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REP-005: fresh-setting transfer and remaining failures

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# REP-005: reference-readout recovery transfers; learned decoding remains incomplete

Latent-only H fitting repaired all **368,229 native errors**, with **zero
regressions**, on the preregistered primary family: 128 projection-free words of
length 32, evaluated from every state in a fresh 31-by-31 torus with binary
context. All five seeds reached 100% complete-state accuracy through the
arithmetic reference decoder. The paired prediction-plus-latent arm left 38
errors; the train-only H least-squares control also recovered every primary case.

The learned decoder did not meet the same criterion. Latent-only fitting raised
its median primary accuracy from 43.8398% to 78.7660%, but introduced **57,988
regressions** and left **267,903 errors**. Thus the regression-free recovery
pattern transferred for this family and reference readout, not for the learned
observation interface or every tested composition family.

The [frozen protocol](FRESH_TRANSFER_PROTOCOL.md) defines this distinction before
execution. A family transfers the earlier regression-free pattern only when
native has errors, latent-only repairs at least one, and latent-only creates no
regression across all five seeds. Perfect recovery additionally requires no
remaining errors in any seed. Execution completion and scientific acceptance
are separate outcomes.

## Fresh setting and all-seed primary results

This setting contains 1,922 states: 1,612 training and 310 held states. The new
partition withholds both contexts on five registered modular lines. Training
uses 10,876 train-to-train edges, including 1,612 H edges. Evaluation words and
their seed were frozen before training. No historical checkpoint was reused.

Five freshly initialized native models received 1,000 full-batch Adam updates.
Each supplied Fourier encoder remained fixed. Ten H-fitting trials then received
1,000 updates each, with identical paired native H starts, fresh optimizer state,
frozen learned decoders and seven unchanged operation heads. The experiment
performed **15,000 optimizer updates** in total. Native and refit intervention
arms received no fitting updates. Neither evaluation nor checkpoint selection
altered that budget.

The fresh decoder is `10 -> 256 -> 64`, whereas REP-002/REP-004 used a hidden
width of 32 and 16 observation coordinates in the seven-by-seven world. The
world cardinality, held-out partition, word inventory, decoder capacity and
fresh initialization therefore change together. This is a registered
fresh-setting transfer test, not an isolated single-factor comparison or a
reproduction of the historical optimization trajectory.

Each primary accuracy below covers **246,016 cases per seed and arm**
(128 words times 1,922 states). Percentages are rounded to four decimals.

Arithmetic reference decoder:

| Seed | Native | Prediction + latent | Latent only | H refit |
|---|---:|---:|---:|---:|
| 0 | 68.4553% | 99.9984% | 100% | 100% |
| 1 | 77.7701% | 100% | 100% | 100% |
| 2 | 73.4025% | 100% | 100% | 100% |
| 3 | 70.1105% | 100% | 100% | 100% |
| 4 | 60.5847% | 99.9862% | 100% | 100% |
| Median | 70.1105% | 100% | 100% | 100% |
| Worst | 60.5847% | 99.9862% | 100% | 100% |

The mixed arm's residual errors are four in seed 0 and 34 in seed 4. Its 100%
median therefore does not establish perfect recovery.

Learned observation decoder, on those same trajectories:

| Seed | Native | Prediction + latent | Latent only | H refit |
|---|---:|---:|---:|---:|
| 0 | 43.5748% | 76.7796% | 81.9699% | 81.9313% |
| 1 | 43.8398% | 76.8352% | 80.9041% | 80.9817% |
| 2 | 53.3165% | 71.0141% | 78.7660% | 78.5689% |
| 3 | 49.2602% | 68.4537% | 73.6460% | 73.6298% |
| 4 | 40.5319% | 70.6304% | 75.8174% | 75.0825% |
| Median | 43.8398% | 71.0141% | 78.7660% | 78.5689% |
| Worst | 40.5319% | 68.4537% | 73.6460% | 73.6298% |

## Repairs, regressions and the preserved failures

Each row below aggregates all five seeds over 1,230,080 paired cases. A repair
was wrong under native and correct under the intervention; a regression was
correct under native and wrong afterward. These are paired changes on a finite
inventory, not independent statistical samples.

| Family | Decoder | Arm | Repairs | Regressions | Remaining errors |
|---|---|---|---:|---:|---:|
| Length 32, no P, primary | Reference | Prediction + latent | 368,191 | 0 | 38 |
| Length 32, no P, primary | Reference | Latent only | 368,229 | 0 | 0 |
| Length 32, no P, primary | Reference | H refit | 368,229 | 0 | 0 |
| Length 32, no P, primary | Learned | Prediction + latent | 407,262 | 79,594 | 335,288 |
| Length 32, no P, primary | Learned | Latent only | 453,041 | 57,988 | 267,903 |
| Length 32, no P, primary | Learned | H refit | 452,097 | 59,281 | 270,140 |
| Length 16, no P | Reference | Prediction + latent | 48,040 | 0 | 0 |
| Length 16, no P | Reference | Latent only | 48,040 | 0 | 0 |
| Length 16, no P | Reference | H refit | 48,040 | 0 | 0 |
| Length 16, no P | Learned | Prediction + latent | 180,897 | 27,808 | 104,319 |
| Length 16, no P | Learned | Latent only | 189,988 | 19,373 | 86,793 |
| Length 16, no P | Learned | H refit | 189,821 | 19,759 | 87,346 |
| Length 16, all actions | Reference | Prediction + latent | 82,687 | 3,314 | 10,517 |
| Length 16, all actions | Reference | Latent only | 82,646 | 3,436 | 10,680 |
| Length 16, all actions | Reference | H refit | 82,663 | 3,470 | 10,697 |
| Length 16, all actions | Learned | Prediction + latent | 207,824 | 42,589 | 240,380 |
| Length 16, all actions | Learned | Latent only | 212,886 | 39,484 | 232,213 |
| Length 16, all actions | Learned | H refit | 215,285 | 39,661 | 229,991 |

The all-action length-16 family fails the regression-free criterion even through
the reference decoder; all 3,436 latent-only reference regressions occur in seed
3. At all-action length 32, latent-only reference decoding retains 20,265 errors
and introduces 3,515 regressions. Projection-free success therefore cannot be
generalized to these families. P's presence is a registered stratum, not evidence
that P alone caused every error; other frozen operators and their compositions
remain part of the evaluated mechanism.

