# RESULT — 064 language-vector: translation is NOT a constant z-offset, and the offset is causally near-inert

**Tier: T3-exploratory. DONE + SELF-HARVESTED in-session.** tmux c100_064 launched
17:16:12Z, DONE 17:21:56Z (5.7 min wall: smoke ~65 s, dev-split encode 26 s, decode
sharded over 3 GPUs ~4 min, analyze 1 s), 0 errors. One post-run ANALYZE-ONLY fix
(langid mixed-rule; see instrument note) — decodes untouched, re-analyzed in 1 s.
Train = FLORES dev (997 rows) → v_L = μ_L − μ_eng; eval = devtest (z reused from 063's
npz, 1012/lang; steering on first 200). Langs deu/tur/jpn/zho/arb (+eng). Greedy, chrF.
All gates PASS.

## Verdict
★ **Both halves of the row question come back NO — informatively. (a) Per sentence,
translation displacement is ~91% NOT the constant offset: v_L explains only 9–13% of
displacement energy (EV_const deu .092 / tur .088 / jpn .134 / zho .115 / arb .106),
residual/displacement ≈ 0.92–0.94, mean cos(d_i, v_L) ≈ 0.33–0.39. Yet v_L is
essentially the OPTIMAL constant vector — the in-sample-oracle constant only adds
+0.002 EV, cos(v_train, mean devtest displacement) = 0.989–0.992, norm ratio ≈ 1.00.
The "language vector" is real, tiny (‖v‖/‖z‖ 0.18–0.29), and hyper-stable in the mean,
while per-sentence cross-lingual displacement (‖d‖ ≈ 3×‖v‖) is dominated by
sentence-idiosyncratic residual that averages out. (b) Causally, adding α·v_L is
near-INERT: with the ENG decoder token, steering NEVER flips output language (0% flip
at α=1 AND α=2, all 5 langs; eng share ≥95%; graceful content cost 87→78–85 chrF-vs-src
as α→2); with the TARGET token, steering changes translation quality by at most ±1.8
chrF vs plain token-switch (α=0). Output language is set by the decoder token, not by
z-arithmetic — completing 063: the offset is removal-safe, addition-inert, and
translation in SONAR is done by the token.**

Answers to the design questions: adding v_L to an English z does NOT make the English
decoder emit the other language (0% at all α ≤ 2); the language-matched decoder emits a
clean translation WITH OR WITHOUT v_L (token-switch alone = 80–88% of the round-trip
ceiling); the linear approximation never "breaks" by α=2 because ‖v‖ is so small
(0.042 for deu vs mean ‖z‖ 0.24) that even 2·v barely moves the decode — quality dips
only 0.4–2.7 chrF from α=1 to α=2.

## Key tables (full JSON: out/results_064_full.json)
Offset constancy (all 1012 devtest rows, v from dev split — out-of-sample):
| lang | EV_const | EV_oracle(mean) | cos(v,d̄) | mean cos(d_i,v) | ‖v‖/‖z‖ | ρ(resid,len) / ρ(disp,len) |
|---|---|---|---|---|---|---|
| deu | .092 | .094 | .990 | .329 | .178 | .27 / .27 |
| tur | .088 | .090 | .989 | .326 | .202 | .32 / .34 |
| jpn | .134 | .137 | .992 | .391 | .289 | .36 / .34 |
| zho | .115 | .117 | .991 | .362 | .271 | .33 / .31 |
| arb | .106 | .108 | .990 | .351 | .208 | .20 / .19 |

Steering, TARGET token (chrF vs L reference, n=200):
| lang | ceiling z_L→L | α=0 (token-switch) | α=0.5 | α=1 | α=1.5 | α=2 | Δ(α1−α0) [CI] |
|---|---|---|---|---|---|---|---|
| deu | 71.6 | 57.7 | 59.6 | 59.3 | 58.8 | 58.9 | +1.58 [−0.05, 3.23] |
| tur | 58.7 | 50.5 | 49.8 | 51.0 | 50.3 | 50.3 | +0.57 [−0.67, 2.05] |
| jpn | 34.7 | 23.5 | 22.6 | 23.5 | 22.9 | 21.4 | −0.00 [−1.37, 1.35] |
| zho | 35.7 | 24.1 | 24.3 | 23.8 | 22.3 | 21.3 | −0.32 [−1.75, 0.90] |
| arb | 56.0 | 49.4 | 48.6 | 47.6 | 47.0 | 46.3 | −1.80 [−3.12, −0.48] |

Steering, ENG token: language-flip rate 0.000 at every α ∈ {0.5,1,1.5,2} for all 5
langs (eng fraction .95–.975, mixed ≤ .05 ≈ the ~5% false-mixed base rate by
construction); content preservation chrF-vs-eng-src: α=0.5 86.4–87.5 → α=1 82.4–85.3 →
α=2 77.5–84.9 (eng round-trip anchor 89.8). Midpoint α=0.5: winner-take-all — eng token
→ 96% English, target token → 87–99% language L; no code-switched regime (feeds 065).
Geometry (deu shown; all langs alike): ‖z_eng+αv‖ 0.241→0.252 (α 0→2), nearest real
z_L is the correct parallel translation for 100% of items at EVERY α (retrieval is that
saturated), nn-cos peaks exactly at α=1 (0.837→0.852→0.841) — v points the right way,
it is just tiny and the decode does not care.

