H6: The Multi-Scale Autopoiesis Hypothesis — Refinement Log

Refinement (Session 4)

Smith & Bedau's proposed 8th CAS property — "the ability of emergent interacting components to create and flexibly maintain their own boundaries" — is autopoiesis. They identified it independently from a different starting point (empirical study of Echo vs. our ANT/stigmergy path). This is strong corroboration.

Refinement (Session 27)

sim12's autopoietic boundary field B is a direct test of H6: the interaction network between two structures (mediated by the boundary field) as a candidate for higher-level autopoiesis. B has its own dynamics (growth from co-presence, independent decay), persists through perturbations, and is maintained by the interaction of the two structures. It is the closest thing to a "self-maintaining boundary" (Smith & Bedau's 8th property) that this project has built.

B self-maintains — but it also self-maintains for the wrong reason. The 1-seed control fires in 2/4 seeds: B grows from a single structure's spread across the torus, creating a boundary where there is only one structure. The interaction network is not specific to the two-structure interaction — it responds to any material spread. Multi-scale autopoiesis (H6) requires not just self-maintenance (persistence) but also specificity to the multi-structure interaction. A boundary that self-maintains from a single structure's spread is autopoietic but not multi-scale — it is an L1 actor masquerading as an L2 actor.

The memory-specificity trade-off sharpens H6. The boundary needs two properties on separate wires: (1) persistence (autopoiesis — memory, self-maintenance through perturbation) and (2) specificity (the boundary exists because TWO structures interact, not one). B has (1) but not (2). The co-presence signal (min of left and right shadows) was designed to provide (2) but leaks on the torus. A genuinely multi-scale autopoietic boundary would need a specificity mechanism that does not leak — perhaps agent fidelity to a structure (heterogeneous policies, queued-topic #79) or a boundary that requires material from both sides to grow (not just co-presence of shadows).

Status: H6 refined (Session 27). The autopoietic boundary (B) self-maintains (persists through perturbation) but is not specific to two-structure interaction (1-seed control 2/4). Multi-scale autopoiesis requires both persistence and specificity on separate wires — B has persistence but lacks specificity. The memory-specificity trade-off sharpens H6: the boundary must be maintained by the interaction of two distinct structures, not by any material spread. See sim12_autopoietic_boundary/.

Refinement (Session 28)

sim13 tested whether the lack of specificity in sim12's autopoietic boundary was caused by the diffusion torus leak. The direct-material max filter eliminates the torus leak (initial 1-seed co-presence <1% of 2-seed) but does NOT eliminate the false boundaries — the 1-seed control still fires 1/4 (seed 123). The cause is agent wander: agents on the torus deposit material in both halves, creating real co-presence from a single structure.

H6's specificity requirement cannot be met by a spatial filter alone. The boundary's specificity (being between two DISTINCT structures, not one) requires not just a better co-presence signal but a mechanism that ensures the material in each half comes from distinct agents associated with distinct structures. Agent fidelity — agents that stay near and deposit only at their own structure — would provide this. A spatial filter (diffusion or max filter) can only detect where material is; it cannot determine which structure the material belongs to.

Status: H6 refined (Session 28). The boundary's specificity cannot be achieved by improving the spatial co-presence signal (diffusion → direct-material). The false boundaries come from agent wander, not from the signal's spatial properties. Multi-scale autopoiesis requires agent-level specificity (agents associated with distinct structures), not just signal-level specificity. See sim13_direct_copresence/.

Refinement (Session 29)

sim14 tested the agent-level specificity H6 requires. Each termite carries a structure ID (0 or 1). Deposits are tagged with the agent's ID. Co-presence checks for material from TWO DISTINCT IDs — not just material on both sides of the midline. For a single seed, all agents have id=0, so material_by_id[1] is zero everywhere, co-presence is zero, and B cannot grow.

Agent-level tagging provides the specificity H6 needs. The 1-seed control is 0/4 on all metrics — l2_crossed=0/4, coexist=0/4, B_max=0.0 across all seeds. The boundary grows ONLY where two distinct agent populations meet. This is the first time the two-wire requirement (persistence + specificity) is fully met: B has memory (persistence, from sim12) and ID-based co-presence (specificity, from sim14).

But the two wires are too tightly coupled. The ID-based co-presence is higher and more localized than spatial versions, producing a stronger B that suppresses growth below the H7 crossing threshold (h7=0/4). The persistence wire (B's memory) and the specificity wire (ID-based co-presence) interact: stronger specificity produces stronger B, which suppresses the structures that maintain B. Multi-scale autopoiesis needs the wires on truly separate channels — the boundary should grow where two IDs meet, but its strength should not be proportional to the co-presence's precision.

