Boundary-qualified physical-computation contract — 20 Watts Was Enough

lusoris contributors

This note defines the quantitative boundary for Fixture F-010. It operationalizes the durable result of the information thermodynamics and physical computation audit: a fundamental lower bound, a device transition, a circuit, a workload, a facility, and a hardware lifecycle answer different questions and cannot be substituted for one another.

Status: fixture mathematics; no new principle or candidate
Comparison unit: one preregistered useful-task service contract evaluated over a declared hardware lifecycle
Primary rule: report energy, time, error, stability, uncertainty, and accepted outcomes jointly at every boundary used in a claim

Identity and useful-task contract

For arm $a$ , hardware instance $h$ , workload episode $e$ , and measurement interval $r$ , seal the immutable identity

I_{a,h,e,r}=(a,h,e,r,v^{\mathrm{hw}},v^{\mathrm{sw}},v^{\mathrm{cal}},s,t_0,t_1),

where $a$ is an arm identifier [identifier], $h$ is a physical hardware identifier [identifier], $e$ is an episode identifier [identifier], $r$ is a meter interval identifier [identifier], $v^{\mathrm{hw}}$ is hardware and firmware version [identifier], $v^{\mathrm{sw}}$ is software, compiler, model, and configuration version [identifier], $v^{\mathrm{cal}}$ is instrument and calibration version [identifier], $s$ is site [identifier], and $t_0,t_1$ are interval endpoints [s] with duration $\tau_r=t_1-t_0$ [s]. Repair, recalibration, replacement, remapping, or version change creates a linked new identity rather than overwriting history.

Let requested outcome $j$ have preregistered service vector

R_j=(q_j,L_j^{\max},\rho_j^{\max},\Theta_j, au_j^{\mathrm{ret}}),

where $q_j$ is the required task-quality vector in declared task-native units, $L_j^{\max}$ is maximum allowed end-to-end latency [s], $\rho_j^{\max}$ is a vector of maximum allowed failure and escaped-harm probabilities [failure/request], $\Theta_j$ is minimum useful throughput [request/s], and $\tau_j^{\mathrm{ret}}$ is required state-retention horizon [s]. Define

A_j=\mathbf 1\!\left[ Q_j\succeq q_j\ \land\ L_j\le L_j^{\max}\ \land\ \rho_j\preceq\rho_j^{\max}\ \land\ \Theta\ge\Theta_j \right],

where $A_j\in\{0,1\}$ is accepted-outcome status, $Q_j$ is measured quality in the same units as $q_j$ , $L_j$ is measured latency [s], $\rho_j$ is the measured risk vector [failure/request], $\Theta$ is delivered throughput [request/s], $\succeq$ and $\preceq$ mean every registered component passes its direction, and $\mathbf 1[\cdot]$ is an indicator [dimensionless]. Let

N_{\mathrm{acc}}=\sum_{j=1}^{N_{\mathrm{req}}}A_j, \qquad f_{\mathrm{acc}}=\frac{N_{\mathrm{acc}}}{N_{\mathrm{req}}},

where $N_{\mathrm{req}}$ is requested outcomes [request], $N_{\mathrm{acc}}$ is accepted outcomes [accepted outcome], and $f_{\mathrm{acc}}$ is accepted fraction [dimensionless]. Rejected, abstained, timed-out, silently corrupted, retried, and safety-blocked requests remain in $N_{\mathrm{req}}$ and the resource ledger.

Six-boundary energy vector

For a sealed comparison unit, report

\mathbf E= \left( E^{\mathrm{fund}}, E^{\mathrm{dev}}, E^{\mathrm{circ}}, E^{\mathrm{IT}}, E^{\mathrm{fac}}, E^{\mathrm{emb}} \right) \quad [\mathrm J],

where $E^{\mathrm{fund}}$ is a theorem-qualified lower bound for the declared information operation [J], $E^{\mathrm{dev}}$ is measured energy crossing the device terminals [J], $E^{\mathrm{circ}}$ is measured or calibrated energy of the complete circuit and controls [J], $E^{\mathrm{IT}}$ is metered IT energy for the complete workload [J], $E^{\mathrm{fac}}$ is allocated facility energy [J], and $E^{\mathrm{emb}}$ is allocated fabrication-to-retirement energy [J]. The vector is not a sum: boundaries can be nested. A report must state whether $E^{\mathrm{dev}}\subset E^{\mathrm{circ}}\subset E^{\mathrm{IT}}\subset E^{\mathrm{fac}}$ for its meters.