## Gates (all PASS)
- G1 in-regime positive control: PC (z_L→eng token) vs 063's B1 c=1 per lang:
  66.3/66.9, 60.6/61.9, 54.2/53.4, 56.1/55.3, 64.3/65.8 — max |Δ| 1.5 ≤ 5.
- G2 eng round-trip 89.8 ≥ 70 (063: 89.7).
- G3 langid ≥ 0.95 on 200 real devtest sents/lang: min 0.995 (script rules + FLORES-dev
  char-trigram NB for eng/deu/tur).
- G4 norm lint: max steered/real mean-norm ratio 1.113 < 5.
- G5 token-switch baseline emits language L: deu .935 / tur .94 / jpn .91 / zho .87 /
  arb .995 ≥ 0.8.

## Predictions → Brier (frozen in PREREG_LITE)
| pred | P | outcome | Brier |
|---|---|---|---|
| P1 EV_const ∈ [0.15,0.55] for ≥4/5 | 0.55 | **FALSE** — all BELOW band (.088–.134) | 0.3025 |
| P2 eng-token flip ≤10% at α=1, all | 0.75 | **TRUE** (0% everywhere) | 0.0625 |
| P3 |Δ chrF(α1 vs α0)| < 3 for ≥4/5 | 0.55 | **TRUE** (5/5; max |Δ| 1.8) | 0.2025 |
| P4 α=2 drop ≥10 vs α=1 for ≥3/5 | 0.60 | **FALSE** (max drop 2.4) | 0.3600 |
| P5 midpoint: ≥80% eng, <10% mixed, all | 0.65 | **TRUE** (96% eng, ≤4.5% mixed) | 0.1225 |

**Mean Brier = 0.210.** P1 and P4 miss in the SAME direction: the offset is even
smaller/weaker than the "substantial minority" I preregistered — constancy below band,
and no breakdown by α=2 because 2‖v‖ is still a small perturbation.

## Instrument note (honesty)
First analyze pass flagged 99% of Japanese decodes as "mixed" (G5 jpn 0.01): the
mixed-rule required a SINGLE raw script ≥0.85 dominance, but normal Japanese splits
between kana and CJK. Fixed to language-appropriate script groups (kana+cjk for jpn),
analyze-only, decodes untouched; G5 jpn → 0.91. G3 (classification acc) was never
affected (1.00 for jpn). Lesson-2 (canonicalization) instance, caught by gate G5.

## Limitations / what did NOT run
- α ≤ 2 only; some larger α might eventually flip language, but geometry (‖2v‖ ≈ 0.35
  of ‖z‖, norm ratio 1.11) says any flip would be far off the α·v ray's tested range.
- chrF jpn/zho levels inherit 063's cross-script deflation (deltas within language are
  fair; flip rates are chrF-free).
- mixed/code-switch detector has a ~5% false-positive floor by construction (5th-pctile
  margin threshold); flip-rate 0.000 is threshold-free (script-based).
- Residual-vs-content analysis limited to length correlation (ρ ≈ displacement's own
  ρ → length is not a special residual driver, it is norm scaling); no semantic
  decomposition of the 91% residual (follow-up).
- Single encoder/decoder pair, greedy, news domain, n=200 steering / 1012 constancy.
- Nothing truncated; all preregistered cells + gates ran at full n.

## Follow-up worth funding? **Y (narrow).**
1. What IS the 91% residual? It is sentence-specific but averages to ~0: test whether
   it is (i) encoder noise (re-encode paraphrases), (ii) content-language interaction
   (probe residual for POS/morphology), or (iii) chrF-invisible register/style.
2. 065 midpoint tie-in: the no-code-switching winner-take-all here says decoder output
   language is discrete in the token — 065 should test WITHIN-z mixtures (interpolate
   z_eng↔z_deu of the SAME sentence, fixed token) instead of adding v.
3. Practical: token-switch alone is 80–88% of round-trip ceiling — SONAR "free MT"
   needs no z surgery at all; steering can be dropped from any pipeline design.

## Provenance / hygiene
Repo: PREREG_LITE.md (frozen pre-compute), src/{run_064.py,run_064.sh},
out/{results_064_full.json, decodes_064_s{0,1,2}.json, run.log}. Box 064 dir 25 MB
(z_dev npz box-only); 063 z npz + FLORES read in place (read-only). GPUs verified free
pre-claim (35/15/15 MiB, hard-guard in script) and free at exit; tmux session
self-ended; box tmux server empty; no foreign process touched. Local commit, no push.