# The full matrix: items 1–31 (as of 2026-07-17 late)

Scored source of truth: PROTOCOL_UNIFIED.md. All items pre-registered before running.

## Arc I — Band-loop retrofit (MBPP; frozen E2B + merge adapter)

| # | tried | key result | control/reference | verdict |
|---|---|---|---|---|
| 1–4 | unified merge adapter, k-loop over prompt | MBPP hard 3.6→28.6 (k=2); GSM hard 0→6.3 | k=0 same harness | loop works on code; GSM fails from day one |
| 5 | same-size adapter, no recurrence | 17.9 hard | vs 28.6+ looped | loop > weights — recurrence load-bearing |
| 6 | mixed-task training | both tasks regressed | single-task arms | interference, no synergy |
| 7 | band-location ablation | L14–30: 43.6 vs early 23.6 / shifted 21.8 | width-matched | lens's "where" confirmed; some bands structurally null (KV-share) |
| 9 | anchor sweep 13/12/11 | 34/31/25% overall, monotone collapse | L14 anchor | L14 boundary special |
| 10 | L9 anchor (full-attention layer) | catastrophic (≤21.4 hard) | anchors 11–13 | lens boundary, not layer type |

## Arc II — Adapter-class factorial

| # | tried | key result | verdict |
|---|---|---|---|
| 11 | unconstrained RecurrentAdapter | ρ→4.5, easy 98→69, no depth gain | 4× params bought nothing |
| 12 | Parcae (ρ<1 certified) | robust training, saturates, easy still 71% | stability ≠ fidelity — independent dials |
| 13a | per-depth adapters (LTV) | hard content depth-stranded (17.9 @ k=2) | weight-sharing load-bearing |
| 13b | free-ACT probe | no state fixed point; no difficulty gradient | output-stable orbit; no free halting |
| 14 | tied-alpha (anchored B) | easy 93 preserved; α never moves | free B = fidelity culprit; 0.3 optimal |
| 15 | randk / noise-s₀ / h2048 / seeds | 50–54 cells → seed means 37–46 | lucky seeds; only seed means are levels |
| 16 | cross-task transfer | code adapter on GSM toxic (easy →28–45%) | content task-local, monotone ladder |

## Arc III — Gates & the GSM boundary

| # | tried | key result | verdict |
|---|---|---|---|
| 17 | GSM-only training, best recipe | hard ≤8.7 | structural → supervision-density diagnosis |
| 18/19 | learned halting heads (E1a/b/c) | all lose to E0 frozen probe; E1c easy routing 95.9 @ 0.11 iters | classifier quality binds; hard recall regressed |
| 20 | threshold curve + oracle | oracle 59.6 @ 0.24 iters; hards depth-diverse | gate worth ~9.6 pts, unclaimed |

## Arc IV — Hybrid & internalization ladder (GSM)

| # | tried | matched | ablated/control | verdict |
|---|---|---|---|---|
| 21 | carry + dense self-distilled scratchpads | **57.4** | FF control 54.7 | 5× prior best; recurrence edge = drop bucket, p=0.0094 |
| 22 | delete steps d=1/2/3, +10 pauses each | 31.6 / 18.4 / 19.1 | base 10.9, cold 9.4 | breaks at d=1; plateau 2× cold (p=0.0025) |
| 23a | 3× training steps | val ↑ (overfit) | — | time not binding |
| 23b | 3× pauses | 29.3 | 31.6 | bandwidth not binding |
| 24 | loop-only band-LoRA r16 | stopped (fit unchanged) | — | expressivity not binding; k=0 bit-exact validated |

## Arc V — Lens/state supervision of the latent chain

| # | tried | matched | ablated | verdict |
|---|---|---|---|---|
| 25 | lens-CE: pause j ↔ deleted token j | 31.2 | — | lce 10.3→1.9 yet flat: writing ≠ computing |
| 26 | result-staging on pre-'=' spans | 24.2 / 15.6 combined | — | harmful — violates just-in-time schedule |
| 27 | zero-pause 10-iter burst + lens | 34.0 | 32.4 (p=0.45) | best nominal, ns; pause tape dead weight |
| 28 | teacher-state endpoint distillation | 30.1 | 29.7 | cos .113→.044, function absent; easy damaged |

## Arc VI — 2026-07-17 designs (Nils)

| # | tried | matched | ablated/ref | verdict |
|---|---|---|---|---|
| 29 | trajectory TF (10 waypoint transitions) | **39.1, p=0.045** | 39.1 burst-off (p=1.0) | first significant positive — a training signal, not an inference loop; +fr 30.5 (hurts); answer-only 15.6 < 19.1 |
| 30 | metacog readiness head on carried state | AUC 0.798 | FF AUC 0.791 | signal real & cheap, NOT recurrence-specific; early-stop loses; oracle +3.9 |
| 31 | synthetic KV memory (per-layer prefix) | 39.5 | 39.1 (p=1.0) | flat — gates frozen at −10 (init gradient-trap confound; −3 rerun open) |
| 32 | discrete latent chain ("latent paper": lens-snapped symbols fed back) | TF 20.3 / ST 27.0 | 39.1 | net-harmful — exposure catastrophe (TF) and quantization noise (ST) both lose to the pure analog carry; architecture tree closed |

Instrument (unnumbered): whiteboard microscopy — three specimens + carry-vs-FF divergence (probe_discount*/probe_gsm*; board artifact).

## Standing positives
MBPP loop-vs-weights gap · GSM drop-bucket reach (p=0.0094) · the 57.4 hybrid · trajectory-TF as a gradient (p=0.045) · 0.8-AUC readiness probe.

## Standing walls
Consumption (8 write-side axes + 1 read-path attempt) · internalization (4 capacity axes + 4 supervision forms) · learned gates < frozen probe.

## Open threads
Seeds for 39.1 · trajectory TF on rung A (move 57.4) · KV gate-init −3 · extension/deferral gating · g into the depth gate.

## Final architecture verdict (item 32 closes the tree)
Pauses, bursts, KV memory, analog TF chains, and discrete chains all have controlled answers.
The loop is a plan machine; tokens are the executor — they win by discreteness PLUS a verified
commitment distribution (the LM head is trained to commit; the lens readout is not).
