The Key Handoff: Retrieval in Hybrid Language Models
Organizations: Georgia Institute of Technology, USA · University of Texas at Austin, USA
Abstract
A two-hop question makes a language model retrieve twice: once to produce a bridge entity, and once to retrieve with it. Transformers resolve that entity in their early layers. Hybrid models replace most of the attention with a recurrent state, so where the key becomes usable, and where it is spent on an answer, is not known. Answering "Where is the ball?" from "the ball belongs to Alice" and "Alice is in the garden" turns on Alice, a name the question does not mention. A model could reach garden through Alice, the key it computed, or through where the fact sits in the prompt. Across twelve models, dense and hybrid, we move a hidden state from one story into another where the two routes lead to different places, and read off which place the model gives. An attention layer converts the key in every model we tested, and crossing that layer removes its usable effect, all of it where no attention follows. In sequential hybrids this makes the answer a handoff: recurrent layers carry the key forward, and attention spends it. Retrieval does not always stop there. Writing a different fact into the memory of the recurrent layers that follow the last attention layer can move the answer toward that fact, multiplying its odds by 1.3 to 2.7, and which hybrids do this is not settled by their architecture or training. That read is addressed by the key, not by position: recurrent state in a hybrid is not only a carrier, but a memory that later layers can query.
Figures & tables
| Nemotron-H | Granite-H | Nano | |
| Top-1 among seven (%), chance 14 | |||
| rebinding | 86 | 71 | 67 |
| row mismatch | 39 | 35 | 28 |
| Causal scrubbing: donor shares only … ( ) | |||
| the key | 3.42 | 3.18 | 3.29 |
| its own answer | 0.62 | 0.62 | 0.61 |
| 8-head | All heads | Random sets | |
|---|---|---|---|
| injection | clamped | beaten | |
| Nemotron-H (L40) | 100% | 0% | 100% |
| Granite-H (L35) | 69–75% | 0% | 100% |
| Nano (L33) | 93–96% | 36–39% | 100% |
| Test | Control | Transposed | |
| Alice | Garden | Garden | Kitchen |
| Bob | Kitchen | Kitchen | Garden |
| Carol | Hall | Hall | Hall |
| Question | Where is the ball? | Where is the cup? | Where is the cup? |
| Own answer | Garden | Hall | Hall |
| Nemotron-H | Granite-Small | |
|---|---|---|
| Key over row | 1.9 | 1.4 |
| Key over test prompt’s | 2.4 | 1.5 |
| Row over test prompt’s | 1.3 | 1.1 |
Appendix figures & tables39 assets
Supplementary material from the paper’s appendix.
Appendix
| Stage | Intervention | Data | Role |
|---|---|---|---|
| Flow localization | Residual patch | 20 paired | Exploratory |
| Head ranking | Head-output patch | 30 discovery + 300 held-out | Confirmatory |
| Fixed-donor crossing | Whole-state transplant | 200 graphs / 600 crosses | Confirmatory |
| Fixed-recipient crossing | Whole-state transplant | 200 graphs / 600 crosses | Confirmatory |
| Common assay: factorial | Whole-state transplant | 200 identities / 1,800 cells | Confirmatory |
| Common assay: path patching | Head-delta injection, clamps | Same 200 identities | Confirmatory |