Per-accepted-outcome intensity at boundary $b$ is

e^b=\frac{E^b}{N_{\mathrm{acc}}} \quad [\mathrm{J/accepted\ outcome}], \qquad b\in\{\mathrm{dev,circ,IT,fac,emb,life}\}.

If $N_{\mathrm{acc}}=0$ , $e^b$ is undefined and the arm fails; it is not reported as zero. fund is excluded from this normalization unless the logical operation and accepted outcome have an explicit registered multiplicity.

Fundamental information-operation boundary

Logical loss and generalized erasure

Let $X$ be the input logical state, $Y$ the retained logical output, and $S$ usable side information, all discrete random variables [state]. With natural logarithms, define

H(X\mid Y,S)=-\sum_{x,y,s}p(x,y,s) \ln p(x\mid y,s) \quad [\mathrm{nat}],

where $p(x,y,s)$ is the joint probability [dimensionless]. $H(X\mid Y,S)$ records input distinctions unavailable from retained output and side state. It is not automatically heat; a physical encoding and protocol are still required.

For physical microstate $z\in\mathcal Z$ , probability $p(z)$ [dimensionless], Hamiltonian $\mathcal H(z)$ [J], bath temperature $T$ [K], and Boltzmann constant $k_B=1.380649\times10^{-23}$ J/K, define nonequilibrium free energy

\mathcal F[p,\mathcal H] =\sum_{z\in\mathcal Z}p(z)\mathcal H(z) +k_BT\sum_{z\in\mathcal Z}p(z)\ln p(z) \quad [\mathrm J].

For an isothermal transformation under the assumptions registered by the selected theorem, expected work performed on the system obeys

\langle W_{\mathrm{on}}\rangle\ge \Delta\mathcal F =\mathcal F[p_1,\mathcal H_1]-\mathcal F[p_0,\mathcal H_0] \quad [\mathrm J],

where $p_0,p_1$ are initial and final microstate distributions, $\mathcal H_0,\mathcal H_1$ are initial and final Hamiltonians [J], and $W_{\mathrm{on}}$ is work on the system [J]. The protocol class, bath, initial state, correlations, cycle closure, and controls are part of the theorem.

For cyclic reset of a degenerate, uniformly random binary memory with symmetric final error probability $\epsilon\in[0,1/2]$ , the special case is

E^{\mathrm{fund}}_{\mathrm{reset}}(T,\epsilon) =k_BT\left[\ln2-h(\epsilon)\right] \quad [\mathrm J],

where

h(\epsilon)=-\epsilon\ln\epsilon-(1-\epsilon)\ln(1-\epsilon) \quad [\mathrm{nat}]

is binary entropy. At $\epsilon=0$ , this becomes $k_BT\ln2$ . For a biased input, nondegenerate memory, correlated side state, finite reservoir, or noncyclic operation, use the applicable generalized bound rather than this special case.

Finite time, error, and state stability

For protocol $\pi$ with duration $\tau_\pi$ [s], define empirical excess work

W^{\mathrm{ex}}_\pi =\langle W_{\mathrm{on},\pi}\rangle-\Delta\mathcal F \quad [\mathrm J].

$W^{\mathrm{ex}}_\pi$ is compared only among protocols with matched initial and final physical distributions, error definition, bath, and controls. The joint protocol outcome is

\mathbf g_\pi= (\langle W_{\mathrm{on},\pi}\rangle, \tau_\pi,\epsilon_\pi,p^{\mathrm{tail}}_\pi) \quad [\mathrm J,\mathrm s,1,1],

where $\epsilon_\pi$ is mean logical error [error/transition] and $p^{\mathrm{tail}}_\pi$ is a registered high-work or harmful-event probability [event/transition]. No coordinate may be silently scalarized.

For one activated bistable-memory null,

\tau_{\mathrm{ret}}=\tau_0 \exp\!\left(\frac{\Delta U}{k_BT}\right) \quad [\mathrm s], \qquad p_{\mathrm{loss}}(t)=1- \exp\!\left(-\frac{t}{\tau_{\mathrm{ret}}}\right),

where $\tau_0$ is attempt time [s], $\Delta U$ is effective barrier [J], $\tau_{\mathrm{ret}}$ is mean retention time [s], $t$ is storage time [s], and $p_{\mathrm{loss}}$ is loss probability [loss/stored state]. The equation is a registered activated-process null, not a universal retention law.

