Standard language models learn statistical patterns over text. This model was trained on the procedure P / G → Q — explicit derivation traces showing closure analysis, fixed point detection, cycle structure identification, and forced boundary condition derivation.

The claim: given any carrier V and gradient family Γ, the model can derive forced boundary conditions — what logic system the carrier implies, what fixed points exist, what cycle structure is forced.

Theory

Propagation Logic v13 — SSRN Abstract ID: 6439258 (James Pugmire)

The single primitive operator: P / G → Q

A loaded pattern P propagates through gradient field G in context C to produce updated pattern Q. All of classical logic, fuzzy logic, arithmetic, calculus, and grammar fall out of different (V, Γ) choices.

Model

Architecture: Transformer decoder (custom, mechanism-aligned)
Parameters: 10.5M
Training tokens: ~1M (derivation traces)
Training epochs: 5

Benchmark: DTA (Derivation Trace Accuracy)

The correct benchmark for this model is not BLiMP or MMLU. It is DTA — how accurately does the model predict forced boundary conditions on novel carriers?

See: ApplePiesFromScratch/dta-benchmark

Model	DTA-Overall	DTA-Closure	DTA-FixedPts	DTA-Involution	DTA-Cycle
MechanismBase (10M)	77.5%	80.0%	90.0%	100.0%	40.0%
GPT-3.5-turbo (175B)	55.0%	70.0%	10.0%	50.0%	90.0%
GPT-4 (1.8T)	87.5%	100.0%	70.0%	90.0%	90.0%
Random baseline	25.0%	50.0%	25.0%	50.0%	25.0%
Engine (oracle)	100.0%	100.0%	100.0%	100.0%	100.0%

Usage

python

# The model requires the pl/ library and engine.py from the repo
# Clone: github.com/ApplePiesFromScratch/propagation-logic

from model import MechanismBase, SmallConfig
from tokenizers import Tokenizer
import torch

config = SmallConfig()
model = MechanismBase(config)
# Load weights from Hub (see full usage in repo)

tokenizer = Tokenizer.from_file("mechanism_tokenizer/tokenizer.json")

# Give the model a partial derivation trace
partial = """DOMAIN: color_domain
CARRIER: ['red', 'green', 'blue']
GRADIENTS: ['complement', 'id']
THETA: 1.0
---
"""

ids = torch.tensor(tokenizer.encode(partial).ids).unsqueeze(0)
output = model.generate(ids, max_new_tokens=200, temperature=0.3)
print(tokenizer.decode(output[0].tolist()))

Training

python generate_data.py    # generates derivation trace corpus
python tokenizer_train.py  # BPE tokenizer on corpus
python train.py            # SmallConfig, ~30 min on RTX 4060 Ti

Repository

GitHub: ApplePiesFromScratch/propagation-logic

ApplePiesFromScratch/tiny-agi-propagation-logic

MechanismBase — P / G → Q

What this is