| Symbol | Meaning |
|---|---|
| , ; | Donor and recipient prompts; the answer-position state entering layer (“pre-L ”) |
| , , | At the final token: the residual state entering layer ; the output a recurrent layer adds to it ( ); the recurrent layer’s memory, accumulated over the preceding tokens. Transplants replace , writer swaps , memory swaps |
| Change in the logit of candidate when the donor’s state replaces the recipient’s (Eq. 1 ) | |
| ; ; | The donor’s answer; the values the recipient binds to the three keys; the recipient’s own answer |
| , , | The fixed-answer, position, and key causal models |
| ; , | Selectivity of a candidate over the other two bindings; mapping (fixed-donor) and key (fixed-recipient) selectivity (Eq. 8 ) |
| Checkpoint | Revision | Class | Layers | Task | Site | Outcome |
| nvidia/Nemotron-H-8B-Base-8K | 94ea861e | H | 52 | Pass | pre-L40 | Primary model |
| ibm-granite/granite-4.0-h-micro-base | 372ede0b | H | 40 | Pass | pre-L35 | Both crossings pass |
| ibm-granite/granite-4.0-h-small-base | 4b4faa80 | H | 40 | Pass | — | Memory swap only |
| Qwen/Qwen2.5-7B | d1497293 | D | 28 | Pass | pre-L22/26 ‡ | Balanced / reference |
| mistralai/Mistral-7B-v0.3 | caa1feb0 | D | 32 | Pass | pre-L19 | Profile panel |
| Zyphra/Zamba2-2.7B | 31afeeac | H | 54 | Fail § | — | Below accuracy gate |
| Quantity (logits) | Crossed assay | Common assay | Normalized |
|---|---|---|---|
| Recipient margin, vs. runner-up | 1.45 | 1.71 0.21 | 1 |
| Mapping selectivity, | 2.37 | 1.48 0.29 | 0.88 0.21 |
| Key selectivity, | 1.02 | 1.14 0.10 | 0.66 0.09 |
| Mapping selectivity, pre-L39 | — | 1.12 0.20 | 0.67 0.15 |
| Key selectivity, pre-L39 | — | 0.85 0.08 | 0.50 0.07 |
| minus pre-L39, mapping | — | 0.36 0.09 | — |
| Donor’s decisive row at position | |||
|---|---|---|---|
| Donor’s key | 1 (Alice’s fact) | 2 (Bob’s fact) | 3 (Carol’s fact) |
| Alice | Garden / Garden | Garden / Kitchen | Garden / Hall |
| Bob | Kitchen / Garden | Kitchen / Kitchen | Kitchen / Hall |
| Carol | Hall / Garden | Hall / Kitchen | Hall / Hall |
| Nemotron-H, pre-L40 | Granite-H, pre-L35 | ||
|---|---|---|---|
| Fixed donor | Mapping selectivity (logits) | 2.37 0.21 | 2.48 0.22 |
| Mapped vs. donor answer (logits) | 1.57 0.19 | 1.67 0.24 | |
| Mapped vs. recipient answer (logits) | 4.17 0.27 | 4.84 0.31 | |
| Tracking rate (%) | 80.8 4.5 | 86.0 3.8 | |
| Top-1 rate among seven (%) | 85.8 4.5 | 70.8 5.5 | |
| Fixed recipient | Key selectivity (logits) | 1.02 0.12 | 0.99 0.14 |
| Nemotron-H | Granite-H | ||
| Fixed-donor crossing | Unmodified donor accuracy (%) | 88.5 | 82.0 |
| Unmodified recipient accuracy (%) | 71.7 | 84.7 | |
| Donor prefers over (%) | 95.5 | — | |
| Recipient prefers over (%) | 92.2 | — | |
| Fixed-recipient crossing | Unmodified donor accuracy (%) | 85.5 | 82.0 |
| Unmodified recipient accuracy (%) | 82.0 | 84.7 |
| Nemotron-H | Attention | Recurrent, before L40 | Recurrent, after L40 |
|---|---|---|---|
| Arrow task | 0.947 | 0.036 | 0.016 0.005 |
| Word task | 0.862 | 0.046 | 0.092 0.010 |
| Numeric twin | 0.936 | 0.036 | 0.028 0.005 |
| Site | Key | Position | Class | |
|---|---|---|---|---|