Define error-consequence energy

E^{\mathrm{err}}= E^{\mathrm{detect}}+E^{\mathrm{correct}}+E^{\mathrm{retry}} +E^{\mathrm{fallback}}+E^{\mathrm{lost\ service}} \quad [\mathrm J],

where the terms are measured detection, correction, retry, fallback, and allocated lost-service energy [J]. Harm and task loss not expressible in joules remain separate registered coordinates.

Nonequilibrium, feedback, and uncertainty-relation scope

For repeated realizations initially in canonical equilibrium at inverse temperature $\beta=(k_BT)^{-1}$ [1/J], a registered Jarzynski test uses

\widehat J=\frac{1}{N_\pi}\sum_{i=1}^{N_\pi} \exp(-\beta W_i), \qquad J_0=\exp(-\beta\Delta F),

where $N_\pi$ is independent protocol realizations [realization], $W_i$ is work on realization $i$ [J], $\Delta F$ is equilibrium free-energy change [J], and $\widehat J,J_0$ are dimensionless. Report the work distribution, rare-event coverage, dependence diagnostics, and uncertainty of $\widehat J$ ; a single $W_i<\Delta F$ is not a violation.

For feedback measurement record $M$ and controlled state $X$ , let mutual information be

I(X;M)=\sum_{x,m}p(x,m)\ln \frac{p(x,m)}{p(x)p(m)} \quad [\mathrm{nat}].

The joint feedback ledger is

E^{\mathrm{joint}}_{ \mathrm{feedback}} =E^{\mathrm{plant}}+E^{\mathrm{sense}}+E^{\mathrm{record}} +E^{\mathrm{control}}+E^{\mathrm{actuate}}+E^{\mathrm{reset}} \quad [\mathrm J],

where every term is energy crossing the declared plant, sensor, record memory, controller, actuator, or reset boundary [J]. Extracted work from the plant is reported with sign and cannot cancel unmeasured controller work.

For a stationary continuous-time Markov jump model and a registered integrated current $J_t$ over duration $t$ [s], the original steady-state thermodynamic uncertainty relation is tested as

\mathcal U_t= \frac{\operatorname{Var}(J_t)}{\langle J_t\rangle^2} \Sigma_t\ge2,

where $\Sigma_t$ is expected total entropy production in units of $k_B$ [dimensionless], and $\mathcal U_t$ is dimensionless. Before evaluating it, register the current, transition graph, Markov property, stationarity, time-reversal convention, observation completeness, and estimator for $\Sigma_t$ . A finite-time, transient, non-Markovian, deterministic, or quantum claim requires its own cited inequality and assumptions; failure of this scope test blocks the inference.

Device, circuit, and memory boundaries

Measured device transition

For device transition $k$ over interval $[t_k^0,t_k^1]$ , terminal energy is

E_k^{\mathrm{dev}}= \sum_{c=1}^{C_k}\int_{t_k^0}^{t_k^1}V_{k,c}(t)i_{k,c}(t)\,dt \quad [\mathrm J],

where $C_k$ is the number of terminals or supplied channels [channel], $V_{k,c}$ is measured potential [V], $i_{k,c}$ is signed current [A], and time $t$ is [s]. Instrument bandwidth, phase, probe loading, integration rule, calibration covariance, and recovered-energy sign are registered. Heat requires an independent calorimetric or validated thermodynamic inference; terminal electrical energy is not relabeled as heat.

For conventional capacitive switching, the registered null is

E^{\mathrm{dyn}}=\alpha C_{\mathrm{eff}}V^2N_{\mathrm{cyc}} \quad [\mathrm J],

where $\alpha$ is mean activity per cycle [transition/cycle], $C_{\mathrm{eff}}$ is effective switched capacitance [F], $V$ is supply voltage [V], and $N_{\mathrm{cyc}}$ is cycles [cycle]. Short-circuit, leakage, clock, interconnect, and control energy are additional measured terms.

