---
language:
  - hbo  # Ancient Hebrew
  - grc  # Ancient Greek (Koine)
  - la   # Latin
library_name: peft
base_model: Qwen/Qwen2.5-0.5B-Instruct
tags:
  - lora
  - peft
  - geometric-ai
  - biblical-hebrew
  - koine-greek
  - latin-vulgate
  - e8-lattice
  - hallucination-reduction
  - sovereign-engine
license: other
license_name: sectl-1.0
license_link: https://github.com/JLeeV/sovereign-engine/blob/main/LICENSE
---

# Titulus_E8 — Geometric LoRA Adapter

**Titulus_E8** is a LoRA fine-tuning adapter for causal language models, trained on the trilingual Biblical corpus
(Hebrew Tanakh · Koine Greek NT/LXX · Latin Vulgate) with a **Topological Coherence Loss** that anchors the
model's embedding space to the [E8 lattice](https://en.wikipedia.org/wiki/E8_lattice).

The adapter is part of the **Sovereign Geometric Model (SGM)** architecture from
[Sovereign Engine](https://github.com/JLeeV/sovereign-engine), a distributed geometric AI system that uses
discrete lattice mathematics to eliminate LLM hallucinations by construction.

---

## The Name

The *Titulus Crucis* — the inscription nailed above the cross — was written in three languages: Hebrew, Latin,
and Greek (John 19:20). It is one of the most historically significant trilingual documents in existence and the
conceptual anchor for this system. The trilingual structure mirrors the three corpus languages exactly.

---

## Architecture

```
Base Model  (Qwen2.5-0.5B-Instruct)
    │
    ├── LoRA Adapter  ← Titulus_E8
    │     rank=32, alpha=64
    │     target: q_proj, v_proj
    │
    └── E8 Logit Mask  (inference-time geometric constraint)
          - every vocabulary token → 8D IPA phonetic coordinate
          - coordinate snapped to nearest of 240 E8 roots (Babai CVP)
          - logits attenuated for tokens that drift beyond geodesic radius
```

### Training Objective

The adapter is trained with a **dual loss**:

```
L = λ_lm · CE_loss + λ_topo · TopologicalCoherenceLoss

TopologicalCoherenceLoss = mean( min_j ||h_i - e8_root_j||² )
```

Where `h_i` are the final hidden-state vectors and `e8_root_j` are the 240 roots of the E8 lattice,
projected into the model's hidden dimension. This forces semantically related embeddings to cluster
near valid lattice coordinates — making hallucination geometrically costly rather than just statistically
unlikely.

---

## Training Data

| Language | Corpus | Source |
|---|---|---|
| **Biblical Hebrew** | Westminster Leningrad Codex (Masoretic Text) | `christos-c/bible-corpus` |
| **Koine Greek** | Nestle-Aland NT + Septuagint (LXX) | `christos-c/bible-corpus` |
| **Latin** | Clementine Vulgate | `christos-c/bible-corpus` |

Each training sample interleaves all three translations of a canonical verse:

```
[HE] בְּרֵאשִׁית בָּרָא אֱלֹהִים אֵת הַשָּׁמַיִם וְאֵת הָאָרֶץ
[GR] Ἐν ἀρχῇ ἐποίησεν ὁ θεὸς τὸν οὐρανὸν καὶ τὴν γῆν
[LA] In principio creavit Deus caelum et terram
```

The model learns to associate semantically equivalent expressions across three typologically distinct
language families — forcing its latent space to develop representations that are stable across linguistic
surface variation.

---

## Usage

### As a standard PEFT adapter

```python
from transformers import AutoTokenizer, AutoModelForCausalLM
from peft import PeftModel

base_model_id = "Qwen/Qwen2.5-0.5B-Instruct"
adapter_id    = "JLeeV/Titulus_E8"

tokenizer = AutoTokenizer.from_pretrained(base_model_id)
model     = AutoModelForCausalLM.from_pretrained(base_model_id)
model     = PeftModel.from_pretrained(model, adapter_id)

inputs = tokenizer("In the beginning", return_tensors="pt")
output = model.generate(**inputs, max_new_tokens=50)
print(tokenizer.decode(output[0]))
```

### With Geometric Logit Mask (full SGM pipeline)

```python
from transformers import AutoTokenizer, AutoModelForCausalLM, LogitsProcessorList
from peft import PeftModel
from sov_heart.logit import GeometricLogitMask

base_model_id = "Qwen/Qwen2.5-0.5B-Instruct"
tokenizer = AutoTokenizer.from_pretrained(base_model_id)
model     = PeftModel.from_pretrained(
    AutoModelForCausalLM.from_pretrained(base_model_id),
    "JLeeV/Titulus_E8"
)

# Build geometric constraint interceptor
processor = GeometricLogitMask.as_logits_processor(
    tokenizer,
    radius=3.0,        # geodesic tolerance (tighter = stricter)
    soft_mask=True,    # Gaussian attenuation vs hard zeroing
    cache_path="/tmp/titulus_token_coords.npy",  # cache for fast reload
)

inputs = tokenizer("Explain the concept of logos", return_tensors="pt")
output = model.generate(
    **inputs,
    max_new_tokens=200,
    logits_processor=LogitsProcessorList([processor]),
)
print(tokenizer.decode(output[0]))
```

---

## Installation

```bash
pip install peft transformers torch

# For the full SGM geometric constraint system:
git clone https://github.com/JLeeV/sovereign-engine
cd sovereign-engine && pip install -e .
```

---

## Geometric Coordinate Mapping

Each token in the vocabulary is mapped to an **8-dimensional E8 coordinate** using IPA phonetic features:

| Dimension | Feature |
|---|---|
| 0 | Stop consonant ratio (p, b, t, d, k, g, q) |
| 1 | Fricative ratio (s, z, v, ʃ, ħ, θ, f, x) |
| 2 | Nasal ratio (m, n) |
| 3 | Vowel ratio (a, e, i, o, u, y) |
| 4 | Liquid ratio (r, l) |
| 5 | Mean Unicode codepoint (normalised to Hebrew range) |
| 6 | Script class (0=Latin, 0.5=Greek, 1.0=Hebrew/Semitic) |
| 7 | Syllable density (syllables per character) |

The raw 8D vector is then snapped to the nearest of the **240 roots of the E8 lattice** using Babai's
Closest Vector Problem (CVP) algorithm — guaranteeing all token coordinates are valid lattice points.

---

## License

This adapter is released under the **Sovereign Engine Cooperative and Topological License (SECTL) v1.0**.
See [LICENSE](https://github.com/JLeeV/sovereign-engine/blob/main/LICENSE) for full terms.

The training corpus texts (Westminster Leningrad Codex, NA28, Clementine Vulgate) are in the public domain.

---

## Citation

```bibtex
@misc{titulus_e8_2026,
  author       = {JLeeV},
  title        = {Titulus\_E8: A Geometric LoRA Adapter Anchored to the E8 Lattice},
  year         = {2026},
  publisher    = {HuggingFace},
  howpublished = {\url{https://huggingface.co/JLeeV/Titulus_E8}},
  note         = {Part of the Sovereign Engine geometric AI architecture}
}
```