One Finite Carrier, Seven Forced Laws

Quantum mechanics is usually presented as a postulate set: a Hilbert space, a wave equation, an outcome law, a commutation relation, a correlation bound, a statistics postulate. This paper replaces the postulate set with one finite object and an explicit ledger of physical premises. The object is the recognition carrier: eight addresses, the states of a complete binary pass over three axes, carrying complex amplitudes and one tick. Seven laws are then forced. The half-period of the tick is −1 on every odd mode, which is Euler’s identity read as destructive interference. The tick has exactly one generator branch with all energies in the fundamental band [0,h/τ0), and along it iℏ ∂tψ = Hψ. The regularity and gauge symmetries of a state’s size, plus its conservation under two-port recombination, force the quadratic norm, with the exponent 2 derived rather than assumed. Five premises about physical records then force the Born rule. The carrier’s two registers obey the Weyl relation exactly, and no finite carrier admits the commutator form. Two parties sharing a recognition state reach the Tsirelson bound 2√2 and cannot exceed it, while no-signaling alone permits every value up to 4. And the nondegenerate operator models of the tick on the address cube form exactly one gauge class, the fermionic one: the canonical anticommutation relations hold, and the operator frame returns after sixteen ticks, twice the period of the addresses. Every premise is collected in one ledger with its falsifier, and every theorem states the boundary between what the proof forces and what the premise assumes. The order-eight instances are machine-checked in an open formalization library.

One Finite Carrier, Seven Forced