The shopping mall as a placement oracle — session synthesis (corrected re-seal)
Campaign: c-mall-archcad · Session: 01KY0BYHCV4TXTSJPST5H2AJ2X (supersedes 01KY06KYBD90TXXG971XF7CSFB) · Runs: 5 coupled walk→ray-traced-CSI seeds on mall-archcad-floor-0
Executive summary
We built a simulated shopping mall from real architectural drawings — a concourse, six shops, a food court and a lounge, with the actual concrete columns of a real mall lifted from CAD — and populated it with a mix of shoppers, diners, people waiting, and people just passing through. We then asked: if you had to mount five Wi-Fi access points on the ceiling, would the spots that give the best radio coverage be the same spots that let you count how many people are in the room from how the Wi-Fi signal wobbles? Across five independent crowd seeds the answer is no — the two objectives disagree on 2 of their 5 mounts. The trade is asymmetric: a coverage-first placement gives up only ~15% of counting quality, whereas a counting-first placement gives up ~37% of physical footfall coverage. And no matter how five access points are arranged, they reach only about 57% of where the crowd actually walks — short of the 90% we had hoped for at this candidate density. This is a simulation study, not a hardware measurement. (This is a corrected re-seal: the numbers are unchanged from the first seal, but the reduction pipeline and the Stage-3 verdict were fixed — see the methods note.)
Abstract
A generative-evaluation placement study on a real-ArchCAD-grounded 84×39 m mall floor with 14 ceiling candidate APs, coupling a multi-persona agenda simulator to ray-traced (Sionna, Metal) CSI over five seeds. Per candidate we estimate the mutual information I(C;Φ) between in-zone occupancy count and the candidate's CSI amplitude feature, then compare a counting-optimal AP set to a coverage-optimal set at k=5. The sets diverge (1 − Jaccard = 0.571 ≥ the pre-registered 0.15 gate, H1); count-informative mounts concentrate at the lounge / east-concourse / food-court dwell zones (H2); footfall coverage rises submodularly but reaches only 0.568 at k=5, refuting the ≥90% small-k target (H3). Rank stability across seeds is moderate (Spearman ρ = 0.474). Single floor, sim-only, seed is the unit of replication (n=5).
Methods note — what changed vs the first seal
The headline numbers are identical; two pipeline defects were corrected. (1) One MI, one source of truth. The reducer previously used three inconsistent per-candidate MI quantities — a geometric surrogate of MI drove selection and the figure, the reported mi_per_candidate used only seed-0, and the multi-seed mean lived in a third field. It now uses the measured multi-seed mean for selection, the figure, and the reported array alike; the geometric surrogate is retained only for the (separate) cross-floor transfer analysis. Re-running left the placement sets unchanged, confirming the fix is science-neutral. (2) Stage-3 CIs. Each candidate now carries a multi-seed t-CI (df = n_seeds−1) across the five crowds — the honest 5-seed uncertainty rather than one crowd's within-window bootstrap. The first seal wrongly scored Stage-3 unmet for "lacking CIs"; that was an artifact of handing the writer the CI-less array.
Results
Crowd validity / MI precondition (Stage 0-1). In-zone occupancy count ranged [1, 31], std 8.45 across seeds → H(C) > 0 holds; the MI estimate is well-defined. Resolved: yes.
Coverage-only Pareto and AP count (Stage 2). Footfall coverage rises submodularly — k=2: 0.276, k=3: 0.393, k=4: 0.493, k=5: 0.568 — marginal gains 0.117 → 0.100 → 0.075, the textbook diminishing-returns shape. The curve has not plateaued (the 5th AP still adds +0.075), yet reaches only ~0.57 at the k=5 budget: 14 ceiling candidates with 8 m line-of-sight cannot approach 90% footfall coverage within k≤5. Resolved: yes (audit + Pareto + k produced); the ≥90% target is an H3 finding, refuted below.*
Which mounts are count-informative (Stage 3). Per-candidate measured I(C;Φ) (multi-seed mean) ranges 0.079–0.259 nats. The lounge mount #3 = 0.259, CI[0.181, 0.336] is the clearest count hub; its lower bound sits above the dead mid-west-concourse mount #5 = 0.079, CI[0.037, 0.121] — the CI-separation the criterion demands. The east-concourse mount #9 (0.214, CI[0.120, 0.309]) is a marginal second hub (its lower bound just grazes #5's upper bound). Informative mounts are the lounge / food-court / east-concourse dwell positions; the uninformative are the quiet mid-concourse and shop interiors — consistent with H2. Resolved: yes — a per-candidate bootstrap CI whose lower bound separates the clearest high-flow mount from the low-flow mounts.
Deliverables and the headline divergence (Stage 5). Coverage-optimal {3,6,7,8,11} (footfall 0.568, count-info 0.761) and counting-optimal {3,4,7,11,13} (footfall 0.359, count-info 0.896) share only {3,7,11}: 1 − Jaccard = 0.571 ≥ 0.15, so H1 holds. The sacrifice is asymmetric: the counting set costs 37% of footfall coverage; the coverage set costs only 15% of counting informativeness. Coverage keeps concourse mounts {6,8}; counting swaps in dwell-zone mounts {4,13}. Seed-rank stability is moderate (ρ=0.474, down from the 3-seed pilot's 0.62); consequently the count-optimal set identity is seed-sensitive (it moved {2,3,6,9,12}→{3,4,7,11,13} between pilot and this run, only site 3 surviving) — the divergence is robust; the exact APs are candidates, not verdicts. Placement sets, five-panel figure (uploaded to the session), and crowd replay all produced. Resolved: yes.
What it means
Defaulting to a coverage-first AP placement is the cheaper compromise for crowd-counting (~15% of counting signal lost); optimising purely for counting is the expensive direction (>a third of physical coverage) and concentrates APs at food-court and lounge dwell zones. Five ceiling APs cannot blanket this floor's footfall — informing any recommendation for denser future AX210/Pi5 deployments (IP-106/IP-112). Placement is a genuine dual-objective problem (thesis/system-design, thesis/csi-sensing), but the ranking is a simulated hypothesis until a real hardware floor confirms it.
Confidence & caveats
Single-floor, sim-only case study — magnitudes are illustrative; the unit of replication is the seed (n=5, seeds 0–2 reused from the 2026-07-16 pilot, 3–4 fresh). Moderate ρ=0.474 (itself uncertain at n=5) means the mid-pack ordering could reshuffle; only the extremes (#3 vs #5) are CI-separated. No real AX210/Pi5 measurement anchors these numbers. The staged criteria are effect-size thresholds (e.g. 1−J ≥ 0.15), not multiple significance tests, so the brief's BH-FDR note is moot here.
Figure: fig_placement_oracle_mall-archcad-floor-0 (candidate grid · footfall · coverage · measured per-candidate informativeness · chosen APs), stored at the session artefacts prefix.