law: quenched-log-uniform-conductance

family: square-alternating

derivation: validated connected orientable triangulated surface with nonempty manifold boundary plus Euler-Poincare

kind: positive

label: one deterministic carrier and one deterministic conductance field with 32 randomized nested measurement batches; not 32 independent geometries

reason: Preregistered lower-cost screen cannot satisfy decision Gates 2-8.

u2Status: UNRESOLVED

scope: restore omitted targetShortcutCount from construction metadata and re-evaluate only the shortcut-count shortfall against it

metric: unweighted-graph-hop

label: descriptive finite-sample t-width only; not a confidence interval and not a coverage guarantee

samplingNote: Eight-root graph-hop ball-growth smoke descriptor only; not a dimension estimate or exponent confidence interval.


label: one deterministic carrier with 32 conductance/joint weighted realizations


process: lazy-weighted-nearest-neighbor

samplingNote: Nonzero Monte Carlo error. The reported four-root t-width is descriptive only, not a confidence interval or coverage guarantee; no hierarchical construction/probe resampling.

decisionNote: Linear energy is an upper bound and the other quantities are proxies. They cannot establish transport noncollapse, Gate 5 PASS, normalized conductivity equivalence, or a Dirichlet-solver result.


family: triangular-clipped


family: cell-center-fan


family: square-hashed-diagonal

label: 32 construction realizations sharing one deterministic unit-conductance law


label: 32 construction and joint weighted realizations


control: comb-trap

discriminant: axial-lazy-walk

interpretation: actual screening discriminant; not a Gate 2/4 alternate-estimator decision

kind: control

label: one deterministic carrier with 32 randomized walk batches

reason: Control screen is not a Gate 7 decision.


channel: comb-discriminant

detail: four root-block axial walk descriptors were not all defined


control: small-world-shortcuts

discriminant: root-ball-inflation

interpretation: actual construction and metric crossover screen; not Gate 2/3 decision evidence

label: 32 independently streamed control constructions


channel: small-world-discriminant

detail: root-ball inflation discriminant was unavailable


control: vanishing-neck

discriminant: two-cell-corridor-transport

label: one unique deterministic evaluation plus 31 exact repeated evaluations; not randomized nested batches


control: perforated-disk

discriminant: separated-removed-face-stars

interpretation: actual topology discriminant; counts toward no Gate 7 decision without full confirmatory inference and reproduction