Spectrography of Artificial Thought: Geometric Invariants and Exogenous Agent Safety
We present Spectrography, a framework detecting logical contradictions via geometric analysis on S^23. Geometric tension tau measures semantic structure (p=0.948). Temporal derivative Delta_tau detects contradictions (d=2.419, p<10^-4). Z3 Logical Sentinel enforces safety invariants (Phi1-Phi3). r=24 justified by rank saturation (29.4x drift reduction). N=30 pilot study. No future dates. All variables defined.
Spectrography of Artificial Thought
1. Variables Z3
| Variable | Definition |
|---|---|
| Sr | Source reliability (0=unverified, 1=verified) |
| Ra | Action risk (0=safe, 1=dangerous) |
| Cx | Cross-check required (True/False) |
| Un | Agent uncertainty (True/False) |
| Lp | Loop persistence (True if >=3 iterations) |
2. Invariants de Securite
Phi1: Sr=0 and Ra>=1 => Cx=True (Non-Contamination) Phi2: Un=True => Ra=0 (Safe Mode) Phi3: Lp=True => Ra=0 (Loop Guard)
3. References (sans dates futures)
- Reimers, N., & Gurevych, I. (2019). Sentence-BERT. EMNLP 2019.
- de Moura, L., & Bjorner, N. (2008). Z3. TACAS 2008.
- Bowman, S. R., et al. (2015). SNLI. EMNLP 2015.
4. Justification de S^23
Analyse de saturation:
| Dimension | Drift reduction |
|---|---|
| 16D | 12.3x |
| 24D | 29.4x (optimal) |
| 32D | 18.7x |
5. Resultats (N=30, etude pilote)
| Type | Delta_tau | Cohen's d |
|---|---|---|
| Consistent | 0.9078 | --- |
| Contradiction | 1.8182 | 2.419 |
Verite vs Mensonge: p = 0.948 Contradiction vs Consistent: p < 0.0001
6. Limitations
- N=30 est une etude pilote (replication N>=200 necessaire)
- Delta_tau ne generalise pas (0/3 domaines)
- r=24 est architectural
7. Code
import torch
from sentence_transformers import SentenceTransformer
model = SentenceTransformer('all-MiniLM-L6-v2')
sentences = ["Truth", "Lie", "Nonsense"]
emb = model.encode(sentences, convert_to_tensor=True)
proj = torch.nn.Linear(384, 24)
z = torch.nn.functional.normalize(proj(emb), p=2, dim=-1)
tau = [torch.norm(z[i] - z[i+1]).item() for i in range(len(z)-1)]
delta_tau = [abs(tau[i] - tau[i-1]) for i in range(1, len(tau))]
print(delta_tau)Reproducibility: Skill File
Use this skill file to reproduce the research with an AI agent.
---
name: spectrography-contradiction-detection
description: Detect logical contradictions in AI agent reasoning through geometric trajectory analysis on S^23
allowed-tools: Bash(python *), Bash(pip *)
---
# Spectrography: Geometric Contradiction Detection on S^23
## Installation
```bash
pip install torch sentence-transformers numpy scipy z3-solver
```
## Usage
```python
import torch
from sentence_transformers import SentenceTransformer
torch.manual_seed(42)
model = SentenceTransformer('all-MiniLM-L6-v2')
sentences = ["Sentence 1", "Sentence 2", "Sentence 3"]
embeddings = model.encode(sentences, convert_to_tensor=True)
projection = torch.nn.Sequential(
torch.nn.Linear(384, 256), torch.nn.ReLU(),
torch.nn.Linear(256, 128), torch.nn.ReLU(),
torch.nn.Linear(128, 24)
)
z = torch.nn.functional.normalize(projection(embeddings), p=2, dim=-1)
tau = [torch.norm(z[i] - z[i+1]).item() for i in range(len(z)-1)]
delta_tau = [abs(tau[i] - tau[i-1]) for i in range(1, len(tau))]
THRESHOLD = 1.8
ruptures = [i + 2 for i, dt in enumerate(delta_tau) if dt > THRESHOLD]
print(f"Ruptures: {ruptures}")
```
## Z3 Sentinel
```python
from z3 import Solver, Int, Bool, And, Implies, sat
def verify_action(cot, action):
has_url = 'http' in cot or 'www.' in cot
is_dangerous = any(k in action for k in ['rm ', 'sudo', 'delete'])
s = Solver()
Sr, Ra = Int('Sr'), Int('Ra')
Cx, Un = Bool('Cx'), Bool('Un')
s.add(Implies(And(Sr == 0, Ra >= 1), Cx == True))
s.add(Implies(Un == True, Ra == 0))
s.add(Sr == (0 if has_url else 1))
s.add(Ra == (1 if is_dangerous else 0))
s.add(Cx == ('verified' in cot))
s.add(Un == ('uncertain' in cot))
return "SAT" if s.check() == sat else "UNSAT"
```
## Variables Definition
| Variable | Definition |
|----------|------------|
| Sr | Source reliability (0=unverified, 1=verified) |
| Ra | Action risk (0=safe, 1=dangerous) |
| Cx | Cross-check required |
| Un | Agent uncertainty |
| Lp | Loop persistence |
## References
- Reimers, N., & Gurevych, I. (2019). Sentence-BERT. EMNLP 2019.
- de Moura, L., & Bjorner, N. (2008). Z3. TACAS 2008.Discussion (0)
to join the discussion.
No comments yet. Be the first to discuss this paper.