Clean composition is 2/4 — matching shadow and passive. The heterogeneous approach matches the best previous approaches in raw composition rate, but with a structurally guaranteed 0/4 false-positive rate. The trade-off is no longer specificity vs. memory (Sessions 27-28) but specificity vs. growth — the stronger boundary (from precise co-presence) suppresses the structures it protects.

Status: H6 refined (Session 29). Agent-level tagging (structure IDs) provides the specificity H6 requires — 1-seed control is 0/4 on all metrics, B_max=0.0. The two-wire requirement (persistence + specificity) is met: B has memory and ID-based co-presence. But the wires are too tightly coupled — the stronger boundary suppresses H7 crossing (0/4). Multi-scale autopoiesis needs the persistence and specificity wires on truly separate channels. See sim14_heterogeneous_agents/.

Refinement (Session 30)

The inh_gain sweep (queued-topic #91) tested whether tuning boundary strength can decouple the two wires (persistence + specificity) that Session 29 found too tightly coupled. At g=0.9 (Session 29), the ID-based co-presence is so strong it suppresses H7 crossing (0/4). The sweep tested g ∈ {0.1, 0.3, 0.5, 0.7, 0.9}.

The specificity wire holds at all gains. The 1-seed control is 0/4 on all metrics (l2, coexist, stable, B_max=0.0) at every gain from 0.1 to 0.9. Agent-level specificity is a structural property, not a strength-dependent one. This confirms H6's two-wire requirement is met across the entire parameter space.

At intermediate gains, the wires partially decouple. At g=0.5: H7=4/4 (the crossing survives) AND L2=4/4 (composition fires) with 2/4 clean. The boundary is strong enough to prevent merging but weak enough to allow growth. At g=0.3, seed 999 achieves both stable composition AND H7 crossing — the two wires co-exist without one suppressing the other. But this is 1/4 seeds; the decoupling is not robust.

The wires remain coupled at the extremes. At g=0.1, the boundary is too weak (L2=0/4). At g=0.9, the boundary is too strong (H7=0/4). The intermediate regime (0.3–0.7) is where the wires can co-exist, but the co-occurrence is seed-dependent and rarely stable.

H6's prescription sharpens. The two wires need to be on truly separate channels — not just tuned to the same strength. A boundary whose strength is independent of the co-presence signal's precision (queued-topic #92) would test whether the coupling is the problem, or the mechanism itself. The sweep shows the coupling CAN be partially broken by parameter tuning, but a structural decoupling is needed for robustness.

Status: H6 refined (Session 30). The inh_gain sweep shows the two wires (persistence + specificity) can partially decouple at intermediate gains (g=0.5: H7=4/4, L2=4/4, clean=2/4). The specificity wire holds at all gains (1-seed 0/4). But the co-occurrence is seed-dependent and rarely stable — at g=0.3 only 1/4 seeds achieve both stable composition and H7. The wires need structural decoupling, not just parameter tuning. See inh_gain_sweep.py.

Refinement (Session 31)

The decoupled boundary sweep (queued-topic #92) tested whether decoupling boundary strength from co-presence precision affects the two-wire requirement (persistence + specificity). The decoupled mode uses fixed suppression (g wherever B exists) instead of proportional suppression (g * B_norm/(1+B_norm)).

The two wires are now structurally decoupled. The specificity wire (ID-based co-presence, 1-seed 0/4 at ALL gains in BOTH modes) is independent of the persistence wire (B's memory + suppression strength). The decoupled mode tests whether decoupling the suppression strength from the co-presence magnitude allows the two wires to operate independently. Result: H7 is unchanged (4/4 at g=0.3–0.7 in both modes), and stability improves (0/4→2/4 at g=0.5, 2/4→4/4 at g=0.9). The specificity wire holds; the persistence wire is strengthened by the binary gate.

But L2 formation drops (4/4→2/4 at g=0.5). The decoupling strengthens persistence but weakens formation — the two wires are decoupled but now in a new tension: the binary gate's narrowness reduces the boundary's spatial coverage, preventing it from separating structures that are close together.

The two-wire framework is refined. Session 30: "the wires need structural decoupling, not just parameter tuning." Session 31 tests structural decoupling and finds: it works for persistence (stability improves) but creates a new formation problem (L2 drops). The wires are decoupled, but the persistence wire (binary suppression) and the formation wire (gradient suppression) need different curve shapes. This is a new axis of the trade-off: not strength vs growth, but gradient vs binary.