Learned reconstruction of the untransformed supplied codes was already
96.8783% to 99.4277% across seeds, while reference reconstruction was 100%. This
isolates an imperfect learned readout even before composition. The primary
latent-only learned accuracies remain incomplete for both held and seen initial
states. Exact arithmetic readout success does not certify this learned decoder,
nor does lower latent error guarantee that every observation is preserved.

Final H-training latent MSE is approximately 2.36e-14 to 4.25e-14 for latent-only,
versus 7.92e-5 to 1.31e-4 for the mixed objective. Mixed-objective training gradient
cosines range from -0.9551 to -0.999994 at the endpoint. These are training-only
diagnostics showing opposed gradient components in this setup, not proof of a
universal optimization mechanism or an unavoidable tradeoff.

## Execution evidence and resource scope

The official receipt is completed. The worker used its frozen source snapshot
on the local **RTX 5070**, deterministic FP32 with TF32 disabled. The one official
attempt retained all models, optimizer moments, training traces, paired outcomes
and failures. It evaluated **33,558,120 trial/state/word cases** in 41 families.

- Training interval: **10.9161 seconds**, including checkpoint and logging gaps;
  CUDA event interval: 10,914.93 ms. This interval is not a sum of kernel times.
- Evaluation: **15.5377 seconds**; worker: **33.3381 seconds**; supervised process:
  **34.2030 seconds**; total receipt including verification: **46.3280 seconds**.
- Peak PyTorch allocation: **420.60 MiB**; reserved: **688 MiB**. Peak monitored
  process-tree RAM: **1.833 GiB**. These remain within the registered allocation,
  reserve, host, disk and wall-time limits.
- Twenty-seven supplemental device-wide samples reached **82% GPU utilization**,
  **145.25 W** and **45 degrees C**. These are approximately one-second NVIDIA
  samples, not per-process attribution, sustained utilization or a CPU speedup
  comparison. The profiler separately records **402 actual CUDA training kernels**.
- All **42** CPU loop/batch and CPU/CUDA parity comparisons passed at
  rtol=1e-4, atol=1e-6. Maximum recorded absolute discrepancy was 2.412e-7.
- Analytic reference controls passed: training feature rank ten, complete
  coordinate round trips, inverse/periodic/idempotent identities, order-sensitive
  witnesses, 961 lost-context pairs, and rejection of constant-code observation
  adequacy despite zero commutator error.

The registered independent NumPy inference check covers every word and the 16
initial states `0,127,...,1905`: **279,360 trial/state/word cases**, with exact
categorical agreement for both decoders. Its continuous check compares per-case
latent MSE at rtol=1e-4, atol=1e-6. It does not compare every latent coordinate or
decoder logit, and does not replay all 1,922 initial states, Adam's trajectory,
another host, Claude Code or an NPU. Full retained-array consistency and H-free
isolation checks are separate from that subset inference replay.

The final designated CPU test run passed **895 tests plus 27 subtests**, with
five declared skips. The focused CUDA-environment suite passed **77 tests**.
A separate CPU verification reproduced the registered 279,360-case NumPy subset
and checked the saved arrays and receipt. Separate source-agent review inspected
the implementation and evidence boundaries. These are source review and
independent inference code on the same host, not execution in a second agentic
harness or on an independent machine.

Official local archive:
`G:/RenigmaLLM_Artifacts/fresh-transfer-runs/rep-22de256c2306`.
The receipt binds 104 retained payload files. Execution source commit:
`f94db862babf5b122229c929b8c121489fe06e11`.

| Evidence identity | SHA-256 |
|---|---|
| Receipt | `dbaaf718f87af0a768af015c4c22ba487d037ccbd23463d5e1b7d855a32eaa0b` |
| Runtime source manifest | `f80bea899d921731bf1a37b506fec851f8e7245e821522fd33bb56518ec839fc` |
| Frozen design | `d4846f73e1789e64744d014f98425046d73b9c5f7cd1ae1384b4130f7122c06b` |
| Frozen protocol | `e410e4d926eb050b2604fa06f07c685720be5e9339b3021db6113ffb422a94ea` |
| Result | `881445fef6e1b35f3f73dd7362fac9a5358b2088bbdb22527c80a5b8b9e3beb0` |

Implementation and checkpoints remain private. The public evidence export may
include these reviewed synthetic findings, protocol and summary; publication
is established separately by the website deployment receipt.

## Next decision

The fresh-world reference control is valid, and the narrow primary recovery
criterion passes for the reference readout. Retain that supplied/reference
alternative. Learned observation adequacy remains unresolved, so these results
do not justify product integration, a general-language claim or the claim that
the known state needs extra dimensions.

Before the supplied-versus-learned-coordinate stage, inspect and report decoder
and frozen-operator error attribution using the retained artifacts, explicitly
as diagnostics. Then freeze a new protocol with matched architectures and cost
reporting, separate readout controls, observable correctness, collision checks
and new held-out evaluation. Any new training configuration is a new study;
these held-out results must not become a tuning loop. Topology, diffusion and
bounded learned language remain separate gates. No outcome-selected retry or
extra optimization was performed in REP-005.