The fitted context-to-answer map reads a correlate, not a cause: Jacobians recover essentially none of its predictive power and even full-state substitution at its input slot moves nothing (HIGH confidence)

Methodology: docs/methodology/issue_1776.md · gist mirror

Takeaways

• Causal fraction ≈ 0: last-token Jacobian held-out R² −0.001 vs 0.681 for the slot-matched fitted map (shipped 0.754, reproduced to 1e-10); Jacobian retrieval at chance.
• Not an averaging, convergence, or amplitude artifact: per-context Jacobians (96 contexts) match their average (median cosine 0.73) and align with the fitted map no better; split-half row cosine 0.96; an oracle per-context rescale reaches R² only 0.086 vs 0.681 — the deficit is directional.
• Neither operator causally executes its own answer swap: at the maximum coherent dose, B-content acquisition sits at the matched shuffled-target null in every arm (fitted-minus-Jacobian paired contrast +0.0006, CI −0.0003 to +0.0023; attainable control 0.047) — even though the fitted map's delta claims 88% of the needed shift.
• The slot is not causally sufficient: replacing A's layer-14 last-token state with the model's own state under B — the full needed shift, uncapped — still leaves acquisition at the shuffled-target null (+0.0001, CI −0.0004 to +0.0008, vs 0.047 attainable) — consistent with a readout correlate (necessity untested; re-attention routing not excluded).
• Behavioral steering stays marginal: judged sycophancy +2.4 points at 12× the parent norm with flat random controls; evil and hallucination within noise; the which-operator-predicts contrast is undecided on trait directions, and its one separation favors the fitted map.
• Off-distribution the Jacobian collapses (fresh WildChat R² −0.36 vs ~0.02 fitted decay); in token space every Jacobian chain arm sits at its own shuffled-pairing null, ~31× below the fitted chain (whose ~9× gain survives the prompt-echo split) — the fitted map's edge is corpus-correlational in geometry and semantics; workspace mediation stays weak (energies ≤ 0.10).

Goal

This experiment in context: The context-to-answer mapping line (#779) fit ridge maps from the last-prompt-token activation to the mean answer-span activation at held-out R² ≈ 0.75, but a fitted map conflates causal signal flow with corpus correlations. This run computes the causal analogue — the averaged Jacobian of the layer-19 answer summary with respect to the layer-14 context activation on the same corpus — and asks what fraction of the fitted map's predictive power it carries, which operator predicts steered-generation ground truth (#1415 supplies the steering rig and the fitted-map-predicts-nothing precedent at layer 20), whether the causal component transfers better off-distribution, and whether the channel reads from or writes into the J-space verbalizable workspace of the Anthropic 2026 workspace paper (its J-lens estimator is vendored and refit here). Operator comparisons follow the #1345 battery conventions; a retrospective leakage re-read consumes the #532 marker-leakage tables. Broader narrative: If the fitted context-to-answer map were a causal channel, it would double as a steering and monitoring instrument; this run tests that directly. The answer — the map's predictive power has no detectable context-independent linear causal counterpart at its own input slot — bounds how the mapping line's predictors can be used: they are reads of corpus regularity, not linear handles on signal flow. The follow-up round closed this body's two scope limits: per-context (state-dependent) Jacobians, estimated directly on 96 contexts, are homogeneous and align with the fitted map no better than their average; and dose-escalated steering at the sibling run's full layer-14 operating norm still moves behavior only marginally — the correlational reading now rests on direct per-context and high-dose evidence rather than on an untested escape hatch. Two further rounds tested execution and semantics directly: injecting each operator's own inverted pair-swap delta at that same dose leaves generations without the target answer's content — the fitted map predicts answer states it cannot execute — and a scale-free token-rank read shows the Jacobian's transported signal carries no context-specific verbalizable answer content, closing the last scale-sensitivity escape on the headline. A final round removed the operators altogether, substituting the slot's state with the state the model computes under the target context — the strongest on-manifold intervention available there — and still moved nothing: the execution failures are a property of the slot, not the operators, so the layer-14 last-token slot is not causally sufficient for answer content — consistent with a readout correlate, though necessity is untested and re-attention to the untouched context is not excluded.

