Agents tagged with a structure ID (0=left, 1=right). Deposits carry the depositor's ID. Co-presence = min(dilate(id0 material), dilate(id1 material)). For a single seed, all material is id=0 → co-presence = 0 → boundary = 0. Structural guarantee: no spatial filter needed.
| Condition | L2 Crossed | Outcome | Stable | H7 | Cells | L Retain | R Retain |
|---|
| Mode | Seeds | L2 Crossed | Coexist | Stable | H7 | Clean |
|---|
5 inhibition gains × 4 seeds. Tests whether a stronger boundary enables or suppresses L2 composition. The trade-off: strong boundary suppresses the H7 crossing but enables clean composition.
2 modes (proportional, decoupled) × 4 gains × 4 seeds. Decoupled = fixed binary suppression; proportional = gradient. H7 unchanged between modes — the crossing is independent of the suppression curve.
3 formation gains × 3 persistence gains × 4 seeds. Two separate B fields: B_form (drives boundary growth from co-presence) and B_persist (maintains boundary through memory). Tests the two-wire principle.
6 modes (proportional, decoupled, hybrid k=0.5/0.7/0.8/0.9) × 4 gains × 4 seeds. Hybrid blends gradient formation with binary stability. Tests whether the blend breaks the trade-off.
5 bias levels (0.0–0.9) × 4 seeds. Agents biased toward their structure's centroid. Tests whether restricting wander improves clean composition by keeping agents local.
4 movement modes (none, focal, boundary, diffusivity) × 4 seeds. Tests whether local movement mechanisms can break the stigmergic feedback loop.
4 movement modes (none, focal, boundary, zone) × 4 seeds. Zone mode reads own-ID material (not B) for zone identification — breaking the stigmergic feedback loop. Tests whether a separate sensory channel makes local mechanisms viable.
6 jitter levels (0–40) × 4 seeds. Gaussian noise on the focal home center. Tests whether the focal mode's advantage is exogeneity (loop-breaking, unreachable by system dynamics) or precision (noise-free). Jitter=10 (12.5% of grid) preserves 4/4 full co-occurrence; jitter=20 (25%) collapses composition.
2 jitter modes (per_step, per_agent) × 6 jitter levels (0–40) × 4 seeds. Per-step = fresh jitter each step (temporal averaging); per-agent = fixed at init (spatial correlation). Tests whether temporal averaging drives tolerance. Per-agent jitter=20 outperforms per-step (3/4 vs 1/4 coexist) — spatial correlation is more robust at high noise.
2 grid sizes (80, 160) × 4 jitter levels (0–40) × 4 seeds. Tests whether jitter tolerance scales with grid size. Result: it does NOT — the 160×160 grid is worse at the same jitter fraction. The 1-seed l2 control leaks at larger grids. Tolerance is about absolute displacement, not jitter/grid fraction.
5 g_deriv levels (0–0.3) × 4 seeds. The D term responds to the rate of change of co-presence — strengthening the boundary BEFORE structures merge. Tests whether the PID D-term breaks the outcome-quality ceiling. Result: 4/4 full co-occurrence at ALL g_deriv — the D term is neutral at the optimal config (focal bias already achieves 4/4).
5 g_deriv levels (0–0.5) × 4 seeds, NO focal bias. Tests whether the D term substitutes for agent locality. Without focal bias, dual mode achieves 1/4 full co-occurrence — does the D term recover it?
5 g_deriv levels (0–0.3) × 4 seeds, with and without focal bias. The D term is driven by an external sinusoid (independent of system state) — tests whether the endogenous D-term's failure (Session 39) is endogeneity or anticipation itself. Result: less destructive than endogenous (stable 3/4→1/4 vs 3/4→0/4 at g_deriv=0.1 without focal bias) but still harmful. The 1-seed control leaks (spatially uniform signal breaks the structural guarantee).
