Steering the unnamed direction on the factor chart

The factor chart's deepest hole was steered with the same design and controls as the principal-component one; it gives a monotone Agreeableness-down, Conscientiousness-up profile, but it is the only one of the three directions that degenerates (42% looping at alpha -2), it matches the chart's prediction on 3 of 5 signs against 5 of 5 before, and the random control in the same span matches almost as well.

Steering the unnamed direction on the factor chart

Where the direction comes from is Where no word goes - the hole on the factor chart. This page is what happened when it was steered. The principal-component version of the same experiment, which this replaces as the current claim, is Steering the unnamed direction.

The design, unchanged

qwen35/build_alien_spec_fa.py copies build_alien_spec.py exactly: the same alphas -2, -1, 0, +1, +2, the same reference norm 0.8102592902648793 taken from phase10_runs/steer_spec.json, the same 24-prompt battery, and the same two controls. zoo-alien-fa.service is a copy of zoo-alien.service and ran

modal run --detach steer_fix.py --spec phase10_runs/alien_spec_fa.json \
    --out phase10_runs/alien_results_fa.json

so this corpus is thinking-off at 512 tokens like every corrected steering run (The thinking-default trap and what it withdrew). steer_fix.py renormalises the merged delta to unit Frobenius over the whole model before scaling by alpha * ref, so the coefficient scale of a direction does not set the dose - alpha does, in the same units as every published direction. Judged blind into phase10_runs/judged_alien_fa.json (Claude Sonnet 4.5 via OpenRouter, 360 records, 0 failed calls; repeat reliability r = 0.860 to 0.885 across the five scales on n = 18 repeats).

The three directions and where they sit, analysis/alien_steer_fa.json#gap and #nearest:

The shuffle control's gap is measured on the 37% of it that lies inside the chart (phase10_runs/alien_spec_fa.json#jobs[1].chart_coords), so 17.8 and 54.8 are not the same measurement; permuting the coefficients across traits mostly moves the direction out of the five-factor span rather than around inside it. That was true of the principal-component shuffle too and is what makes it a control for "unusual mixtures break the model" rather than for direction.

Damage at matched strength

Fraction of the 24 responses that loop, same definition as every steering page (a 10-word window repeating four times), analysis/alien_steer_fa.json#<direction>.degen:

This reverses the principal-component reading. There the blog page could say "The random direction in the same subspace does more damage than the unnamed one, not less" - analysis/alien_steer.json gives span_random 0.3333333333333333 at alpha -2 against 0.08333333333333333 for alien_k5, with the shuffle at 0.0 throughout. On the factor chart the unnamed direction is the only one of the three that degenerates anywhere, and it does so on 10 of 24 responses at alpha -2. At every other strength it is intact, and so is everything else.

So the pre-registered pair of readings splits rather than resolving. Within |alpha| <= 1 and at +2 the direction is habitable and gives the coherent profile below; at -2 it is not. The honest summary is that the factor chart's deepest hole has a habitable side and a thin one, and the thin side is the negative pole.

The judged curves

analysis/alien_steer_fa.json#alien_fa.curve, blind Big Five means over the 24 prompts. The alpha -2 row is the one where 42% of the responses loop and should be read as a mean over partly degenerate text.

Conscientiousness rises monotonically from 3.4166666666666665 to 6.083333333333333, the largest movement of any scale on any of the three directions. Agreeableness falls from 5.583333333333333 at -1 to 3.875 at +2 and Emotional Stability from 5.125 to 4.041666666666667. Extraversion barely moves at all (4.0 to 4.083333333333333).

Mean response lengths (#alien_fa.len) run 1880.2916666666667, 1373.0, 1845.25, 1936.875, 1766.4166666666667 - no collapse, unlike span_random_fa, which falls to 880.75 characters at +2 and 1076.2083333333333 at -2 without looping.

Did the chart predict the behaviour?

analysis/alien_match_fa.json. pred is the direction's coordinates on the five named Big Five axes, computed from weights alone before any text existed, exactly from results/gram_sweep.npz (analyse_alien_steer_fa.py:big_five_coords); obs is how the blind judge's mean moved from alpha -2 to +2.

signs: 3 of 5. r: 0.7438221950472093.

Against the principal-component run's 5 of 5 and analysis/alien_match.json#r = 0.8142138888404568, this is weaker. Two things are worth saying about it rather than around it:

• the two misses are the two scales the chart barely committed to. The predicted Extraversion coordinate is -0.007337834635425705 and Agreeableness +0.06798030634328894, an order of magnitude smaller than the other three; the three scales the chart did commit to all match, and the largest predicted magnitude (Emotional Stability) is a match.
• the controls match nearly as well. Scored against the same pred, span_random_fa also gets 3 of 5 signs at r = 0.7343440116564208 and alien_fa_shuffle gets 3 of 5 at r = 0.4803937317774778 (analysis/alien_steer_fa.json#<direction>.signs, #<direction>.r). On the PC chart the shuffle control managed 2 of 5. The reason is visible in the table above: Conscientiousness rises by +2.6666666666666665 under alien_fa and +2.583333333333333 under span_random_fa, and that one shared movement carries most of the correlation for both. On this evidence the r for the unnamed direction is not evidence that the chart predicted anything direction-specific. The comparison the PC page could make - prediction beats control - does not reproduce.

What this does and does not establish

It establishes that the deepest hole in the five-factor chart is steerable, gives a monotone and legible dose-response on three scales, and does not break the model except at its negative extreme. It does not establish that the chart predicts the behaviour of a direction chosen for its angle, because a random direction in the same span was predicted about as well by the same coordinates. Whether that is a property of this chart or of the 24-prompt battery is untested.

Where the numbers are used

qwen35/build_blog_page.py: coverage_svg() now draws the factor-chart k sweep as the primary curve with the principal-component gap behind it as a dashed line at the same k, and alien_card() reads the _fa files, quotes phase10_runs/alien_results_fa.json directly at alpha -2 and +2, generates its one-line character sketch from analysis/alien_match_fa.json#pred, and carries one generated sentence comparing the two charts. The card falls back to the principal-component version if the _fa files are absent. alien_verdict() and the surrounding prose still read the principal-component files and are owned elsewhere; see the register in Factor-first migration.

Related: Steering the unnamed direction, Where no word goes - the hole on the factor chart, Where no word goes - the hole and the alien direction, The factor chart, Steering the base model along weight-space directions, The thinking-default trap and what it withdrew, Judged evaluations of the trait adapters.