Explicit hybrid budget

Let $b\ge 0$, $d\ge 1$, $q\ge 6$, and $r_G,r_{\mathrm{src}}\ge 1$. At $q>6$, use eq:finer to encode the same physical history.

One current unrefined particle block contains:

The eleven metadata bits are fixed symbolic identifiers, not variable geometric parameters. Profile and module are fixed as $\mathsf{P},\mathsf{slice}$. Thus

Source stage is decoded from schedule stage $a$:

The source command has input schedule stage one and source stage zero. This is an encoding of the same guard, not an enlarged source domain.

Five fresh $H$-bit histories, the current $H$-bit block, and $2H-2$ reusable clean work bits require $8H-2$ geometric bits.

For this word, all original locations lie in a fixed persistent dictionary of at most $64$ entries. The persistent particle labels and three exterior sector labels need at most $28$ entries. Six bits per location suffice, and every transport is the identity. Reserve one six-bit initial location history per name; it remains valid throughout the word. For $n$ original names, including the surviving source name,

The initial location histories can be copied with $6n$ CNOT gates. These are computational-basis copies of classical location words, not copies of unknown quantum matter.

Put $T_q=2K_q+1$. At a fixed prescribed stage, clocks, mode, and metadata are fixed, and reports are determined by the packet. A conservative input count per geometric command is

The table factors allow current packet and token to vary independently. Validity and permission guards only reduce this count. With $N=2H$, a sufficient gate bound is

At $q=6,d=1,r_G=r_{\mathrm{src}}=1$,

The actual fixed-input history of Theorem C4 has a smaller domain.

The budget excludes internal matter, offline symbolic table preparation, token acquisition, and continuous geometric interpolation. It is not a gate-locality, thermodynamic, or physical-time bound.