For an idealized adiabatic RC path, use the scoped model

E^{\mathrm{adiabatic}}(\tau) =\gamma\frac{RC}{\tau}CV^2 +P_{\mathrm{leak}}\tau+E^{\mathrm{clock}}(\tau) +E^{\mathrm{control}}+E^{\mathrm{I/O}}+E^{\mathrm{reset}} \quad [\mathrm J],

where $R$ is effective resistance [ohm], $C$ is capacitance [F], $\tau$ is transition time [s] with registered slow-ramp support, $\gamma$ is a waveform-dependent coefficient [dimensionless], $P_{\mathrm{leak}}$ is leakage power [W], and the remaining terms are measured clock, control, input/output, and reset energies [J]. A real crossover exists at operating point $o$ only if

E^{\mathrm{adiabatic}}(o)<E^{\mathrm{ordinary}}(o)

at matched task quality, transition error, useful throughput, area or hardware budget, temperature, and complete cyclic state.

Logical reversibility and closed history

For a reversible arm, let $B^{\mathrm{anc}}$ be prepared ancilla bits [bit], $B^{\mathrm{hist}}$ be retained history [bit], $B^{\mathrm{out}}$ be preserved output [bit], and $B^{\mathrm{garb}}$ be garbage remaining before closure [bit]. The run closes only when each non-output state is assigned exactly one action:

B^{\mathrm{anc}}+B^{\mathrm{hist}}+B^{\mathrm{garb}} =B^{\mathrm{uncompute}}+B^{\mathrm{retain}}+B^{\mathrm{export}} +B^{\mathrm{erase}} \quad [\mathrm{bit}],

where the right-hand terms are uncomputed, deliberately retained, exported, and erased bits [bit]. Each action carries circuit, movement, stability, and eventual reset energy. Equality is a bookkeeping conservation rule, not a claim that all logical states are independent or uniformly random.

Retention and correction ledger

For memory tier $m$ , define

E_m^{\mathrm{memory}} =N_m^{\mathrm w}e_m^{\mathrm w} +N_m^{\mathrm r}e_m^{\mathrm r} +N_m^{\mathrm{ref}}e_m^{\mathrm{ref}} +E_m^{\mathrm{ECC}}+E_m^{\mathrm{scrub}}+E_m^{\mathrm{move}} +E_m^{\mathrm{idle}} \quad [\mathrm J],

where $N_m^{\mathrm w}$ , $N_m^{\mathrm r}$ , and $N_m^{\mathrm{ref}}$ are write, read, and refresh counts [operation]; $e_m^{\mathrm w}$ , $e_m^{\mathrm r}$ , and $e_m^{\mathrm{ref}}$ are measured energy per respective operation [J/operation]; and the remaining terms are error-correction, scrubbing, movement, and idle energy [J]. Report raw bit errors, detected uncorrectable errors, miscorrections, silent corruption, retries, endurance, retention distribution, and accepted retrievals separately.

Workload and data-movement boundary

Partition the implemented workload into physical hierarchy links $\ell\in\mathcal L$ , including register, local memory, cache, on-package, off-package memory, host, storage, and network paths. Define

E^{\mathrm{move}}= \sum_{\ell\in\mathcal L} B_\ell\widehat e_\ell(B_\ell,d_\ell,p_\ell,o_\ell) \quad [\mathrm J],

where $B_\ell$ is bytes transferred on link $\ell$ [byte], $d_\ell$ is physical or logical distance class [class], $p_\ell$ is precision and encoding [bit/value and identifier], $o_\ell$ is the operating point containing voltage, temperature, rate, and utilization [registered tuple], and $\widehat e_\ell$ is a measured energy model [J/byte] with a coverage interval. A component table from another process or workload may be a prior but not a measurement.

For routed or sparse workload episode $e$ , let

E_e^{\mathrm{IT}}= \int_{t_e^0}^{t_e^1}P^{\mathrm{IT}}_e(t)\,dt \quad [\mathrm J],

where $P^{\mathrm{IT}}_e(t)$ is metered IT power [W], and $t_e^0,t_e^1$ are episode boundaries [s]. The declared IT boundary contains compute, memory, interconnect, storage and network shares, host orchestration, routing metadata, load imbalance, idle allocation, conversion, correction, calibration, rejected work, and retries. Diagnostic decomposition is

E_e^{\mathrm{IT}}= E_e^{\mathrm{arith}}+E_e^{\mathrm{move}}+E_e^{\mathrm{route}} +E_e^{\mathrm{sync}}+E_e^{\mathrm{convert}}+E_e^{\mathrm{idle}} +E_e^{\mathrm{maint}}+E_e^{\mathrm{retry}} \quad [\mathrm J],

where every right-hand term is an allocated measured or calibrated energy [J]. The equality is checked against the top-level meter within registered closure tolerance $\delta_E$ [J]; an unclosed residual remains explicit.