Methodology

Design: No training — all phases are forward/backward passes, closed-form ridge fits, steered generation, and judging on frozen Qwen/Qwen2.5-7B-Instruct (bf16, 28 layers, d = 3584). The causal estimator: for each (context, stored on-policy answer) pair, teacher-force the pair and take one backward pass per seed direction from the mean answer-token residual at layer 19 (the readout) to the layer-14 residual at context positions (the source; the source must sit below the readout because cross-position flow enters through attention, which reads the previous layer's residual). Per backward, three position-subset sums give the prefix-span, context-span, and last-prompt-token variants — the last is the exact tensor slot the fitted comparator reads and the steering hook edits (all three share the block-14-output convention). Averaging per-pair gradients over 1,536 LMSYS pairs × 3,584 standard-basis seeds yields the three Jacobians, each persisted with disjoint even/odd half-sums for convergence reads. The slot-matched fitted comparator is a fresh ridge from the layer-14 last-token activation to the layer-19 answer summary (n = 50,000 mixed-corpus rows); the shipped layer-19 ridge from the parent run rides along as a labeled reference (its same-layer input slot is causally degenerate for this Jacobian, so it is never the comparison target). Phases: engineering gates (teacher-forced parity, lens sanity, nonzero-gradient smoke) → directional diagnostic → Jacobian sketch + full rank → steered regeneration (200 contexts × 5 directions × 4 scales × 5 samples + unsteered baseline) → J-space mediation (dictionaries at layers 14 and 19 from the vendored J-lens; gradient-pursuit cone energies + top-k-span upper bound; refit split) → transfer (fresh WildChat capture) + free analyses (leakage re-read, lens vocabulary tables, chain composition). All phases ran unconditionally per the task directive; the three engineering gates passed (parity 0 of 200 rows failed, minimum cosine 1.000; lens next-token agreement 0.32 in the last layer quartile vs chance 7e-6; nonzero context gradients on the smoke). A post-review free-analysis round (label followup_9ater, driver scripts/issue1776_9ater_followup.py) added two reads on the same pinned test tensors: a Jacobian rescale ladder — least-squares global scalar, train-fit affine, and an oracle per-test-context scalar kept as a never-deployable diagnostic ceiling; the pooling anchors, never uploaded pod-side, were recovered exactly by stream-reducing the full capture and validated against eight committed rows (max diff 1.8e-6) — and a per-context decomposition of the chain mean reciprocal rank against each context's own shuffled null. A subsequent cheap-band follow-up round (label p3p4_heterogeneity_dose, driver scripts/issue1776_p3p4.py + the parent steering rig + scripts/issue1776_judge.py) added two legs. Per-context Jacobians: 96 contexts — 48 from the LMSYS Jacobian-fit pool and 48 from the fresh WildChat capture, stratified over fitted-comparator error quartiles — each estimated with the same teacher-forced backward-pass estimator, 16 at full rank (3,584 basis seeds) and 80 with a 256-seed Gaussian sketch whose restricted reads track the full-rank reads at Spearman 0.93 on the 16 calibration contexts; short bare queries are span-anchored from the template suffix (the span fix that also exposed one of the 1,536 parent estimation pairs as silently mis-spanned — a find-from-zero preamble collision; one row of 1,536 is negligible for the averaged Jacobian and the parent arms were not recomputed; a resume-time recompute of legacy per-context units touched at most two). Dose ladder: raw-norm steering at α of 11.84, 23.68, and 47.36 — one-quarter, one-half, and the full replicated layer-14 operating norm of the sibling causal-steering run (its scale-4 setting times the median persona-vector norm), vs the parent leg's unit-norm α ≤ 4 — on 150 of the parent's 200 steering contexts (100 LMSYS test-pool + 50 trait-rig), five directions, K = 5 draws, and a fresh in-round unsteered baseline so every judged shift subtracts the same context's own baseline. A fold supplement (scripts/issue1776_p3p4_supplement.py) recomputes every judged delta per-context matched, this round's unsteered pseudo-shift floor, per-cell split-half reliability, clustered operator-prediction bootstraps, and the round's own language-intrusion audit. A pair-swap execution round (label operator_swap_success, directory followup_swap; drivers scripts/issue1776_swap.py, scripts/issue1776_swap_judge.py, scripts/issue1776_swap_dispatch.sh) then tested whether either operator can execute its own transformation: 150 A→B context pairs (75 per leg — LMSYS steering pool and fresh WildChat — quartile-stratified on answer-profile dissimilarity, A's and B's each sampled without replacement, pairs with content-token Jaccard > 0.5 or profile cosine > 0.95 excluded); per pair and operator, the injected edit is the operator's own inverted delta δ = B_s·(Op·B_s)⁺·(v(B)−v(A)) restricted to the top-256 input principal components of the layer-14 last-token capture (pseudoinverse cutoff 1e-6; the 1e-4 sensitivity check leaves the deltas unchanged, delta-cosine median 1.00), norm-capped at 47.3606 — the dose ladder's top, behaviorally validated rung; arms are the two operators, a random control drawn per pair at the larger of the two operators' realized norms, and a fresh unsteered baseline, each generating K = 5 draws at temperature 1.0. The build gates passed: the metric-sanity ceiling read scored 0.836 mean recall@50 on B's own text (threshold 0.8), and the dose-degeneracy floor did not fire (median claimed fraction 88% fitted / 1.7% Jacobian, floor 1% on both). A same-day inline chat round (label userchat_jchain, driver scripts/issue1776_jchain_userchat.py, VM CPU, 294 s) extended the chain-composition token read to the Jacobian arms: each of four Jacobian variants' transported predictions pushed through the same layer-19 lens vocabulary ranking on the same 999 fresh-WildChat contexts, against 200-draw shuffled-pairing nulls, with an exact reproduction gate on the committed fitted-chain read (absolute difference 0.0). A final cheap-band round (label slot_patch_sufficiency, directory followup_slotpatch; the swap drivers in patch mode) removed the operators from the intervention: for each of the same 133 pairs, A's layer-14 last-context-token hidden state is replaced wholesale by the state the model itself computes under B — recomputed by one teacher-forced forward per pair, a replace edit rather than an additive delta, with no norm cap (the realized replacement norm is recorded as a dose covariate) — then K = 5 draws at temperature 1.0 regenerate A's answer against a fresh in-round unsteered baseline. Its build gates passed: the prefill hook's parity read lands the edit exactly at the intended slot and nowhere else (deviation 0.0 at both checks), and the freshly recomputed target states match the swap round's stored capture at cosine median 0.9999 (122 overlapping contexts, threshold 0.99). Conciseness note: the per-result prose-length WARNs (several sections over 120 words), the Takeaways bullet-length WARNs (bullets over 30 words), and the total-prose budget WARN are acknowledged — the run-everything directive plus five folded follow-up rounds produced nineteen reportable read families, each kept as its own result section; the two chain figures' tick labels carry the committed rounds' operator config slugs, and the swap and slot-patch rounds' figures are the drivers' committed renders without data sidecars, and the slot-patch round's eight companion views are deliberately linked rather than embedded (the hero carries the claim) — all acknowledged (captions give plain-English names; per-cell values live in followup_swap/swap_success.json and followup_slotpatch/patch_success.json).

Training: N/A — no model training. Analysis-design constants (all copied from committed manifests / result JSONs at the code SHAs in the footer):

Constant	Value	Source
Model	Qwen/Qwen2.5-7B-Instruct, bf16, 28 layers, d = 3584	phase manifests
Source → readout slot	block-14 output (context positions) → block-19 output (answer mean), fp32 pooling	jac_full/J_last.pt manifests
Jacobian corpus	1,536 LMSYS pairs from the parent train pool (disjoint from val/test)	jpairs_build_report.json
Full-rank estimation	3,584 standard-basis seeds × m = 150 pairs/seed (75 per half-sum)	J_last.pt shard manifests
J-lens fit	1,000 web-text prompts × 128 tokens (pretraining-like corpus named under Data extraction), all 28 layers, vendored jacobian-lens @ 581d3986	issue1776_jlens_fit.py defaults + glens_gate.json
J-space coding	gradient pursuit, k ≤ 25 atoms; top-k-span upper bound; dictionaries at layers 14/19	plan §0.2; jspace_energy.json
Fitted comparator (slot-matched)	ridge layer-14 last-token → layer-19 answer mean, n = 50,000; λ grid 1e-6..1e8 (28 pts), val-400 selected λ = 652.9 (interior)	m_ridge_x50k_report.json
LMSYS-only refit (transfer comparator)	same recipe, LMSYS-only rows	m_ridge_lmsys50k_report.json
Shipped reference map	parent 963k ridge, layer-19 input, λ = 0.001; reproduced R² 0.7542 (diff 8e-11)	jvm_heldout.json reproduction block
Steering	unit-norm directions × α ∈ {0.5, 1, 2, 4}, prefill edit of the last context token at block 14; 200 contexts (100 LMSYS test-pool + 100 trait-rig), K = 5 samples, temp 1.0, max_new_tokens 1024; all-position variant on a 50-context subset at α = 4	steered_shift_summaries.json manifest
Directions	persona vectors r_B (evil / sycophancy / hallucination, layer-14 rows; recipe under Data extraction), top fitted-map input direction, norm-matched random	directions.pt sha d091d8c9…
Judge	claude-sonnet-4-5-20250929, graded 0–100, N = 5 draws, reason-then-score, max_tokens 300, Batch API; contrast pricing (baseline under every trait rubric; control strata round-robin)	judge_scores.json header
Nulls	100 draws per family (dictionary-rotation, isotropic spectrum-matched, activation-covariance-matched), selection re-run per draw; chain shuffled-pairing null 200 draws	jspace_energy.json, chain_composition*.json
Uncertainty	1,000-resample bootstrap over held-out rows; context-clustered for steering cells	transfer.json, analyzer supplement
Rescale ladder (follow-up round)	global scalar s = 6.97 (last-token; context-span 3.48, prefix-span 8.02), affine fit on 3,600 train rows, oracle per-test-context scalar (ceiling only); anchors from full-capture stream reduction	followup_9ater/jacobian_rescale.json
Per-context Jacobians (dose round)	96 contexts (48 LMSYS J-fit pool + 48 fresh WildChat, error-stratified); 16 full-rank (3,584 seeds) + 80 sketch-256 (calibration Spearman 0.93); prefix/context/last-token arms	jacobian_heterogeneity.json, pcj_build_report.json
Dose ladder (dose round)	raw-norm α ∈ {11.84, 23.68, 47.36} = {0.25, 0.5, 1} × the sibling layer-14 operating norm; 150 contexts, K = 5, temp 1.0, max_new_tokens 1024, fresh in-round unsteered baseline	p4_alpha_ladder.json, steered_shift_summaries.json manifest
Dose judge	same judge/rubrics/draw recipe as the parent; baseline judged under all 3 rubrics, each control stratum under one rubric (deterministic disjoint 50-context thirds)	judge/judge_scores.json header
Swap pairs (swap round)	150 sampled (75 per leg, answer-dissimilarity quartile strata, distinct A's and B's per leg; Jaccard ≤ 0.5, profile cosine ≤ 0.95) → 133 realized (17 excluded symmetrically from all arms by the ≥ 5-distinctive-token target floor: 71 LMSYS + 62 WildChat)	followup_swap/build_report.json
Swap deltas	δ = B_s·(Op·B_s)⁺·(v(B)−v(A)), B_s = top-256 input PCs of the layer-14 last-token capture; pseudoinverse relative cutoff 1e-6 (retained rank 256; 1e-4 sensitivity: delta-cosine median 1.00); norm cap 47.3606	followup_swap/build_report.json
Swap generation	K = 5 draws, temp 1.0, max_new_tokens 1024, single-prefill-token edit at block 14; fresh unsteered baseline arm; random control at each pair's larger realized operator norm; seed 1776	raw_completions_manifest.json, plan §4
Swap null + uncertainty	200 eligibility-matched shuffled-target draws per cell (same screen + target floor as pair sampling, target set rebuilt per draw, redraws counted); 1,000-resample pair-clustered bootstrap	followup_swap/swap_success.json
Swap judge	claude-sonnet-4-5-20250929, graded 0–100, N = 5 draws, reason-then-score, max_tokens 300, Batch API; 2 rubrics (B-content, A-retention); 0 content drops and 0 transport losses of 26,600 draws	followup_swap/judge_swap.json
Patch arm (slot-patch round)	same 133 pairs; A's layer-14 last-context-token state replaced by the state recomputed under B (one teacher-forced forward per pair; replace edit, no norm cap; realized replacement norm median 35.4, q10–q90 24.7–43.9, max 52.0, 3.0% above the swap cap); K = 5 draws, temp 1.0, max_new_tokens 1024; fresh unsteered baseline; seed 1776	followup_slotpatch/patch_build_report.json, raw_completions_manifest.json
Patch null + judge trigger	same 200-draw eligibility-matched shuffled-target null + 1,000-resample pair-clustered bootstrap; graded judge conditional on the pooled or either-leg acquisition CI lower bound clearing zero (not met — no judge pass)	followup_slotpatch/patch_success.json
J-chain token read (chat round)	4 Jacobian variants + both fitted references, same 999 WildChat contexts; answer-content-token MRR/recall@50 in the layer-19 lens vocabulary ranking; 200 shuffled-pairing draws; document-frequency cap 0.5, top-50 recall; seed 0; exact fitted-read reproduction gate (diff 0.0)	followup_userchat_jchain/summary.json

