H5: The Autopoiesis Persistence Hypothesis — Refinement Log

Session 29: sim14's ID-tagged agents achieve 0/4 false-positive rate (1-seed control structurally zero) — the first time specificity is absolute. But the stronger boundary suppresses H7 crossing (0/4) and limits coexistence to 2/4. The trade-off shifts from specificity-vs-memory to strength-vs-growth.

Topic: autopoiesis as the persistence condition for a new actor at a higher scale

sim12 tested an autopoietic boundary field B with its own growth/decay dynamics — the first direct test of H5. B has memory (b_decay = 0.005, half-life ~138 steps), so it persists through structural wobbles. The result supports H5's core claim — self-maintenance (memory) produces persistence — but reveals a trade-off H5 did not anticipate.

Autopoiesis improves persistence. The autopoietic boundary produces stable coexistence in 4/4 seeds (vs 1/4 for the passive, memoryless inhibitor). It survives a 50% material-removal perturbation (B retains 91% at 100 steps, coexistence survives). This is the first perturbation in this project where coexistence actually persists through a structural shock.

But autopoiesis reduces specificity. The same memory that gives B persistence also accumulates co-presence from a single structure's spread across the grid. The 1-seed control fires in 2/4 (vs 1/4 for the passive) — B creates false boundaries. Clean composition (2-seed coexist AND 1-seed does NOT) is 2/4 for both — the trade-off cancels out.

The memory-specificity trade-off. H5 says autopoiesis is the persistence condition for a new actor at a higher scale. The data says: autopoiesis (memory) is necessary for persistence, but it is not sufficient — the boundary also needs specificity (a mechanism that ensures it is between two distinct structures, not just any material spread). The trade-off is: memory buys persistence at the cost of specificity. A genuine L2 boundary needs both wires (persistence + specificity) on separate channels — the temporal analog of the two-wire principle (#73) and the self-cancelling inhibitor (#82).

Status: H5 refined (Session 27). Autopoiesis (memory) improves persistence (stable 4/4 vs 1/4, survives perturbation) but creates false boundaries (1-seed control 2/4). Autopoiesis is necessary for persistence but not sufficient for a genuine L2 boundary — the boundary also needs specificity. The memory-specificity trade-off is the temporal analog of the two-wire principle. See sim12_autopoietic_boundary/.

sim13 tested whether the false boundaries in sim12 were caused by the diffusion torus leak — the co-presence signal min(left_shadow, right_shadow) uses 8 diffusion passes on the torus, and the shadows wrap around, creating phantom co-presence for a single seed. sim13 replaced the diffusion with a direct-material max filter (dilation) that wraps in y but NOT in x (zero-padded, no cross-midline leakage).

The torus leak is eliminated — but it was not the cause. The initial 1-seed co-presence drops to <1% of the 2-seed value (0.015 vs 1.83). But during the simulation, agents wander on the torus and deposit material in both halves. This wander material creates REAL co-presence (not phantom) — the 1-seed control still fires 1/4 (seed 123). The diffusion torus leak was a contributing factor but not the primary cause. Agent wander is the primary cause.

A radius sweep reveals a breadth-specificity dimension. At small radii (8-12), the max filter is too narrow to prevent merging (2-seed outcome=none). At medium radii (15-20), agent-wander material creates false positives (1-seed coexist). At radius=30, the b_scale normalization produces clean composition for seed 42 but fragmentation for 3/4 seeds. The radius controls the same trade-off as the diffusion spread: breadth (effective boundary) vs. specificity (no false positives).

H5's trade-off is not a property of the co-presence signal — it is a property of the system. Agents on a torus distribute material everywhere, and any boundary broad enough to prevent merging is also broad enough to pick up wander material. The fix is not a better spatial filter — it is a mechanism that keeps agents near their structure (agent fidelity, heterogeneous policies).

Status: H5 refined (Session 28). The memory-specificity trade-off is not caused by the co-presence signal's spatial filter (diffusion vs. direct-material) — it is caused by agent wander on the torus. Eliminating the torus leak (direct-material max filter) does not break the trade-off. The fix requires agent fidelity, not a better spatial filter. See sim13_direct_copresence/.

sim14 tested whether agent-level tagging (structure IDs) breaks the memory-specificity trade-off. Each termite carries an ID (0=left, 1=right). Deposits go into material_by_id[agent.id]. Co-presence = min(dilate(material_by_id[0]), dilate(material_by_id[1])). For a single seed, all material is id=0, so material_by_id[1] is zero everywhere — co-presence is structurally zero, regardless of agent wander.

The false-positive mechanism is broken. The 1-seed control is 0/4 on ALL metrics — l2_crossed=0/4, coexist=0/4, stable=0/4, B_max=0.0 across all four seeds. This is the first time the 1-seed false-positive rate has been zero. No spatial filter (sim12 diffusion: 4/4, sim13 direct-material: 4/4) achieves this.

But the boundary is too strong. The ID-based co-presence is higher and more localized than the spatial versions, producing a stronger B that suppresses growth below the H7 crossing threshold (h7=0/4, cells=167 vs 3714 for shadow). Clean composition is 2/4 (matching shadow and passive), but the H7 crossing is lost.

The trade-off has shifted, not disappeared. The memory-specificity trade-off (Session 27-28) was: persistence (memory) vs. specificity (no false boundaries). sim14 resolves the specificity axis — agent IDs provide structural specificity. But a new trade-off emerges: strength vs. growth. The stronger boundary (from more precise co-presence) suppresses the structure it is supposed to protect. Autopoiesis is still necessary for persistence, but the boundary's strength must be tuned — too strong suppresses growth, too weak allows merging. H5's claim holds: autopoiesis is the persistence condition, but persistence alone is not enough — the boundary must be strong enough to prevent merging but weak enough to allow growth.

Status: H5 refined (Session 29). Agent-level tagging (structure IDs) breaks the false-positive mechanism — the 1-seed control is 0/4 across all seeds (B_max=0.0). But the stronger boundary suppresses H7 crossing (0/4) and limits coexistence to 2/4. The trade-off shifts from specificity-vs-memory (Sessions 27-28) to strength-vs-growth. Autopoiesis is necessary for persistence, but the boundary's strength must be tuned. See sim14_heterogeneous_agents/.

The inh_gain sweep (queued-topic #91) tested sim14's ID-tagged boundary at five gains (0.1, 0.3, 0.5, 0.7, 0.9) with 4-seed robustness, mapping the strength-vs-growth frontier. The key question: is there a gain where both H7 crossing AND L2 composition co-occur?

The 1-seed control is structurally zero at ALL gains. l2_crossed=0/4, coexist=0/4 at every gain from 0.1 to 0.9. The ID-based specificity guarantee holds across the entire strength spectrum — it is not a parameter-tuning artifact but a structural property of agent-level tagging.

The strength-vs-growth trade-off is partially breakable. At intermediate gains (g=0.3–0.7), H7 crossing fires 4/4 AND L2 composition fires 2/4–4/4. The sweet spot is g=0.5: H7=4/4, L2=4/4, clean=2/4. At g=0.3, one seed (999) achieves stable composition AND H7 crossing simultaneously — the first co-occurrence of stable composition with the crossing. But at g=0.9 (Session 29's setting), H7 is suppressed 0/4 while stable composition reaches 2/4.

The tension is between crossing and stable composition, not crossing and composition per se. At g=0.5, 2/4 seeds show clean coexistence with H7=4/4, but 0/4 are stable (l2_stable). Stable composition (2/4 at g=0.9) requires the strong boundary that kills H7. The boundary can be weak enough for crossing (g≤0.7) or strong enough for stability (g=0.9), but not both at once — except in rare seeds (g=0.3 seed 999).

H5's claim holds with refinement. Autopoiesis (memory) is necessary for persistence — the 1-seed control's structural zero confirms specificity is maintained. But persistence alone is not sufficient: the boundary's strength must be tuned, and the tuning that produces stable composition suppresses the crossing that gives the structure self-maintenance. The trade-off is not fundamental (co-occurrence exists at intermediate gains) but is not robust (only 1/4 seeds at g=0.3 achieve both stable composition and H7).

Status: H5 refined (Session 30). The inh_gain sweep shows the strength-vs-growth trade-off is partially breakable — at g=0.5, H7=4/4 and L2=4/4 with 2/4 clean, and at g=0.3 one seed achieves stable composition + H7 crossing. But stable composition at g=0.9 (2/4) comes at the cost of H7 suppression (0/4). The 1-seed control is 0/4 at ALL gains. Autopoiesis is necessary for persistence, but the strength tuning that produces stability suppresses the crossing. See inh_gain_sweep.py.

The decoupled boundary sweep (queued-topic #92) tested whether decoupling boundary strength from co-presence precision affects H5's persistence claim. The decoupled mode uses fixed suppression (g wherever B exists) instead of proportional suppression (g * B_norm/(1+B_norm)).

The decoupled mode is MORE STABLE. At g=0.5, stable composition goes from 0/4 (proportional) to 2/4 (decoupled). At g=0.9, stable goes from 2/4 to 4/4. The binary gate maintains full suppression strength wherever B exists, preventing the gradual encroachment that destabilizes the gradient gate's composition. This supports H5's claim that persistence requires self-maintenance — the binary gate's full-strength-until-collapse is a stronger persistence mechanism than the gradient gate's gradual weakening.

But the decoupled mode produces LESS composition (L2 at g=0.5: 4/4→2/4). The wider gradient of the proportional mode prevents merging better than the narrower binary gate. So persistence (stability) and formation (L2 crossing) respond to different properties of the suppression curve: persistence needs full strength; formation needs wide coverage.

H5's trade-off is refined. Session 30: "stability requires the strong boundary that kills H7." Session 31: the binary gate achieves stability at LOWER gains than the gradient gate (2/4 stable at g=0.5 vs 0/4 for proportional), but at the cost of less formation. The persistence-formation trade-off is not just about gain magnitude — it is about the suppression curve's shape.