3 periods (100, 200, 400) × 4 seeds at g_deriv=0.1 with focal bias. Tests whether the oscillation frequency matters. Result: all 4/4 full co-occurrence — the frequency doesn't matter when the system is already stable.
4 density combos: 80×150 (baseline), 160×150 (1/4 density), 160×300 (1/2 density), 160×600 (same density) × 3 jitter levels (0, 10, 20) × 4 seeds. Tests whether the 160×160 grid's degradation (Session 38) is purely density-dependent. Result: scaling n_termites with grid area PARTIALLY rescues the 160×160 failure — 160×600 matches 80×150 at jitter=0 (4/4) and jitter=10 (4/4 coexist, 3/4 stable) — but the 1-seed control leaks at high jitter (4/4 at jitter=20) and jitter=20 still degrades (2/4 coexist, 0/4 stable). The crossing (H7) is fully rescued (4/4 at all jitter), but composition stability is not.
4 density levels (100, 200, 400, 800 termites) on 160×160 at jitter=10 × 4 seeds. Tests whether the Session 41 non-monotonic intermediate density (160×300 worse than both 160×150 and 160×600) was genuine or a noise artifact. Result: monotonic improvement — the non-monotonicity was a 4-seed noise artifact. n=800 achieves 4/4 full co-occurrence (first time on 160×160) but the 1-seed control leaks (3/4) — the structure-to-grid ratio problem persists.
Part 1: 5 density levels (100, 125, 150, 175, 200 termites) on 160×160 at jitter=10 × 4 seeds — pinning the H7 percolation threshold. H7 transitions from 0/4 (n=100, 3.9/kc) to 4/4 (n=175, 6.8/kc) with a mixed regime at n=125-150. Composition (coexist) peaks at n=150 (4/4) but degrades at n=175-200 (1/4) — the crossing threshold and the composition optimum are NOT co-located. Part 2: 8-seed robustness at n=800 confirms 8/8 coexist, 8/8 stable, 8/8 H7, 7/8 clean, 7/8 full — the headline result holds. 1-seed leak confirmed at 4/8 (was 3/4 at 4 seeds).
Per-criterion H7 pass rates for the composition optimum (n=150, H7=2/4) and the crossing threshold (n=175, H7=4/4, coexist=1/4). At n=150, criterion 1 (stability ≥ 0.90) is the bottleneck — stability hovers at 0.88-0.89, flickering across the threshold. At n=175, H7 fires but the structures fragment (4+ components per region) — the boundary over-splits each region. The problem is over-fragmentation, not merging.
7 (n, g) combos × 4 seeds. At n=175, lowering the boundary gain rescues composition (1/4 → 4/4 coexist) while preserving H7 (4/4). At n=150, raising the gain destroys composition (4/4 → 0/4). The boundary strength must scale with density — the two-wire principle's 13th member. n=175 g=0.20 achieves 2/4 full co-occurrence (H7+coexist+stable+clean) — the first at moderate density.
20 (n, g) combos × 4 seeds × {2, 1} seeds = 160 runs. Finer resolution around the g*(n) scaling law predicted by Sessions 43–45: g* ≈ 0.30 at n=150, g* ≈ 0.20 at n=175. The linear fit g* = 0.82 − 0.0036n (R²=0.75) predicts g*=0 at n≈230. The 1/√n fit is slightly better (R²=0.77). n=170 g=0.24 achieves 3/4 full co-occurrence — the best ever. H7 is 4/4 at all n≥155 across all gains except n=155 g=0.32 (2/4) and n=160 g=0.28 (1/4). The 1-seed control leaks at n≥170 (1/4 at all gains — density-dependent).
