# RESULT — 034 negation-operator (Campaign100 MANIFEST row 034)

**Tier: T3-exploratory.** Verdict: ★ **POSITIVE, certified.** A single linear direction in SONAR
z-space is a **causal, dose-responsive, content-specific negation operator that GENERALIZES from
templated to NATURAL sentences** — promoting 033's templated finding. All 6 gates pass; all 5
frozen predictions resolve TRUE (**Brier 0.1375**). One honest caveat: the latent offset does **not
beat a naive rule-based "insert-not" string baseline** on correctness/preservation — its value is
mechanistic (a linear negation code exists and is causal), not practical.

## What ran
- **Stimuli (natural, NOT templated).** 021's 1500-sentence real corpus (C4/cpool family). LOCAL
  neutral codex negated 100 TRAIN affirmatives (varied devices: not 78 / no 7 / never 7 / cannot 5 /
  fails_to 2 / lacks 1) and produced counterparts for 56 held-out TEST affirmatives (55 declarative +
  1 question; long n=3) and 40 naturally-negative sentences (for undo). TRAIN/TEST are **disjoint
  sentence sets**.
- **Box GPU decode** (phys GPU0 / CVD=0, tmux c100_034): encode all, fit `offset_nat =
  mean(z_neg−z_aff)` over 100 TRAIN pairs; refit `offset_tmpl` from 033's templated negation-train
  pairs; `offset_rand` = norm-matched Gaussian null. 688 greedy decode jobs (add/undo × 4 doses +
  baseline/ceiling/templated/random), re-encode + chrF. 90 s, det_ok True.
- **LOCAL codex judge** (744 records, neutral `flipped`/`preserved`, no attack vocab, **0 parse
  fails**) → analysis. Manager hand-check **14/15** agree (1 borderline: an α=2.0 double-negative).

## Offset geometry (the headline mechanism)
| offset | ‖off‖ | diff_align (1=perfectly linear) |
|---|---|---|
| natural (100 pairs) | 0.038 | **0.653** |
| templated (033, refit) | 0.058 | 0.839 |
| random (norm-matched) | 0.038 | — (cos_to_nat 0.027) |

**cos(offset_nat, offset_tmpl) = 0.856** — the natural-text and templated negation directions are
nearly parallel. z-norms flat (aff 0.205 / neg 0.208). Natural negation is a *slightly noisier but
same* direction as the clean templated one.

## Causal results (held-out natural sentences)
**ADD (56 aff → negate), dose-response — textbook rise-then-garble:**

| α | flip-rate | soft-flip | preserved | chrF(flip vs base-decode) |
|---|---|---|---|---|
| 0.5 | 0.00 | 0.00 | 0.93 | 98.6 |
| 1.0 | 0.64 | 0.68 | 0.93 | 93.8 |
| **1.5** | **0.84** | 0.92 | 0.84 | 91.2 |
| 2.0 | 0.59 | 0.79 | 0.66 | 89.4 |

Peaks at α=1.5 (offset norm 0.038 is under-scaled for longer natural sentences; needs ~1.5× to fully
cross the polarity boundary), then **over-steers into garble** at α=2.0 (flip falls, preservation
0.93→0.66, double-"not" and content corruption, e.g. *"As the storm did not rag…"*). At α=1.0 clean:
*"film production is **not** a meticulous process"*, *"military operations against ISIS have **not**
intensified"*.

- **Generalizes across categories** (@α=1.5): short 1.00 (n=13), long 1.00 (n=3), question 1.00
  (n=1), declarative 0.77 (n=39). (long/question underpowered — the corpus yielded few; caveat.)
- **UNDO (40 naturally-negative → affirmative):** flip 0.23 / 0.63 / 0.63 / **0.65** at α
  0.5/1/1.5/2. Best 0.65 (>0.5), near its own harder ceiling (0.80 — double-negatives like *"not
  without its challenges"* are hard to affirm). e.g. *"**not** everyone is enthusiastic" → "everyone
  is enthusiastic"*.
- **Specificity:** among successful flips, chrF(flip vs the model's own baseline decode) = **0.921** —
  the offset changes essentially only polarity, not content.

## Gates / baselines (all PASS)
| gate | value | pass |
|---|---|---|
| G_ceiling (true-neg decodes as neg) | 0.93 ≥ 0.90 | ✓ |
| G_baseline (unchanged z flip) | 0.00 ≤ 0.15 | ✓ |
| G_random (norm-matched dir flip) | **0.00** ≤ 0.15 | ✓ |
| G_parse | 0/744 | ✓ |
| G_det | True | ✓ |
| G_norm (aff≈neg norm) | 0.205 / 0.208 | ✓ |

Random norm-matched direction **never flips** (0.00) → the flip is offset-*specific*, not a norm
artifact. Baseline (no offset) 0.00.

## Predictions (frozen in PREREG_LITE) → Brier 0.1375
| # | prediction | p | outcome |
|---|---|---|---|
| a | natural flip-rate > 0.6 @ best α | 0.70 | **TRUE** (0.84) |
| b | dose-response monotone-then-saturate/garble | 0.82 | **TRUE** (rise 0→0.64→0.84, garble@2.0) |
| c | undo > 0.5 on naturally-negative | 0.55 | **TRUE** (0.65) |
| d | specific — content chrF > 0.6 among flips | 0.60 | **TRUE** (0.921) |
| e | templated-033 offset transfers > 0.4 | 0.55 | **TRUE** (0.71) |

All five hit; Brier 0.1375 is **under-confident** (the 033 prior justified higher c/d/e). The
templated offset transferring at **0.71** flip (preserved 0.79) is the cleanest confirmation that
negation is one direction across template and natural text.

## Honest caveat / negative sub-finding
The deterministic **"insert-not" STRING baseline beats the latent offset**: flip 0.89 (vs offset best
0.84) and preservation **0.98** (vs 0.84). So the offset is NOT a better *practical* negator than
naive string editing — string insertion is a strong, high-precision baseline. The offset's
contribution is **mechanistic**: it demonstrates negation is encoded as a single causal linear
direction in the sentence embedding, recoverable and steerable, which string editing says nothing
about. The string baseline also only produces mechanical "not"/"It is not the case that"; the offset
naturally realizes varied devices (does not / never / no).

## Limitations
One AE (SONAR), one corpus family, greedy decode, single codex judge (14/15 hand-agree). long/question
categories underpowered (n=3/1). Undo ceiling itself only 0.80 (affirming double-negatives is hard) so
the undo result is bounded by stimulus difficulty, not just the operator. Natural offset align 0.653 <
templated 0.839 — the direction is real but noisier on diverse text, consistent with the α≈1.5 optimum.

## Follow-up worth funding? **Y (narrow).**
- The negation direction as a **latent monitor / steering primitive** (feeds 080 sonar-causal-steering,
  086 latent-monitor): a single vector whose addition provably flips a semantic property.
- `diff_align` again pre-screens linearity (0.65 natural vs 0.84 templated predicts the mild
  degradation) — cheap "is T linear" gauge, consistent with 033.
- Dose-optimum >1.0 for natural text (offset under-scaled) is a general lesson for latent operators fit
  by mean-difference on short templates then applied to long text.

Artifacts: `out/{stimuli,points,offsets,meta,judge,analysis}.json`, `src/`, this file. Box out kept;
GPU0-only honored (GPU2/GPU3 + all foreign tmux untouched); 021/033 out read-only; local commit, no push.