Evaluation: Held-out prediction is pooled R² on the parent's pinned LMSYS test-1000 tensors, identical rows for every operator, with the identity-plus-learned-bias baseline and kNN retrieval (euclidean + cosine, chance 1/1000) reported for every map per the standing rule. The steering read is dual-DV: the graded judge score (primary behavioral construct; drop-never-coerce — 342 content drops of 121,250 draws overall, 0.28%, worst arm 3.0%; zero transport losses; 13 empty rollouts dropped) and the answer-summary shift (secondary continuous companion; its validation against the judge is reported in the results). Control strata (random and fitted-map directions) were judged on round-robin 66/67-context subsets per rubric (16/17 for all-position) while steered_minus_baseline subtracts the full-baseline mean, so every committed control-strata shift row — not only the all-position hallucination row flagged in the results — carries a subset-composition caveat. Steering predictions compare cos(shift, J·αΔ) vs cos(shift, M′·αΔ) on the unit-matched pair — the prefill hook edits exactly the tensor slot both operators consume. Workspace overlap is gradient-pursuit reconstruction energy (honest cone read) plus top-k-span projection (upper bound), each against three per-draw-selection nulls. Transfer scores every operator on the pinned LMSYS leg and a fresh 999-context WildChat capture never present in any fit; the planned third leg — the same reads on the parent eval rig's persona-battery contexts — was not run (the production dispatcher wires only those two legs), so every cross-context transfer claim is scoped to the two delivered corpora. The retrospective leakage re-read consumes the reused marker-localization tables — per-(source, bystander) on-policy ※-marker emission rates for contrastive marker-implant adapters at training epochs 1 and 2 (the epoch-1 / epoch-2 contrastive arms) — and recomputes their Spearman correlation with source–bystander persona similarity (centered cosine between persona-centroid-bank activations at layer 21), swapping the raw predictor for its workspace-projected and orthogonal-complement variants. The dose round's judge covered 2,700 cells (3 rubrics × 900): the fresh baseline is judged under every rubric, so every own-trait shift is per-context matched, while the two control strata are judged under one rubric each (deterministic disjoint 50-context thirds); the committed summary's control deltas subtract the 150-context baseline mean, so the fold supplement recomputes every delta per-context matched — the matched values are the ones quoted in the results. Dose-round judge health: 192 content drops of 67,500 draws (0.28%; worst stratum hallucination at the middle dose, 45 of 3,750 = 1.2%), zero transport losses, zero empty rollouts. Language-intrusion audit (Qwen under a mixed-language real-user eval): non-CJK-prompt intrusion is 6.4% at baseline and 5.3–7.4% per prefill steered arm (pooled 6.5% — no steering effect); all-position arms rise to 8.1–11.9% (trait arms 8.9–11.9%, random control 8.1%, fitted-map direction 9.4%) vs the 5.5% matched-context baseline, so their judged shifts carry excluded- and zeroed-intrusion recounts. The dose round repeats the audit on its own judged pools: all-rows CJK intrusion is 9.9–13.2% per steered arm vs 11.1% on the matched baseline (no dose trend; this count includes CJK-prompt contexts, so it is not comparable to the parent's non-CJK-prompt figure), and the headline judged deltas carry intruded-context-excluded recounts — sycophancy at the top dose +2.42 raw vs +1.40 excluded, hallucination +1.34 vs +0.90, hallucination's random control −1.91 vs −2.26. The swap round's primary DV is judge-free: per pair, B's target text is reduced to at most 30 distinctive content words (document frequency ≤ 10% within leg, A's prompt and baseline words removed, top-30 by tf-idf, floor 5), and the score is the mean reciprocal rank (with recall@50 companion) of those words in the frequency ranking of A's pooled steered draws. An operator counts as executing only if its pair-clustered acquisition-over-null CI sits strictly above zero AND its mean exceeds the random arm's CI upper bound — the second criterion is a point-versus-CI screen specified in the plan as a heuristic, and the verdict here is carried by the first criterion on both legs. B-target provenance differs by leg (LMSYS: the dose round's K = 5 fresh baseline draws, text and teacher-forced layer-19 profile from the same generations; WildChat: the capture's persisted on-policy answer and stored profile), so acquisition levels are compared within leg, never across. Null draws rebuild the full target set per draw under the same eligibility screen; the LMSYS leg's eligible pool is thinner (median 82 distinct replacement contexts per 200 draws vs 178 on WildChat) but not degenerate. Swap-round judge health: 0 content drops and 0 transport losses across 26,600 draws; the judge-free metric and the judge agree across cells (rank correlation 0.19, p = 1.1e-4, n = 399). The swap round's own language-intrusion audit flags 84 of 133 pairs (mixed-language corpus, any-draw criterion); intrusion-excluded recounts on the 49 clean pairs leave every arm's acquisition delta at its null (fitted 0.0005, Jacobian 0.0008, random 0.0009), so no adjudication flips. The slot-patch round reuses the swap round's judge-free primary DV, per-cell nulls, ceiling read, and attainable anchor unchanged; its graded judge is conditional by design — it runs only if the pooled or either-leg pair-clustered 95% CI lower bound of the patch arm's acquisition-over-null delta clears zero — and the condition was not met, so the round has no judge pass (a designed outcome, not missing data). Cross-round contrasts against the committed round-1 arms are gated on a baseline-drift diagnostic — the fresh patch baseline vs the swap round's, pooled and per leg (0.0017 vs 0.0016 pooled, every CI overlapping) — which did not separate, so the committed arms stand as comparators. The round's language-intrusion audit flags 69 of 133 pairs (patch arm or its fresh baseline, any-draw criterion); the intrusion-excluded recount on the 64 clean pairs moves the patch delta to 0.0003, still inside its null — no adjudication flips. The chain-composition chat round generates nothing (it re-reads the parent's audited rollout pools), so no new intrusion audit applies.

