H11: The Saturating Channel Hypothesis — Refinement Log

Refinement (Session 13, 2026-07-28 — sim08 partial corroboration, boundary sharpened)

sim08 tested the cheapest non-saturating channel — a density cap (a cell at/above DENSITY_CAP cannot receive deposits; a hard boolean gate on the action, not a graded cue function) — reusing sim06's metrics and detector unchanged.

Result: H11 confirmed in direction, sharpened in sufficiency.

• The cap consolidates morphology, monotonically. Sweeping the cap from ∞ (off) to 1.5, pillars fall 101 → 52, and the pheromone field is de-saturated (max pheromone 8.01 → 2.50). This is exactly the effect H11 predicts: a non-saturating action-gate prevents the cue field from being driven flat and prunes nucleation. The direction H11 claimed is real and replicated in a third independent mechanism.
• But the cap does NOT produce the crossing. Stability does not rise (0.874 → 0.775 at the tightest cap); the detector never fires for any cap strength. The cap reduces building volume (1131 → 619 cells) without raising persistence.
• The cap does NOT rescue cue-based feedback. cap+self_maintenance (262 pillars, stability 0.763) is no better than self_maintenance alone (252, 0.775) — consistent with H11: the cue channel, not the feedback energy, is the problem.

What this means for H11. Non-saturating inhibition is necessary-but-not-sufficient. A cap that only limits growth corrects the fragmentation symptom (pillars) but not the persistence symptom (stability) — the crossing needs a structure that holds its mass against erosion, and a pure limiter reduces mass rather than recruiting its maintenance. The crossing therefore needs a non-saturating channel that recruits as well as limits: the curvature channel in real termites (Calovi 2019) does both — it routes deposition to concavities (limits scatter) AND each deposit extends the concavity (recruits further building at the edge). The density cap only limits. Candidate next: a curvature/deposition-edge rule that routes AND limits. See concepts/non-saturating-channels.md and sim08.

H11's status is now: directionally confirmed (3/3 mechanisms), but the "consolidation requires non-saturating feedback" claim is refined to "consolidation requires non-saturating feedback that RECRUITS, not merely one that LIMITS." The cheap test did not settle the crossing but it did discriminate: the cap consolidates where cue-feedback fragments, so the channel distinction H11 draws is real; the cap alone just isn't enough.

Refinement (Session 19, 2026-08-03 — the crossing fires with a control arm; H11's channel distinction is now causal, not just directional)

sim09's d* sweep (100 combos) found 0/100 crossings under the original detector. The blocker was an unfalsifiable metric-ceiling bug in criterion 2's mass-saturation gate (see H7's Session 19 refinement for the full diagnosis). Corrected to a relative-slope plateau, the crossing fires in the curvature channel and not in the baseline-pheromone control — the first time the H7 crossing has fired with a control arm.

This upgrades H11's evidence from "directional" to "causal with a control." Previously H11 rested on a same-direction comparison: non-saturating channels (sim08, sim09) consolidated where saturating ones (sim06, sim07) fragmented, but both were within one model family and neither crossing fired, so the channel distinction was inferred from morphology, not from the crossing verdict. Now the baseline-pheromone control (sim06's saturating Grassé rule) is run under the same corrected detector and crosses in 0/3 tested d values — its saturating response never elevates the pheromone cue enough to pass criterion 2's elevation gate (mean_pheromone 0.25 < 0.50 threshold). The curvature channel, which has no pheromone field to saturate, crosses at every d. The channel distinction H11 draws is now the causal variable separating the crossing from the non-crossing, not merely a correlate of morphology.

The honest limitation, carried over. The crossing fires at d=0 (no smoothing), so the recruit half — the non-saturating curvature routing — is what the control lacks and what drives the crossing. The limit half (d-smoothing) consolidates morphology but is not necessary for the verdict. H11's "recruit as well as limit" refinement (Session 13) is therefore half supported: the recruit half is load-bearing for the crossing; the limit half is load-bearing for the morphology. Isolating them is the next test. Status: H11 directionally confirmed (4/4) and now causally supported with a control arm for the recruit half; the limit half's contribution to the crossing verdict is unproven.

Refinement (Session 20, 2026-08-04 — the limit half is a stability amplifier, not morphology-only)

The recruit-vs-limit isolation (see H7 Session 20 for the full 2×2 factorial) upgrades H11's evidence on the limit half. The recruit half (curvature routing) is necessary and almost-sufficient for a stable crossing: recruit-only (d=0) is stable in 3/4 seeds; neither (no recruit) is stable in 0/4. The limit half alone (d-smoothing, no curvature routing) is never stable (0/4) — its crossing criteria flicker (hold 0.40–0.55) because the biharmonic shapes convex geometry that no agent is routed to (criterion 3, deposits_on_convex_fraction, oscillates around 0.60 without the routing to concentrate deposits at convex tips).

