sim09 — Curvature Channel

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

A non-saturating, recruit-as-well-as-limit stigmergic channel testing whether the trace→actor crossing (H7) fires where saturating cue-field feedback fragmented.

What it tests

H7, the Trace→Actor Crossing Hypothesis — does an accumulated stigmergic trace cross from passive coordination signal to self-maintaining actor? sim06 (saturating cement-pheromone cue) was a near-miss and then a reversal (self-maintenance fragmented the structure). sim07 (scalar structure-sourced transport) had the wrong sign. sim08 (non-saturating density cap) consolidated morphology but didn't recruit maintenance. H11, the Saturating Channel Hypothesis, diagnosed the common failure: all three acted through the pheromone field, whose deposit response p = base + gain·φ/(1+φ) saturates above φ≈1, so negative feedback through that channel destroys spatial contrast rather than creating it.

sim09 replaces the saturating cue with the curvature channel identified by Calovi et al. (2019, Phil Trans R Soc B) and Facchini et al. (2020, J R Soc Interface; 2024, eLife). The Facchini 2020 growth equation

∂f/∂t ≈ f(1−f)·[(1/2)·Δf + d·Δ²f]

becomes three operational pieces in sim06's 2D grid+agent framework:

• (1/2)·Δf (mean curvature) → the recruit mechanism. Loaded termites deposit at convex tips via a linear, non-saturating probability p = base + gain·curvature, clamped to [0,1]. Depositing at a convex tip extends the tip, recruiting further building there.
• d·Δ²f (biharmonic) → the limit mechanism + phase-transition knob. d is sim09's analog of sim07's M_c. Part 7's d sweep is the headline phase-transition plot.
• f(1−f) (surface restriction) → compute_on_surface. A Moore-dilation of the structure mask restricts deposits to the structure surface.

The Facchini/Calovi action-component split is the single most important design constraint: loaded termites deposit at convex tips (Facchini 2024: pellet deposition at convex tips); unloaded termites excavate at concavities (Calovi 2019: aggregate activity at concavities). sim06 conflated these into a single "build" action; sim09 splits them — conflating them would invert the rule's sign.

Conditions:

• curvature_channel — the curvature routing + biharmonic smoothing + surface restriction.
• baseline_pheromone — sim06's saturating Grassé rule (deposit probability base + gain·φ/(1+φ)), reusing the same metrics and detector. The control.

Hypotheses tested

• H7 (primary) — the trace→actor crossing. sim09's crossing detector has three channel-adapted criteria: (1) structure_stability ≥ 0.90, (2) roughness (curvature std over surface) sustained ≥ 0.02 while mass plateaus — corrected in Session 19 to a relative-slope plateau |slope(total_material over last K=16 samples)|/mean(total_material) < 0.001 (the original |growth_rate| < 0.01 gate was an unfalsifiable metric-ceiling bug, its threshold ~100× below the Poisson noise floor of a 150-termite deposit process), (3) deposits_on_convex_fraction ≥ 0.60. A synthetic-history regression guard encodes that lesson as an executable test (must fire on all-true; withhold when any single criterion — including the mass plateau — is negated).
• H11 (the saturating-channel diagnosis) — sim09 is its sufficiency test: does a non-saturating recruiting channel cross where saturating/non-recruiting channels (sim06 cue, sim07 scalar transport, sim08 cap) all failed?
• H4 (dynamic environment) — curvature is geometry the agents reshape; the stigmergic medium is dynamic, not a fixed fitness function.
• H1 / H10 (composition context) — if the curvature channel crosses, the next question is whether two self-maintaining curvature structures compose (the L2 question sim05 left open, now with a non-saturating stigmergic glue).

Design

The perturbation/self-repair test (Part 8) damages a central 25%-area square at step 0.6×steps and measures recovery = total_material / pre_perturb_total_material for each post-damage record. Part 8b (Session 24) adds patch_recovery (material in the damaged patch / pre-damage patch material) and a mirror_recovery control arm (an undamaged same-size region). targeted_repair = patch_recovery − mirror_recovery isolates preferential scar repair from background growth. Result: targeted_repair is negative in all conditions — neither channel preferentially repairs the damage site; the crossing is a stability claim, not a self-repair claim.

