# RESULT — 063 language-capacity-tax: capacity knee per language + the decode cost of language identity

**Tier: T3-exploratory. DONE + SELF-HARVESTED in-session.** tmux c100_063 launched
16:56:10Z, DONE 17:05:29Z (9.3 min wall: smoke 67 s, full build 3 s, encode ~80 s,
decode sharded over 3 GPUs ~7 min, analyze 0.5 s), 0 errors, session self-ended, GPUs
left at 35/15/15 MiB. FLORES-200 devtest (1012 parallel rows) reused from 046; items =
concatenations of c∈{1,2,3,4,6,8} rows × 64/lang/c, 6 langs (eng/deu/tur/jpn/zho/arb),
greedy decode, chrF. All gates PASS; zero truncation exclusions (max item ≤500 tokens).

## Verdict
★ **The language "capacity tax" is a LEVEL tax, not a knee tax — and language identity
is decoder-free: it lives in the target token plus a removable mean offset that near the
knee is actually worth removing.**

(a) **Knee location barely moves across languages once measured fairly; fidelity LEVEL
moves enormously.** Same-language round-trip chrF at c=1 (single sentences): eng 89.7 >
deu 70.2 > tur 59.8 > arb 58.4 > zho 36.1 ≈ jpn 34.5 — the 046 FVU ordering, but as a
penalty paid at ALL lengths, not a shifted cliff. Relative knees (frozen criterion, first
drop below 0.8× own c=1 chrF): **in token space jpn 54.9 / zho 58.7 / tur 60.3 / eng 65.3
/ deu 89.2 / arb 103.1** — NO language crosses the preregistered 0.75×K_eng tax line
(P2 FALSE, 0/5). deu/arb knees sit LATER in tokens for the anti-intuitive reason: their
tokenizations are inflated (same content = 315/336 tokens at c=8 vs eng 251), and the
extra tokens are capacity-free — **capacity is content-bound, not token-bound**. In
content units (FLORES rows) the knee is ~2 sentences everywhere, with a real ~25% deficit
for the 046-hard languages: zho 1.67 / jpn 1.73 / tur 1.74 vs eng 2.14 / deu 2.23 /
arb 2.32.

(b) **Language-ID budget ≈ one removable offset + the target token.**
- Wrong-token decode is clean translation, not garbling: raw z_L decoded with the eng
  token scores chrF-vs-English-reference 53–67 at c=1 (P3 TRUE, all ≥40). The decoder
  takes output language from the token; z's language content doesn't jam it.
- Centering (z − μ_L + μ_eng, offsets 0.18–0.29 of ‖z‖) before eng-decode is **free at
  c=1** (mean Δ = −0.02 chrF; per-lang −1.8..+1.1 — P4 TRUE) and **HELPS at length** for
  deu/tur/jpn (+3.7 to +6.6 chrF at c≥6; B-cell knees shift later: deu 103→137, tur
  88→110, jpn 110→122 tokens; zho/arb ≈ 0). Post-hoc reading: the offset costs nothing
  when the vector has slack and its removal frees usable capacity once the vector is full.
- Centered z decoded with its OWN token still comes out in language L (script fraction
  0.94–1.00), chrF cost only 0–3.4 vs raw (deu 66.8 vs 70.2, tur 58.6 vs 59.8, jpn 31.6
  vs 34.5, zho 32.7 vs 36.1, arb 59.7 vs 58.4) — the offset is not load-bearing for the
  decoder, completing 046 (FVU) and 062 (probes): language identity ≈ mean offset on
  every instrument tried, now including DECODE.

## Key tables (full JSON: out/results_063_full.json)
A-cell mean chrF (same-language round-trip) by c:
| lang | c=1 | c=2 | c=3 | c=4 | c=6 | c=8 | knee(tok) | knee(content) |
|---|---|---|---|---|---|---|---|---|
| eng | 89.7 | 74.7 | 56.4 | 44.9 | 32.7 | 25.7 | 65.3 | 2.14 |
| deu | 70.2 | 59.3 | 47.4 | 37.2 | 28.8 | 22.3 | 89.2 | 2.23 |
| tur | 59.8 | 44.8 | 36.7 | 27.7 | 20.8 | 17.7 | 60.3 | 1.74 |
| jpn | 34.5 | 25.8 | 19.7 | 15.4 | 10.6 | 7.6 | 54.9 | 1.73 |
| zho | 36.1 | 26.3 | 18.9 | 14.3 | 10.1 | 7.9 | 58.7 | 1.67 |
| arb | 58.4 | 49.4 | 42.0 | 33.7 | 25.4 | 19.8 | 103.1 | 2.32 |

