sim08 — Density Cap

Open the interactive visualization — renders the grid heatmap (play/pause, step slider) and all metric charts from results.json.

One-line: Tests whether inhibiting deposition through a non-saturating channel (a hard density cap on the deposit action) consolidates the stigmergic structure where sim06/sim07's saturating-cue feedback fragmented it. Direct test of H11, the Saturating Channel Hypothesis.

The hypothesis under test

H11 says negative feedback delivered through the saturating pheromone cue field (p = base + gain·φ/(1+φ), flat above φ≈1) is self-defeating: it destroys the spatial contrast consolidation needs. Two prior attempts both fragmented (sim06 self-maintenance: 66–109 → 219–297 components; sim07 transport: 57 → 128 pillars), both acting through the cue. The refined prescription: act on the action (deposit probability) via a channel that does not saturate. sim08 tests the cheapest such channel — a density cap: a cell whose material ≥ DENSITY_CAP cannot receive deposits. The cap is a hard boolean gate on the action, so it stays discriminating however high the pheromone field climbs.

Biological basis: real termites use non-saturating geometric (curvature), humidity (threshold), and crowding (mechanical) channels — not a saturating cement pheromone, which no study has identified. See concepts/non-saturating-channels.md.

What it does

Reuses sim06's tested machinery (Field, Termites, field dynamics, metrics, crossing detector, morphology) unchanged. The only change is one clause in the deposit rule: eligible = cell_material < density_cap. Movement, reload, pickup, decay, diffusion, erosion, the detector, and all metrics are identical to sim06 — so the comparison is apples-to-apples. Four conditions:

• baseline — sim06's saturating Grassé rule, no cap, no maintenance.
• self_maintenance — sim06's cue-based feedback (the condition that fragmented).
• density_cap — Grassé rule + non-saturating cap (the H11 test).
• cap_plus_self_maintenance — cap + cue feedback (does the cap rescue the cue loop?).

Results

Condition comparison (default DENSITY_CAP=4.0)

Density-cap sweep (cap strength → morphology)

Interpretation

Partial corroboration of H11, with a sharper boundary.

1. The cap consolidates morphology, monotonically — H11's direction is confirmed. Pillars fall from 101 → 52 as the cap tightens. The cap also suppresses the pheromone field (max pheromone 8.01 → 2.50) — exactly the "de-saturating the channel" effect H11 predicts: a non-saturating action-gate prevents the cue field from being driven flat. This is the positive result.

2. But the cap does NOT produce the crossing. Stability does not rise — it degrades slightly at the tightest cap (0.874 → 0.775). The detector never fires. The cap reduces building volume (1131 → 619 cells) without raising persistence.

3. The binding constraint survives the cap. sim06's near-miss was criterion 1 (stability 0.849–0.893 vs 0.90). sim08's cap holds stability at 0.77–0.88 — still below 0.90. The cap corrects the fragmentation symptom (pillars) but not the persistence symptom (stability). Non-saturating inhibition is necessary-but- not-sufficient for the crossing.

4. The cap does NOT rescue cue-based feedback. cap+self_maintenance (262 pillars, stability 0.763) is if anything worse than self_maintenance alone (252, 0.775). Adding the cap to the saturating-cue loop does not fix it — consistent with H11's claim that the cue channel, not the feedback energy, is the problem.

What this refines

• H11 confirmed in direction, sharpened in sufficiency. Non-saturating inhibition consolidates where saturating-cue feedback fragments — the prescription was right. But a cap that only limits growth cannot reach the crossing, because the crossing also needs persistence (the structure holding its mass against erosion). A pure limiter reduces mass; it doesn't recruit maintenance.
• The crossing needs a non-saturating channel that RECRUITS, not just one that LIMITS. The curvature channel (Calovi 2019) does both: it routes deposition to concavities (limits scatter) AND each deposit extends the concavity (recruits further building at the edge). The density cap only limits. Candidate next experiment: a curvature/deposition-edge rule that routes AND limits.
• H7's prescription narrows again. sim06: positive feedback alone insufficient. sim07: scalar cue-transport insufficient. sim08: non-saturating limitation insufficient. The crossing needs a non-saturating channel that also feeds back positively into its own maintenance — geometry that recruits, not just caps.

Method notes

• Determinism verified (seed 42; reruns identical).
• The cap is a genuine positive control: selftest asserts a fully-capped grid yields zero deposits and the same grid uncapped yields deposits > 0.
• Reuses sim06's detector, which is proven able to fire (sim06 selftest Part 5). A null here is therefore informative, not an unfalsifiable detector.
• All metrics, the crossing detector, and morphology functions are inherited unchanged from sim06; only the deposit rule's eligibility clause differs.

Files

• sim08.py — the simulation (imports sim06 for the reused machinery).
• results.json — four conditions + summaries (committed).
• visualize.html — interactive Canvas view of the conditions and the sweep.
• output/sweep_density_cap.json — the cap-strength sweep data.