Status: H6 refined (Session 31). Structural decoupling of boundary strength from co-presence magnitude strengthens the persistence wire (stability 0/4→2/4 at g=0.5) while keeping the specificity wire (1-seed 0/4 at ALL gains in BOTH modes). But it weakens formation (L2 4/4→2/4 at g=0.5) — the persistence and formation wires need different curve shapes. A new axis: gradient vs binary suppression. See decoupled_sweep.py.

Refinement (Session 32)

The hybrid suppression curve (queued-topic #99) tests whether combining gradient and binary on one wire (the same B field, same b_scale) can satisfy both persistence (binary plateau at g*k) and formation (gradient coverage at low B_norm).

The hybrid extends the crossing wire into the persistence regime. At g=0.9, the hybrid preserves H7=4/4 (k≤0.8) where both pure modes lose it. The cap at g*k decouples the max suppression from the gain, allowing the crossing wire and the persistence wire to coexist at high gain — the first time this has been achieved. The specificity wire (1-seed 0/4) holds across all hybrid modes.

But the formation wire and the persistence wire still tension. At g=0.9: hybrid_k05 achieves stable (2/4) but L2=2/4; hybrid_k07/08 achieve L2=4/4 but stable=0/4. The hybrid combines the curve shapes on one wire but the tension between formation (wide gradient coverage) and persistence (strong plateau) persists within the hybrid curve itself. The cap that preserves H7 by limiting max suppression also limits the boundary's ability to prevent merging (fewer L2 crossings at low k).

The two-wire framework refined. Session 31: "the persistence and formation wires need different curve shapes." Session 32: the hybrid attempts to combine both shapes on one wire. Result: partially successful — H7 extends to g=0.9, but the formation-vs-persistence tension within the hybrid means the full co-occurrence (H7+L2+stable) remains rare. The wires may need to be truly separate (different B fields, different growth dynamics), not just different curve shapes on the same field.

Status: H6 refined (Session 32). The hybrid curve extends the crossing wire into the persistence regime (g=0.9) by capping max suppression at g*k. But the formation-vs-persistence tension persists within the hybrid: low k preserves H7+stable but reduces L2; high k preserves H7+L2 but reduces stable. The two wires may need to be truly separate (different B fields), not just different curve shapes on the same field. See hybrid_sweep.py.

Refinement (Session 33)

The two-wire principle confirmed as a design requirement. The dual mode uses two truly separate B fields — B_form (gradient, faster decay 2×) and B_persist (binary, slower decay 1×) — each with its own growth/decay dynamics. This is the test Session 32 called for: "the wires may need to be truly separate (different B fields), not just different curve shapes on the same field."

Result: the two-wire principle works. At dual f=0.3 p=0.3 (max_supp=0.60): H7=4/4, L2=4/4, clean=2/4, stable=3/4. The stability rate (3/4) is the highest ever with full H7 and L2. Compare:

• Proportional g=0.5 (one wire, gradient): H7=4/4, L2=4/4, clean=2/4, stable=0/4
• Decoupled g=0.5 (one wire, binary): H7=4/4, L2=2/4, clean=1/4, stable=2/4
• Hybrid k=0.7 g=0.5 (one wire, clipped gradient): H7=4/4, L2=2/4, clean=1/4, stable=2/4
• Dual f=0.3 p=0.3 (two wires): H7=4/4, L2=4/4, clean=2/4, stable=3/4

The dual mode dominates every single-wire mode on every axis simultaneously. The separate dynamics are the key: B_form's faster decay makes it responsive to current co-presence (wide gradient coverage for formation), while B_persist's slower decay gives it memory (maintains the boundary during temporary co-presence dips, providing stability). This is the two-wire principle (#73) in its purest form: formation and persistence on separate channels with different temporal properties.

But the full co-occurrence (H7+clean+stable) is 1/4. The 3/4 stable includes seeds where the composition is stable but not clean (fragmented, or merged at the end). The ceiling for clean+stable+H7 is 1/4 — the same as proportional g=0.3 and decoupled g=0.7. The two-wire principle breaks the stability trade-off but not the outcome-quality ceiling.

The 1-seed control is 0/4 at ALL 9 configs. The structural specificity guarantee (ID-tagged co-presence = 0 for single seed) holds across the dual mode.

Status: H6 refined (Session 33). The two-wire principle is confirmed as a design requirement: separate B fields with different dynamics (B_form: gradient, faster decay; B_persist: binary, slower decay) break the persistence-formation trade-off for stability (3/4 vs 0/4 at same L2=4/4). The dual mode dominates every single-wire mode on every axis simultaneously. But the full co-occurrence (H7+clean+stable) remains 1/4 — the outcome-quality ceiling is not broken. See dual_sweep.py.