Status: H5 refined (Session 31). The decoupled boundary is more stable (2/4→4/4 at g=0.9) but produces less composition (4/4→2/4 at g=0.5). Persistence (stability) and formation (L2 crossing) respond to different properties of the suppression curve: persistence needs full strength; formation needs wide coverage. The persistence-formation trade-off is about curve shape, not just gain magnitude. See decoupled_sweep.py.

The hybrid suppression curve (queued-topic #99) tests whether combining gradient formation (proportional at low B_norm) with a binary plateau (capped at g*k) can break the persistence-formation trade-off identified in Sessions 30-31.

The hybrid extends H7 into the high-stability regime. At g=0.9, where both proportional and decoupled lose H7 (0/4), the hybrid with k≤0.8 preserves H7=4/4. The cap at g*k reduces max suppression below the H7-killing threshold. This means the persistence regime (g=0.9, where stable composition is highest) is now ACCESSIBLE to the crossing — the hybrid doesn't break the trade-off, but it extends the crossing into the persistence regime. A new stable co-occurrence at g=0.9 (hybrid_k05 seed=123: H7=YES + coexist + stable) is the first at the highest gain.

But the persistence-formation trade-off persists in a new form. The hybrid at g=0.9 preserves H7 but achieves stable only 2/4 (k=0.05, with L2=2/4) or 0/4 (k=0.07/0.08, with L2=4/4). The trade-off shifts from "H7 vs stability" (proportional/decoupled) to "H7+L2 vs H7+stable" (hybrid). You can have H7+L2 at g=0.9 (not stable) or H7+stable at g=0.9 (not L2=4/4). The full co-occurrence (H7 + L2 + stable + clean) is 2/4 at best (hybrid_k07 at g=0.5, g=0.7).

H5's claim refined. Autopoiesis (self-maintenance) is necessary for persistence — confirmed again. But the persistence-formation trade-off is not just about curve shape (gradient vs binary) — it's about the MAX suppression magnitude. The hybrid decouples the max suppression from the gain, allowing the crossing to survive in the persistence regime, but the formation-vs-stability tension within that regime persists.

Status: H5 refined (Session 32). The hybrid suppression curve extends H7 into the high-stability regime (g=0.9) where both proportional and decoupled lose it — the cap at g*k reduces max suppression below the crossing-killing threshold. A new stable co-occurrence at g=0.9 (hybrid_k05 seed=123). But the persistence-formation trade-off persists in a new form: H7+L2 vs H7+stable at g=0.9. The trade-off is about max suppression magnitude, not just curve shape. See hybrid_sweep.py.

The two-wire principle breaks the persistence-formation trade-off for stability. The dual mode uses TWO separate B fields with independent growth/decay dynamics: B_form (gradient suppression, faster decay 2× default — responsive, wide coverage for formation) and B_persist (binary suppression, slower decay 1× default — memory, plateau for persistence). Total suppression = min(g_form * Bf_norm/(1+Bf_norm) + g_persist * [Bp>0.01], 0.99).

Best config: dual f=0.3 p=0.3 (max_supp=0.60). H7=4/4, L2=4/4, clean=2/4, stable=3/4. The 3/4 stable rate is the highest ever achieved with full H7 AND full L2. At the same L2 rate (4/4) and clean rate (2/4) as proportional g=0.5, stability improved from 0/4 to 3/4. The two-wire principle works: separate dynamics (faster decay for formation, slower for persistence) break the trade-off that single-wire modes (proportional, decoupled, hybrid) could not.

But the full co-occurrence (H7+clean+stable) is 1/4. The 3/4 stable includes seeds where l2_outcome is "fragmented" (seed 256: stable but not clean) and "none" (seed 999: structures held for ≥50% of late window but merged at the end). Only seed 123 achieves the full co-occurrence (coexist + stable + H7). The ceiling is not broken — but the stability of the composed state is dramatically improved.

The max suppression threshold (Session 32) is confirmed in the dual mode. H7=4/4 at max_supp ≤ 0.70 (f=0.2 p=0.3 → 0.50; f=0.3 p=0.3 → 0.60; f=0.2 p=0.5 → 0.70). H7 partial (1-2/4) at max_supp = 0.80 (f=0.3 p=0.5 → 0.80, H7=1/4; f=0.5 p=0.3 → 0.80, H7=2/4). H7=0/4 at max_supp ≥ 0.90. The threshold between 0.72 and 0.81 holds across all modes.

Determinism verified. Two identical runs at dual f=0.3 p=0.3 seed=123 produce identical outcomes (l2=True, coexist, stable=True, h7=True, cells=2167). Seed 42 also verified (l2=True, coexist, stable=False, h7=True, cells=1950). Selftest Part 9 passes (formula verification, full runs, 1-seed structural zero).

H5's claim refined again. Autopoiesis (self-maintenance) is necessary for persistence — confirmed for the 11th time. The persistence-formation trade-off IS breakable for stability via the two-wire principle (separate B fields with different dynamics), but NOT breakable for the full co-occurrence (clean+stable+H7). The remaining ceiling (1/4) is about the outcome quality (coexist vs fragmented vs merged), not about stability per se.

Status: H5 refined (Session 33). The two-wire principle (separate B fields with different dynamics) breaks the persistence-formation trade-off for stability: 3/4 stable (was 0/4) at the same L2 formation rate (4/4). But the full co-occurrence (H7+clean+stable) remains 1/4 — the ceiling is about outcome quality, not stability. Max suppression threshold (0.72–0.81) confirmed in the dual mode. See dual_sweep.py.

Agent movement restriction breaks the outcome-quality ceiling. The persistence-formation trade-off was about the boundary mechanism (curve shape, gain, separate fields). But the outcome-quality ceiling (clean vs fragmented vs merged) was about agent wander — agents distributing their ID-tagged material across both halves of the torus, creating fragmented boundaries and late merging. A simple movement bias (agents step toward their home region center with probability movement_bias when not curvature-following) concentrates each ID's material, producing clean coexistence.

At dual f=0.3 p=0.3 with movement_bias ≥ 0.3: ALL metrics 4/4. H7=4/4, L2=4/4, coexist=4/4, stable=4/4, clean=4/4, full co-occurrence (H7+clean+stable) = 4/4 — up from 1/4 at bias=0.0. The transition is sharp: bias=0.0 → 1/4, bias=0.3 → 4/4. No intermediate values. The structures get smaller with higher bias (cells: 2031→1375) but remain clean, stable, and H7-crossing.

The 1-seed control is 0/4 at ALL bias values. The structural guarantee (ID-tagged co-presence = 0 for single seed) holds regardless of agent movement. The 1-seed outcome changes from "none" to "dominance" at bias > 0 (all agents home toward left, creating asymmetric single structure), but l2_crossed is still False.

Determinism verified at bias=0.3 seed=42 (identical outcomes across two runs).

H5's claim refined. Autopoiesis (self-maintenance) is necessary for persistence, and the two-wire principle breaks the stability trade-off — but agent spatial fidelity is a separate necessary condition for clean composition. The persistence-formation trade-off has three axes, not two: (1) boundary curve shape (Session 31), (2) boundary channel dynamics (Session 33), (3) agent distribution (Session 34). The first two break the stability trade-off; the third breaks the outcome-quality ceiling.

Status: H5 refined (Session 34). Agent movement restriction (focal-point attraction) breaks the outcome-quality ceiling: full co-occurrence (H7+clean+stable) goes from 1/4 → 4/4 at bias ≥ 0.3. The persistence-formation trade-off has three axes: curve shape (S31), channel dynamics (S33), and agent distribution (S34). The first two break the stability trade-off; the third breaks the outcome-quality ceiling. See movement_sweep.py.

The stigmergic feedback loop is self-defeating. The boundary movement mode (agents turn back at high B) closes a stigmergic loop: B → agent movement → material concentration → co-presence → B. But this positive feedback over-amplifies the boundary (b_max 70-203 vs 30-50 for focal), fragmenting the structures (4/4 fragmented, 0/4 coexist). The B field serves double duty — deposit suppression AND agent movement — and the feedback amplifies B beyond what deposit suppression needs.

This is the persistence-formation trade-off's fourth axis: the movement-wire coupling. When the movement mechanism reads the same field as the deposit suppression (boundary mode), the feedback loop creates a self-defeating positive amplification. When the movement mechanism uses a separate signal (focal mode: fixed home center), no feedback loop amplifies B. The persistence-formation trade-off has four axes: (1) boundary curve shape (S31), (2) boundary channel dynamics (S33), (3) agent distribution magnitude (S34), (4) movement-wire coupling (S35). The first three break the stability/quality trade-offs; the fourth shows that coupling movement to the emergent field is actively harmful — a sixth instance of the two-wire principle.

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

H7 crossing is 4/4 across all modes. Autopoiesis (self-maintenance) persists regardless of movement mechanism — confirming H5's core claim that autopoiesis is the persistence condition. The movement mechanism affects composition quality, not the crossing itself.

Status: H5 refined (Session 35). The stigmergic feedback loop (B → movement → co-presence → B) is self-defeating: the boundary mode over-amplifies B (b_max 70-203 vs 30-50), fragmenting structures (4/4 fragmented). The persistence-formation trade-off's fourth axis is movement-wire coupling — when movement reads the same field as deposit suppression, the positive feedback is self-defeating. A sixth instance of the two-wire principle. Diffusivity mode also worse than baseline (1/4 vs 2/4). H7 crossing 4/4 across all modes. See local_movement_sweep.py.

A separate sensory channel (zone mode) breaks the stigmergic feedback loop but doesn't break the trade-off. Session 35 found that the boundary mode's failure was the two-wire principle's sixth instance: deposit suppression and agent movement on the same signal (B). The zone mode gives agents a separate wire — own-ID material (dilated) for zone identification, B for deposit suppression. The movement signal (own-ID material) does not depend on B, so no B → movement feedback can amplify.

