. No real keys are entered; the simulator creates no wallet, signs or broadcasts no transactions and needs no live data.