| Nemotron-H pre-L40 | 1.13 0.12 | 0.36 0.10 | 0.77 0.11 | Key-dominant |
| Nemotron-H pre-L39 | 0.84 0.09 | 0.28 0.07 | 0.56 0.09 | Key-dominant |
| Qwen2.5 pre-L22 | 0.86 0.16 | 0.87 0.14 | 0.02 0.14 | Balanced |
| Qwen2.5 pre-L26 | 0.63 0.12 | 0.02 0.11 | 0.65 0.09 | Neither † |
| Granite-H pre-L35 | 1.07 0.13 | 0.25 0.09 | 0.82 0.10 | Key-dominant |
| Nemotron-H pre-L40 (colon format) | 0.81 0.12 | 0.31 0.08 | 0.49 0.09 | Key-dominant |
| Model | No class | Balanced | Key-dominant |
|---|---|---|---|
| Nemotron-H | pre-L0–L26; pre-L41–L51 (fixed answer) | pre-L27, L28, L31–L33 | pre-L29, L30, L34–L40 |
| Granite-H | pre-L0–L24; pre-L36, L39 (fixed answer) | — | pre-L25 § , L26–L35 |
| Qwen2.5 | pre-L0–L17; pre-L24, L26, L27 (fixed answer) | pre-L18, L19, L21–L23 | pre-L20 |
| Model | Type | Layers | Key peak (class) | , arrow | , binding | , arrow / binding | Attn. share |
| Nemotron-H-8B | Sequential hybrid | 52 (4 attn.) | pre-L40 (key) | 0.68 0.03 | 0.69 0.02 | 1.9 / 1.9 | 0.95 |
| Nemotron-H-4B | Sequential hybrid | 52 (4 attn.) | pre-L40 (key) | 0.63 0.03 | 0.68 0.02 | 1.9 / 1.8 | 0.94 |
| Granite-H | Sequential hybrid | 40 (4 attn.) | pre-L35 (key) | 0.70 0.02 | 0.55 0.02 | 1.8 / 2.0 | 0.96 |
| Falcon-H1-3B | Parallel hybrid | 32 (all) | pre-L21 (key) | 0.59 0.02 | 0.56 0.02 | 4.6 / 4.8 | 1 |
| Falcon-H1-7B | Parallel hybrid | 44 (all) | pre-L29 (balanced) | 0.70 0.02 | 0.73 0.01 | 3.2 / 3.0 | 1 |
| Qwen2.5-7B | Dense | 28 | pre-L22 (balanced) | 0.61 0.02 | 0.54 0.02 | 2.9 / 3.2 | 1 |
| Task | Model | Peak = resolver | Coincide (%) | Peak margin over runner-up |
|---|---|---|---|---|
| Arrow | Nemotron-H-8B | L40 | 100.0 | 0.29 0.04 (L38) |
| Arrow | Nemotron-H-4B | L40 | 100.0 | 0.18 0.02 (L39) |
| Arrow | Granite-H | L35 | 99.4 | 0.01 0.01 (L33) |
| Arrow | RecurrentGemma-9B | L29 | 100.0 | 0.40 0.07 (L28) |
| Arrow | Nemotron-3-Nano-30B | L33 | 100.0 | 0.14 0.04 (L31) |
| Arrow | Falcon-H1-3B | L21 | 97.8 | 0.02 0.01 (L20) |
| Arrow task | Binding task | |||||||||||||
| Model | Attn. blocks | Late attn. | Rise span | Depth | Attn. in span | in | Consumed | Rise span | Depth | Attn. in span | in | Consumed | ||
| Nemotron-H-8B | 4 | 2 | L29–L40 | 0.57–0.78 | 2 | 1.9 | 1.13 | 1.55 | L29–L40 | 0.57–0.78 | 2 | 1.9 | 0.70 | 1.30 |
| Nemotron-H-4B | 4 | 2 | L29–L40 | 0.57–0.78 | 2 | 1.9 | 0.66 | 1.69 | L29–L40 | 0.57–0.78 | 2 | 1.8 | 0.77 | 1.39 |
| Granite-H | 4 | 2 | L25–L35 | 0.64–0.90 | 2 | 1.8 | 1.07 | 1.29 | L25–L35 | 0.64–0.90 | 2 | 2.0 | 0.49 | 1.43 |
| RecurrentGemma-9B | 12 | 6 | L26–L31 | 0.70–0.84 | 2 | 2.0 | 0.83 | 0.56 | — | — | — | — | — | — |
| Nemotron-3-Nano-30B | 6 | 3 | L33–L42 | 0.65–0.82 | 2 | 1.7 | 1.06 | 0.85 | L33–L42 | 0.65–0.82 | 2 | 1.9 | 0.83 | 0.77 |
| Condition | Redirection | Guest lookup | Host lookup | Shared key kept | Host frame |
| Nemotron-H-8B : reader L40, 8 of 32 heads, gate 84/84% | |||||
| Writer L33 swapped | 0.04 0.03 | 0.04 0.04 | 0.95 0.06 | 1.00 0.02 | 0.02 0.04 |
| Control L35 swapped | 0.13 0.02 | 0.14 0.02 | 0.87 0.05 | 1.00 0.01 | 0.13 0.04 |
| All writers L28/L33/L39 swapped | 0.58 0.05 | 0.31 0.09 | 0.10 0.20 | 0.99 0.03 | 0.32 0.14 |
