# exp013_blob_flow — THE CONDITIONING HYPOTHESIS CONFIRMED (CANDIDATE s0; s1 running)

**Hypothesis (Phil, 2026-07-18).** "Blob likely will be less effective for
eps than it will be for flow matching." Mechanism: eps-prediction recovers
structure through x0̂ = (x_t − √(1−ᾱ)·ε̂)/√ᾱ — ill-conditioned at high noise
(vanishing √ᾱ) exactly where blob supervision applies; rectified flow
recovers x0̂ = x_t − σ·v̂ EXACTLY and linearly at every sigma.

**Design.** Identical coupling to exp012 (foreground-weighted LP-x0, HIGH
band, λ=0.5), identical fused data + blob targets, identical multiband beds
— only the substrate changes: base_lune (flow objective, its judged-best
nl77 conditioning). Arms: frozen | uniform-mb3 | blob-mb3; in-bed gauges on
all arms.

**Results** (`results.json`):

| arm | common flow-MSE | HIGH-band blob gauge |
|---|---|---|
| frozen | 0.62989 | 0.18447 |
| uniform mb3 | 0.57249 (−9.1%) | 0.12987 |
| **blob mb3** | 0.57379 | **0.12220** |

| prereg | outcome |
|---|---|
| **P1: blob-gauge move ≥5× the eps reference (+0.03%)** | **HIT — −5.9% relative, ~200×** |
| P2 common gauge undegraded (<0.5%) | HIT (+0.23%) |
| P3 toggle bit-exact | HIT |

**Verdict (candidate, s0).** The SAME supervision that is 2-seed inert on
the eps substrate (exp012) bites hard on the flow substrate — the
conditioning of the x0 recovery is the controlling variable, exactly as
hypothesized. Consequences: (1) blob/structural supervision belongs on
FLOW-objective trunks (or v-pred); (2) exp012 is reframed as this pair's
conditioning control; (3) the undertrained lune trunk pays adapters −9.1%
(largest adapter effect measured in the line — headroom scales inversely
with trunk training, consistent with the "undertrained exemplar" framing).

**Caveats.** s0 (s1 running); one λ; lune ≠ core substrate (the flow-vs-eps
contrast rides on different trunks — a v-pred core arm is the clean
follow-up); blob gauge scale differs across objectives (relative moves are
the comparison, stated as such).

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## SEED-1 (2026-07-18, `results_s1.json`) — PROMOTED: 2-SEED CONFIRMED
s1 relative blob-gauge move −3.7% (s0 −5.9%) — both seeds pass the
preregistered 5× bar by ~125–200× the eps reference; common gauge clean
both seeds. THE CONDITIONING LAW (2-seed): structural/blob supervision
pays where x0 recovery is linear (flow: x0 = x_t − σv) and is inert where
it divides by vanishing √ᾱ (eps at high noise). Scope: lune flow trunk vs
core eps trunk (different trunks — v-pred same-trunk arm remains the
sharpest follow-up); 2 training seeds, shared cache.

---
## DOSE-RESPONSE POINT (2026-07-19, λ=2.0, `results_lambda2.json`)
Monotone: λ=0.5 → −5.9% blob gauge at ~0% common cost; **λ=2.0 → −8.4% at
+0.9% common cost** (now past the 0.5% P2 bound). The coupling-strength
trade surface is real and mapped at two points; λ≈1 interpolation and
pure-band-phase training are the open refinements. (Ops note: this arm
reused the s0 results filename on-pod — the shipped s0 file is canonical;
the config's lambda field disambiguates.)

---
## THE DOSE CURVE COMPLETE (2026-07-19, `results_lambda1.json`)
| λ | blob-gauge move | common-gauge cost | within 0.5% bound |
|---|---|---|---|
| 0.5 | −5.9% | ~+0.2% | yes |
| **1.0** | **−8.3%** | **+0.4%** | **yes — the operating point** |
| 2.0 | −8.4% | +0.9% | no |
Monotone with saturation between λ=1 and 2: λ≈1 captures essentially the
full blob-gauge gain inside the preregistered common-gauge tolerance. All
single-seed dose points on the 2-seed-confirmed conditioning law's flow
substrate.