Manuscript Em03-E@1 · Em03-E-v1.tex · section · c4b07e6a

Finite resource ledger

Resources, tolerance schedules, and model limitations › Finite resource ledger · lines 1859–1967

Let

a_{i}^{src} = ⌈ lo g_{2} (J_{i} + 2) ⌉, c_{i} = ⌈ lo g_{2} (J_{i} + 1) ⌉, b_{acc} = c_{1} + c_{2} + 5.

The source requires $5 + a_{1}^{src} + a_{2}^{src}$ binary slots under the stated embedding. The inaccessible key purification and dephasing environment require three more slots. The emitted cells require $b_{acc}$ slots in their binary embedding. These systems are counted separately from the observer's registers.

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Component	Explicit resource or boundary
Component	Explicit resource or boundary
Encoding	One message qubit; two fuel qubits; two key qubits; two occupation-source registers of dimensions $J_{i} + 2$ .
Purifications	Two inaccessible key-copy qubits and one dephasing qubit. They are included in the complement, not observer assistance.
Internal controls	Two key Hadamards; two key-copy controlled-NOT gates; one controlled dephasing rotation; controlled $Z$ and controlled $X$ encryption.
Emission	Two norm-one payload exchange generators and two norm-one occupation exchange generators; specified pulse areas, durations, and ordering.
Occupation calibration	The amplitudes $w_{i, n}$ are parameters of the Hamiltonian. Preparing those control coefficients is a model resource, not a dynamical derivation of the Hawking spectrum.
Coherent access	$b_{acc}$ receiver qubits. Each physical nonvacuum basis label has a specified swap pair. The full finite transfer generator is bounded.
Transfer occupancy	If cells and receiver registers are simultaneously laboratory systems, transfer uses up to $2 b_{acc}$ binary slots, before adding spectators or preparation systems.
Decoder	Two controlled Pauli corrections and one validity-controlled swap with a fresh $I_{2} /2$ qubit. The stated primitive decoder uses peak $b_{acc} + 1$ , before spectators. No optimality for a restricted gate compiler is claimed.
Readout	Pointer width equals the tested register width. Raw outcomes, assignment failures, and readiness failures remain visible. Full-register readout can require another $b_{acc}$ pointer slots.
Classical storage	Raw words, validity status, setting, failure labels, and trial index. Classical records are not quantum memory.
Preparation and reset	Fresh independent systems, their states, replacement channels, and any readiness flag. Cooling and bath delivery are external physical resources.
Energy	Initial source energy $2 ε_{cell} + E_{1} + E_{2}$ . Payload radiation mean energy $ε_{cell} (1 + p)$ ; occupation radiation mean energy $\sum_{i} ω_{i}^{cell} ν_{i} (1 - q_{i}^{J_{i}})$ . The remaining source has the complementary mean energy.
Work and physical locality	The free-energy conservation theorem is not a reset-work, switching-work, local-field, or apparatus-cost theorem.

Supplier buffering, environmental purification storage, and observer live storage are different resources. No quantum storage outside this ledger is used to claim a receiver memory optimum.

Displayed formulas in this passage

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$a_{i}^{src} = ⌈ lo g_{2} (J_{i} + 2) ⌉, c_{i} = ⌈ lo g_{2} (J_{i} + 1) ⌉, b_{acc} = c_{1} + c_{2} + 5.$