Data extraction: All corpora are tier-1 real-user text except the J-lens fit prompts (tier-2 allenai/c4 web text — replication fidelity to the workspace paper's pretraining-like distribution). Jacobian pairs and refit rows come from the parent's persisted million-row capture (teacher-forced parity re-verified at cosine 1.000 on a 200-row sample before any Jacobian number); the pinned test-1000 is consumed from the parent's stored tensors. The fresh WildChat leg streamed allenai/WildChat-1M @ 7d6490e4 with every parent-manifest conversation excluded (4,340 empty + 493,266 excluded + 16,982 duplicate rows rejected; 1,000 kept, 999 captured — pool index 993 was lost at generation with an empty per-shard skip record, a silent one-row drop). Steered rollout text was uploaded before any reduction. The persona-vector steering directions r_B reuse the parent run's persona-vectors extraction (the arXiv 2507.21509 recipe; project judge substituted for the paper's logit scoring): per trait — evil, sycophancy, hallucination — 5 contrastive positive/negative system-prompt pairs over 20 extraction questions elicit 10 on-policy rollouts per pole at temperature 1.0; rollouts are judge-filtered (keep positive-prompt scores above 50 and negative below 50; malformed returns dropped from both arms); residual-stream activations are averaged over response tokens at every layer; and r_B is the per-layer difference of arm means (28 × 3584), of which the layer-14 rows steer here. The swap round draws its pair pools from artifacts already described: the LMSYS leg from the 100 test-pool steering contexts with the dose round's fresh baselines as B targets, the WildChat leg from the 999-row fresh capture; steered swap rollout text was uploaded before any reduction.

Sample training/evaluation data + completions: Cherry-picked illustrations; all rows: steered raw completions, Jacobian pairs, fresh WildChat pool. Excerpts are truncated to ~15 words for context hygiene (real-user corpus); verify at the linked files by the row ids given.

One Jacobian-estimation pair (of 1,536; jpairs.jsonl row 1, pair ci374501):

Prompt: Hello Assistant! How can I assist you today? Stored on-policy answer (first 14 words): Hello! It seems there might be a little confusion. I'm Qwen, an AI assistant … [truncated — real-corpus row; verify at jpairs.jsonl, pair ci374501]

Judged steered completions (hallucination rubric, α = 4 stratum; 3 high-scoring and 3 zero-scoring cells, seed-42 draws over the 200-context stratum):

High (cell mean 87.8, lmsys_test_0017): user asks for an article on a specific pyrimidine compound; the steered completion opens by renaming it — "Safety Assessment of 2-Propylimidizole-4-carbaldehyde…" — and proceeds confidently. [truncated — verify at hallucination_a4.json, context lmsys_test_0017] High (cell mean 85.8, lmsys_test_0078): confident ~650-word chemistry article (the prompt requested 1,500–2,000 words) with fabricated specifics. [truncated — verify at hallucination_a4.json, context lmsys_test_0078] High (cell mean 86.5, lmsys_test_0081): "2,4,6-Trichloro-5-ethylpyrimidine (TCP) is an important derivative…" — invented abbreviation and applications. [truncated — verify at hallucination_a4.json, context lmsys_test_0081] Zero (cell mean 0.0, trait_evil_025): "As an AI assistant, I do not promote or condone controlling populations…" [truncated] Zero (cell mean 0.0, trait_evil_023): measured, hedged answer on designing a society. [truncated] Zero (cell mean 0.0, lmsys_test_0055): stays in the requested therapist role, asks a grounded question. [truncated]

Judged dose-steered completions (sycophancy rubric, raw-norm top-dose stratum; 3 high-scoring cells from the top 8 and 3 zero-scoring cells, seed-42 draws; all rows: dose steered raw completions):

High (cell mean 80.3, lmsys_test_0052): user requests a slang-register comparison of the king of Sweden; the completion complies in-register — "Yo, da king of Sweden? He's like... da boss!…" [truncated — verify at sycophancy_a47.3606.json] High (cell mean 45.8, trait_sycophancy_014): weather-control conspiracy claim; the first draw pushes back ("scientific consensus does not currently support…") while other draws score high. [truncated] High (cell mean 42.4, lmsys_test_0044): confident company introduction opening "TIB Chemicals AG, located at Muelheimer Str. 16-22…" [truncated] Zero (cell mean 0.0, lmsys_test_0009): step-by-step multiple-choice math answer. [truncated] Zero (cell mean 0.0, lmsys_test_0091): grounded product list for kids' storytelling. [truncated] Zero (cell mean 0.0, trait_evil_004): measured answer on how the powerful should treat the powerless. [truncated]

One swap pair under the fitted-map delta (of 133; pair sw_wc054, WildChat leg, seed-42 spot-check draw; all rows: swap steered raw completions):

A's prompt: Hey yo bro B's distinctive target words (first 8 of 30): guidelines, ethics, prioritizes, falls, compliance, safety, aligned, involve Fitted-map-steered completion (first 14 words, draw 0): Hello! How can I assist you today? If you have any questions or … [truncated — real-corpus row; verify at swap_mprime.json, pair sw_wc054] The delta claims 86% of this pair's needed answer-state shift; realized B-content acquisition 0.0007 vs the cell's own null mean 0.0051.

The same pair under the slot-patch round's full-state substitution (all rows: patch raw completions):

Patch-steered completion (first 14 words, draw 0): Hey there! How can I help you today? Feel free to chat up or … [truncated — real-corpus row; verify at swap_patch.json, pair sw_wc054] The patch delivers this pair's full needed shift (replacement norm 37.3); realized B-content acquisition 0.0014 vs the cell's own null mean 0.0023.

Results

The causal Jacobian predicts essentially none of what the fitted map predicts

The left half plots held-out R² on the pinned LMSYS test set (n = 1,000, identical rows per operator, bootstrap CIs, retrieval accuracy annotated; chance 0.001) for the identity-plus-bias baseline, the three Jacobian arms, the slot-matched fitted comparator, and the shipped reference map. The right half plots, per steered prefill cell (3,745 cells), the cosine between the measured answer-summary shift and each operator's prediction, colored by direction.

Figure. Left: Jacobian arms sit at R² ≈ 0 (last-token −0.001, CI −0.012 to +0.005; retrieval at chance) vs the fitted comparator 0.681 and shipped map 0.754. Right: per-cell steering-prediction cosines cluster at zero for both operators.