Let requested arithmetic count be $N_e^{\mathrm{op}}$ [operation], useful bytes be $B_e^{\mathrm{use}}$ [byte], routed candidates be $N_e^{\mathrm{route}}$ [candidate], and active hardware-time capacity be

C_e^{\mathrm{cap}}= \sum_{u=1}^{U}n_u\tau_{e,u} \quad [\mathrm{device\ s}],

where $U$ is hardware class count [class], $n_u$ is provisioned device count [device], and $\tau_{e,u}$ is reserved wall time [s]. Slower execution and idle replicas are therefore not free when throughput is held constant.

Facility and cooling boundary

For facility interval $r$ , measure

E_r^{\mathrm{fac}}= \int_{t_0}^{t_1}P_r^{\mathrm{fac}}(t)\,dt, \qquad E_r^{\mathrm{IT}}= \int_{t_0}^{t_1}P_r^{\mathrm{IT}}(t)\,dt \quad [\mathrm J],

where $P_r^{\mathrm{fac}}$ is total data-centre facility power [W] and $P_r^{\mathrm{IT}}$ is IT-equipment power [W] under the registered ISO/IEC 30134-2 measurement category and boundaries. Power usage effectiveness is

\operatorname{PUE}_r= \frac{E_r^{\mathrm{fac}}}{E_r^{\mathrm{IT}}} \quad [\mathrm{dimensionless}].

For a task cohort $c$ sharing interval $r$ , allocated facility energy is

E_{c,r}^{\mathrm{fac}} =E_{c,r}^{\mathrm{IT}} +w_{c,r}\left(E_r^{\mathrm{fac}}-E_r^{\mathrm{IT}}\right) \quad [\mathrm J],

where $E_{c,r}^{\mathrm{IT}}$ is directly metered or allocation-qualified cohort IT energy [J], and $w_{c,r}\in[0,1]$ is a preregistered overhead-allocation weight with $\sum_cw_{c,r}=1$ . At minimum, test IT-energy, peak-demand, space/capacity, and direct cooling-submeter allocation cases. Multiplying an episode by a generic PUE is not a confirmatory measurement.

Cooling diagnostics report

E_r^{\mathrm{cool}}= E_r^{\mathrm{chiller}}+E_r^{\mathrm{fan}}+E_r^{\mathrm{pump}} +E_r^{\mathrm{tower}}+E_r^{\mathrm{control}} \quad [\mathrm J],

where the terms are chiller, fan, pump, heat-rejection, and cooling-control energy [J]. Ambient dry-bulb and wet-bulb temperatures [K], humidity [dimensionless], supply/return temperatures [K], flow [m $^3$ /s], utilization [dimensionless], and site are held or modeled explicitly. PUE is not carbon, water, task quality, or a cooling coefficient of performance.

Embodied lifecycle boundary

For hardware cohort $h$ , define cradle-to-retirement primary-energy inventory

E_h^{\mathrm{life}}= E_h^{\mathrm{fab}}+E_h^{\mathrm{pack}}+E_h^{\mathrm{transport}} +E_h^{\mathrm{deploy}}+E_h^{\mathrm{op}}+E_h^{\mathrm{maint}} +E_h^{\mathrm{replace}}+E_h^{\mathrm{EOL}} \quad [\mathrm J],

where the terms are allocated fabrication, packaging, transport, deployment, operation including facility share, maintenance, replacement, and end-of-life primary energy [J]. Credits, if allowed by the preregistered lifecycle method, are signed and shown separately.