| Control set L31/L35/L37 swapped | 0.26 0.03 | 0.26 0.03 | 0.72 0.09 | 1.00 0.02 | 0.24 0.05 |
| Residual after L33 replaced | 0.69 0.02 | 0.74 0.03 | 0.33 0.17 | 0.99 0.04 | 0.80 0.13 |
| Swap | Guest lookup | Host lookup | Paired guest-lookup difference |
| Nemotron-H-8B : writers L28/L33/L39, controls L31/L35/L37, reader L40; pattern: distributed | |||
| L28 alone | 0.12 0.04 | 0.78 0.08 | vs. L31: 0.16 0.05 |
| Control L31 alone | 0.04 0.02 | 0.98 0.04 | |
| L33 alone | 0.04 0.04 | 0.95 0.06 | vs. L35: 0.10 0.05 |
| Control L35 alone | 0.14 0.02 | 0.87 0.05 | |
| L39 alone | 0.14 0.03 | 0.86 0.04 | vs. L37: 0.03 0.03 |
| Paired contrast | Estimate (95%) |
|---|---|
| Later excess over no-key | 0.242 0.097 |
| Q1: L37 interruption drop | 0.154 0.061 |
| L39 comparison drop | 0.005 0.017 |
| Q2: L37 versus L39 drop | 0.159 0.057 |
| Q3: rescue improvement | 0.087 0.050 |
| Rescue shortfall from uninterrupted | 0.067 0.039 |
| Condition | What carries the transplant | Mapping selectivity | Key selectivity | Top-1 (%) |
|---|---|---|---|---|
| Whole state | 1.48 0.29 | 1.14 0.10 | 42 | |
| Top-8 head outputs only | 1.46 0.28 | 1.18 0.10 | 40 | |
| All 32 head outputs | 1.48 0.27 | 1.20 0.10 | 41 | |
| Other 24 head outputs | 0.22 0.06 | 0.17 0.03 | 4 | |
| Bottom-8 head outputs | 0.08 0.03 | 0.07 0.01 | 3 | |
| Residual; heads clamped to recipient | 0.01 0.04 | 0.10 0.02 | 3 |
| Condition | What carries the transplant | Mapping selectivity | Key selectivity | Top-1 (%) |
|---|---|---|---|---|
| Whole state | 1.44 0.29 | 1.09 0.10 | 38 | |
| Top-8 head outputs only | 1.00 0.20 | 0.81 0.08 | 25 | |
| All 32 head outputs | 1.42 0.27 | 1.15 0.10 | 41 | |
| Other 24 head outputs | 0.52 0.11 | 0.41 0.05 | 8 | |
| Bottom-8 head outputs | 0.14 0.04 | 0.12 0.02 | 4 | |
| Residual; heads clamped to recipient | 0.04 0.06 | 0.07 0.04 | 3 |
| Condition | What carries the transplant | Mapping selectivity | Key selectivity | Top-1 (%) |
|---|---|---|---|---|
| Whole state | 1.18 0.25 | 1.11 0.13 | 28 | |
| Top-8 head outputs only | 1.14 0.26 | 1.04 0.13 | 26 | |
| All 32 head outputs | 1.01 0.23 | 0.93 0.12 | 18 | |
| Other 24 head outputs | 0.14 0.04 | 0.12 0.02 | 3 | |
| Bottom-8 head outputs | 0.17 0.05 | 0.14 0.02 | 3 | |
| Residual; heads clamped to recipient | 0.43 0.10 | 0.43 0.06 | 4 |
| Key’s answer against the recipient’s others ( ) | Preservation advantage | ||||
|---|---|---|---|---|---|
| Model | shares the key | shares the answer | shares the row | over answer | over row |
| Nemotron-H | 3.42 0.35 | 0.62 0.04 | 0.47 0.02 | 0.72 0.11 | 0.86 0.11 |
| Granite-H | 3.18 0.35 | 0.62 0.04 | 0.51 0.03 | 0.97 0.12 | 1.08 0.11 |
| Nemotron-3 Nano | 3.29 0.42 | 0.61 0.05 | 0.52 0.04 | 1.14 0.15 | 1.12 0.14 |
| Family | Unit | Learned d.o.f. | Held-out outcome on the common assay |
|---|---|---|---|
| Crossed transplant | Complete residual | 0 | Key-dominant, dual-supported; mapping 1.48, key 1.14 |
| Path patching | Head-output route | 0 (set prespecified) | Top-8 route carries 98–104% of in Nemotron-H, 93–96% in Nano and 69–75% in Granite-H |
| Causal scrubbing | Factor-preserving resample | 0 | Key-preserving scrub preserves, answer- and row-preserving do not, in all three hybrids |