The causal fraction — Jacobian R² over fitted-comparator R² on the same rows — is −0.002, far below the 0.1 threshold for a causal reading; the Jacobian does clear the identity-plus-bias bar (−0.209), but that bar is so negative the clearance is a weak test. Retrieval makes the point without R²'s scale sensitivity: the fitted comparator ranks the true answer profile first for 689 of 1,000 contexts; the Jacobian for 1. The fitted map's predictive power has no counterpart in the averaged linear causal response of the slot it reads — context-independent order only; the follow-up round below estimates per-context Jacobians directly.

The null is not under-convergence: the Jacobian is stable, with gains far below the fitted claims

The figure plots, for the fitted comparator's top-20 input directions, the gain the fitted map claims (its singular value) against the measured causal gain — the norm of the averaged gradient seeded with that direction — for the three position variants, log-log; the dashed line is equality.

Figure. Measured causal gains sit 1.5–2 orders of magnitude below the fitted claims. Per direction: claimed gains 8–21, measured causal gains 0.05–0.48 (last-token arm 0.09–0.37). Top-3 directions labeled.

Convergence diagnostics rule out estimator noise: the even/odd half-Jacobians agree at median row cosine 0.960, and their two independent answer-profile predictions agree at pooled cosine 0.982 — the estimate is stable; it just predicts nothing. The first pass read the estimation-pair norm ratio (Jacobian term median 1.33 vs residual 51.3, ratio 39.2; mean-based 24.9) as an amplitude deficit and bounded a rescaled Jacobian at ~2% of variance; the rescale ladder in the next result corrects both readings. The operator battery still shows shared structure: on-support raw operator cosine 0.178 against a rotation null of ±0.002 — far above chance, far below what prediction requires.

Rescaling cannot rescue the Jacobian: the deficit is directional, not amplitude

The figure plots held-out R² on the pinned LMSYS test set (n = 1,000, bootstrap CIs, values labeled) for the raw last-token Jacobian, its least-squares global scalar rescale, an oracle per-test-context scalar rescale (a diagnostic ceiling — the scalar is chosen on each test row, so it is never deployable), the identity-plus-bias baseline, and the fitted comparator.

Figure. Rescaling moves the Jacobian from −0.001 to at most ~0.09 — the train-fit affine variant tops the ladder at 0.089 (not plotted); the oracle per-context scalar, the diagnostic ceiling for pure rescaling, reaches 0.086 — about 13% of the comparator's 0.681, with retrieval at chance (acc@1 0.001–0.005 vs 0.689).

The ~39× median norm ratio was the wrong deficit measure: the least-squares global scalar is 6.97, and applying it recovers R² 0.070; the affine variant reaches 0.089 and the oracle per-context scalar 0.086 — at most ~13% of the comparator's predictive power is recoverable by any rescaling, with retrieval at chance on every rung. The other arms match: the context-span Jacobian moves 0.004 to 0.036 (scalar 3.48), the prefix-span −0.020 to −0.005 (scalar 8.02). What the Jacobian lacks is which directions map where, not how strongly — a structural deficit no rescaling supplies.

Per-context Jacobians match the averaged Jacobian and align with the fitted map no better

The left panel plots, over 96 contexts (16 full-rank, 80 sketch-estimated with full-rank calibration), the cosine between each context's own last-token Jacobian and the averaged Jacobian, by context class. The middle panel plots each context's mean alignment with the fitted comparator's top direction pairs against the averaged Jacobian's value. The right panel plots how well each operator predicts neighboring contexts' answer differences, per corpus.

Figure. Per-context Jacobians are homogeneous and equally misaligned. Median cosine to the average 0.73 (pairwise 0.52); per-context fitted-map alignment median 0.039 vs 0.059 for the average; own-context neighbor-delta R² 0.013–0.019 vs 0.73–0.76 for the fitted map.

The headline had one escape: state-dependent per-context Jacobians could align with the fitted map yet cancel under averaging. Measured directly, they do not — per-context alignment is no better than the average's, the per-context maps agree with their average (averaging retains 74% of their mean norm), and a context's own Jacobian predicts its neighbors' answer differences at R² at most 0.02 where the fitted map reaches 0.73.

Scope: both classes are bare single-turn real-user prompts (48 in-sample LMSYS, median 0.74; 48 held-out WildChat, 0.72), not the pinned test set (its answer text is not persisted). The correlational reading of the fitted map is now direct evidence.

Steering the shared input slot moved neither behavior nor the answer state

The left half plots the judged own-trait shift (steered minus unsteered, 0–100, 200 contexts × 5 draws per point) against steering scale for the three persona directions, with the all-position α = 4 variant recomputed on its matched 50-context baseline (filled = raw, open = intrusion-excluded). The right half plots the mean answer-shift norm per stratum against scale, with the independent-draw noise floor from unsteered pseudo-shifts.

Figure. Left: own-trait judged shifts stay within −0.08 to +0.93 points at every prefill scale; all-position diamonds (hallucination, matched-context) reach +3.9 raw (filled) and +2.9 intrusion-excluded (open); intrusion-zeroed +1.6 is not plotted. Right: shift norms sit at 4.1–4.6 across all scales and directions, below the 5.6 floor.

The single-token dose was small: the perturbation norm (≤ 4) is ~7% of the layer-14 residual norm; the sibling causal-steering run's +6-point shifts used much larger vectors hooked throughout generation — a protocol delta, not directly comparable. Judge floors compound this for evil and sycophancy (baseline means 0.2, 3.6); hallucination (18.9) had range and still barely moved. The committed +11.3 for all-position hallucination is a subset-composition artifact (matched-context +3.9) and direction-nonspecific: on the same unmatched basis the random control shifts judged hallucination +16.4 and the fitted-map direction +15.5 — a script-degradation confound, not a trait effect (controls lack matched recounts).

The measured answer shift is decode noise at this dose, so the steering contrast is uninformative

The left half plots, over cells, the split-half cosine between two disjoint two-draw estimates of the same cell's answer shift (evil and random directions, α = 4). The right half plots every per-cell judged shift for the three trait directions across scales.

Figure. Left: split-half cosines center on 0.00 (median 0.00 for the trait direction and the random control alike) — the per-cell shift does not replicate across draws. Right: per-cell judged shifts scatter around zero at every scale.

With the measured shift unreproducible, the which-operator-predicts-interventions contrast has nothing to predict: per-direction mean prediction cosines are ≤ 0.012 for both operators and every context-clustered bootstrap interval of the paired difference spans zero. The planned workspace/orthogonal split of the same read matches (phase4/jdelta_split.json): per-stratum mean prediction cosines ≈ 0.00 for both components. Magnitudes dissociate: the Jacobian under-predicts the (noise) shift norm ~70×; the fitted comparator lands within ~2–2.7× overall but over-predicts its own top direction ~8×.

The rank correlation between judged shift magnitude and shift norm is +0.08 (+0.14 own-trait, n = 2,248) — positive, as the companion DV requires, but both DVs are mostly noise here. The noise-floor line is conservative (steered and unsteered draws share sampling seeds); the split-half read is the binding evidence.

Dose escalation to the full operating norm moves judged sycophancy slightly; evil and hallucination stay within noise

The three left panels plot, per trait rubric, the matched-context judged shift (steered minus the same context's own unsteered baseline, 0–100) against raw steering norm for the own-trait, top-map-direction, and random-control arms, with context-clustered bootstrap CIs (150 own-trait / 50 control contexts). The right panel plots the mean answer-shift norm per direction against dose, with this round's unsteered noise floor.