Let $Y_h\in(0,1]$ be accepted packaged yield [accepted device/started device], $N_h^{\mathrm{start}}$ be started units [device], $N_h^{\mathrm{life}}$ be lifetime accepted task outcomes [accepted outcome], and $u_h$ be useful utilization [useful device-second/provisioned device-second]. The lifecycle intensity is

e_h^{\mathrm{life}}= \frac{E_h^{\mathrm{life}}}{N_h^{\mathrm{life}}} \quad [\mathrm{J/accepted\ outcome}],

with $N_h^{\mathrm{life}}$ estimated only over registered deployment demand, support lifetime, failure, maintenance, retirement, and replacement policies. Yield and utilization are reported rather than absorbed into an optimistic denominator.

For new specialized hardware $s$ versus an already available conventional arm $c$ , the operational-energy break-even count is

N^*= \frac{ E_s^{\mathrm{emb}}-E_c^{\mathrm{incremental\ emb}} }{e_c^{\mathrm{op}}-e_s^{\mathrm{op}}} \quad [\mathrm{accepted\ outcome}],

when $e_c^{\mathrm{op}}>e_s^{\mathrm{op}}$ . Here $E_s^{\mathrm{emb}}$ is newly incurred embodied energy [J], $E_c^{\mathrm{incremental\ emb}}$ is additional embodied energy incurred by the conventional option [J], and $e_c^{\mathrm{op}},e_s^{\mathrm{op}}$ are facility-inclusive operational intensities [J/accepted outcome]. If the denominator is nonpositive, no positive energy break-even exists. $N^*$ is reported as a distribution under yield, utilization, service-life, demand, and allocation uncertainty.

Climate, water, material criticality, toxicity, and labor are separate outcome coordinates. For greenhouse-gas inventory,

G_h=\sum_{g=1}^{G}a_{h,g}\chi_g \quad [\mathrm{kg\ CO_2e}],

where $a_{h,g}$ is activity amount in its declared inventory unit, $\chi_g$ is the geography-, time-, and pathway-qualified characterization factor [kg CO $_2$ e/inventory unit], and $G$ is inventory-flow count [flow]. Energy alone does not determine $G_h$ .

Uncertainty, support, and matched comparison

For reported outcome $y$ [native unit], decompose its estimator as

\widehat y=y+b^{\mathrm{meter}}+b^{\mathrm{model}} +b^{\mathrm{alloc}}+\varepsilon,

where $b^{\mathrm{meter}}$ is meter/calibration bias [native unit], $b^{\mathrm{model}}$ is model-form or extrapolation bias [native unit], $b^{\mathrm{alloc}}$ is shared-resource allocation effect [native unit], and $\varepsilon$ is repeatability variation [native unit]. Report a coverage or credible interval for $y$ , calibration lineage, covariance where quantities share meters or models, and sensitivity across registered allocation and lifecycle cases. An interval for repeatability alone is not total uncertainty.

Let $x$ be an episode/regime feature vector in registered native units and $\mathcal S_{\mathrm{val}}$ be validation support. Define a preregistered support distance

d_{\mathrm{sup}}(x)= \inf_{z\in\mathcal S_{\mathrm{val}}} \left\|D^{-1}(x-z)\right\|_2 \quad [\mathrm{dimensionless}],

where $D$ is a diagonal matrix of fixed feature scales in the same units as $x$ , and $\|\cdot\|_2$ is Euclidean norm. Authority is withheld when $d_{\mathrm{sup}}(x)>d_{\max}$ , where $d_{\max}$ is a sealed dimensionless threshold. Other support tests are allowed only when specified before the held-out release.

The primary outcome vector for arm $a$ is

\mathbf Y_a= \left( f_{\mathrm{acc}},Q,L_{0.50},L_{0.99},\rho, e^{\mathrm{IT}},e^{\mathrm{fac}},e^{\mathrm{life}}, E^{\mathrm{err}},C^{\mathrm{cap}},G,W,M \right),

where $f_{\mathrm{acc}}$ is accepted fraction [dimensionless], $Q$ is registered task quality [task-native units], $L_{0.50},L_{0.99}$ are median and 99th percentile latency [s], $\rho$ is the registered risk vector [failure/request], the $e$ terms are energy intensity [J/accepted outcome], $E^{\mathrm{err}}$ is error-consequence energy [J], $C^{\mathrm{cap}}$ is capacity use [device s], $G$ is greenhouse-gas inventory [kg CO $_2$ e], $W$ is water inventory [m $^3$ ], and $M$ is a material/labor burden vector in declared native units. The vector is not reduced to one score after observing results.