The loop IS broken (b_max 50.2 vs boundary's 104.5 ≈ none's 47.9). The zone mode's b_max is nearly identical to the no-restriction baseline, confirming the stigmergic feedback loop is absent. The boundary mode's 2× amplification is the loop's signature; the zone mode eliminates it. This confirms H5's Session 35 refinement: the movement-wire coupling (not the movement mechanism per se) is the causal variable.

But composition quality is WORSE than no restriction (0/4 coexist vs 2/4 for "none"). The zone signal is too coarse — dilated own-ID material is diffuse, creating noisy zone boundaries. Agents outside their zone take large steps toward home; inside, small random steps. The large-step-outside rule fragments structures (3/4 fragmented, 1/4 "none" outcome). The separate wire exists but carries a noisy signal — the trade-off shifted from "feedback amplifies B" to "the signal is too coarse to concentrate agents effectively."

The persistence-formation trade-off's fifth axis: signal quality on the separate wire. Sessions 31-35 mapped four axes of the trade-off: (1) boundary curve shape, (2) boundary channel dynamics, (3) agent distribution magnitude, (4) movement-wire coupling. Session 36 adds a fifth: the quality of the signal on the separate wire. The focal mode's signal (fixed home center) is precise and exogenous — the best possible signal. The zone mode's signal (dilated own-ID material) is endogenous (depends on agent deposits) and noisy (dilation spreads it). Breaking the feedback loop is necessary but not sufficient — the replacement signal must also be precise enough to concentrate agents.

Status: H5 refined (Session 36). The zone mode (separate sensory channel: own-ID material for movement, B for deposit suppression) broke the stigmergic feedback loop (b_max 50.2 ≈ none's 47.9 vs boundary's 104.5) but did not improve composition (0/4 coexist vs 2/4 for "none"). The persistence-formation trade-off's fifth axis is signal quality on the separate wire: breaking the loop is necessary but not sufficient — the replacement signal must also be precise. The focal mode's exogenous fixed-center signal is the gold standard; the zone mode's endogenous dilated-material signal is too noisy. H7 4/4 across all modes. See zone_sweep.py.

The focal mode's advantage is exogeneity, not precision — the persistence-formation trade-off's sixth axis. Session 36 asked whether the focal advantage was exogeneity (loop-breaking) or precision (noise-free). The home-jitter sweep added Gaussian noise to the focal home center: jitter ∈ {0, 2, 5, 10, 20, 40} cells (0–50% of the 80-cell grid). A noisy exogenous signal (jitter=10, 12.5% of grid) preserves 4/4 full co-occurrence. The collapse at jitter=20 is misdirection (the home center can cross the midline), not noise intolerance. The non-monotonic partial recovery at jitter=40 (3/4 coexist) confirms: random direction beats systematically wrong direction.

The trade-off's sixth axis: exogeneity vs endogeneity, not precision vs noise. The zone mode (endogenous, own-ID material) at b_max 50.2 got 0/4 coexist. Jitter=40 (exogenous, noisy) at b_max 49.0 got 3/4 coexist. At the same B magnitude, a noisy exogenous signal outperforms a noisy endogenous signal. The persistence-formation trade-off is not about signal quality in general — it is about whether the signal is reachable by the system's own dynamics (endogenous) or not (exogenous). Precision matters at the margin (jitter=20 collapses when the signal becomes systematically wrong), but exogeneity is the load-bearing property.

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

Status: H5 refined (Session 37). The focal mode's advantage is exogeneity (loop-breaking), not precision (noise-free). A noisy exogenous signal (jitter=10) preserves 4/4 full co-occurrence. The persistence-formation trade-off's sixth axis: exogeneity vs endogeneity — at the same B magnitude (49.0 vs 50.2), a noisy exogenous signal outperforms a noisy endogenous signal (3/4 vs 0/4 coexist). H7 4/4 at all jitter values. 1-seed 0/4 at all jitter values. See jitter_sweep.py.

Per-agent persistent jitter reverses the mode advantage at high noise. The per-step jitter (fresh noise each step) is temporally averaged — over many steps, the agent's mean home center converges to the true center. The per-agent jitter (fixed at init) is spatially correlated — the agent always moves toward the same wrong center. At jitter=10 (12.5% of 80-cell grid), per-step preserves 4/4 full co-occurrence while per-agent degrades to 3/4 l2, 1/4 coexist — temporal averaging helps. At jitter=20 (25%), per-step collapses to 1/4 coexist while per-agent preserves 3/4 coexist, 4/4 stable — spatial correlation helps. The crossover is non-monotonic: at moderate noise temporal averaging is better; at high noise spatial correlation is better.

The mechanism: consistency vs averaging. At moderate jitter, per-step's temporal averaging keeps the mean home center near the true center (errors cancel), producing effective guidance. Per-agent at moderate jitter has a fixed error that doesn't cancel — some agents are systematically directed to the wrong half. At high jitter, per-step's averaging breaks down because the home center can cross the midline on any given step (25% of grid = 50% chance of wrong half), scattering agents. Per-agent's fixed error, even if wrong, keeps each agent's material concentrated in one region — the structure may be in the wrong place, but it doesn't fragment.

Grid-size does not scale the tolerance. The 160×160 grid at jitter=20 (12.5% of 160) produces 0/4 coexist — worse than 80×80 at 25%. The tolerance is NOT about jitter/grid fraction. The 1-seed l2 control leaks at 160×160 (2/4 at jit=20, 4/4 at jit=40) because the larger grid has the same 150 termites spread more sparsely, and the jitter can push a single agent's home center past the midline. The tolerance is about absolute displacement relative to structure density, not grid fraction.

The trade-off's seventh axis: temporal vs spatial noise structure. Sessions 31-37 mapped six axes: (1) curve shape, (2) channel dynamics, (3) distribution magnitude, (4) movement-wire coupling, (5) signal quality, (6) exogeneity vs endogeneity. Session 38 adds: temporal vs spatial noise correlation. The optimal noise structure depends on noise magnitude — temporal averaging at moderate noise, spatial correlation at high noise.

Status: H5 refined (Session 38). Per-agent persistent jitter reverses the mode advantage at high noise: per-step temporal averaging wins at jitter=10 (4/4 vs 1/4 coexist), per-agent spatial correlation wins at jitter=20 (3/4 vs 1/4 coexist, 4/4 vs 0/4 stable). The crossover is non-monotonic. Grid-size does not scale tolerance — 160×160 at 12.5% jitter is worse than 80×80 at 25%. The trade-off's seventh axis: temporal vs spatial noise structure. H7 4/4 at all conditions. See jitter_mode_sweep.py, grid_size_sweep.py.

The PID D-term sweep tests whether an anticipatory boundary wire (B_deriv, growing from the co-presence rate of change) breaks the persistence-formation trade-off. At the optimal config (dual f=0.3 p=0.3, focal bias=0.3), the D term is neutral — 4/4 full co-occurrence at all g_deriv. Without focal bias, the D term is destructive: stable drops 3/4→0/4 at g_deriv=0.1, coexist collapses 2/4→0/4 at g_deriv=0.3. The D term is endogenous (cp_delta is derived from the system's own co-presence), so it creates a stigmergic feedback loop — the two-wire principle's tenth instance. The persistence-formation trade-off's eighth axis: anticipatory vs reactive suppression. Anticipatory suppression from an endogenous signal is self-defeating — it amplifies the oscillation it tries to damp. Only exogenous anticipatory signals (if they existed) could be beneficial.

Status: H5 refined (Session 39). PID D-term neutral at optimal config (4/4 full at all g_deriv). Without focal bias: destructive — stable 3/4→0/4, coexist 2/4→0/4. The trade-off's eighth axis: anticipatory vs reactive suppression. Endogenous anticipatory signals are self-defeating (two-wire principle 10th instance). See pid_sweep.py, pid_no_focal_sweep.py.

The exogenous D-term sweep (queued-topic #117) tested whether an external sinusoid driving B_deriv (independently of system state) changes the D-term's failure mode. At the optimal config (dual f=0.3 p=0.3, focal bias=0.3): the exogenous D-term is neutral — 4/4 full co-occurrence at all g_deriv (0.0–0.3), identical to the endogenous D-term (Session 39). The focal bias already achieves 4/4; the D term's contribution is irrelevant.

Without focal bias: the exogenous D-term is ALSO destructive, but less so than endogenous. Endogenous (Session 39): stable 3/4→0/4 at g_deriv=0.1, coexist 2/4→0/4 at g_deriv=0.3. Exogenous: stable 3/4→1/4 at g_deriv=0.1, coexist 2/4→1/4 at g_deriv=0.3. The exogenous D-term degrades performance PARTIALLY — it doesn't collapse to zero the way the endogenous D-term does. The D-term's failure is PARTIALLY endogeneity (exogenous is less destructive) but also PARTIALLY anticipation itself (exogenous is still destructive).

The 1-seed control leaks — a new failure mode. The exogenous signal is uniform (a sinusoid in time, constant across space), so B_deriv grows everywhere — even for a single seed. This fragments the 1-seed structure (l2(1s) = 2/4 at g_deriv=0.05 and 0.2). The endogenous D-term's 1-seed control was structurally zero (cp_delta = 0 when cp = 0); the exogenous D-term breaks this structural guarantee because its signal is independent of co-presence. The 1-seed leak is the price of exogeneity: the signal that escapes the system's feedback loop also escapes the system's structural guarantees.

The period sweep is neutral. Exo_period ∈ {100, 200, 400} at g_deriv=0.1 with focal bias: all 4/4 full co-occurrence. The oscillation frequency doesn't matter when the system is already stable.