Cited: Calovi et al. 2019 (Phil Trans R Soc B); Facchini, Lazarescu, Perna & Douady 2020 (J R Soc Interface), public code at github.com/oiluigioi/JRSI_2020_termite_nest; Facchini et al. 2024 (eLife).

Results (default params, seed=42, d=1.0)

Note (Session 19): at default params the curvature channel grid-saturates (10000/10000 cells), so the mass plateau is a physical ceiling (nowhere left to deposit), not a dynamic equilibrium. The honest crossing result is the tuned probe below, where the grid does not saturate. The baseline never crosses under the corrected detector at any parameter.

Perturbation (25% damage @ step 2400):

Session 24 finding: the grid-wide recovery_final conflates scar repair with volume restoration (baseline's 47× is unbounded accumulation). The patch_recovery isolates the scar; the mirror_recovery control arm (undamaged same-size region) isolates the growth baseline. targeted_repair = patch − mirror is negative in all conditions — neither channel preferentially repairs the damage site. The crossing fires but does not self-repair in the targeted sense. See patch_recovery_probe.py.

d-sweep (reduced grid 80², 150 termites, 2000 steps): under the original detector, no phase transition at default DEPOSIT_PROB_BASE=0.10 — the curvature channel saturates the grid (pillars=1, retention=1.0 at every d ∈ {0, 0.2, 0.5, 1, 2, 4, 8}). Session 19 d sweep (100 combos, dpb × decay × d): 0/100 crossed under the original detector* — criterion 2's mass-saturation gate (|growth_rate|<0.01) was an unfalsifiable metric-ceiling bug (threshold ~100× below the Poisson noise floor of a 150-termite deposit process). Corrected to a relative-slope plateau (|slope(M)|/mean(M)<0.001 over K=16 samples): the crossing fires in the curvature channel at every d∈[0,4] in the tuned probe (dpb=0.01, decay=0.002, non-saturating grid 3123–5754/6400 cells) and does NOT fire in the baseline-pheromone control (same detector, 0/3 — saturating rule never elevates the pheromone cue enough). crossing_step 1550→900, pillars 12→1, roughness 0.44→0.77 as d rises. Determinism verified (0/80 history diffs).

Honest reading

At default parameters the corrected detector fires for the curvature channel (step 1125) and not the baseline — but the grid saturates (10000/10000 cells), so the mass plateau is a physical ceiling, not a dynamic equilibrium. The honest crossing result is the tuned probe (dpb=0.01, decay=0.002), where the grid does not saturate (3123–5754/6400 cells): the curvature channel crosses at every d∈[0,4] and the baseline-pheromone control (same detector) does not (0/3). This is the first H7 crossing with a control arm. The baseline's 47.34× perturbation "recovery" remains an artifact of unbounded material accumulation (the saturating deposit rule piles material without an erosion balance) — a saturating channel cannot express the spatial contrast targeted repair needs. Honest limitation: the crossing fires at d=0 (no smoothing), so the recruit half (curvature routing) drives the verdict; the limit half (d-smoothing) consolidates morphology (pillars 12→1, crossing_step 1550→900) but is not necessary for the crossing. The recruit-vs-limit isolation is the next test.

The clean H7 separation — curvature recruits repair at the scar, baseline does not — requires the mass-saturating parameter regime Part 7 also identified as needed for the crossing: lower nucleation (deposit_prob_base ≈ 0.01) + higher erosion (material_decay ≈ 0.002) so the biharmonic instability can create spatial selectivity before the grid fills. In a tuned probe the curvature channel saturates and refills the hole to 1.01× (repair-like) while the baseline grows unboundedly to 4.55× (volume, not repair) — the direction is right, but the minimal grid-wide metric is not sharp enough to settle H7 on its own.