Tokens per 100 chars: eng 24.3 / deu 26.3 / tur 26.7 / arb 38.5 / jpn 56.1 / zho 80.5;
tokens per FLORES row (median): jpn 34.5 = eng 34.5 < zho 38 < tur 38.5 < deu 44 < arb 45.
B2−B1 (centering gain, chrF-vs-eng) by c: deu −1.8/+3.9/+5.7/+2.4/+5.6/+4.8;
tur −0.1/+3.7/+4.3/+0.8/+3.8/+4.2; jpn +0.6/+2.2/+2.1/+2.7/+4.8/+6.6;
zho and arb ≈ 0 (−1.5..+1.4). Exact match: eng c=1 17.2%, deu 1.6%, else 0 (long/greedy).
Exploratory: Spearman(offset_rel, content-knee) over 5 non-eng langs = **−0.6** (bigger
language offset ↔ earlier content knee; arb the outlier) — direction consistent with
"tax ∝ offset", n=5, NOT preregistered, descriptive only.

## Gates (all PASS)
- G1 retrieval P@1 en↔X on devtest singles: min 0.998 (jpn) ≥ 0.8.
- G2 decode instrument: eng c=1 chrF 89.7 ≥ 70 (027/058 anchor regime).
- G3 positive control: eng drop c1→c8 = 64.0 chrF ≥ 5 — 028's length axis reproduced.
- G4 norm lint: cross-language mean-‖z‖ ratio ≤ 1.085 per bin (< 5); ‖z‖ grows 0.24→0.32
  with c and saturates by c=4 — the vector "fills up" in norm too (report-only).
- G5 truncation: 64/64 kept in every (lang,c); nothing excluded.

## Predictions → Brier (frozen in PREREG_LITE)
| pred | P | outcome | Brier |
|---|---|---|---|
| P1 eng positive control (strict decrease + drop ≥10) | 0.85 | **TRUE** | 0.0225 |
| P2 ≥2/5 langs token-knee < 0.75×K_eng | 0.55 | **FALSE** (0/5; deu/arb knees LATER) | 0.3025 |
| P3 wrong-token decode = translation, all ≥40 chrF | 0.80 | **TRUE** (53.4–66.9) | 0.0400 |
| P4 centering |Δ| < 3 chrF at c=1 (mean) | 0.55 | **TRUE** (−0.02) | 0.2025 |
| P5 c=4 ordering: eng top, jpn/zho bottom | 0.55 | **TRUE** (eng 44.9; zho 14.3 min) | 0.2025 |

**Mean Brier = 0.154.** P2's miss is the row's finding: the tax hypothesis located the
penalty in the wrong coordinate (knee position in tokens) — it is a level penalty plus a
modest content-knee deficit, and token-count inflation (deu/arb) is capacity-neutral.

## Limitations / what did NOT run
- **chrF cross-script level confound (main caveat):** absolute chrF levels for jpn/zho
  are deflated by punctuation/normalization mismatches (decoder emits ASCII ",." for 、。)
  and logographic char statistics — the eng-vs-jpn/zho LEVEL gap is directionally real
  (matches 046 FVU, and B1-vs-eng-reference scores jump to 53–55) but its magnitude is
  not script-fair. Relative knees partially cancel this; cross-language knee-SHAPE could
  still inherit some chrF nonlinearity. tur (Latin script, chrF-fair) independently shows
  a real level tax (59.8 vs 89.7) and early content knee (1.74).
- B1 > A for jpn/zho (English decode of a Japanese z beats Japanese decode on chrF) —
  likely mostly the same artifact + possible decoder English bias; not over-read.
- Concatenated FLORES rows ≠ natural long sentences (discourse pasting); knee from 6
  bins × 64 items, greedy only, single encoder/decoder pair, news domain.
- The B2−B1 length interaction (centering helps at c≥2) is post-hoc; only c=1 was
  preregistered (P4). No causal steering test of the offset (that is row 064's job).
- Nothing truncated; all preregistered cells + gates ran at full n.

## Follow-up worth funding? **Y (narrow).**
1. Row 064 (language-vector) is now sharpened: the offset is removal-safe and
   removal-HELPS near the knee — test the reverse direction (adding μ_L − μ_eng to an
   English z: does it translate? at what fidelity cost vs token-switch translation?).
2. Script-fair fidelity metric (word/morpheme-level or punctuation-normalized) to
   de-confound the CJK level tax; cheap re-analysis of the saved decodes.
3. The "centering frees capacity past the knee" effect (+5 chrF for deu/tur/jpn) as a
   practical trick + probe of WHAT the freed dimensions carried.

## Provenance / hygiene
Repo: PREREG_LITE.md (frozen pre-compute), src/{run_063.py,run_063.sh}, out/{results_063_
full.json, decodes_063_full_s{0,1,2}.json, run.log}. Box 063 dir 34 MB (items json +
z npz kept box-side); FLORES reused in place from 046 (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.