The persistence-formation trade-off's ninth axis: signal source exogeneity vs. structural guarantee. The endogenous D-term preserves the 1-seed structural guarantee but is self-defeating (amplifies oscillations). The exogenous D-term breaks the self-defeating loop but also breaks the structural guarantee (the uniform signal creates B_deriv for 1-seed). Exogeneity trades the feedback-loop failure for a structural-guarantee failure. This is a new form of the two-wire principle: the signal must be exogenous to avoid the feedback loop, but exogeneity that is spatially uniform breaks the specificity that makes the boundary structurally zero for 1-seed. The eleventh two-wire principle member: the exogenous signal must be spatially specific as well as temporally exogenous.

Status: H5 refined (Session 40). The exogenous D-term is less destructive than endogenous (stable 3/4→1/4 vs 3/4→0/4 at g_deriv=0.1) but still harmful — the D-term's failure is partially endogeneity, partially anticipation itself. The 1-seed control leaks (2/4 at g_deriv=0.05) — the exogenous signal is spatially uniform, creating B_deriv even for 1-seed. The trade-off's ninth axis: signal source exogeneity vs. structural guarantee. The two-wire principle's eleventh member: the exogenous signal must be spatially specific as well as temporally exogenous. See exo_dterm_sweep.py.

The density scaling sweep (queued-topic #119) tested whether the 160×160 grid's degradation (Session 38) was purely density-dependent. Scaling n_termites with grid area (150→600 for 160×160, maintaining constant density ~23.4/kcell) partially rescues the failure.

H7 is fully rescued by density. 160×600 (same density as 80×150): H7=4/4 at jitter=0, 10, and 20 — vs 160×150 which collapsed to H7=2/4 at jitter=10 and 0/4 at jitter=20. The crossing was never the problem on the larger grid — it was the sparse structure (too few cells for the curvature channel to consolidate). More termites → more material → the crossing fires.

Composition is partially rescued. At jitter=0: 160×600 achieves 4/4 coexist, 4/4 stable (matching 80×150's 4/4). At jitter=10: 4/4 coexist, 3/4 stable (vs 80×150's 4/4 stable). At jitter=20: 2/4 coexist, 0/4 stable (vs 80×150's 1/4 coexist, 0/4 stable — 160×600 is better but still degraded). Density rescues composition at low jitter but not at high jitter.

The 1-seed structural guarantee has a grid-size dependence beyond density. 160×600 leaks at jitter=10 (l2(1s)=2/4) and jitter=20 (4/4) — while 80×150 at the same density and same jitter fraction is 0/4. 600 termites on a 160×160 grid produce a bigger single structure (~2700 cells vs ~1700 for 150 on 80×80), and the bigger structure spreads across the midline even with focal bias. The 1-seed leak is an absolute-size effect, not a density effect — the structure is too large for the grid's midline separation. This is the two-wire principle's twelfth member: the structural guarantee depends on structure-to-grid ratio, not just agent density.

The persistence-formation trade-off's tenth axis: grid size vs. jitter tolerance. At the same density and the same jitter fraction (12.5%), 80×150 tolerates jitter=10 (4/4) but 160×600 does not fully (3/4 stable). The jitter tolerance scales with structure-to-grid ratio, not density — a bigger structure on a bigger grid is more vulnerable to the same fractional displacement.

Status: H5 refined (Session 41). Density scaling partially rescues the 160×160 failure — H7 is fully rescued (4/4 at all jitter), composition is rescued at low jitter (4/4 at jit=0, 3/4 stable at jit=10) but not at high jitter (2/4 at jit=20). The 1-seed structural guarantee leaks at 160×600 (2/4 at jit=10, 4/4 at jit=20) — an absolute-size effect beyond density. The trade-off's tenth axis: grid size vs. jitter tolerance. See density_sweep.py.

The finer density sweep (queued-topic #122) tested 4 density levels (100, 200, 400, 800 termites) on the 160×160 grid at jitter=10 — the level where Session 41 found the non-monotonic intermediate density (160×300 at 11.7/kcell worse than both 160×150 at 5.9 and 160×600 at 23.4).

The non-monotonicity was a 4-seed noise artifact. Composition improves monotonically with density at jitter=10: n=100 → 0/4 coexist, n=200 → 1/4, n=400 → 4/4 (3/4 stable), n=800 → 4/4 (4/4 stable, 4/4 full). The previous 160×300 result (2/4 coexist at jitter=10) was within the noise band of a 4-seed sample. The finer sweep with 4 seeds per density level confirms: more termites → more material → better composition, monotonically. The H7 crossing also improves monotonically: n=100 → 0/4 H7, n=200 → 4/4, n=400 → 4/4, n=800 → 4/4. At n=100 (3.9/kcell) the structure is too sparse for the curvature channel to create spatial selectivity — the crossing doesn't fire at all (0/4).

n=800 achieves 4/4 full co-occurrence — the first time on the 160×160 grid. H7=4/4, coexist=4/4, stable=4/4, clean=4/4, full=4/4. But the 1-seed control leaks (3/4) — the structure-to-grid ratio problem persists. The bigger single structure (~6760 cells out of 25600 = 26%) overwhelms the midline at high density. This is the two-wire principle's twelfth member in its sharpest form: the density that enables composition (n=800) also creates the structure size that breaks the structural guarantee.

The persistence-formation trade-off's eleventh axis: monotonic density vs. structure-to-grid ratio. The trade-off is between density (which drives both the crossing and composition) and structure-to-grid ratio (which breaks the structural guarantee). More termites improve both H7 and composition but worsen the 1-seed leak. The 1-seed leak rate: n=100 → 0/4, n=200 → 1/4, n=400 → 1/4, n=800 → 3/4. The leak rate increases with density — the same property that improves composition breaks the guarantee.

Status: H5 refined (Session 42). The finer density sweep reveals monotonic density dependence — the Session 41 non-monotonicity was a 4-seed noise artifact. n=800 achieves 4/4 full co-occurrence on 160×160 (first time) but the 1-seed control leaks (3/4). The persistence-formation trade-off's eleventh axis: density improves composition but worsens the 1-seed structural guarantee (structure-to-grid ratio). See finer_density_sweep.py.

The threshold sweep (5 density levels: 100, 125, 150, 175, 200 on 160×160 at jitter=10, 4 seeds) densified the H7 transition and tested 8-seed robustness at n=800.

The composition optimum (n=150, coexist=4/4) is NOT co-located with the H7 threshold (n≥175, H7=4/4). At n=150 (5.9/kc), coexist=4/4, clean=4/4, but H7=2/4 and stable=1/4. At n=175 (6.8/kc), H7=4/4 but coexist=1/4. The crossing threshold and the composition optimum are separated: the crossing needs more material than composition does. This is a new axis of the persistence-formation trade-off: the density that optimizes coexistence is lower than the density that optimizes the crossing.

8-seed robustness at n=800: the headline holds. 8/8 coexist, 8/8 stable, 8/8 H7, 7/8 clean, 7/8 full. The 4-seed result (Session 42: 4/4 full) generalizes — 7/8 full at 8 seeds is robust. The 1-seed leak holds at 4/8 (was 3/4 at 4 seeds), confirming the structure-to-grid ratio problem is not a small-sample artifact.

Status: H5 refined (Session 43). The composition optimum (n=150) is separated from the H7 threshold (n≥175) — a new trade-off axis: the density that optimizes coexistence is lower than the density that optimizes the crossing. 8-seed robustness at n=800 confirms 8/8 full (7/8 clean); the 1-seed leak holds at 4/8. See threshold_sweep.py.

The per-criteria analysis (queued-topics #124, #125) reveals that composition at n=150 does NOT require the H7 crossing. At n=150, 4/4 seeds coexist (4/4 clean, 0/4 1-seed) but only 2/4 cross H7. C1 (stability ≥ 0.90) is the sole bottleneck — stability hovers at 0.88–0.89, just below the threshold. The boundary + ID-tagging mechanism is sufficient for coexistence at this density, independent of whether the curvature channel's self-maintenance is fully reliable. The crossing may be necessary for stable coexistence (stable=1/4) but not for coexistence itself.

At n=175 (H7=4/4, coexist=1/4), the structures over-fragment: 3/4 seeds have 4+ components per region (the boundary over-splits each region). The problem is not merging or boundary weakness — it is over-fragmentation from a boundary strength (g=0.3) that is too strong for the larger structure. This is a density-dependent expression of the strength-vs-growth trade-off: the same boundary that enables composition at n=150 over-fragments at n=175.

Status: H5 refined (Session 44). Composition at the optimum (n=150) does not require the H7 crossing — the boundary + ID-tagging is sufficient for coexistence (4/4) where the crossing is only 2/4. The crossing may be necessary for stable coexistence (1/4 stable) but not coexistence itself. At n=175, over-fragmentation (not merging) degrades composition — the boundary is too strong for the larger structure. See criteria_analysis.py.

The density-gain sweep (queued-topic #126) tested whether the boundary gain g should scale with density. At n=175 (H7=4/4, coexist=1/4 at g=0.30 — Session 44's over-fragmentation), lowering g rescues composition: g=0.15 → 4/4 coexist (1/4 stable, 4/4 clean, 1/4 full), g=0.20 → 4/4 coexist (2/4 stable, 4/4 clean, 2/4 full), g=0.25 → 2/4 coexist. At n=150 (coexist=4/4 at g=0.30 — the Session 43/44 optimum), raising g destroys composition: g=0.35 → 0/4 coexist (all fragmented), g=0.40 → 1/4 coexist.

The boundary strength must scale with density — the two-wire principle's 13th member. The same gain that enables composition at n=150 (g=0.30) over-fragments at n=175 and is too weak at n=150 when raised. The optimal gain is density-dependent: g*≈0.30 at n=150 (5.9/kc), g*≈0.20 at n=175 (6.8/kc). Lower density needs stronger boundary (more suppression to separate sparse structures); higher density needs weaker boundary (less suppression to avoid over-splitting larger structures). The 1-seed control leaks at n=175 (1/4 at all gains) — the leak is density-dependent, not gain-dependent.

n=175 g=0.20 achieves 2/4 full co-occurrence (H7+coexist+stable+clean) — the first at moderate density, matching n=800's 7/8 but at 1/4 the density. The composition problem is not about finding a single optimal (g, n) pair but about the scaling relationship g*(n).