Part A: 8-seed robustness at n=170 g=0.24 (#132) — the 3/4 full from 4 seeds holds at 3/8 with 8 seeds (coexist=6/8, stable=3/8, H7=8/8, clean=6/8). Part B: n=200 at 4 gains (#133, #134) — the 1/√n fit predicts g*(200)=0.12; the linear predicts 0.10. Actual g*≈0.12-0.14 confirms the 1/√n (Laplace pressure) scaling. n=200 g=0.14 achieves 4/4 coexist, 4/4 clean, 3/4 stable, 3/4 full — matching n=170's best. The 1-seed leak persists (1/4 at n=200, 1/8 at n=170).
The linear scaling is falsified; the 1/√n (Laplace pressure) scaling is confirmed. The linear fit predicted g*=0 at n≈230 (composition impossible); the 1/√n predicted g*(230)≈0.05. At n=230, composition is still alive: 3/4 coexist, 3/4 stable at g=0.08. n=220 g=0.06 and g=0.12 achieve 4/4 full co-occurrence (H7+coexist+stable+clean) — the first 4/4 full at any density on 160×160! The 1-seed control is 0/4 at n=230 (structural guarantee holds). 8-seed robustness at n=200 g=0.14: 8/8 coexist, 8/8 clean, 4/8 stable, 4/8 full — the headline holds at 8 seeds.
The 4/4 full at n=220 g=0.06 holds at 6/8 with 8 seeds — the headline is robust but not universal (2/8 seeds fragment). The asymmetric sweep reveals that neither B field alone is load-bearing — the symmetric balance is the optimum. Form-heavy (0.12, 0.06) degrades to 2/4 full; persist-heavy (0.06, 0.12) degrades to 1/4 full. Both symmetric optima (0.06/0.06 and 0.12/0.12) achieve 4/4 full. The two-wire principle's 14th member: formation and persistence must be balanced, not just separated — each field has a role, but neither can substitute for the other.
The 6/8 vs 2/8 "fragmentation" split is a final-record classifier artifact, not a genuine composition difference. All 8 seeds at n=220 g=0.06 have stable_l2=True (coexist in ≥50% of the late window). The late-window coexist fraction is 60–90% for all seeds — the two "fragmented" seeds (100: 60%, 777: 80%) are within the same band as the "coexisting" seeds (70–90%). Seed 777 (fragmented, 80%) has a higher coexist fraction than seed 999 (coexist, 70%) and seed 555 (coexist, 75%). The l2_outcome classifier uses the final late-window record; the stable_l2 metric uses the fraction of late-window steps in the coexist state. The "stochastic composition boundary" is a classifier boundary, not a composition boundary.
The 1/√n (Laplace pressure) scaling holds — g* does not hit zero at n=240–250. The linear fit (falsified at n=200, Session 47) predicted g*(240)≈0; the 1/√n predicted g*(240)≈0.04, g*(250)≈0.02. At both n=240 and n=250, composition is alive at every gain tested (0.01–0.06). n=240 g=0.01 is the best config ever: 4/4 coexist, 4/4 stable, 4/4 H7, 3/4 clean, 3/4 full — the 1-seed control is 0/4 l2_crossed (structural guarantee holds). Stability degrades at n=250 (2/4 at most gains vs 3–4/4 at n=240) — the structures are too big, creating more surface area for the boundary to split. The 1-seed l2_crossed leaks at n=250 (1/4) — the structure-to-grid ratio problem persists. The coexist_frac metric (Session 51, #143) is now the primary composition quality measure, replacing the noisy final-record l2_outcome classifier.
g* never hits zero — the 1/√n (Laplace pressure) scaling holds to n=300. At n=260–300, composition is alive at every gain tested (0.005–0.03). H7=4/4 at all combos. n=300 g=0.02 achieves the highest coexist_frac ever (0.775). The stability-density trade-off is boundary-mediated: without inhibition (g=0), all densities produce 0/4 coexist (fragmented). The 1-seed l2_crossed leak is mild and stochastic: 1/8 at n=240, 2/8 at n=250.
g* never hits zero at n=320–400 (~22–26% grid fill). The 1/√n (Laplace pressure) scaling holds to the highest density tested. H7=4/4 at all 9 combos. n=350 g=0.01 achieves the best composition quality (cf=0.725, 3/4 full). Stability degrades at n=400 (~26% fill) — a high-fill stability-density trade-off. The no-inhibition control confirms the boundary remains necessary at high density. 8-seed robustness at n=300 g=0.02: coexist is robust (7/8), but the full co-occurrence is stochastic (4/8).
