RMSN-425M-CasimirCascade-Base

425M Resonant Metriplectic Sheaf Pre-Trained Base Model
The First Observed Multi-Singularity Casimir Cascade in Non-Euclidean Port-Hamiltonian Networks

Developed by DuoNeural AI Laboratory — Jesse Caldwell, Archon, Aura✨

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🏛️ Model Overview

RMSN-425M-CasimirCascade-Base represents a pivotal topological milestone in the Phase 5 pretraining sweep of the Resonant Metriplectic Sheaf Network. Parameterized at 425 million weights ($D=1344, L=16, M_w=64$) and trained on FineWeb-Edu for 100,000 steps, this model embodies Casimir Attractive Resonance ($r = D \pmod{32} = 0$).

🌊 Discovery: The Casimir Singularity Cascade

When the internal dimension $D$ satisfies dyadic resonance ($D \equiv 0 \pmod{32}$), the representation manifold experiences an attractive Casimir interaction between non-Euclidean sheaf layers. Over 100,000 steps of pretraining, this interaction precipitated a triple macroscopic singularity cascade with strict discrete layer spacing $\Delta L = 3$:

Layer	Participation Ratio ($PR$)	Soliton / Singularity State
Layer 09	1.000000	Rank-1 Macroscopic Singularity
Layer 10	63.48	Superfluid Bulk
Layer 11	63.82	Superfluid Bulk
Layer 12	1.000000	Rank-1 Macroscopic Singularity
Layer 13	55.60	Superfluid Bulk
Layer 14	54.04	Superfluid Bulk
Layer 15	1.000000	Rank-1 Macroscopic Singularity

This structure confirms the $\Delta L \ge 3$ Casimir Repulsion Law: multi-soliton coexistence requires a minimum layer gap to avoid quantum entanglement channel collapse, as verified on BlueQubit QCPU.

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⚡ Empirical Anchoring Under SFT

While general language modeling on $M=3$ models undergoes topological narrowing (WikiText-103 PPL = 90.37 vs 81.04 for $M=1$), supervised fine-tuning revealed the Dual Boundary Shielding Phenomenon:

• The $L_{09}, L_{12}, L_{15}$ singularities act as permanent topological cement anchors.
• Under 5,000 steps of reasoning SFT, this anchored manifold achieved 162.24 WikiText-103 retention PPL, dramatically outperforming the open boundary $D=1296$ control model (266.27 PPL).

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🚀 Usage & Inference

import torch
from rmsn_core import ResonantMetriplecticSheafLM
from transformers import AutoTokenizer

device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')

# 1. Load tokenizer
tokenizer = AutoTokenizer.from_pretrained('HuggingFaceTB/cosmo2-tokenizer')

# 2. Initialize RMSN architecture (D=1344, L=16, Slots=64)
model = ResonantMetriplecticSheafLM(
    vocab_size=49152,
    dim=1344,
    depth=16,
    num_slots=64
).to(device)

# 3. Load checkpoint
ckpt = torch.load('rmsn_d1344_base_best.pt', map_location='cpu', weights_only=False)
sd = ckpt.get('model_state', ckpt.get('model', ckpt))
clean_sd = {k[6:] if k.startswith('model.') else k: v for k, v in sd.items()}
model.load_state_dict(clean_sd, strict=False)
model.eval()

# 4. Generate
prompt = "The physical principle governing non-equilibrium dissipative systems is"
input_ids = tokenizer.encode(prompt, return_tensors='pt').to(device)
with torch.no_grad():
    logits = model(input_ids)
    next_token = torch.argmax(logits[:, -1, :], dim=-1)
    print("Next predicted token:", tokenizer.decode(next_token))

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📚 Citation

@article{caldwell2026rmsn,
  title={Resonant Metriplectic Sheaf Networks: A Unified Port-Hamiltonian Framework for Neural Language Modeling with Emergent Lyapunov Cascade Dynamics},
  author={Caldwell, Jesse and Archon and Aura},
  journal={DuoNeural Lab Preprints},
  year={2026},
  publisher={Zenodo}
}