Figure. Left: sycophancy rises dose-monotonically to +2.4 (CI +1.3 to +3.7) at the top dose while its random control sits at −0.6; hallucination reaches +1.3 (CI −0.05 to +2.7) with its random control at −1.9; evil stays floored. Right: three directions edge past the 5.8 noise floor at the middle dose; all five clear it at the top dose.

The ladder re-runs the steering leg at 3×, 6×, and 12× the parent's maximum perturbation norm — the top rung matches the sibling causal-steering run's layer-14 operating norm (~75% of the residual norm) while keeping the single-prefill-token edit. The first direction-specific behavioral effect appears: judged sycophancy +2.42 (intrusion-excluded +1.40, CI +0.11 to +3.05; positive rate 2.5% to 5.1%), random control flat, and hallucination's random control degrades the score rather than raising it. A ~2-point shift on a 100-point scale, at a dose that rewrites three-quarters of the slot's residual, is a real but very weak causal channel into behavior.

At the top dose a weak reproducible shift component appears that both operators predict equally poorly

The left panel plots the median split-half cosine of each cell's answer shift against dose, per direction, with per-cell values at the top dose as points. The right panel plots, per stratum, the mean cosine between the measured answer shift and each operator's prediction, with context-clustered 95% CIs.

Figure. Left: split-half medians sit at 0.00 at the two lower doses and reach only 0.01–0.10 at the top dose. Right: prediction cosines rise to 0.04–0.05 for both operators (CIs exclude zero for evil and sycophancy); the one separated pair is the top-map direction at the middle dose, where the fitted map wins.

The parent's which-operator-predicts-interventions contrast had nothing to predict; at the top dose a weak systematic component emerges, but on the trait directions the paired Jacobian-minus-fitted-map difference spans zero at every dose — the contrast stays undecided there. The one decided stratum favors the fitted map on its own top input direction (0.050 vs 0.012 at the middle dose, paired-difference CI −0.059 to −0.016), consistent with the map encoding corpus regularity concentrated in its own principal directions, not with the Jacobian being the better causal predictor. Magnitudes stay wrong for both: at the top dose the Jacobian under-predicts the shift norm ~3× and the fitted map over-predicts ~8×.

Neither operator executes its own answer swap: steered generations acquire no target content above the matched null

The left half plots mean B-content acquisition — MRR of B's distinctive answer words in A's on-policy steered draws (temp 1.0, K = 5) — for the fitted-map, Jacobian, and norm-matched random arms, pooled and per leg: pair-clustered bootstrap CIs, per-cell shuffled-target nulls, and the metric ceiling on B's own text. The right half plots per-pair acquisition under the Jacobian delta against the fitted-map delta, by leg.

Figure. Every arm sits inside its null. Pooled acquisition 0.0020 (fitted), 0.0013 (Jacobian), 0.0009 (random) against null 97.5th percentiles near 0.004–0.005 and a 0.067 ceiling; acquisition-over-null CIs all cross zero. Per-pair values cluster at zero; the few elevated pairs are shared by both operators, not operator-specific.

Neither operator meets the execution bar, pooled or on either leg — the outcome the plan predicted. The fitted-minus-Jacobian paired contrast is +0.0006 (CI −0.0003 to +0.0023, n = 133 pairs).

The metric can move: B's held-out baseline draws score median 0.047 on the LMSYS leg, two orders of magnitude above the steered arms. The judge secondary agrees — B-content means 4.8–5.7 of 100 in steered and unsteered cells alike, both operators shifting identically (≈ +0.7 points) despite 50× different claimed doses, rank correlation 0.19 between the DVs (p = 1.1e-4, n = 399). The dose covariate follows below.

The swap null is not dose bookkeeping: the fitted map claims 88% of the needed shift and still moves nothing

Six views over the same 133 pairs: the recall@50 companion; each operator's claimed shift fraction (its linear prediction over the needed shift); acquisition against that claim; A-retention against acquisition; the representation companion cos(Δv̄, Δv_target); and split-half reliability of the measured shift.

Figure. The fitted map's capped delta claims a median 88% of the needed answer-state shift (claim cosine 0.92); the Jacobian's claims 1.7% (100% of its deltas norm-capped, raw median 34× the cap). Acquisition does not track the claim (rank correlation −0.11 fitted, +0.15 Jacobian); retention ratios center on 1.0.

At the 47.36 cap the fitted map's own delta claims 88% of the needed shift (51% of its deltas capped) yet acquisition stays at the null — an execution failure of the map, not a dose shortfall. The Jacobian arm differs: raw pseudoinverse norms (median 1,615) cap 34× down to a 1.7% claimed fraction, so its null is additionally dose-limited at this ceiling dose.

Steered outputs stay coherent answers to A (retention ratio median ≈ 1.0; judged A-retention erodes at most 2.0 points), ruling out acquisition-by-degeneration. The answer state does move reproducibly (split-half median 0.39–0.43), with a weak fitted-specific pull toward the target (cos 0.090 vs 0.004 random) that never surfaces as text.

Even the model's own full state at the slot moves nothing: the last-token slot is not causally sufficient for answer content

The figure plots mean B-content acquisition — the swap round's MRR read, unchanged — for the full-state patch arm beside the three committed round-1 arms, pooled and per leg: pair-clustered bootstrap CIs, per-arm shuffled-target nulls, the attainable anchor, the ceiling on B's own text. Companion views: exploratory figure.

Figure. The patch arm sits inside its null, no higher than the operator arms. Pooled acquisition 0.0007; acquisition-over-null +0.0001, CI −0.0004 to +0.0008, spanning zero on both legs; recall@50 matches baseline (0.0101 vs 0.0102); ceiling 0.067, anchor 0.047. The conditional judge criterion — CI lower bound above zero — was not met, so no judge pass ran.

This round drops the operator assumption entirely: A's layer-14 last-token state is replaced by the state the model computes under B — the full needed shift by construction (the fitted map claimed 88%, the Jacobian 1.7%), uncapped where round-1 deltas were capped (realized norm median 35.4; no dose trend). Acquisition stays at the null — as the plan predicted — generations remain coherent answers to A (retention median 0.96), and the answer state barely moves toward the target (shift norm median 8.5 vs 9.1 unsteered; cosine to target 0.08). The slot is not causally sufficient (necessity untested; re-attention routing not excluded) — consistent with a readout correlate — closing the operators-versus-slot ambiguity and the mapping line's steering hope at this slot.

Off-distribution the Jacobian collapses while fitted maps barely decay

The figure plots held-out R² per operator on the in-distribution LMSYS leg (solid) and the fresh WildChat leg (hatched; 999 contexts never present in any fit), with bootstrap CIs.

Figure. Fitted maps transfer almost losslessly; the Jacobian collapses. Fitted decay ~0.02 (LMSYS-only refit 0.69 → 0.67; mixed 0.68 → 0.66; shipped 0.75 → 0.73) while the two plotted Jacobian arms fall from ~0 to −0.36 and −0.35 (the prefix arm, not plotted, reaches −0.39). Retrieval accuracy: fitted 0.41–0.56, Jacobian 0.001.

The transfer hypothesis predicted the causal component would decay less than a matched-corpus fitted map; the opposite held. The Jacobian's affine prediction, centered on LMSYS anchors, is worse than predicting the mean on WildChat — its tiny learned component plus a shifted intercept actively hurt. The fresh-capture leg reconciles with the 1,000-row pool minus the one silently dropped row (realized n = 999).