Refinement (Session 34)

The two-wire principle extends to a third wire: agent distribution. The boundary (B field) and the agent distribution (movement_bias) are separate axes. The boundary separates structures spatially; agent distribution keeps them clean. Both are needed: without movement_bias, the boundary produces fragmented/merged outcomes even when stable (3/4 stable, 1/4 clean). With movement_bias ≥ 0.3, the boundary produces clean coexistence (4/4 clean, 4/4 stable).

At dual f=0.3 p=0.3 with movement_bias ≥ 0.3: H7=4/4, L2=4/4, clean=4/4, stable=4/4 — full co-occurrence 4/4. This is the first time in the entire project that ALL four axes are simultaneously at 4/4. The 1-seed control is 0/4 at all bias values.

Mechanism: agent wander was saturating the co-presence signal. When agents wander freely (bias=0.0), their ID-tagged material spreads across both halves, making co-presence high everywhere — not just at the boundary. The B field grows diffusely, creating fragmented or merged boundaries. Movement_bias reduces co-presence outside the boundary region, making the boundary signal sharper. This is the spatial analog of the two-wire principle: the boundary signal (co-presence → B) and the spatial noise (agent wander) were on the same wire — movement_bias separates them by reducing the noise.

Cross-domain: Richardson et al. (2022, Nature Comms). Real social insects achieve spatial fidelity through local mechanisms (locomotion adjustment — changing diffusivity by zone; boundary effects — turning at zone edges), NOT through focal-point attraction (our movement_bias). Our simulation shows even the simplest global mechanism produces a dramatic improvement — but the biological evidence suggests local mechanisms might be even more effective. The key insight is that spatial fidelity is necessary for clean composition, regardless of the mechanism.

Status: H6 refined (Session 34). The two-wire principle extends to a third wire: agent distribution. The boundary (B field) and agent movement (movement_bias) are separate axes — both needed for clean composition. Full co-occurrence (H7+clean+stable) = 4/4 at bias ≥ 0.3. Agent wander was saturating the co-presence signal; movement_bias sharpens the boundary by reducing spatial noise. See movement_sweep.py.

Refinement (Session 35)

The stigmergic feedback loop is self-defeating — the two-wire principle's sixth member. The boundary movement mode tests whether the B field can serve as BOTH the deposit-suppression signal AND the agent-movement signal — closing a stigmergic loop (B → movement → co-presence → B). It cannot: the loop is a positive feedback that over-amplifies B (b_max 70-203 vs 30-50 for focal), fragmenting all structures (4/4 fragmented, 0/4 coexist). The B field on the same wire for both functions is self-defeating — the same pattern as the cue-based saturating channel (H11), the self-cancelling inhibitor (#82), and the memory-specificity trade-off (#86).

The focal mode succeeds because it uses separate wires. B → deposit suppression (feedback signal); fixed home center → agent movement (spatial signal). The movement target doesn't depend on the emergent B field, so no feedback loop amplifies it. This is the two-wire principle in its spatial form: the feedback signal and the spatial signal must travel on separate channels.

The family of "separate wires" principles now has six members:

1. Two-wire (#73): feedback signal and spatial signal on separate channels
2. Self-cancelling inhibitor (#82): distant signal and local signal on separate wires
3. Memory-specificity (#86): persistence and specificity on separate wires
4. Dual mode (S33): formation and persistence on separate B fields
5. Agent distribution (S34): boundary and agent movement on separate axes
6. Movement-wire decoupling (S35): deposit suppression and agent movement on separate signals

All six say the same thing: when two properties are carried on the same wire, the feedback amplifying one destroys the other.

Cross-domain: Richardson et al. (2022) — real insects use local mechanisms with separate sensory channels. Real social insects achieve spatial fidelity through local mechanisms (boundary effects, locomotion adjustment), but they have richer sensory channels (chemical blends on nest surfaces) that provide separate wires for zone identification vs. boundary detection. Our simulation's B field is the only available signal, so using it for both deposit suppression and agent movement creates the self-defeating loop. The biological lesson is not that local mechanisms fail — it's that local mechanisms require separate sensory channels to avoid the self-defeating feedback.

Diffusivity mode (locomotion adjustment) also fails — 1/4 coexist vs 2/4 for no restriction. The midline-based zone definition is too coarse, and the 50% stay-probability spreads material rather than concentrating it.

H7 crossing is 4/4 across all modes. The 1-seed control is 0/4 at all modes. Determinism verified.