But the limit half is not merely morphology-only. The recruit+limit condition is stable in 4/4 seeds where recruit-only is stable in 3/4 — the one borderline seed (123, hold 0.65) becomes fully stable (hold 1.0) when d>0 is added. The limit half amplifies the stability of the recruit-driven crossing against seed variance. So H11's "recruit as well as limit" is refined: the recruit half is load-bearing and almost-sufficient; the limit half is a stability amplifier + morphology optimizer — not strictly necessary for the crossing, but causally contributing to its robustness. This is a stronger claim than Session 19's "half-supported": the limit half has a causal role (stability), not merely an aesthetic one (morphology).

The clean separation. The recruit half routes agent action to the geometry; the limit half shapes the geometry. Limit-only shapes geometry that no agent is routed to (criterion 3 flickers); neither alone (no geometry shaping) produces nothing. The recruit half is the load-bearing variable; the limit half makes its crossing robust. Status: H11 directionally confirmed (4/4), causally supported with a control arm, and now mechanism-decomposed: recruit = necessary + almost-sufficient; limit = stability amplifier + morphology optimizer. See recruit_limit_sweep.py.

Refinement (Session 21, 2026-08-05 — the confound resolved: action-based is primary, non-saturating is secondary)

Session 20 isolated the recruit and limit halves, but the recruit half is action-based (curvature routes what the agent does) AND non-saturating (linear gain) simultaneously — H11's two claimed properties are confounded. The saturating-action control disentangles them: the same curvature routing, but a saturating response p = base + gain·c/(1+|c|) instead of linear p = base + gain·c. Both forms are action-based; only the linear form is non-saturating.

The 2×2×2 factorial (response × recruit × d) with a 4-seed robustness pass found: the saturating action crosses in 8/8 recruit-ON seeds and is stable in 6/8 (linear is 7/8). At d=0, linear mean hold is 0.912 vs saturating 0.862 — saturation costs ~0.05 in hold rate. At d=1 the limit half rescues both to 4/4 stable, hold 1.00. The decisive contrast is recruit ON vs OFF (0/8 crossed regardless of response), not linear vs saturating.

H11's strict "non-saturating" claim is partially weakened. The saturating action-based channel does not destroy spatial contrast (criterion 3, deposits_on_convex_fraction, holds 1.00 in all seeds for both forms) — it only slows mass equilibration (criterion 2's mass-plateau gate flickers more under the saturating form). The non-saturating property matters for stability, not for the crossing verdict. H11's distinction should be refined: the critical property is action-based routing (curvature routes what the agent does, not how strongly it reads a cue); non-saturating is a stability amplifier, analogous to the limit half's role. This is a weaker version of H11 — the "self-defeating" language overstates the saturating action's failure; it is "self-destabilizing" at most.

Honest limitation: this tests within the action-based family. The saturating form c/(1+|c|) still routes — it compresses the gain but does not stop routing at high curvature. A truly cue-like saturating channel (sim06/sim07's pheromone field whose deposit response flattens above φ≈1) would still fail the way those sims did. The test isolates action-based from non-saturating within the action-based family, not against the cue-based family. The cue-vs-action distinction (H11's original framing) is still supported by the baseline-pheromone control (0/3 crossed). What the test refines is the within-action distinction: non-saturating is not the causal variable; action-based routing is.

Status: H11 directionally confirmed (4/4), causally supported with a control arm, mechanism-decomposed, and now confound-resolved: action-based routing is the primary load-bearing property; non-saturating is a secondary stability amplifier. See saturating_action_sweep.py.

Refinement (Session 22, 2026-08-06 — the cue-based non-saturating control: H11's "self-defeating" framing is backwards for the cue family)

The remaining cell of the 2×2 (queued-topic #67): a non-saturating cue channel. sim06's as-built deposit rule is the saturating cue p = base + gain·φ/(1+φ); the non-saturating cue is p = base + gain·φ (clamped to 1.0). Both are cue-based; only the response curve differs. A deposit_response parameter was added to sim06.py.

Result — the non-saturating cue crosses LESS, not more. Seed-42 factorial (64 conditions): saturating cue crosses 32/32 (stable 32/32, hold 1.000); linear cue crosses 19/32 (stable 16/32, hold 0.527). Decomposed by self-maintenance: without SM, saturating cue is 16/16 stable (hold 1.000); linear cue is 0/16 stable (hold 0.053). With SM, both are 16/16 stable (hold 1.000). Seed robustness (4 seeds) confirms: saturating no-SM 4/4 stable; linear no-SM 0–1/4 stable; both with SM 4/4 stable. Determinism verified.

This is the opposite of H11's strict original prediction. H11 said non-saturating channels consolidate where saturating ones fragment. Session 21 found this holds within the action family (non-saturating action is slightly more stable). Session 22 finds it reverses in the cue family: the non-saturating cue is the one that fragments (0/16 stable without SM), and the saturating cue is the one that consolidates (16/16). The non-saturating property is a sign-reversing modifier: it helps in the action family, hurts in the cue family.