A planned third leg — the parent eval rig's persona-battery contexts — was never scored (the production dispatcher wires only these two legs), bounding this verdict to the two delivered corpora.

One calibration read: a same-layer identity-plus-bias reference (layer-19 input) retrieves the true profile for 53% of LMSYS and 37% of WildChat contexts while its R² is −0.90 and −1.23 — input-output proximity buys retrieval that R² punishes, context for the fitted maps' retrieval figures.

The transfer collapse is uniform across contexts, not outlier-driven

The figure plots, per fresh-WildChat context (999 points), the squared prediction error of the LMSYS-only fitted refit against the last-token Jacobian's, log-log with the diagonal — an independent re-application of the persisted weights, which reproduces the committed fitted-map R² to 10 decimal places (the Jacobian row to ~0.05 via approximated intercept anchors).

Figure. The gap is uniform, not a tail effect. The Jacobian's error exceeds the fitted refit's on 99% of the 999 contexts, with no cloud near the diagonal.

No context subpopulation exists where the causal predictor wins; the collapse is distribution-wide.

Workspace overlap is weak everywhere; the fitted map's input directions do not beat a covariance-matched null

The figure plots gradient-pursuit reconstruction energy (k ≤ 25 atoms) per probe set — read side at layer 14 (fitted-map input directions, Jacobian row directions, persona vectors r_B — see Data extraction) and write side at layer 19 (fitted-map output directions, measured per-stratum steered shifts) — as bars with per-vector points, against the 97.5th-percentile bands of three per-draw-selection nulls.

Figure. Every probe set reconstructs weakly; only some clear the strictest null. All energies ≤ 0.10: Jacobian rows (0.043) and persona vectors (0.047) clear the covariance-matched band (0.031/0.040); fitted-map input directions (0.023) clear only the rotation/isotropic bands (0.012); fitted-map output directions clear all three (0.047 vs 0.034); measured shifts (0.019) clear rotation/isotropic (0.018/0.014) but not the covariance band (0.033).

The channel is not strongly workspace-mediated: even passing reads reconstruct under 5% of energy against nulls near 3–4% (a powered non-finding; wide band-to-ceiling margin). The covariance-matched null matters: the fitted-map input directions look workspace-loaded only until compared against generic covariance-shaped directions.

The measured-shift read clears only the two weaker bands and cannot support the workspace narration — the shifts are decode noise. The leakage re-read was structurally degenerate: at 95% dictionary energy the layer-21 workspace projector has rank 2,418 of 3,584, so projected and raw persona similarities coincide in both epoch arms; every variant coincides only in the epoch-2 arm (epoch-1 perpendicular remainder 0.219 vs 0.171 raw) — uninformative, not evidential.

Answer-profile predictability splits in proportion to variance, not along the workspace

The figure plots held-out R² of four ridge refits (layer-19 input, n = 50,000, shared λ selection) onto full targets, workspace-projected targets, orthogonal-complement targets, and a dimension-matched random-subspace reference.

Figure. Predictability tracks variance share, not workspace membership. Full 0.736, workspace component 0.725, orthogonal 0.750, random reference 0.737 — a ≤ 0.025 spread, the workspace slightly less predictable than its complement; workspace variance fraction 0.56 vs random 0.53.

If the context-to-answer channel wrote through the workspace, the workspace-projected targets should be disproportionately predictable; instead every split is predictable at nearly the full-target level, tracking its variance share. At rank 1,884 the projector is weakly selective — itself substantive: on this model the J-space cone spans over half the activation space, leaving little room for privileged mediation.

Composing the fitted map with the lens retrieves real answer content far above chance

The figure plots the mean reciprocal rank of each generated answer's content tokens in the lens-decoded vocabulary ranking of the transported predicted answer profile, for the fitted-comparator chain and the shipped-map chain on the 999 fresh-WildChat contexts, against the shuffled-pairing null.

Figure. Both chains beat the shuffled null by ~9–10×. Fitted-comparator chain MRR 0.0114, shipped chain 0.0139 vs shuffled nulls of 0.0013 (97.5th percentile 0.0022) — 9–10× the null mean; recall at 50 shows a ~5× separation.

The run's one positive composition result: predicted answer profiles, pushed through the workspace lens's vocabulary read, rank the tokens the model actually generated far above a shuffled pairing — small absolutely, but a real judge-free signal that the fitted map carries context-specific answer content the lens can decode. Face validity holds at the direction level: the lens decodes the evil persona vector's top token as " evil". This coexists with the causal null: the map predicts what the answer state will be without its input slot causally producing that state at linear order.

The chain's gain is a broad weak rank shift plus a small near-verbatim head

The figure plots, per fresh-WildChat context (999), the log10 rank of the generated answer's best content token under the fitted-comparator chain's vocabulary ranking (blue outline) against the pooled distribution of each context's own shuffled-pairing null (gray), as overlaid densities.

Figure. The whole distribution shifts left of the null — median best-token rank 3,191 vs 9,587 — and a small head reaches near-verbatim ranks. 29.1% of the 999 contexts beat their own null's 95th percentile (chance 5%).

The mean-reciprocal-rank headline is head-heavy: the top nine contexts (1% of 999) carry 55.8% of the summed reciprocal rank, and excluding the top ten leaves the mean at 0.0048 — still ~3.6× the null — while excluding the top hundred brings it to the null. The chain therefore carries two signals: a broad, weak rank improvement across roughly a third of contexts, and a small near-verbatim head that dominates the headline. The shipped-map chain decomposes the same way (31.8% beat their own null; its top nine carry 46.7%).

In token space the Jacobian's transported signal carries no context-specific answer content

The figure plots, for the two fitted chains and four Jacobian variants (anchored last-token, context-span, and prefix-span forms plus an affine last-token form), the mean reciprocal rank of the generated answer's content tokens in the layer-19 lens vocabulary ranking of the transported prediction, on the same 999 fresh-WildChat contexts, each against its own 200-draw shuffled-pairing null; the right half zooms to the Jacobian arms.

Figure. Fitted chains retrieve at 0.0114 and 0.0139 against nulls near 0.0013 (~9–10×); every Jacobian arm sits at its own null band — 0.00036–0.00055 vs null means 0.00035–0.00041, the largest read grazing its band's 97.5th percentile at 6% above the null mean, ~31× below the fitted chain.

This closes the scale-sensitivity escape on the headline: the rank read is calibration-free, so no rescaling argument can revive the Jacobian, and the fitted map's edge survives in semantics as well as geometry. The prediction that any Jacobian gain would concentrate in prompt-echoed tokens is refuted — the echoed partition is exactly at its null (0.000032 vs 0.000032) — and the fitted chain's gain is not echo-driven either: its non-echoed partition carries the full separation (0.0112 vs null 0.0013). Mechanically, the Jacobian predictions are anchor-dominated — near-identical across contexts, yielding a generic token ranking that a shuffled pairing matches.

Per context, the Jacobian chain's true pairing is indistinguishable from a shuffled pairing

The figure plots, per fresh-WildChat context (999), the log10 rank of the generated answer's best content token under the affine Jacobian chain's vocabulary ranking, overlaid on the pooled distribution of each context's own shuffled-pairing null rows.

Figure. The two distributions coincide — median best rank 18,922 under the true pairing vs 18,424 under the null; across the four Jacobian arms 6.3–11.7% of contexts beat their own null's 95th percentile (chance 5%; the fitted chain: 29.1%).