| Study | Manipulation | What it identifies | What crossing adds |
|---|---|---|---|
| Feng & Steinhardt (2024) | Binding-ID vectors added to, or swapped between, entity–attribute pairs | A binding subspace shared across entities and its geometry | A reference baseline and a key position factorial, so that “binding” splits into the bound value and the bound row, each with a preregistered bound |
| Gur-Arieh et al. (2026) | Counterfactual prompt pairs that vary one retrieval cue (positional, lexical, reflexive) with activation patching | Which retrieval mechanism a model uses at a site, and that the mechanisms mix | Computed-key assembly in hybrids compared with dense models; a reference baseline and prespecified factorial classification |
| Sharma et al. (2026) | Patching a predicate (filter) representation between list prompts | A general filter-head circuit that selects list items | The key and position of a bound variable rather than a predicate, and three intervention families compared on one assay |
| Condition or paired contrast | Original (95%) | Fresh template (95%) |
|---|---|---|
| Shifted lookup | 0.418 0.063 | 0.126 0.066 |
| All five outputs clamped | 0.012 0.023 | 0.004 0.032 |
| L42/L44 clamped | 0.111 0.045 | 0.010 0.049 |
| L46/L48 clamped | 0.290 0.053 | 0.104 0.057 |
| Same-key, different-answer rescue | 0.406 0.057 | 0.117 0.060 |
| Different-key, same-answer control | 0.041 0.050 | 0.053 0.046 |
| Model | Incoming state | Key over row | Key over test prompt’s | Row over test prompt’s | Identities, key row |
|---|---|---|---|---|---|
| Nemotron-H | Ordinary execution | 0.65 0.04 | 0.89 0.05 | 0.24 0.03 | 98% |
| Shifted | 0.82 0.05 | 1.00 0.07 | 0.18 0.03 | 100% | |
| Granite-Small | Ordinary execution | 0.31 0.03 | 0.40 0.02 | 0.09 0.01 | 98% |
| Shifted | 0.38 0.03 | 0.48 0.03 | 0.10 0.01 | 100% |
| Template | Execution | All five memories | L44 memory only |
|---|---|---|---|
| Original | Shifted | ||
| Original | Ordinary | ||
| Fresh wording | Shifted | ||
| Fresh wording | Ordinary |
| Accuracy | : over the memory prompt’s answer | : over the test prompt’s answer | Consistent | |||||
|---|---|---|---|---|---|---|---|---|
| Model (recurrent layers after last attention) | Task version | (S / R / M, %) | Shifted | Ordinary | Shifted | Ordinary | identities (%) | Read |
| Nemotron-H-8B (5 Mamba-2) | Word | 71 / 68 / 69 | 0.33 0.04 | 0.70 0.04 | 0.67 0.07 | 0.98 0.06 | 100 | Both conditions |
| Story | 64 / 61 / 63 | 0.11 0.02 | 0.37 0.03 | 0.23 0.04 | 0.53 0.03 | 99 | Both conditions | |
| Paragraph | 71 / 66 / 70 | 0.44 0.04 | 0.79 0.05 | 0.89 0.09 | 1.09 0.06 | 100 | Both conditions | |
| Short word | 76 / 74 / 78 | 0.33 0.04 | 0.78 0.04 | 0.68 0.08 | 1.05 0.06 | 99 | Both conditions | |
| Numeric twin | 88 / 87 / 86 | 0.00 0.01 | 0.00 0.00 | 0.00 0.01 | 0.00 0.01 | 18 | Not detected | |
| Increase in supplied location’s score relative to | ||
| Incoming state after the last attention layer | Memory’s own answer | Recipient’s answer |
| Nemotron-H : both factors contribute | ||
| Ordinary execution | 0.735 0.048 | 1.006 0.057 |
| Own pre-attention state, attention skipped | 0.678 0.046 | 1.241 0.075 |