Arm $p$ Pareto-dominates null $n$ only if its simultaneous uncertainty region is no worse on every hard-gated coordinate and strictly better on at least one preregistered primary coordinate under every required sensitivity case. Let

D_{p,n}=1

denote that decision [dimensionless], and $D_{p,n}=0$ otherwise. A component energy win with worse quality, risk, latency, capacity, or another required boundary cannot set $D_{p,n}=1$ .

The illustrative simultaneous-decision figure shows the uncertainty regions and hard gates without assigning measured values to any system.

Equal-budget constraints

For resource $r\in\mathcal R$ , require

B_{a,r}\le B_r^{\max},

where $B_{a,r}$ is arm- $a$ consumption in the native unit of resource $r$ and $B_r^{\max}$ is the shared ceiling in that unit. The registered resource set is

\mathcal R=\{ \text{data},\text{design work},\text{fabrication},\text{area}, \text{memory},\text{sensors},\text{controls},\text{reserve}, \text{training compute},\text{wall time},\text{capacity}, \text{operational energy},\text{maintenance},\text{replacement} \}.

Each resource has its own unit; unlike quantities are never summed. If an arm uses less of a capped resource, the unused amount remains reported and is not converted into post-hoc credit. If an arm violates any hard ceiling, its result is infeasible rather than penalized by a chosen scalar.

Required nulls and ablations

The complete null stack contains, when technically compatible:

source/channel coding, compression, quantization, pruning, batching, memoization, caching, compiler elimination, and recomputation;
clock and power gating, dynamic voltage/frequency scaling, near-threshold operation, mixed precision, structured sparsity, tiling, data reuse, and hierarchy-aware placement;
reversible logic with closed ancilla/history accounting, adiabatic or energy-recovery logic with measured power clock, and conventional logic at matched throughput and process;
ECC, checksums, retry, checkpoint/replay, guardbands, calibration, redundancy, and abstention;
matched digital, analog, in-memory, optical, and neuromorphic implementations including conversion, communication, control, drift, thermal, and host work;
direct facility metering and registered shared-overhead allocations; and
ISO 14040/14044 lifecycle cases with common functional unit, yield, utilization, lifetime, replacement, geography, and uncertainty.

Ablations remove exactly one of: generalized physical-state modeling; finite-time optimization; finite-error accounting; retention/correction; closed reversible history; power-clock recovery; feedback-controller boundary; TUR scope gate; hierarchy-aware routing; facility metering; embodied inventory; or uncertainty/support gating. Recalibrate each ablation only within the same development budget. An ablation that makes an arm infeasible is recorded as such, not silently retuned with additional resources.

Held-out regimes and hard retirement

Confirmation splits group by physical device, fabrication cohort, circuit and clock instance, software/model version, workload family, data-layout and hierarchy regime, task shift, transition duration, final error target, temperature, retention horizon, sensor/controller version, facility/site, season, electricity case, and future time. Random transitions or requests from the same group are development diagnostics only.

Retire the broad physical-efficiency composition if any of the following holds:

a claimed lower bound lacks its state distribution, Hamiltonian, bath, correlations, final error, duration, or cycle boundary;
a device advantage disappears when waveform source, parasitics, control, correction, and full transition closure are measured;
a reversible advantage excludes history, ancillae, output preservation, uncomputation, retention, export, or eventual erasure;
an adiabatic advantage disappears at matched useful throughput, hardware capacity, error, and leakage-inclusive power-clock cost;
a feedback or information-engine gain disappears when sensing, memory, control, actuation, and reset share one boundary;
a thermodynamic uncertainty inference fails its process, current, stationarity, observation, or entropy-production scope test;
a memory advantage fails the required retention, endurance, correction, silent-corruption, or replacement contract;
arithmetic savings are offset by routing, data movement, synchronization, conversion, imbalance, or idle capacity;
a facility claim uses component power, TDP, or a generic PUE instead of calibrated interval evidence;
lifecycle superiority depends on an unsupported yield, utilization, lifetime, demand, allocation, electricity, or replacement assumption;
no Pareto gain survives the strongest compatible null stack, held-out regimes, and required uncertainty sensitivities; or
the result lowers quality, safety, latency, retention, or coverage relative to the sealed useful-task contract.

Passing this contract supplies evidence only for the already named candidate scope in Fixture F-010. It creates no project-wide claim, principle, or candidate by itself.