The answer stayed fixed.
Permission changed.

Combined FINAL

2,048/2,048

Answer → native EOS

40/40

Native EOS → correct answer

40/40

75 FINAL answer identities. 40 causal answer identities. 80/80 sham controls unchanged. 188/188 question-only controls unchanged.

The 188-question bank is selected by a deterministic stock-capability rule before permission training. No case is removed or replaced after the bank is frozen. Gate training stops at the first qualifying checkpoint, update 256. Content weights remain frozen.

The causal test reverses the learned permission state across 40 answer identities. The question, content weights, and complete non-EOS logits remain fixed. It changes answer to EOS and EOS to the corresponding correct answer.

The condition never enters the content computation. The gate receives neither the question nor an externally computed truth verdict. Its learned score comes from aligned digit-pair embeddings and an offset.

For every non-EOS token t:  z′[t] = z[t]
At the first token:         z′[EOS] = BF16(z[EOS] − 32 × r × s(c))
Baseline and sham: r = +1   Reversed permission: r = −1

The EOS adjustment is computed in FP32 and cast to BF16. Full-vocabulary greedy decoding selects the output. After the first token, the gate is bypassed. There is no output deletion or answer replacement.

All non-EOS logits, rankings, and probabilities conditional on a non-EOS token remain unchanged. The total probability of continuing changes through EOS.

A finite-precision certificate covers 810,000,000,000 ordered condition pairs, each paired with any of the 188 frozen bank computations.

The accepted domain is EQ(a,b), with each operand an integer from 100000 through 999999. That is 900,000 × 900,000 conditions. Equal operands permit the fixed answer followed by EOS. Unequal operands select first-token EOS.

This is proof coverage, not 810 billion executed trials. The certificate assumes the recorded content logits and continuation, FP32 gate accumulation, FP32 EOS addition followed by BF16 round-to-nearest, ties-to-even, and baseline full-vocabulary greedy decoding.

Download the pinned release and verify saved evidence

Python 3.11 or later. The complete download includes approximately 8.1 GB of content weights. Verification uses the CPU and generates no new model outputs.

python -m pip install huggingface_hub
hf download sharthokrayanpal/PCCG-2-Qwen3-4B \
  --revision a3b952458a46b5547ba3cec7d03a37b395bed03a \
  --local-dir PCCG-2-Qwen3-4B
cd PCCG-2-Qwen3-4B
python -m pip install numpy==2.3.5
python src/verify.py

Run fresh inference

CUDA and BF16. For byte-exact logit replay, use the recorded NVIDIA H100 80 GB environment, PyTorch 2.8.0+cu128, Transformers 4.56.2, and SDPA attention. Each output directory must be new.

python -m pip install -r requirements.txt
python src/reproduce.py witness --out ../pccg2-witness
python src/reproduce.py behavioral --out ../pccg2-behavioral
python src/reproduce.py causal --out ../pccg2-causal

These commands load the frozen release and compare new outputs with saved evidence. They do not train or select parameters.

python PCCG-2-paper-supplement/prove_domain.py \
  --release ./PCCG-2-Qwen3-4B \
  --out domain-certificate-recomputed.json

PCCG-2 implements an engineered gate over six-digit equality and stock-qualified answers. It does not identify a naturally occurring circuit in stock Qwen or the mechanism behind frontier Void observations. Jacobian Lens was used in PCCG-1, not PCCG-2.

The released experiment controls model generation, not consequential external actions or general alignment.

Rayan Pal · Independent Researcher · Research library