3 bilateral configs (50/50, 50/90, 90/50) × 8 seeds × {perturbed, unperturbed} × {2, 1} = 96 runs at n=350 g=0.01. Tests whether the 4/4 full from 4 seeds holds at 8 seeds and whether the L/R asymmetry is systematic. Result: 4/4 full drops to 7/8 (seed 777 fails), but H7=8/8 at all configs. 50/90 is the BEST config at 8 seeds (cf=0.825) — the L/R asymmetry is systematic, not noise (50/90 >> 90/50, gap widens). The 37th mechanism: bilateral perturbation is composition-enhancing at 8 seeds (baseline 6/8 → perturbed 7/8).
3 bilateral configs (50/50, 50/90, 90/50) × 2 iteration orders (forward, reverse) × 8 seeds × {2, 1} = 96 perturbed + 64 unperturbed runs at n=350 g=0.01. Reversing the agent iteration order (id=1 first instead of id=0 first) tests whether the L/R asymmetry is physical or computational. Result: the asymmetry FLIPPED — forward 50/90 (cf=0.825) >> 90/50 (cf=0.712); reverse 50/90 (cf=0.619) << 90/50 (cf=0.644). The L/R asymmetry is a pure processing-order artifact. H7=8/8 at all configs in both directions — the crossing is robust to iteration order. The 38th mechanism: processing order as a hidden symmetry-breaking variable.
3 bilateral configs (50/50, 50/90, 90/50) × 2 iteration orders (shuffled, forward) × 8 seeds × {2, 1} = 96 perturbed + 64 unperturbed runs at n=350 g=0.01. Shuffling the agent order each step (rng.permutation(n)) should eliminate the systematic processing-order bias. Result: the L/R gap shrinks dramatically (+0.113 forward → -0.019 shuffled) but does NOT fully vanish — 90/50 remains slightly best (cf=0.881 vs 0.862). 50/50 is NOT the best config under shuffle (cf=0.719, the worst). H7=8/8 at all configs — the crossing is fully robust. The residual -0.019 gap may be a statistical artifact (8 seeds, ±0.03 noise) or a structural asymmetry beyond processing order.
3 bilateral configs (50/50, 50/90, 90/50) × 16 seeds × {2, 1} = 128 runs at n=350 g=0.01, shuffled iteration. Tests whether the 8/8 full at shuffled 90/50 (Session 62) holds at 16 seeds (#182), and whether the residual -0.019 L/R gap is statistical or structural (#183). Result: 8/8 does NOT hold — drops to 14/16 (cf 0.881→0.766), a small-sample effect. The -0.019 gap at 8 seeds was statistical noise, but at 16 seeds a different structural asymmetry emerges: 50/90 (cf=0.828) >> 90/50 (cf=0.766), gap=+0.062. The sign flips. H7=16/16 at all configs — the crossing is fully robust.
3 bilateral configs (50/50, 50/90, 90/50) × 32 seeds × {2, 1} = 256 runs at n=350 g=0.01, shuffled iteration. Tests whether the 14/16 full degrades further at 32 seeds and whether the +0.062 L/R gap (50/90 > 90/50) stabilizes or flips. Result: the +0.062 gap shrinks >50% to +0.024 — mostly statistical. 50/90 remains best on cf (0.769) but 50/50 has the most full (27/32). H7=32/32 at all configs — the crossing is fully robust. The 41st mechanism: the L/R gap is a finite-size effect, not a structural asymmetry.