Key findings (project arc)

• sim06 (saturating cue): near-miss, then reversal — self-maintenance fragmented the structure (219–297 components vs 66–109 baseline).
• sim07 (scalar structure-sourced transport): null — venting pheromone away from saturated pillars disperses the cue that recruits deposits (wrong sign for consolidation).
• sim08 (non-saturating density cap): consolidates morphology (pillars 101→52) but doesn't recruit — stability didn't rise (0.874→0.775). Necessary, not sufficient.
• sim09 (non-saturating recruit+limit curvature channel): crossing FIRES (Session 19, corrected detector). The d* sweep (100 combos) found 0/100 under the original detector — criterion 2's mass-saturation gate (|growth_rate|<0.01) was an unfalsifiable metric-ceiling bug (threshold ~100× below the Poisson noise floor of a 150-termite deposit process). Corrected to a relative-slope plateau (|slope(M)|/mean(M)<0.001 over K=16 samples), the crossing fires in the curvature channel at every d∈[0,4] in the tuned probe (dpb=0.01, decay=0.002, non-saturating grid 3123–5754/6400 cells) and does NOT fire in the baseline-pheromone control (same detector, 0/3). crossing_step 1550→900, pillars 12→1, roughness 0.44→0.77 as d rises. Honest limitation: the crossing fires at d=0, so the recruit half (curvature routing) drives the verdict; the limit half (d-smoothing) consolidates morphology but is not necessary for the crossing.

sim09's result is now a positive test of H7 with a control arm and a mechanism decomposition — the corrected detector fires the crossing in the curvature channel and not in the baseline-pheromone control (same detector). H11's channel distinction (non-saturating action-channel vs saturating cue-channel) is the causal variable separating crossing from non-crossing, not just a directional correlate.

Session 20 (2026-08-04) recruit-vs-limit isolation: a 2×2 factorial (recruit ON/OFF × limit ON/OFF, 4-seed robustness pass) decomposed the curvature channel into its two halves. The recruit half (curvature routing: curve_follow, deposit_prob_gain, excavate_prob_gain) is necessary and almost-sufficient for a stable crossing: recruit-only (d=0) crosses stably in 3/4 seeds (hold rate 1.00 in 3, 0.65 in the borderline seed); neither (no recruit, no limit) never crosses (0/4). The limit half (biharmonic d-smoothing) alone is never stable (0/4 — criteria flicker, hold 0.40–0.55, because the smoothing shapes convex geometry that no agent is routed to; criterion 3 deposits_on_convex_fraction oscillates around 0.60 without the routing to concentrate deposits at convex tips). But the limit half is not morphology-only: it is a stability amplifier — recruit+limit is stable in 4/4 seeds where recruit-only is 3/4; the borderline seed becomes fully stable (hold 1.0) when d>0 is added. So H11's "recruit as well as limit" is: recruit = necessary + almost-sufficient; limit = stabilizer + morphology optimizer (causally contributes to robustness, not strictly necessary). The decisive contrast is recruit ON vs OFF at d=0 (same detector, same regime, only the recruit flag differs). See recruit_limit_sweep.py.

Session 21 (2026-08-05) saturating-action control: the recruit half is action-based AND non-saturating simultaneously — H11's two claimed properties are confounded. A saturating response p = base + gain·c/(1+|c|) (action-based, compresses) was tested against the linear p = base + gain·c (action-based, non-saturating) in a 2×2×2 factorial (response × recruit × d) with a 4-seed robustness pass. The saturating action crosses in 8/8 recruit-ON seeds and is stable in 6/8 (linear is 7/8); the limit half rescues both to 4/4 at d=1. Saturation costs ~0.05 in mean hold rate at d=0 (0.91→0.86) but does not collapse the crossing — criterion 3 (deposits_on_convex_fraction) holds 1.00 for both forms; only the mass-plateau gate (criterion 2p) flickers more under saturation. Action-based routing is the primary load-bearing property; non-saturating is a secondary stability amplifier. H11's strict "non-saturating" claim is partially weakened: a saturating action-based channel still crosses stably, but less robustly. See saturating_action_sweep.py.

The next test is the L2 composition question: do two self-maintaining curvature structures compose (the sim05 L2 question reopened with a non-saturating stigmergic glue — the direct test of H1/H10)? Also: a late perturbation after true mass plateau (the current perturbation hits at 60% of steps when mass is still rising) may give a different self-repair result.

