Occupancy-qualified spatial transition — 20 Watts Was Enough

lusoris contributors

This note defines the narrow built-environment stress track for Candidate 001. Its purpose is to expose state and cost that disappear when a topology edit is represented as an instantaneous graph operation.

The contract applies only when physical or service topology changes while people, critical services, or hazardous inventory remain inside the affected dependency boundary. If the asset can be isolated and a fixed approved sequence dominates, ordinary change control is the relevant baseline.

Typed transition state

For transition version $v$ and step $k$ , keep the state tuple

X_{v,k}= \left( G, Y, O, R, F, S, U, H, C, E \right)_{v,k}.

The fields are deliberately not collapsed:

$G$ : surveyed physical and service topology, including uncertainty;
$Y$ : required service by user group, location, and time;
$O$ : observed or forecast occupancy, ability, familiarity, and assistance;
$R$ : ordinary, accessible, construction, emergency, responder, and goods routes, including capacity and closures;
$F$ : detection, alarm, suppression, compartment, smoke and heat state, and scenario-specific evacuation timing;
$S$ : structural, utility, control, and indoor-environment state;
$U$ : ownership, permits, operating restrictions, acceptance authority, stop-work power, and their expiry;
$H$ : material and work state—installed, removed, stored, in transit, reusable, damaged, waste, temporary, and irreversible;
$C$ : cost, energy, carbon, water, waste, and disruption accounts; and
$E$ : evidence support, timestamp, version, calibration, coverage, uncertainty, and invalidation dependencies.

A plan or model is an input to $E$ ; it is not a substitute for $G$ , $O$ , $F$ , or $S$ . Likewise, an actuator command belongs to the control record while verified equipment response belongs to $S$ .

Intermediate-state admissibility

Let $\mathcal H$ be the preregistered set of hard constraints. The step gate is

\mathcal A_{v,k} = \mathbf 1 \left[ \bigwedge_{h\in\mathcal H} g_h(X_{v,k})\ge 0 \right] \mathbf 1[E_{v,k}\text{ is sufficient and current}] \mathbf 1[U_{v,k}\text{ permits the step}],

where every indicator is dimensionless. Each $g_h$ retains its own physical unit and threshold; the conjunction does not add seconds, newtons, contaminant concentration, and route availability into a fictitious scalar score.

For fire scenario $s$ , one necessary margin is

m^{\mathrm{egress}}_{s,v,k} =ASET_{s,v,k}-RSET_{s,v,k}-M_s\quad[\mathrm{s}],

with $m^{\mathrm{egress}}_{s,v,k}\ge0$ . Here $ASET$ is available safe egress time, $RSET$ is required safe egress time, and $M_s$ is the frozen scenario margin, all in seconds. Passing this one margin does not establish structural, accessibility, utility, or environmental admissibility.

For user group $g$ , define accessible route availability as

a_{g,v,k} = \mathbf 1[\exists\text{ usable route for }g] \mathbf 1[q_{g,v,k}\ge q_g^{\min}],

where $a$ is dimensionless, route capacity $q$ and its minimum $q^{\min}$ use the same declared unit such as persons per second, and “usable” includes the group's mobility and assistance requirements. A graph path that is blocked, untenable, too narrow, or unsupported does not satisfy the predicate.

The controller may execute step $k$ only when $\mathcal A_{v,k}=1$ . Otherwise it must abstain or enter a pre-approved restricted, decanted, isolated, or safe-stop state. It cannot average one hard violation against an energy saving.

Evidence-age gate

For evidence item $j$ , let measurement time be $t_j$ , current decision time be $t$ , and maximum permitted age under the current hazard and work state be $\tau_j(X_{v,k})$ , all in seconds. Its freshness indicator is

f_j(t,X_{v,k})= \mathbf 1[t-t_j\le\tau_j(X_{v,k})] \mathbf 1[d_j(X_{v,k})=0],

where $d_j$ is a dimensionless invalidation flag. Moving a wall, isolating a circuit, changing occupancy, impairing suppression, or changing the sensor support can set $d_j=1$ even before the clock expires. Required evidence is current only when $\prod_{j\in\mathcal J_{v,k}} f_j=1$ .