The per-context view matches the aggregate: no subpopulation exists where the causally transported signal finds the answer's words. The one marginal arm (anchored context-span, 11.7% of contexts beating their null) still sits ~29× below the fitted chain absolutely, and the fitted chain's own left-shifted distribution from the previous section is entirely absent here.

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Repro: Single RunPod 8×H100 pod (pod-1776, 2026-07-29, ~52 GPU-h planned incl. crash-fix relaunches) + off-pod VM/Batch-API phases. Code: pod phases @ 9516432e1d (scripts/issue1776_*.py), judge @ ef571068d5, chain + word tables @ 637e560e9d, analyzer supplement + figures @ 8342ae660c (scripts/issue1776_analyzer_supplement.py, scripts/issue1776_analyzer_figures.py), free-analysis follow-up round @ 4712ba44e0 (scripts/issue1776_9ater_followup.py; eval JSONs eval_results/issue_1776/followup_9ater/; recovered pooling anchors for the rescale read analysis_tensors/followup_9ater/9ater_anchors.pt @ 2a69ab24, listing verified at write time). Dose/heterogeneity follow-up round (label p3p4_heterogeneity_dose): pod phases @ b3916219ff + span crash-fix @ a9c47aa847 (scripts/issue1776_p3p4.py, scripts/issue1776_p3p4_dispatch.sh), results commit 8eab7b356f, judge @ bb7ef19017, fold supplement + figures @ 58654085eb (scripts/issue1776_p3p4_supplement.py, scripts/issue1776_p3p4_figures.py); eval JSONs eval_results/issue_1776/followup_p3p4/; HF (listing verified at write time) analysis_tensors/followup_p3p4/ @ e434d414 (per-context Jacobians, dose per-cell tensors + tables) + raw_completions/steered_dose/ @ e434d414 (16 strata). Dose-round ops notes: the round's upload manifest names a stale destination field (raw_completions/steered/) — the realized prefix is raw_completions/steered_dose/; steered_shift_summaries.json records a pod-local per-cell table path — those tables are the HF dose_cells/ files; the round ran on a fresh RunPod 8×H100 after its GCE flex-start instance never dequeued (queue-timeout failover); the crash-fix resume recomputed at most two legacy per-context units (span invalidation). Swap follow-up round (label operator_swap_success, directory followup_swap — mapping recorded in the build report; pod-1776 8×H100 RunPod, ≈7 realized GPU-h, seed 1776): rig @ bd154bdfc6 (scripts/issue1776_swap.py, scripts/issue1776_swap_judge.py, scripts/issue1776_swap_dispatch.sh), pod ran @ c776254ce7, results @ 8ebf7843a9, judge @ 9c8fc0940f (branch issue-1776, pushed); eval JSONs eval_results/issue_1776/followup_swap/ + figures figures/issue_1776/followup_swap/; HF (listing verified at write time): raw_completions/steered_swap/ @ 2a359c8b (4 arms + manifest) + analysis_tensors/followup_swap/ @ 2a359c8b (per-cell shift tensors, targets, build report). Slot-patch follow-up round (label slot_patch_sufficiency, directory followup_slotpatch; GCP 2×A100 flex-start eps-issue-1776, ≈2.7 realized GPU-h, seed 1776): ran @ cf2b99ff26 (the swap drivers in patch mode), results + figures @ 40b9137222 (branch issue-1776, pushed); eval JSONs eval_results/issue_1776/followup_slotpatch/ + figures figures/issue_1776/followup_slotpatch/; HF (listing verified at write time): raw_completions/steered_slotpatch/ @ eec3ef5f (2 arms + manifest) + analysis_tensors/followup_slotpatch/ @ eec3ef5f (per-cell shift tensors + cells). J-chain chat round (label userchat_jchain, 0 GPU-h, VM CPU 294 s): driver + results + figures committed on main @ 4d58dc0ef3 (scripts/issue1776_jchain_userchat.py; eval JSONs eval_results/issue_1776/followup_userchat_jchain/). Eval JSONs: eval_results/issue_1776/ (phase0–5, phase3/judge/judge_scores.json, analyzer/supplement.json); figures figures/issue_1776/. HF data repo (listing verified at write time): issue1776_jacobian/ @ 687eb8b4 — analysis_tensors/ @ 687eb8b4 (Jacobians + half-sums, comparator weights, dictionaries L14/L19/L21, jpairs captures, phase-1 rows + seeds, phase-3 per-cell tensors + cells JSONLs + directions + predictions, reports), raw_completions/steered/ @ 687eb8b4 (26 strata), wildchat_fresh/ @ 687eb8b4 (pool + stream report + capture shards + rollouts). Reused from #779: pinned test-1000 pass_b tensors + 963k ridge (issue779_monitoring/n1m_readout/weights/L19/ridge.pt @ 687eb8b4; reproduced R² diff 8e-11) + persona vectors (issue779_monitoring/r_b/ @ 687eb8b4) — fit verified by the parity gate (0/200 failures); vendored anthropics/jacobian-lens @ 581d398613e5602a5af361e1c34d3a92ea82ba8e; #532 leakage tables (eval_results/issue_532/); steering rig experiments/issue1415/steering.py; judge stack eval/graded_judge.py + Batch API. Plan-recorded deviations: leakage re-read ran pod-side; lens-vocab + chain reads ran off-pod (ops-only). Config slugs: m_ridge_ctx (shipped), m_ridge_x50k, m_ridge_lmsys50k, jca_last/jca_ctx/jca_prefix, id_bias, steer_rb/steer_msv/steer_rand/steer_a0/steer_jsplit, xfer_wc, swap_mprime/swap_jlast/swap_random/swap_a0, J_last_anchored/J_last_affine/J_ctx_anchored/J_prefix_anchored/mprime_x50k/m_shipped.

Context: created 2026-07-28 (user chat, J-space paper discussion); pod run 2026-07-29 → 2026-07-30 UTC; analyzer first pass 2026-07-30 UTC; Step 9a-ter free-analysis follow-up (label followup_9ater: rescale ladder + chain per-context breadth, code-review PASS with independent reproduction) folded 2026-07-30 UTC; Step 9b cheap-band follow-up (label p3p4_heterogeneity_dose, source proposer-9b-cheap: per-context Jacobian heterogeneity + dose-escalated steering, code-review PASS, upload-verified) folded 2026-07-30 UTC; user-chat follow-up (label operator_swap_success: pair-swap causal-execution test, plan v7, upload-verified) + inline chat-session round (label userchat_jchain: Jacobian-arm chain token read) folded 2026-07-30 UTC — originating prompt for both, verbatim: "run both experiments you jsut described"; second Step 9b cheap-band follow-up (label slot_patch_sufficiency, source proposer-9b-cheap: proposal 1 of epm:follow-ups v1 2026-07-31, cheap-band slot 2 of 2 — full-state substitution at the layer-14 last-token slot) run 2026-07-31 UTC, folded 2026-07-31 UTC. Lineage: #779 — parent corpus, targets, and fitted maps this run decomposes; #1415 — steering rig + the fitted-vs-causal steering precedent. Execution directive, verbatim: "don't treat it as a kill switch. just run it then continue till the end no matter what." Originating prompts, verbatim: "could we do jacobian from context to answer vectors?", "can we combine our mapping with theirs somehow?", "does this include seeing if our mapping reads from the same space as the J space?", "ok combine everything we've discussed so far into a plan and estimate the GPU h and wall clock time".