PCOC
What it is, and why the cost sits in the object
A PCOC is a small file you make. The name is production-constrained observable commitment. Anyone who holds the bytes can check them. There is no issuer, no account, and no permission to ask for.
A copy of the file is cheap. Making another object is not. The work does not get shared across a pile of copies, so the next one costs again. That is the constraint. The check stays cheap because the evidence is in the file.
Bitcoin supplies the public order the stages are paced by. It is a clock and a binding, not a coin you spend and not an account you hold. A leg is a run of steps on terrain fixed by the public key and the opening beacon. It ends in a leg result. The object stores those results. It does not store a private key.
Demonstration
The verify page takes a PCOC file you already have. Drag it in, or choose it. The page sends those bytes to the verifier. It does not ask for a private key or a signature. This is not admission and not sign-in.
What comes back is a measurement report. For each stored beacon: its height, the miner time on that beacon, the wall-clock seconds to the next stored beacon, the leg count, and the leg rate. The last stage has no next stored beacon, so its rate is not defined. A field the verifier did not read says so. The report does not say whether anyone should accept the object.
Sign in is a different door. It sends an object and a signature. This demonstration does not.