Service and transition burden

For user group $g$ over transition interval $[t_0,t_1]$ , service loss is

L_g= \int_{t_0}^{t_1} \left[Q_{g,\mathrm{ref}}(t)-Q_g(t)\right]_+dt.

If $Q_g$ is usable service places, $L_g$ is place-hours; if $Q_g$ is flow in persons per hour, $L_g$ is persons. The service unit must be declared, and the vector $\mathbf L=(L_1,\ldots,L_G)$ remains visible so an aggregate cannot hide loss concentrated on one group.

Transition burden is reported as a vector rather than an automatic weighted sum:

\mathbf B= \left( \mathbf L, T_{\mathrm{transition}}, E_{\mathrm{transition}}, GWP_{\mathrm{transition}}, C_{\mathrm{transition}}, W_{\mathrm{material}}, N_{\mathrm{defect}}, N_{\mathrm{hard\ violation}} \right).

The components use, respectively, declared service-unit-hours, seconds, joules, kilograms CO $_2$ e, currency, kilograms, a defect count, and a hard- violation count. Any scalarization must publish its weights, units, and decision authority. The primary feasibility condition is $N_{\mathrm{hard\ violation}}=0$ for every protected scenario—not a favorable mean.

Fast reversible allocation and slow structural adaptation therefore retain different action, deficit, build, carry, and stranded-capacity coordinates (C-1496).

Commitment and recovery

Let $K_{v,k}$ be the set of material or legal commitments already made. A software rollback is physically available only if a tested predecessor state $X_{v,k^-}$ remains reachable under the current $K_{v,k}$ , resources, authority, and time. Define

r_{v,k}=\mathbf 1[X_{v,k^-}\in\mathcal R(X_{v,k},K_{v,k})],

where $r$ is dimensionless and $\mathcal R$ is the set of reachable, verified states. When $r_{v,k}=0$ , the record must name a reachable safe-stop or forward- recovery state; calling the transition reversible is false.

Recovery after a demand-regime reversal is part of the structural decision, not an optional endpoint after the selected regime has already been scored (C-1496).

Recovery is complete only after target service, evidence validity, open-defect limits, and reserve are restored. For each service component $m$ ,

T^{\mathrm{recover}}_m = \inf\{t\ge t_f: Q_m(t:t+\Delta)\ge Q_m^{\mathrm{target}} \land R_m(t:t+\Delta)\ge R_m^{\min}\}-t_f,

where $t_f$ is fault or interruption time, $\Delta$ is the frozen sustainment window, $Q$ and reserve $R$ use declared service units, and $T^{\mathrm{recover}}$ is seconds. Reopening without reserve restoration is reported separately.

Equal-budget comparison and rejection

The residual contract is compared with the complete ordinary stack: surveyed as-built records, code and professional review, permits, impairment control, configuration management, construction sequencing, commissioning, post- occupancy evaluation, and lifecycle asset management. All arms receive the same asset, staff time, information, sensors, professional review, material, construction window, compute, maintenance, and whole-life budget.

Reject or merge the residual when any of the following holds:

the asset can be isolated and a fixed approved sequence matches outcomes;
a protected-user accessibility or life-safety constraint is violated;
the advantage disappears when stale evidence, failed actuators, occupancy changes, transition duration, irreversible work, and common causes are represented;
mature change control plus commissioning matches the protected-service and lifecycle frontier; or
apparent recovery omits displaced exposure, defects, reserve restoration, or the next disruption.

The editable transition diagram is occupancy-qualified-spatial-transition.mmd. The evidence boundary is developed in the built-environment audit.