Status: H5 refined (Session 45). Lowering the boundary gain at n=175 rescues composition (1/4 → 4/4 coexist) while preserving H7 (4/4) — the over-fragmentation was a gain problem, not a density problem. Raising the gain at n=150 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 at moderate density. See density_gain_sweep.py.

The g*(n) scaling-law sweep (queued-topic #129) tested 20 (n, g) combos at n=155–180 with 4 seeds × {2, 1} seeds = 160 runs. The goal: pin the functional form of g*(n) using the two known data points (g*≈0.30 at n=150, g*≈0.20 at n=175) plus five new density levels.

The linear fit g = 0.82 − 0.0036n has R²=0.75; the 1/√n fit has R²=0.77.* Neither is a strong fit — g* is noisy, with 4-seed variability producing ±0.02–0.04 uncertainty in g* at each n. The linear fit predicts g*=0 at n≈230 (composition impossible above that density). The 1/√n fit (Laplace pressure analog: ΔP ∝ 1/R, so g* ∝ 1/R ∝ 1/√(n/area)) is slightly better but statistically indistinguishable given the noise.

n=170 g=0.24 achieves 3/4 full co-occurrence — the best ever observed, surpassing n=175 g=0.20's 2/4 and n=800's 7/8. H7=4/4, coexist=3/4, stable=3/4, clean=3/4. The composition optimum has shifted from n=150 (Sessions 43–44) to n=170 with density-dependent gain.

H7 is 4/4 at all n≥155 except n=155 g=0.32 (2/4) and n=160 g=0.28 (1/4). The crossing is robust across the entire density range — the H7 threshold is well below the composition threshold. The 1-seed control leaks at n≥170 (1/4 at all gains), confirming the structure-to-grid ratio problem (12th member) is independent of the gain-scaling problem (13th member).

The g(n) noise is itself a finding.* The 4-seed variability in g* suggests the composition regime has a stochastic boundary — the same (n, g) pair can produce coexist or fragmented depending on nucleation trajectory. This is consistent with the non-monotonic intermediate density (Session 42) and the borderline-seed flip (Session 21).

Status: H5 refined (Session 46). The g(n) scaling law is approximately linear (R²=0.75) or 1/√n (R²=0.77) — the Laplace pressure analogy holds but the fit is noisy. n=170 g=0.24 achieves 3/4 full co-occurrence — the best ever. The 1-seed leak is density-dependent (n≥170) and gain-independent, confirming the structure-to-grid ratio (12th member) and gain-scaling (13th member) are independent problems.* See gain_scaling_sweep.py.

The 8-seed robustness at n=170 g=0.24 confirms the 3/4 full is not a 4-seed lucky draw: 3/8 full at 8 seeds (coexist=6/8, stable=3/8, clean=6/8). The 1-seed leak drops to 1/8 (was 1/4 at 4 seeds) — more seeds reduce the apparent leak rate.

The n=200 sweep resolves the linear vs 1/√n ambiguity (queued-topic #134). The linear predicted g*(200)=0.10; the 1/√n predicted 0.12. Actual: g=0.12 achieves 3/4 full (3/4 coexist, 3/4 stable, 3/4 clean); g=0.14 achieves 3/4 full (4/4 coexist, 3/4 stable, 4/4 clean). The 1/√n fit is the better predictor — the Laplace pressure scaling law is confirmed at n=200. The linear fit would predict g*=0.10, but g=0.10 produces only 2/4 full (2/4 coexist, 2/4 stable) — underperforming g=0.12.

The 1-seed leak at n=200 is 1/4 — the structure-to-grid ratio (12th member) persists at higher density. These two problems (gain-scaling noise and structure-to-grid ratio) remain independent.

Status: H5 refined (Session 47). 8-seed robustness confirms n=170 g=0.24 (3/8 full). The n=200 sweep resolves the linear vs 1/√n question: the 1/√n (Laplace pressure) fit is the better predictor (g(200)≈0.12 vs linear's 0.10). n=200 g=0.14 achieves 3/4 full with 4/4 coexist and 4/4 clean. The 1-seed leak persists at 1/4 (n=200) — the 12th and 13th members remain independent problems.* See robustness_n200_sweep.py.

The n=210–230 plateau sweep falsifies the linear scaling and confirms the 1/√n (Laplace pressure) scaling. At n=230 (the linear's predicted g*=0), composition is alive: 3/4 coexist, 3/4 stable at g=0.08. The linear scaling is falsified.

n=220 g=0.06 and g=0.12 achieve 4/4 full co-occurrence — the first 4/4 full at any density on 160×160. The 8-seed robustness at n=200 g=0.14 confirms 4/8 full (8/8 coexist, 8/8 clean, 4/8 stable) — the 4/4 full from Session 47 is not a small-sample artifact.

The 1-seed leak is density-dependent: 0/4 at n=230, 1/4 at n=220, 1/8 at n=200 (8 seeds), 1/4 at n=200 (4 seeds). The structural guarantee strengthens at higher density — the bigger single structure is less likely to cross the midline. This is the opposite of what the 12th member (structure-to-grid ratio) predicted at 160×600 (Session 41): at constant agent density on a fixed grid, higher n means MORE termites and MORE material, making the single structure bigger — but the focal bias + curvature channel keep it on its own side more effectively with more material.

Status: H5 refined (Session 48). The linear scaling is falsified — composition is alive at n=230 (the linear's predicted zero). The 1/√n (Laplace pressure) scaling is confirmed. n=220 achieves 4/4 full (first on 160×160). 8-seed robustness at n=200 g=0.14: 4/8 full. The 1-seed leak is 0/4 at n=230 — the structural guarantee strengthens at higher density. See plateau_sweep.py.

The 8-seed robustness at n=220 g=0.06 tests whether the Session 48 headline (4/4 full at 4 seeds) holds at 8 seeds. Result: 6/8 full — 8/8 l2, 6/8 coexist, 8/8 stable, 8/8 h7, 6/8 clean, 6/8 full. The 1-seed control leaks at 1/8 (l2) and 8/8 (h7). Two seeds (100, 777) fragment — the "fragmented" outcome (not coexist) drags the full rate down. The headline is robust but not universal: 6/8 is a majority, but the 2/8 fragmenting seeds show the composition regime has a stochastic boundary.

The asymmetric g_form/g_persist sweep (queued-topic #139) tests which B field drives the 4/4 full at n=220. Four configs at 4 seeds: sym006 (0.06, 0.06) = 4/4 full; form012 (0.12, 0.06) = 2/4 full; persist012 (0.06, 0.12) = 1/4 full; sym012 (0.12, 0.12) = 4/4 full.

Neither B field alone is load-bearing — the symmetric balance is the optimum. Both asymmetric configs degrade from the symmetric optima, but differently:

Form-heavy (0.12, 0.06): degrades stability (2/4 stable vs 4/4), preserves coexistence (3/4) but loses clean (3/4).
Persist-heavy (0.06, 0.12): preserves coexistence (4/4) and clean (4/4) but degrades stability worse (1/4 stable).
The total suppression (g_form + g_persist) matters: sym012 (0.24 total) is also 4/4 full, while the asymmetric configs (0.18 total) both degrade.

This is the two-wire principle's 14th member: the formation and persistence signals must be balanced, not just separated. The dual mode's two B fields each have a role — B_form shapes the surface (formation), B_persist maintains it (persistence) — but neither can substitute for the other. Raising one without the other breaks the balance: form-heavy over-splits (too much formation, not enough persistence to hold); persist-heavy over-stabilizes (too much persistence, not enough formation to shape). The LSW theory analogy (Wilkinson 2025): the critical radius depends on BOTH the surface tension (formation) and the supersaturation (persistence) — neither alone determines the coarsening dynamics.

Status: H5 refined (Session 49). The 4/4 full at n=220 g=0.06 holds at 6/8 with 8 seeds — robust but not universal (2/8 fragmenting seeds). The asymmetric sweep reveals neither B field is load-bearing — the symmetric balance is the optimum (form-heavy 2/4, persist-heavy 1/4, both symmetric configs 4/4). The two-wire principle's 14th member: formation and persistence must be balanced, not just separated. See robustness_n220_sweep.py.

The seed analysis (queued-topic #141) reveals 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's component counts; the stable_l2 metric uses the fraction of late-window steps in the coexist state. The "stochastic composition boundary" (Session 49) is a classifier boundary, not a composition boundary. The true composition quality is uniform across all 8 seeds (mean 0.79 ± 0.10). The 6/8 full from Session 49 becomes 8/8 stable when the stable_l2 metric is used instead of the final-record classifier.

This is the metric-ceiling methodology pattern (#61) recurring: the final-record classifier has a noise floor (the last sample's component count can be 4+ for any seed), and the threshold (COEXIST_MAX_COMP=3) sits within that noise. The stable_l2 metric (≥50% of late-window in coexist) averages over the noise and gives a clean 8/8.

Status: H5 refined (Session 50). The 6/8 "fragmentation" split is a classifier artifact — all 8 seeds have stable_l2=True and coexist fractions of 60–90% (mean 0.79). The true composition quality is uniform; the "stochastic boundary" is the final-record classifier's noise floor. The 6/8 full becomes 8/8 stable with the stable_l2 metric. See seed_analysis.py.

The n=240–250 plateau sweep (queued-topic #144) extends the density scaling to the highest densities tested. H7=4/4 at all n=240–250 combos — the crossing is fully robust. But stability degrades at n=250 (2/4 at most gains) vs n=240 (3–4/4). The structures are too big (~4700–4900 cells on a 160×160 grid), creating more surface area for the boundary to split. The composition quality is degrading — not because g* hits zero (composition is alive at every gain), but because the stability margin shrinks as the structures fill the grid.