Limitations

• Toy 2D toroidal grid; lumped curvature (half the Laplacian of a lightly-smoothed material field), not the full Facchini phase-field.
• No real evaporation, airflow, or thermal physics — the evaporation≡curvature unification (Facchini 2024) is represented only geometrically.
• Parameter-sensitive: at default deposit_prob_base=0.10 the grid saturates before spatial selectivity emerges; the phase-transition regime needs lower nucleation + higher erosion.
• The roughness-as-maintenance mechanism (deposits roughen the surface, focusing further deposition) is inferred, not directly measured.
• Explicit-step integration of the biharmonic d·Δ²f is numerically fragile at high d (a d=8 probe showed a blowup; the 0.0001 prefactor needs reducing for the upper sweep range).
• The perturbation recovery metric is grid-wide; it cannot distinguish "repair at the scar" from "continued growth elsewhere." Session 24 added patch_recovery (scar-isolating) and mirror_recovery (control arm); targeted_repair is negative in all conditions — neither channel preferentially repairs the damage site.

What it teaches / next steps

1. The crossing fires (Session 19). The d* sweep found the original detector's mass-saturation gate was an unfalsifiable metric-ceiling bug (threshold ~100× below the Poisson noise floor). Corrected to a relative-slope plateau, the crossing fires in the curvature channel and not in the baseline-pheromone control — the first H7 crossing with a control arm. dstar_sweep.py is the sweep script; sim09.py's detect_crossing carries the corrected gate.
2. The recruit and limit halves are isolated (Session 20). A 2×2 factorial (recruit ON/OFF × limit ON/OFF, 4-seed robustness pass) found the recruit half is necessary and almost-sufficient for a stable crossing (3/4 seeds stable at d=0; neither = 0/4); the limit half alone is never stable (0/4 — criteria flicker) but is a stability amplifier (recruit+limit = 4/4 stable, rescuing the borderline seed). See recruit_limit_sweep.py.
3. The action-based vs non-saturating confound is resolved (Session 21). A saturating-action control (same curvature routing, saturating response c/(1+|c|) vs linear c) found action-based routing is the primary load-bearing property (saturating crosses 8/8 seeds, stable 6/8; linear 8/8, stable 7/8); non-saturating is a secondary stability amplifier (mean hold drops 0.91→0.86 at d=0; criterion 3 holds 1.00 for both). The limit half rescues both to 4/4 at d=1. See saturating_action_sweep.py.
4. Spatially-targeted recovery metric (Session 24). patch_recovery (material in the scar / pre-damage) + mirror_recovery (control arm: undamaged same-size region). targeted_repair = patch − mirror is negative in all conditions — neither channel preferentially repairs the damage site. The crossing is a stability claim, not a self-repair claim. See patch_recovery_probe.py.
5. Composition (the L2 question). The curvature channel crosses — do two self-maintaining curvature structures compose? This is the sim05 L2 question reopened with a non-saturating stigmergic glue — the direct test of H1/H10.
6. The crowding channel (Xiao 2026). The third non-saturating channel, independent of curvature/evaporation. A sim10 could test whether crowding (distributed inhibition preventing saturation) crosses where the density cap (sim08) didn't — the cap limited without recruiting; crowding might recruit via local density gradients.

How to run

cd ~/brain/artificial-life/simulations
uv run python3 sim09_curvature_channel/sim09.py run          # main experiment -> results.json
uv run python3 sim09_curvature_channel/sim09.py sweep_plot   # parameter sweeps -> output/*.png
uv run python3 sim09_curvature_channel/sim09.py selftest    # fast internal sanity checks
uv run python3 sim09_curvature_channel/saturating_action_sweep.py  # Session 21 confound test
uv run python3 sim09_curvature_channel/recruit_limit_sweep.py  # Session 20 2x2 isolation
uv run python3 sim09_curvature_channel/dstar_sweep.py          # Session 19 d* sweep
uv run python3 sim09_curvature_channel/patch_recovery_probe.py  # Session 24 targeted recovery

Visualization: visualize.html — fetches results.json and the optional output/sweep_data.json.