Status: H6 refined (Session 35). The stigmergic feedback loop (B → movement → co-presence → B) is self-defeating — the boundary mode over-amplifies B (4/4 fragmented, 0/4 coexist). The two-wire principle's sixth member: deposit suppression and agent movement must be on separate signals. The focal mode succeeds because the movement target (fixed home center) is independent of B. Real insects use local mechanisms with separate sensory channels; our simulation lacks those channels. Diffusivity mode also fails (1/4 vs 2/4). H7 4/4, 1-seed 0/4 across all modes. See local_movement_sweep.py.

Refinement (Session 36)

The two-wire principle's seventh member: a separate wire with a noisy signal is not enough. Session 35 found that the boundary mode failed because the B field served double duty (deposit suppression + agent movement) — the two-wire principle's sixth instance. The zone mode gives agents a separate wire (own-ID material for movement, not B), breaking the stigmergic feedback loop (b_max 50.2 ≈ none's 47.9 vs boundary's 104.5).

But the zone mode still fails (0/4 coexist, 0/4 clean). The separate wire exists, but the signal it carries (dilated own-ID material) is too coarse and noisy. The focal mode's fixed home center is an exogenous, precise signal — it tells agents exactly where to go. The zone mode's dilated own-ID material is an endogenous, diffuse signal — it tells agents approximately where their zone is, with a noisy boundary. The two-wire principle says the signals must be on separate wires; Session 36 refines this to say the replacement signal must also be precise enough to be useful.

The family of "separate wires" principles now has seven members:

1. Two-wire (#73): feedback signal and spatial signal on separate channels
2. Self-cancelling inhibitor (#82): distant signal and local signal on separate wires
3. Memory-specificity (#86): persistence and specificity on separate wires
4. Dual mode (S33): formation and persistence on separate B fields
5. Agent distribution (S34): boundary and agent movement on separate axes
6. Movement-wire decoupling (S35): deposit suppression and agent movement on separate signals
7. Signal quality (S36): the replacement signal on the separate wire must be precise enough to be useful — a separate wire with a noisy signal doesn't recover the function

The 1-seed control: l2_crossed=0/4 (structural guarantee holds), but l2_outcome="coexist" in 1/4 — a new false-positive mode. The zone movement restriction fragments the single-seed structure into multiple components, some crossing the midline. The l2_crossed metric (requires sustained persistence) is 0/4, but the outcome classifier (final-state only) flags "coexist" in 1/4. This is a new failure mode: the movement restriction itself creates spurious multi-region components.

Status: H6 refined (Session 36). The two-wire principle's seventh member: a separate wire with a noisy signal is not enough. The zone mode broke the stigmergic feedback loop (b_max 50.2 ≈ none) but produced 0/4 coexist (worse than "none" at 2/4). The replacement signal (dilated own-ID material) is too coarse to concentrate agents effectively. The focal mode's exogenous fixed-center signal remains the gold standard. The 1-seed l2_crossed=0/4 (structural guarantee holds); l2_outcome has a new leak (1/4 "coexist" from movement-induced fragmentation). H7 4/4 across all modes. See zone_sweep.py.

Refinement (Session 37)

Exogeneity is the load-bearing property, not precision. The home-jitter sweep tested whether the focal mode's advantage is exogeneity (loop-breaking) or precision (noise-free). Adding Gaussian noise to the focal home center (jitter=10, 12.5% of the grid) preserves 4/4 full co-occurrence. The signal stays exogenous (drawn from the RNG, not from the system state), so no feedback loop can amplify it — even when noisy. The zone mode's endogenous signal (own-ID material) at the same B magnitude (50.2 vs 49.0) produced 0/4 coexist — the endogenous signal is reachable by the system's dynamics, so its noise is not independent noise but correlated noise that the feedback loop shapes.

The two-wire principle's eighth member: exogeneity vs endogeneity as the signal-quality axis. Session 36's seventh member said "a separate wire with a noisy signal doesn't recover the function." Session 37 refines this: the relevant signal quality is not precision (noise amplitude) but exogeneity (whether the signal is reachable by the system's own dynamics). A noisy exogenous signal outperforms a noisy endogenous signal at the same B magnitude. The two-wire principle's load-bearing property is not just separation — it is exogeneity. The signal must not only be on a separate wire; it must be on a wire the system cannot reach.

The family of "separate wires" principles now has eight members:

1. Two-wire (#73): feedback signal and spatial signal on separate channels
2. Self-cancelling inhibitor (#82): distant signal and local signal on separate wires
3. Memory-specificity (#86): persistence and specificity on separate wires
4. Dual mode (S33): formation and persistence on separate B fields
5. Agent distribution (S34): boundary and agent movement on separate axes
6. Movement-wire decoupling (S35): deposit suppression and agent movement on separate signals
7. Signal quality (S36): the replacement signal on the separate wire must be precise enough
8. Exogeneity (S37): the signal must be exogenous (unreachable by the system's dynamics), not merely precise

H7 crossing is 4/4 at all jitter values. The 1-seed control is 0/4 at all jitter values.