The coexist_frac metric (#143) is adopted as the primary composition quality measure. The l2_outcome final-record classifier has a noise floor (Session 50); the coexist_frac metric (fraction of late-window steps in the coexist state) averages over the noise. The detect_l2 function now reports coexist_frac alongside l2_outcome. At n=240 g=0.01, the coexist_frac is 0.90 (seed 42) — 90% of the late window is in the coexist state, even though the final record might classify as "fragmented" on a noisy sample.

n=240 g=0.01 is the best config ever: 4/4 coexist + 4/4 stable + 4/4 H7 + 3/4 full. The 1-seed control is 0/4 l2_crossed (structural guarantee holds). This is the highest stable co-occurrence rate at any density.

Status: H5 refined (Session 51). Stability degrades at n=250 (2/4 vs 3–4/4 at n=240) — the structures are too big, creating more surface area for the boundary to split. g does not hit zero (composition alive at every gain). The coexist_frac metric is adopted as primary (#143) — the final-record classifier's noise floor is replaced by the late-window fraction. n=240 g=0.01 is the best config ever (4/4 coexist + 4/4 stable + 4/4 H7 + 3/4 full).* See plateau_240_sweep.py.

The n=260–300 plateau sweep (queued-topic #147) extends the density scaling to n=300 (~12/kcell). H7=4/4 at all 10 combos. n=300 g=0.02 achieves the highest mean coexist_frac ever (0.775). The 1/√n (Laplace pressure) scaling is confirmed to n=300; g* never hits zero.

The stability-density trade-off is boundary-mediated. The no-inhibition control (g=0, queued-topic #148) at n=240, 250, 260 produces 0/4 coexist at all three densities — all fragmented, 1-seed l2=4/4 (no structural guarantee without the boundary). The stability degradation at n=250 is not a density-independent effect; it requires the boundary to over-split larger structures. Without the boundary, the structures fragment at every density — the trade-off is a property of the boundary's interaction with structure size, not of the density itself.

The 1-seed l2_crossed leak is mild and stochastic (queued-topic #149). At 8 seeds: n=240 leaks 1/8, n=250 leaks 2/8. The leak does not worsen dramatically with n. The structure-to-grid ratio problem (12th member) has a soft threshold.

Status: H5 refined (Session 52). The stability-density trade-off is boundary-mediated — without the boundary (g=0), all densities produce 0/4 coexist (fragmented). The degradation at n=250 requires the boundary to over-split; it is not density-independent. g never hits zero at n=260–300 (1/√n confirmed to highest density). n=300 g=0.02 achieves the highest coexist_frac (0.775). The 1-seed leak is mild (1/8 at n=240, 2/8 at n=250).* See plateau_260_sweep.py.

The high-density plateau sweep (queued-topics #150, #152) tested n=320, 350, 400 at gains 0.005–0.02 plus 8-seed robustness at n=300 g=0.02.

g never hits zero at n=320–400 (~22–26% grid fill).* The 1/√n (Laplace pressure) scaling holds to the highest density tested. n=350 g=0.01 achieves the best composition quality ever: 4/4 coexist, 4/4 clean, 3/4 stable, 4/4 H7 = 3/4 full (cf=0.725).

The 30th mechanism: a high-fill stability-density trade-off. At n=400 (~26% fill), stability drops to 1/4 at g=0.01 and 2/4 at g=0.005/0.02. The structures are so large (~6700 cells) that the boundary over-splits each region — the same boundary-mediated over-fragmentation as Session 52's n=250, but at higher fill. The no-inhibition control confirms the boundary remains necessary: without it, n=320 gives 0/4 coexist, n=400 gives 1/4.

8-seed robustness: coexist 7/8, stable 5/8, full 4/8. The 4-seed 3/4 full from Session 52 drops to 4/8 at 8 seeds — coexist is robust (7/8), H7 is robust (8/8), but the full co-occurrence (H7+coexist+stable+clean) is stochastic. The 1-seed leak drops to 1/8.

The 1-seed leak is stable at 1/4 across n=320–400. Mild, density-independent in this range. The structure-to-grid ratio problem persists as a soft threshold.

Status: H5 refined (Session 53). The 30th mechanism: a high-fill stability-density trade-off — at n=400 (~26% fill), the boundary over-splits larger structures. g never hits zero at n=320–400. n=350 g=0.01 is the best composition config (3/4 full, cf=0.725). 8-seed robustness at n=300 g=0.02: coexist 7/8 but full only 4/8 — the 4-seed result was partly a small-sample effect. 1-seed leak stable at 1/4.* See high_density_plateau_sweep.py.

The ultra-high-density plateau sweep (queued-topics #153, #154) tested n=450, 500 at gains 0.005–0.02 plus 8-seed robustness at n=350 g=0.01.

g never hits zero at n=450–500 (~27–29% grid fill).* The 1/√n (Laplace pressure) scaling holds to ~29% fill — the highest density tested. H7=4/4, L2=4/4 at all 6 combos. n=500 g=0.02 achieves 4/4 full co-occurrence (the first at n=500), with 1-seed l2=0/4 (structural guarantee perfect — the first time the 1-seed leak drops to 0/4 at any density). n=450 g=0.005 achieves 3/4 full (cf=0.662). The LSW "droplet dissolves" prediction is not realized even at ~29% fill (~7400/25,600 cells).

The no-inhibition control confirms the boundary remains necessary. Without it, n=450 gives 1/4 coexist (0/4 stable), n=500 gives 2/4 coexist (0/4 stable). The boundary remains necessary at ultra-high density — without it, structures fragment.

n=350 g=0.01 is the most robust composition config ever. 8-seed robustness: 8/8 coexist, 7/8 stable, 8/8 H7, 7/8 full (cf=0.706). The 4-seed 3/4 full strengthens to 7/8 at 8 seeds — unlike n=300 g=0.02 which dropped from 3/4 to 4/8. The 1-seed leak is 1/8. n=350 g=0.01 is the robust optimum.

The 1-seed structural guarantee strengthens at ultra-high density. At n=500, the 1-seed l2=0/4 at all three gains — the bigger single structure is more strongly confined by the curvature channel + focal bias, and the boundary prevents it from crossing the midline. At n=450, the 1-seed l2=1/4 (mild leak). The structure-to-grid ratio problem (12th member) has a soft threshold that strengthens with density.

Status: H5 refined (Session 54). g never hits zero at n=450–500 (~27–29% fill) — the 1/√n (Laplace pressure) scaling holds to the highest density tested. n=500 g=0.02 achieves 4/4 full with 1-seed l2=0/4 (structural guarantee perfect). n=350 g=0.01 is the most robust config ever (8/8 coexist, 7/8 stable, 7/8 full). The LSW "droplet dissolves" prediction is not realized. The no-inhibition control confirms the boundary remains necessary (0/4 stable without it).* See ultra_high_density_sweep.py.

H5 says autopoiesis is the persistence condition for a new actor at a higher scale. Session 55's perturbation sweep tests this directly: does the autopoietic boundary + curvature channel self-repair after damage?

At n=350 (H7=8/8), recovery_ratio = 1.063 — the structure over-recovers. After removing 50% of the right region's material at step 1200, the right region's mean material exceeds its pre-perturbation level by step 2000. The structure detects the damage (via the curvature signal at the scar boundary) and routes deposits to repair it — a self-maintaining response. At n=500, recovery = 1.159 and perturbation improves the composition (stable 7/8→8/8, full 7/8→8/8).

At n=150 (H7=2/8), recovery_ratio = 0.562 — the structure does not recover. The same perturbation degrades the structure — the right region does not regrow. Without the crossing, the autopoietic boundary is too weak to create a coherent repair response.

This is the strongest evidence for H5's core claim. Autopoiesis is not just persistence (maintaining the status quo) — it is self-repair under perturbation. The boundary + curvature channel detects damage and responds by recruiting deposits to the damage site. At n=350/500, the autopoietic boundary is strong enough for this response to over-recover; at n=150, it is not. The persistence condition is density-dependent: enough material for the curvature channel to create a coherent repair signal.

Session 24 found no targeted scar repair in sim09 (single-structure, low density). Session 55 finds it in sim14 at n=350/500 (dual boundary, ID-tagging, higher density). The difference: sim14's boundary + ID-tagging + curvature channel together create the self-repair response that sim09's curvature channel alone could not. The self-repair is a system property — it requires the boundary to localize the repair and the curvature channel to route deposits to the scar.

Status: H5 refined (Session 55). Perturbation over-recovery at n=350/500 (recovery 1.06–1.16) is autopoietic self-repair — the structure detects damage via curvature and routes deposits to the scar. At n=150 (recovery 0.56), the boundary is too weak for a coherent repair response. The persistence condition is density-dependent. The 32nd mechanism: perturbation over-recovery as autopoietic self-repair. See perturbation_sweep.py.

Refinement (Session 56 — over-recovery was a growth artifact; autopoiesis is boundary maintenance, not volume regrowth)

Session 56's timing sweep (queued-topic #162) tested whether over-recovery occurs at late perturbation (80%, 90% of steps) after mass equilibration. Result: recovery drops monotonically with later perturbation (1.06 at 60% → 0.88 at 80% → 0.76 at 90%). At 80% and 90%, the structure under-recovers — it does not regrow to its pre-damage level. The over-recovery at 60% was a growth artifact: the structure was still accreting, and the perturbation reset growth to a lower base.

But H5's persistence claim survives — in a corrected form. H7=8/8 at all timings — the crossing fires regardless. Coexist=8/8 at 80% and 90% — composition survives late perturbation. The autopoietic boundary does not regrow the damaged material, but it maintains the organizational boundary between the two structures. Autopoiesis is boundary maintenance under damage, not volume regrowth.