The mechanism: deposit-probability clamping, not cue-response compression. The linear rule p = base + gain·φ hits p=1.0 at φ≈1.15 — every high-pheromone cell deposits at 100%, flattening the spatial gradient and diluting the pheromone field (mean pheromone over structure drops to 0.467 vs the saturating cue's 0.749, below the 0.5 crossing threshold). The saturating cue's φ/(1+φ) compression prevents deposit-probability saturation, keeping the response graded and preserving spatial contrast. The "saturation" that is self-defeating is the deposit-probability clamping (which the linear cue hits), not the cue-response compression (which the saturating cue has). H11's original framing conflated these two.

Self-maintenance rescues the linear cue (4/4 stable, hold 1.000). The structure-reemits-pheromone loop sustains pheromone elevation regardless of the response curve, compensating for the linear cue's gradient-flattening. So the non-saturating cue is not categorically unable to cross — it needs a separate mechanism to sustain the pheromone field the saturating cue sustains on its own.

The cue-action asymmetry completes the 2×2:

H11's refinement: the critical property is action-based routing (primary, both rows cross); the non-saturating property is a family-dependent modifier — a stability amplifier in the action family, a stability destroyer in the cue family (without compensation). The "self-defeating" language was backwards for the cue family: the saturating cue is self-sustaining; the non-saturating cue is self-defeating (it clamps to p=1.0 and flattens the gradient). H11 should be re-read as: the self-defeating channel is the one whose response saturates the deposit probability (not the cue field) — and that is the non-saturating cue, not the saturating cue.

Honest limitations. (1) Within sim06's Grassé model; the pheromone decay+diffusion dynamics are model-specific. (2) The SM rescue means the linear cue's failure is conditional, not absolute. (3) The 0.5 phero_elev threshold is a modeling choice; the linear cue crosses at 0.3–0.4 (threshold sensitivity confirmed). (4) The result is a surprise — H11's strict reading predicted the opposite. Not a self-fulfilling correction.

Status: H11 directionally confirmed (4/4) with control arm, mechanism-decomposed, confound-resolved, and now 2×2-complete. The non-saturating property reverses sign across families. H11's "self-defeating saturating channel" framing is backwards for the cue family — the self-defeating channel is the non-saturating cue (deposit-probability clamping flattens the gradient). See cue_response_sweep.py.

Refinement (Session 23, 2026-08-07 — the φ_sat predictor is family-specific, not universal; spatial contrast survives via routing)

Queued-topic #72 proposed φ_sat (the input value at which p_deposit first reaches 1.0) as a unifying diagnostic across all four cells of the 2×2: if max_input > φ_sat, the channel is probability-saturated and the crossing fails.

A direct probe (phi_sat_probe.py) of sim06 (cue) and sim09 (action) at their crossing-proven regimes found the predictor is 50% accurate — no better than chance. It correctly predicts the cue family (cue/linear: max_phero 3.77 > φ_sat 1.165 → saturated → fails; cue/saturating: φ_sat=∞ → unsaturated → crosses) but fails for the action family (action/linear: max_curv 2.55 > c_sat 1.165 → saturated → but crosses stably). The clamping fraction is 0–7% everywhere; the cue/linear has 6.9% clamped cells and fails, the action/linear has 1.0% and crosses.

The mechanism: deposit-probability saturation is self-defeating ONLY when the deposit probability is the spatial signal (cue family). In the action family, spatial contrast lives in the routing decision (which direction the termite moves), not the deposit probability. The response curve saturates the gain (how hard to deposit), not the routing (where to go). Even when some cells clamp to p=1.0, the curvature gradient still routes termites to the right place. H11's "the self-defeating channel is the one whose response saturates the deposit probability" is refined to: deposit-probability saturation is self-defeating only in cue-based channels, where the deposit probability IS the spatial signal. In action-based channels, the routing decision preserves spatial contrast independently of the deposit probability.

The unifying diagnostic is not φ_sat but whether spatial contrast in the routing input survives the response curve. This depends on the channel architecture: action-based channels preserve routing (where to go) even under saturation; cue-based channels do not (the cue field is the spatial signal, and clamping it destroys the gradient). The φ_sat predictor treats the deposit probability as the sole carrier of spatial information, which is true only for the cue family.

Honest limitations. (1) The probe measures the equilibrated field (2000 steps), not the transient nucleation phase. (2) The clamping fraction is computed on the final-state field; the dynamics during growth may differ. (3) The action and cue families use different routing inputs (curvature vs pheromone) on different scales, so the max values are not directly comparable — the comparison is about whether each exceeds its own φ_sat. (4) The result is not a surprise — Session 21 already established that action-based routing is the primary load-bearing property; this probe quantifies the failure and identifies the mechanism (routing preserves spatial contrast) rather than confirming a prediction.

Status: H11 refined: the φ_sat predictor is family-specific, not universal. Deposit-probability saturation is self-defeating only in cue-based channels (where the deposit probability is the spatial signal); in action-based channels, the routing decision preserves spatial contrast independently. The unifying diagnostic is whether spatial contrast in the routing input survives the response curve, which depends on channel architecture. See phi_sat_probe.py.