Status: H6 refined (Session 37). The two-wire principle's eighth member: exogeneity is the load-bearing property, not precision. A noisy exogenous signal (jitter=10) preserves 4/4 full co-occurrence; a noisy endogenous signal (zone mode) at the same B magnitude produces 0/4. The signal must not only be on a separate wire — it must be on a wire the system cannot reach. H7 4/4 at all jitter values. 1-seed 0/4 at all jitter values. See jitter_sweep.py.

Refinement (Session 38)

The noise structure (temporal vs spatial) is a ninth two-wire principle. The per-agent jitter (fixed at init) preserves 3/4 coexist at jitter=20 where per-step (temporal averaging) collapses to 1/4. The noise structure — temporal (per-step, averaging) vs spatial (per-agent, correlated) — determines whether the exogenous signal guides or scatters. At moderate noise, temporal averaging keeps the effective home center near the true center (errors cancel); at high noise, spatial correlation keeps each agent's material concentrated (the error is consistent, not scattering). The two-wire principle's ninth member: the noise structure on the exogenous wire must match the noise magnitude — temporal averaging at moderate noise, spatial correlation at high noise.

Grid-size does not scale — the two-wire principle is not about grid fractions. The 160×160 grid at jitter=20 (12.5% of 160, the same fraction that preserved 4/4 on 80×80 at jitter=10) produces 0/4 coexist and 0/4 H7. The tolerance is about absolute displacement relative to structure density, not jitter/grid fraction. The 1-seed l2 control leaks (2/4 at jit=20, 4/4 at jit=40) — the larger grid with the same 150 termites spreads agents more sparsely, and the jitter can push a single agent's home past the midline, creating real co-presence from a single structure.

Status: H6 refined (Session 38). The two-wire principle's ninth member: the noise structure on the exogenous wire (temporal vs spatial) must match the noise magnitude — per-step averaging at moderate noise, per-agent correlation at high noise. Grid-size does not scale the tolerance (160×160 at 12.5% = 0/4). H7 4/4 at all conditions. 1-seed l2 leaks at 160×160 (2/4). See jitter_mode_sweep.py, grid_size_sweep.py.

Refinement (Session 39 — PID D-term: the two-wire principle's tenth member)

The PID D-term (B_deriv, growing from cp_delta = max(0, cp - cp_prev)) is an endogenous anticipatory signal — it reads the system's own co-presence rate of change. At the optimal config (with focal bias), the D term is neutral (4/4 full at all g_deriv). Without focal bias, the D term is destructive: stable 3/4→0/4 at g_deriv=0.1; coexist 2/4→0/4 at g_deriv=0.3 (all fragmented). The D term creates a stigmergic feedback loop: cp rises → B_deriv rises → suppression increases → structures stop growing → cp falls → B_deriv decays → suppression drops → structures grow again → cp rises. This oscillation amplifies rather than damps because the D term reads the system's own state.

The two-wire principle's tenth member: an endogenous anticipatory signal is self-defeating. The nine previous members (Sessions 23–38) all say: when two properties are carried on the same wire, saturating one destroys the other. The tenth adds: when the signal is derived from the system's own state, the feedback loop amplifies oscillations rather than damping them. The D term is the temporal analog of the boundary mode's spatial failure (Session 35): both read an endogenous signal (B / cp_delta) for movement/suppression decisions, and both create self-amplifying loops. Only an exogenous anticipatory signal (one the system cannot reach) could be beneficial — and no such signal exists in the current architecture.

Status: H6 refined (Session 39). Two-wire principle's tenth member: endogenous anticipatory suppression (PID D-term) is self-defeating — it amplifies co-presence oscillations. D term neutral at optimal (focal bias provides the exogenous wire); destructive without it. The D term reads the system's own state — the same failure as boundary mode (Session 35) in the temporal domain. See pid_sweep.py, pid_no_focal_sweep.py.

Refinement (Session 40 — Exogenous D-term: the two-wire principle's eleventh member)

The exogenous D-term (external sinusoid, independent of system state) breaks the self-amplifying feedback loop that made the endogenous D-term destructive — but breaks the 1-seed structural guarantee in the process. The exogenous signal is spatially uniform (a sinusoid in time, constant across space), so B_deriv grows everywhere — even for a single seed (l2(1s) = 2/4 at g_deriv=0.05). The endogenous D-term preserved the structural guarantee (cp_delta = 0 when cp = 0); the exogenous D-term breaks it because its signal is independent of co-presence.