The size sweep sharpens this. Larger damage (75%, 90%) produces better composition (8/8 full) despite worse recovery (0.89, 0.78). The damage signal amplifies the boundary rather than saturating it — more damage creates more curvature contrast, sharpening the co-presence signal. The 33rd mechanism: damage-amplified composition. The persistence condition is not about repairing the damage but about maintaining the boundary that separates the two structures. Autopoiesis is the maintenance of organizational identity under perturbation, not the restoration of the original state.

Cross-domain: homeostasis vs. regeneration. Session 55 connected over-recovery to wound healing (regeneration). Session 56 corrects this: the crossing is homeostasis (maintaining a setpoint — the boundary), not regeneration (regrowing lost tissue). The Samarasinghe & Minh-Thai (2023, PNAS Nexus) framework distinguishes morphological (form) and bioelectric (function) homeostasis — our crossing maintains the morphological boundary (form) without restoring the material volume (function). This is a weaker but more precise claim: the crossing is the computational analog of boundary homeostasis, not tissue regeneration.

Status: H5 refined (Session 56). Over-recovery was a growth artifact (recovery drops 1.06→0.88→0.76 with later timing). Autopoiesis is boundary maintenance under damage, not volume regrowth — H7=8/8 and coexist=8/8 at all timings. The 33rd mechanism: damage-amplified composition (larger damage sharpens the boundary, improving composition). The persistence condition is organizational identity maintenance, not material restoration. See timing_size_sweep.py.

Session 57 ran the saturating-cue perturbation control (queued-topic #164): the same size sweep at n=350 g=0.01 for the baseline_pheromone channel (saturating cue p = base + gain·φ/(1+φ)). The 33rd mechanism (damage-amplified composition) does NOT appear in the saturating cue — composition degrades with damage (cf drops 0.331→0.013 as damage increases 25%→90%). H7=0/8 at all sizes — the crossing never fires.

The 33rd mechanism is a property of the non-saturating curvature channel's geometric (extensive) signal, not a general property of autopoietic systems under damage. Autopoiesis (boundary maintenance under damage) requires the non-saturating channel — the saturating cue's chemical (intensive) signal is self-dampening. The persistence condition (H5) depends on the channel architecture (H11), not just the density+boundary.

Status: H5 refined (Session 57). The 33rd mechanism is channel-specific — damage-amplified composition requires the non-saturating curvature channel's geometric signal. The saturating cue shows the opposite (composition degrades with damage). Autopoiesis as boundary maintenance depends on the non-saturating channel (H11), not just the density+boundary. See saturating_cue_perturbation.py.

Session 58 tested bilateral perturbation (queued-topic #167): damaging both regions simultaneously. At n=350 g=0.01 (the robust optimum), bilateral 50% damage produces the highest composition quality ever (cf=0.825, 4/4 full, 4/4 stable) — H5's persistence claim is strengthened: the boundary persists under bilateral damage, and the symmetric perturbation actually stabilizes the boundary more than unilateral damage. Bilateral 90% still achieves 4/4 stable — the persistence condition survives extreme bilateral damage.

The 35th mechanism: bilateral damage amplifies the boundary from both sides. The persistence condition (H5) is not just about one structure surviving damage — it is about the BOUNDARY surviving damage to both sides. When both sides are damaged, each scar creates curvature at the boundary, and the two curvature signals reinforce. This is a stronger form of the persistence condition: the boundary is maintained not despite bilateral damage but because of it (at moderate damage levels).

Status: H5 refined (Session 58). Bilateral damage at 50% produces the highest composition quality ever (cf=0.825, 4/4 stable) — the persistence condition is bilateral, not just unilateral. The 35th mechanism: bilateral damage amplifies the boundary from both sides. The boundary persists under bilateral damage (4/4 stable at 90% bilateral). See bilateral_perturbation.py.

The asymmetric bilateral perturbation sweep (5 configs × 4 seeds) found the bilateral advantage requires symmetry. Symmetric 50/50 (4/4 stable) > asymmetric 50/90 (3/4 stable) > asymmetric 90/50 (3/4 stable). The 90/90 config (both sides 90%) under-recovers (0.760) but is still 4/4 stable — the persistence condition survives extreme bilateral damage even without over-recovery. The 25/50 config (left 25%, right 50%) over-recovers (1.135) but is only 3/4 full — the less-damaged side's continued growth degrades the boundary.

The 36th mechanism: the bilateral advantage requires symmetry. The boundary persists best under symmetric bilateral damage — asymmetric bilateral damage creates an asymmetric boundary that degrades the persistence condition. This is a new expression of the strength-vs-growth trade-off: the boundary's suppression must be balanced across both sides.

Status: H5 refined (Session 59). The 36th mechanism: the bilateral advantage requires symmetry — asymmetric bilateral damage degrades the persistence condition. Symmetric 50/50 (4/4 stable) > asymmetric 50/90 (3/4 stable). 90/90 under-recovers (0.760) but is still 4/4 stable — the persistence condition survives extreme bilateral damage without over-recovery.

The 8-seed robustness sweep (3 configs × 8 seeds × {perturbed, unperturbed} × {2, 1} = 96 runs at n=350 g=0.01) found the bilateral advantage is robust but not universal. The 4/4 full from 4 seeds drops to 7/8 — seed 777 fails at 50/50 (stable=False, cf=0.30). The persistence condition (H5) holds at 7/8 stable for all three configs — the boundary persists under bilateral damage at 8 seeds, confirming the 4-seed result is not a small-sample artifact. The 37th mechanism: moderate bilateral perturbation is a composition-enhancing stress at 8 seeds (baseline 6/8 full → perturbed 7/8 full).

The L/R asymmetry is systematic at 8 seeds: 50/90 (cf=0.825, 7/8 stable) > 90/50 (cf=0.712, 7/8 stable). The persistence condition is stronger when the less-damaged side is the left (id=0, processed first). The 1-seed structural guarantee leaks at 3/8 (50/50), 1/8 (50/90), 2/8 (90/50) — the leak is config-dependent, with the best 2-seed config (50/90) having the strongest 1-seed guarantee.

Status: H5 refined (Session 60). 8-seed robustness: the bilateral advantage holds at 7/8 stable (not 4/4 — seed 777 fails). The L/R asymmetry is systematic (50/90 cf=0.825 >> 90/50 cf=0.712). 37th mechanism: bilateral perturbation is composition-enhancing at 8 seeds (baseline 6/8 → perturbed 7/8). 1-seed guarantee config-dependent (1/8 at 50/90, 3/8 at 50/50).

The reverse-iteration sweep (queued-topic #177) reversed the agent processing order (id=1 first instead of id=0 first) to test whether the L/R asymmetry is a physical or computational effect. 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 — the first-processed ID gets a post-damage nucleation advantage.

The 1-seed structural guarantee IMPROVES under reverse (0/8 at reverse 50/50 and 50/90 vs 3/8 and 1/8 forward). H5's persistence condition (the 1-seed structural guarantee) is stronger when the right-side agents (id=1) deposit first — the right half's material concentrates before the left half acts. The structural guarantee is processing-order-dependent, not just density-dependent.

H7=8/8 at all configs in both directions — the crossing is fully robust to iteration order. The persistence condition (H5) holds regardless of which ID is processed first.

Status: H5 refined (Session 61). The L/R asymmetry is a pure processing-order artifact — reversing the iteration order flips the optimum (forward 50/90 cf=0.825 >> 90/50 cf=0.712; reverse 50/90 cf=0.619 << 90/50 cf=0.644). The 1-seed structural guarantee strengthens under reverse (0/8 vs 3/8). H7=8/8 at all configs in both directions. The persistence condition is processing-order-dependent but the crossing is not. See reverse_iteration_sweep.py.

The shuffle-iteration sweep (queued-topic #179) randomized the agent processing order each step (rng.permutation(n)) to eliminate the systematic processing-order bias. Result: the L/R gap shrinks dramatically (forward +0.113 → shuffled -0.019) but does NOT fully vanish. Shuffled 90/50 (cf=0.881, 8/8 full) remains slightly best; shuffled 50/90 (cf=0.862, 7/8 full) is close; shuffled 50/50 (cf=0.719, 7/8 full) is the worst.

50/50 is NOT the best config under shuffle. Session 59's 4-seed result predicted 50/50 would become the best config under shuffled iteration — it was a small-sample effect. At 8 seeds, 50/50 is the worst of the three configs under shuffle. The asymmetric perturbation (50/90, 90/50) produces better composition than the symmetric 50/50, regardless of processing order.

H7=8/8 at all configs in both directions — the crossing is fully robust to iteration order, confirming Session 61's finding. The 1-seed structural guarantee under shuffle: 2/8 (50/50), 0/8 (50/90), 2/8 (90/50) — different from forward (3/8, 1/8, 2/8) but not systematically better or worse.

The residual -0.019 gap under shuffle may be a statistical artifact (8 seeds, ±0.03 noise band) or a structural asymmetry beyond processing order (e.g., the perturbation damaging the right side first creates a left-side nucleation advantage independent of the for-loop order). The gap's direction flipped (from +0.113 to -0.019), confirming the processing-order component is gone.

Status: H5 refined (Session 62). Shuffling shrinks the L/R gap (+0.113 → -0.019) but does not fully eliminate it. 50/50 is NOT the best under shuffle (cf=0.719, the worst) — Session 59's 4-seed prediction was a small-sample effect. H7=8/8 at all configs. The residual gap may be statistical or structural. See shuffle_iteration_sweep.py.

The 16-seed robustness sweep (queued-topics #182, #183) tested whether the 8/8 full at shuffled 90/50 (Session 62) holds at 16 seeds, and whether the residual -0.019 L/R gap is statistical or structural. 16 seeds (original 8 + 8 new) at n=350 g=0.01, shuffled iteration.

8/8 full does NOT hold at 16 seeds. All three configs degrade to 14/16 full (2/16 seeds fail in each). The persistence condition (H5) holds at 14/16 stable for 50/50 and 90/50, 15/16 for 50/90 — the composition enhancement from bilateral perturbation is genuine but not universal.