| Foreign prompt’s pre-attention state | 0.365 0.045 | 0.740 0.080 |
| Ordinary minus own state (attention ran) | +0.058 0.014 | 0.236 0.030 |
| Condition (final token only) | Baseline (%) | Intervened (%) | Paired drop (points, 95%) | Correct wrong | Wrong correct |
| Word wording : source 70.7%, recipient 62.0%, 100 identities | |||||
| Post-attention outputs, calibration means (primary) | 69.8 | 67.3 | 9.0 | 12.6 | |
| Earlier five recurrent outputs, calibration means | 69.8 | 62.2 | 17.9 | 16.2 | |
| Post-attention outputs, zeros | 69.8 | 50.7 | 34.1 | 15.6 | |
| Earlier five recurrent outputs, zeros | 69.8 | 32.3 | 61.0 | 16.9 | |
| Post-attention minus earlier, means | |||||
| Variant | Model | Gate (%) | Site | Class | |||
|---|---|---|---|---|---|---|---|
| Filler context | Nemotron-H-8B | 65/66 | pre-L40 | 0.81 0.12 | 0.36 0.09 | Key-dominant (dual) | 0.90 0.02 |
| Filler context | Qwen2.5-7B | 66/66 | pre-L22 | 0.53 0.13 | 0.53 0.13 | Balanced | 0.52 0.02 |
| Filler context | Llama-3.1-8B | 83/86 | pre-L16 | 0.78 0.10 | 0.37 0.08 | Key-dominant (dual) | 0.35 0.01 |
| Word-valued attributes | Nemotron-H-8B | 70/77 | pre-L40 | 0.82 0.12 | 0.20 0.08 | Key-dominant (dual) | 0.89 0.01 |
| Word-valued attributes | Granite-H | 66/62 | pre-L35 | 0.66 0.09 | 0.10 0.06 | Key-dominant (dual) | 0.89 0.04 |
| Word-valued attributes | Qwen2.5-7B | 66/68 | pre-L21 | 0.39 0.10 | 0.33 0.08 | Balanced | 0.32 0.01 |
| Model | Task | Site | Preregistered class | Classes across the grid | Layers changed (max / mean) |
|---|---|---|---|---|---|
| Nemotron-H-8B | Arrow | pre-L40 | Key-dominant (dual) | Key-dominant (dual) | 4 / 1.3 of 52 |
| Nemotron-H-8B (pre-L39) | Arrow | pre-L39 | Key-dominant (dual) | Key-dominant (dual) | 4 / 1.3 of 52 |
| Nemotron-H-8B | Colon | pre-L40 | Key-dominant (dual) | Key-dominant (dual) | 0 / 0.0 of 2 |
| Nemotron-H-8B | Binding | pre-L40 | Key-dominant (dual) | Key-dominant (dual) | 0 / 0.0 of 52 |
| Nemotron-H-4B | Arrow | pre-L40 | Key-dominant (dual) | Key-dominant (dual) | 0 / 0.0 of 52 |
| Nemotron-H-4B | Binding | pre-L40 | Key-dominant (dual) | Key-dominant (dual) | 4 / 1.3 of 52 |
| Arrow task | Binding task | ||||||
| Model | Attn. blocks | ||||||
| Nemotron-H-8B | 4 | 0.71 | 2.9 | 1.9 | 0.72 | 2.9 | 1.9 |
| Nemotron-H-4B | 4 | 0.66 | 2.7 | 1.9 | 0.71 | 2.8 | 1.8 |
| Granite-H | 4 | 0.73 | 2.9 | 1.8 | 0.57 | 2.3 | 2.0 |
| RecurrentGemma-9B | 12 | 0.80 | 9.6 | 2.0 | — | — | — |
| Nemotron-3-Nano-30B | 6 | 0.78 | 4.7 | 1.7 | 0.75 | 4.5 | 1.9 |
| Alternative | Evidence against it |
|---|---|
| Fixed donor answer | One donor tracks three recipient bindings on 81% of crosses; scrub destroys the effect |
| Recipient keeps its own answer | logits |
| Query token, not key, is transferred | Recipient maps away from in 97% of cells; excluding the rest leaves unchanged |
| State is only a row pointer | The key beats the position by 0.77 logits with a reference baseline; scrub destroys the effect |
| Any nearby site works | Pre-L39 whole residual carries three quarters of the effect, same class |
| Any eight heads carry it | Top-8 path exceeds all 255 random eight-head paths |