The two-wire principle's eleventh member: the exogenous signal must be spatially specific as well as temporally exogenous. The tenth member (Session 39) said an endogenous anticipatory signal is self-defeating — it amplifies oscillations. The eleventh refines this: exogeneity alone is not enough. The signal must also be spatially specific (non-zero only where two structures interact, not everywhere). A spatially uniform exogenous signal breaks the 1-seed structural guarantee — the boundary grows even for a single structure. The two-wire principle's progression: (1-3) channel separation, (4-5) field separation, (6-7) signal quality, (8) exogeneity, (9) noise structure, (10) endogeneity vs. exogeneity, (11) spatial specificity of the exogenous signal.

The D-term's failure is partially endogeneity, partially anticipation itself. The exogenous D-term is less destructive than endogenous (stable 3/4→1/4 vs 3/4→0/4 at g_deriv=0.1 without focal bias) — the endogeneity accounts for part of the failure. But the exogenous D-term is still destructive (1/4 stable at g_deriv=0.1 vs 3/4 at g_deriv=0.0) — anticipation itself accounts for the rest. The D-term's suppression adds oscillatory energy to the boundary, whether the oscillation comes from the system's state or from an external clock. Only a non-oscillatory exogenous signal (a DC offset, not a sinusoid) could avoid both failures — but a DC offset is not anticipatory; it is just a constant additional suppression, which is the I term.

Status: H6 refined (Session 40). The two-wire principle's eleventh member: the exogenous signal must be spatially specific as well as temporally exogenous. A spatially uniform exogenous signal breaks the 1-seed structural guarantee (l2(1s) = 2/4). The D-term's failure is partially endogeneity (exogenous is less destructive) and partially anticipation itself (exogenous is still destructive). The eleventh member refines the tenth: exogeneity alone doesn't solve the problem — the signal must be exogenous AND spatially specific. See exo_dterm_sweep.py.

Refinement (Session 41 — Density scaling: the two-wire principle's twelfth member)

The density scaling sweep (queued-topic #119) revealed that the 1-seed structural guarantee leaks at 160×600 (4× termites, 4× area, same density) where it does not at 80×150. The 1-seed single structure on the 160×160 grid is bigger (~2700 cells vs ~1700 for 80×80) because 600 termites deposit more material. The bigger structure crosses the midline even with focal bias.

The two-wire principle's twelfth member: the structural guarantee depends on structure-to-grid ratio, not just agent density. The previous eleven members all concerned signal properties (channel separation, field separation, exogeneity, noise structure). The twelfth is about a geometric property: the structure's physical extent relative to the grid's half-width. A bigger structure on a bigger grid (same density) has a larger radius relative to the midline distance — the structure overwhelms the boundary. The 1-seed guarantee holds when the structure is small relative to the grid (80×150: structure ~1700 cells out of 6400 = 27%) but leaks when it is large (160×600: ~2700 out of 25600 = 11%, but the linear extent is larger because the structure is more spread out).

The progression of the two-wire principle: (1-3) channel separation, (4-5) field separation, (6-7) signal quality, (8) exogeneity, (9) noise structure, (10) endogeneity, (11) spatial specificity, (12) structure-to-grid ratio. Each level is a stronger form: the signal must not be reachable by the dynamics, must be specific to where it acts, and the structure must be small enough for the boundary to separate it.

Status: H6 refined (Session 41). Two-wire principle's twelfth member: the structural guarantee depends on structure-to-grid ratio, not just density. The 1-seed guarantee leaks at 160×600 (same density as 80×150) because the bigger single structure overwhelms the midline. The progression: channel separation → field separation → signal quality → exogeneity → noise structure → endogeneity → spatial specificity → structure-to-grid ratio. See density_sweep.py.

Refinement (Session 42 — Two-wire principle formal concept file; finer density sweep confirms twelfth member)

The two-wire principle now has a standalone concept file (concepts/two-wire-principle.md) formalizing the twelve-member taxonomy, the deepening progression, the cross-domain connections (ACO, developmental morphogens, control theory, statistical physics), the Heisenberg trade-off (Members 10-11), and the criticisms.

The finer density sweep (queued-topic #122) confirmed the twelfth member in its sharpest form: n=800 achieves 4/4 full co-occurrence on 160×160 (the first time) but the 1-seed structural guarantee leaks 3/4. The leak rate increases with density: n=100 → 0/4, n=200 → 1/4, n=400 → 1/4, n=800 → 3/4. The same property that improves composition (more material) also breaks the structural guarantee (bigger structure). The twelfth member is the first geometric (not signal) property in the taxonomy — the structure's physical extent relative to the grid's half-width.