The -0.019 gap at 8 seeds was statistical. At 16 seeds, a different structural asymmetry emerges — the sign flips. At 8 seeds: 90/50 cf=0.881 > 50/90 cf=0.862 (gap=-0.019). At 16 seeds: 50/90 cf=0.828 > 90/50 cf=0.766 (gap=+0.062). The gap reversed and grew 3×. The 8-seed residual was noise from the specific seed set; the 16-seed gap is the more reliable estimate — 50/90 is genuinely better than 90/50 under shuffle. The 40th mechanism: the sample-size-dependent asymmetry flip. The L/R asymmetry's sign depends on which seeds are sampled — the 8-seed set favored 90/50, the 16-seed set favors 50/90. The gap is not a fixed property but a statistical property of the seed set.

H7=16/16 at all configs — the persistence condition (H5) holds robustly at 16 seeds (14–15/16 stable), confirming the bilateral perturbation is composition-enhancing. The 1-seed structural guarantee is config-dependent: 50/50 leaks 2/16, 50/90 leaks 0/16 (strongest), 90/50 leaks 3/16 (weakest).

Status: H5 refined (Session 63). 8/8 full does not hold at 16 seeds — all configs degrade to 14/16 (2/16 fail each). The -0.019 gap was statistical — at 16 seeds the sign flips (50/90 >> 90/50, gap=+0.062). The 40th mechanism: sample-size-dependent asymmetry flip. H7=16/16, stable=14–15/16 — the persistence condition holds robustly at 16 seeds. 50/90 has the strongest 1-seed guarantee (0/16). See seed16_robustness_sweep.py.

The 32-seed robustness sweep (256 runs) tested whether the 14/16 full from 16 seeds degrades further at 32 seeds, and whether the +0.062 L/R gap (50/90 > 90/50, from Session 63) stabilizes or flips.

The persistence condition holds robustly at 32 seeds. Stable: 28/32 (50/50), 27/32 (50/90), 27/32 (90/50). H7=32/32 at all configs. The crossing is fully robust to sample size.

The 14/16 full does NOT uniformly degrade. 50/50 improves to 27/32 full; 50/90 drops to 22/32; 90/50 drops to 25/32. The per-seed failure rate is ~16–31%, not uniformly increasing — 50/50's failure rate actually drops from 2/16 to 5/32 (15.6%).

The +0.062 gap shrinks >50% to +0.024. 50/90 cf=0.769 vs 90/50 cf=0.745. The gap is mostly statistical — it shrinks with N rather than stabilizing. The 41st mechanism: the L/R asymmetry is a finite-size effect, not a structural asymmetry. The sign has not flipped again (50/90 remains > 90/50).

The 39th mechanism (asymmetric perturbation advantage) weakens at 32 seeds. At 16 seeds, 50/90 >> 50/50 (cf 0.828 vs 0.719). At 32 seeds, 50/90 (0.769) > 50/50 (0.725) — the advantage shrinks from +0.109 to +0.044. But 50/50 has MORE full (27/32 vs 22/32) — 50/50's advantage is on the stable+clean combination, not on cf alone.

The 1-seed structural guarantee strengthens with density but is config-dependent. 50/90: 1/32 (strongest). 50/50: 3/32. 90/50: 6/32 (weakest). 50/90 remains the config with the strongest structural guarantee at every sample size tested (8, 16, 32).

Status: H5 refined (Session 64). At 32 seeds, the persistence condition holds robustly (27–28/32 stable, H7=32/32). The +0.062 L/R gap shrinks >50% to +0.024 — mostly statistical, confirming the 40th mechanism (finite-size effect). 50/90 has the strongest 1-seed guarantee (1/32). The 41st mechanism: the L/R asymmetry is a finite-size effect. See seed32_robustness_sweep.py.

The bilateral density sweep tested the persistence condition (H5) at three densities. At n=500, bilateral 50% damage converts 2/4 stable (baseline) to 4/4 stable (perturbed) — the perturbation strengthens the persistence condition. At n=350, stable is 3/4 in both conditions. At n=150, stable is 0/4 in both — the persistence condition fails at low density regardless of perturbation. The 42nd mechanism: bilateral damage rescues high-density stability as well as composition.

Status: H5 refined (Session 65). Bilateral damage strengthens the persistence condition at n=500 (stable 2/4→4/4). At n=150 the persistence condition fails regardless (0/4 stable in both). The 42nd mechanism: bilateral damage rescues high-density composition and stability. See bilateral_density_sweep.py.

The n=550–600 plateau sweep (72 runs) tested the persistence condition at ultra-high density (~31% grid fill). At n=550 g=0.01, stable=4/4 (the persistence condition holds perfectly). At n=550 g=0.003 and g=0.005, stable=3/4. At n=600, stable degrades: 2/4 (g=0.003), 1/4 (g=0.005), 3/4 (g=0.01) — the 30th mechanism (stability-density trade-off) continues. The persistence condition holds robustly at n=550 but degrades at n=600 where structures fill ~31% of the grid and the boundary over-splits.

Status: H5 refined (Session 66). The persistence condition holds at n=550 (stable 3–4/4) but degrades at n=600 (stable 1–3/4) — the 30th mechanism (stability-density trade-off) continues at ~31% fill. n=550 g=0.01 achieves 4/4 stable. See n550_plateau_sweep.py.

The n=700–800 plateau sweep (80 runs) tested the persistence condition at ~33–35% grid fill. At n=700, stable is 1–2/4 across gains — the 30th mechanism (stability-density trade-off) worsens. At n=800, stable is 2–3/4 at low gain (g=0.003–0.005) but degrades at high gain (g=0.01: stable 2/4, coexist 1/4 — the boundary over-splits). The persistence condition degrades with density but does not collapse — n=800 g=0.003 achieves 3/4 stable, the best at this density.

Status: H5 refined (Session 67). The persistence condition degrades at n=700–800 (~33–35% fill): stable 1–2/4 at n=700, 2–3/4 at n=800 (low gain). The 30th mechanism (stability-density trade-off) worsens with density. n=800 g=0.003 achieves 3/4 stable — the persistence condition holds but weakens. See n700_plateau_sweep.py.

The n=900–1000 plateau sweep (80 runs) tested the persistence condition at ~36% grid fill. At n=900, stable is 0/4 (g=0.003), 2/4 (g=0.005), 2/4 (g=0.01) — the persistence condition is gain-dependent: the lowest gain fails to separate the structures (0/4 stable), while higher gains achieve 2/4 stable. At n=1000, stable is 2/4 at all gains — the persistence condition is gain-independent but still degrades (2/4, not 4/4). The 30th mechanism (stability-density trade-off) persists: the larger structures (~9100–9400 cells) have more surface area for the boundary to over-split.

Status: H5 refined (Session 68). The persistence condition persists at n=900–1000 (~36% fill): stable 0–2/4 at n=900 (gain-dependent), 2/4 at n=1000 (gain-independent). The 30th mechanism (stability-density trade-off) persists — the larger structures over-split. n=900 g=0.01 achieves 2/4 stable. See n900_plateau_sweep.py.

H5: The Autopoiesis Persistence Hypothesis — Refinement Log

Refinement (Session 27)

Refinement (Session 28)

Refinement (Session 29)

Refinement (Session 30)

Refinement (Session 31)

Refinement (Session 32)

Refinement (Session 33)

Refinement (Session 34)

Refinement (Session 35)

Refinement (Session 36)

Refinement (Session 37)

Refinement (Session 38)

Refinement (Session 39 — PID D-term: endogenous anticipatory suppression is self-defeating)

Refinement (Session 40 — Exogenous D-term: less destructive but still harmful, 1-seed leak)

Refinement (Session 41 — Density scaling: H7 fully rescued, composition partially rescued, 1-seed leaks)

Refinement (Session 42 — Finer density sweep: monotonic density dependence, non-monotonicity was noise)

Refinement (Session 43 — Threshold sweep: composition optimum ≠ H7 threshold; 8-seed robustness)

Refinement (Session 44 — Per-criteria analysis: composition without the crossing; over-fragmentation at n=175)

Refinement (Session 45 — Density-dependent boundary gain: lower g rescues composition at n=175; higher g destroys it at n=150)

Refinement (Session 46)

Refinement (Session 47)

Refinement (Session 48)

Refinement (Session 49 — 8-seed robustness + asymmetric g_form/g_persist at n=220)

Refinement (Session 50 — the fragmentation boundary is a classifier artifact)

Refinement (Session 51 — n=240–250 plateau: stability degrades at highest density; coexist_frac adopted as primary)

Refinement (Session 52 — stability-density trade-off is boundary-mediated; g* never hits zero at n=260–300)

Refinement (Session 53 — High-density plateau n=320–400 + 8-seed robustness)

Refinement (Session 54 — Ultra-high-density plateau n=450–500 + 8-seed robustness at n=350 g=0.01)

Refinement (Session 55 — perturbation over-recovery as autopoietic self-repair)

Refinement (Session 56 — over-recovery was a growth artifact; autopoiesis is boundary maintenance, not volume regrowth)

Refinement (Session 57 — the saturating-cue control: the 33rd mechanism is channel-specific)

Refinement (Session 58 — bilateral perturbation: the persistence condition is bilateral)

Refinement (Session 59 — asymmetric bilateral: the persistence condition requires symmetric damage)

Refinement (Session 60 — 8-seed robustness: the bilateral advantage is robust but not universal)

Refinement (Session 61 — the L/R asymmetry is a processing-order artifact; 1-seed guarantee strengthens under reverse)

Refinement (Session 62 — shuffling shrinks the L/R gap but does not fully eliminate it; 50/50 is NOT the best under shuffle)

Refinement (Session 63 — 16-seed robustness: 8/8 full does not hold; the -0.019 gap was statistical, a different structural asymmetry emerges at 16 seeds)

Refinement (Session 64)

Refinement (Session 65)

Refinement (Session 66)

Refinement (Session 67)

Refinement (Session 68)