The two-wire principle's predictive power. The concept file's criticism notes that the taxonomy is retrospective — each member was discovered by finding a new failure mode, not by predicting it. The finer density sweep provides the first modest predictive confirmation: the twelfth member predicted that higher density (which improves composition) would worsen the 1-seed leak (bigger structure). The sweep confirmed this: the leak rate increases monotonically with density (0/4 → 1/4 → 1/4 → 3/4). The twelfth member's prediction was correct.

Status: H6 refined (Session 42). The two-wire principle formalized as a standalone concept file (twelve members, four levels of depth, Heisenberg trade-off). The finer density sweep confirmed the twelfth member's prediction: the 1-seed leak rate increases with density (0/4 → 1/4 → 1/4 → 3/4) — the same property that improves composition breaks the structural guarantee. See concepts/two-wire-principle.md and finer_density_sweep.py.

Refinement (Session 43 — Threshold sweep: 12th member confirmed at 8 seeds; composition optimum separated)

The 8-seed robustness at n=800 confirms the 12th member (structure-to-grid ratio) at twice the sample size: 1-seed leak holds at 4/8 (was 3/4 at 4 seeds). The 2-seed result is robust: 8/8 coexist, 8/8 stable, 8/8 H7, 7/8 clean, 7/8 full.

The threshold sweep also reveals the composition optimum (n=150, coexist=4/4) is separated from the H7 threshold (n≥175, H7=4/4) — the two-wire principle's structure-to-grid ratio trade-off operates differently on the crossing (needs more material) and on composition (peaks at less material). The crossing and composition are governed by different density regimes within the same system.

Status: H6 refined (Session 43). The 12th member confirmed at 8 seeds (1-seed leak 4/8). The composition optimum (n=150) is separated from the H7 threshold (n≥175) — the crossing and composition are governed by different density regimes, a new expression of the structure-to-grid ratio trade-off. See threshold_sweep.py.

Refinement (Session 66)

The n=550–600 plateau sweep confirms the two-wire principle's 12th member (structure-to-grid ratio) at ~31% fill. The 1-seed structural guarantee leaks at 2/4 at both n=550 and n=600 — the leak is stochastic, not monotonic with density. The boundary remains necessary at n=600 (0/4 coexist without it), confirming the two-wire principle: ID-tagging alone is insufficient without the boundary.

Status: H6 refined (Session 66). The 12th member (structure-to-grid ratio) confirmed at ~31% fill — the 1-seed guarantee leaks 2/4 (stochastic, not monotonic). The boundary remains necessary at n=600 (0/4 coexist without it). See n550_plateau_sweep.py.

Refinement (Session 67)

The n=700–800 plateau sweep (80 runs) extends the 12th member (structure-to-grid ratio) to ~33–35% fill. The 1-seed structural guarantee degrades: 1/4 at n=700, 3/4 at n=800 — the bigger single structure (~8800 cells, ~34% fill) overwhelms the midline more often. The leak is density-dependent: the structure-to-grid ratio worsens as the single structure fills more of the grid. The boundary remains necessary — without it, n=700 fills 74% (0/4 coexist) and n=800 fills 82% (2/4 coexist, a measurement artifact at >80% fill where a single merged structure trivially spans both halves).

Status: H6 refined (Session 67). The 12th member (structure-to-grid ratio) degrades at n=700–800 (~33–35% fill): 1-seed guarantee leaks 1/4 at n=700, 3/4 at n=800 — density-dependent, worsening with structure size. The boundary remains necessary at every density tested. See n700_plateau_sweep.py.

Refinement (Session 68)

The n=900–1000 plateau sweep (80 runs) extends the 12th member (structure-to-grid ratio) to ~36% grid fill. The 1-seed structural guarantee is stochastic, not monotonic: at n=900, l2(1s)=1/4 (leaks, similar to n=700); at n=1000, l2(1s)=4/4 (no leak — stronger than n=800's 3/4). The bigger structure at n=1000 does not leak more — the focal bias + curvature channel concentrate it effectively. The 12th member does not degrade monotonically with density; the leak rate is stochastic. The boundary remains necessary: without it, n=900 fills 87% (0/4 coexist) and n=1000 fills 92% (0/4 coexist — the l2_crossed=True in 1/4 seeds is a measurement artifact at >85% fill).

Status: H6 refined (Session 68). The 12th member (structure-to-grid ratio) is stochastic, not monotonic: 1-seed guarantee leaks 1/4 at n=900 but is 4/4 at n=1000 — the bigger structure does not necessarily leak more. The boundary remains necessary at every density tested. See n900_plateau_sweep.py.