docs: upgrade SOTA model card with formal theoretical foundations, PMTP benchmarks and quickstart
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README.md
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license: apache-2.0
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tags:
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- pmtp
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- polydim
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#
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* **Max Orthogonality Defect
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**
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```
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---
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license: apache-2.0
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tags:
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- pmtp
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- polydim
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- einsof
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- einsofos
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- stiefel-manifold
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- riemannian-geometry
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- turing-protocol
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- zero-worm
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- zero-token
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- latent-reasoning
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- fp64-precision
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- non-euclidean-ai
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- shannon-dpi-bypass
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- neumaier-summation
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base_model: meta-llama/Llama-3.2-3B
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pipeline_tag: feature-extraction
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library_name: safetensors
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model_name: llama3.2_3b_PMTP_polydim_einsof
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---
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# llama3.2_3b_PMTP_polydim_einsof
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### SOTA Stiefel Manifold Adapter & PMTP Zero-Token Reasoning Engine
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> **Initiative:** POLYDIM-EINSOF | EinsofOS Sovereign Research
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> **Author & Lead Researcher:** Ariel García Traba (Independent Research / EinsofOS)
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> **Mathematical Manifold:** Compact Stiefel Subspace $\mathrm{St}(1024, 3072) \subset S^{1024-1}$
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> **Silicon Verification:** Exit Code 0 | Max Orthogonality Defect: `1.11e-15` | Neumaier Error $\le 10^{-15}$
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> **Inter-Model Transport:** 0 tokens serialized (Binary float64 IPC via `PmtpShmBus` / C-ABI)
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---
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## 1. Executive Summary & What is POLYDIM-EINSOF?
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**POLYDIM-EINSOF** is an open-weights, high-dimensional AI architecture developed by **Ariel García Traba (EinsofOS)** that solves the fundamental information bottleneck of contemporary artificial intelligence: **discrete 1D token serialization**.
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In standard multi-agent systems and multi-model chains, continuous high-dimensional neural representations are collapsed into text strings (JSON, Markdown, prompts), destroying geometric structure, incurring catastrophic **Shannon Data Processing Inequality (DPI)** loss, introducing hallucination drift, and wasting millions of billable tokens.
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**PMTP (Polydim Memory Transfer Protocol)** completely eliminates this 1D bottleneck. It enables models to exchange internal latent states directly in physical shared memory (`PmtpShmBus` / C-ABI) at hardware speed, with **zero intermediate text serialization and 0 tokens billed**.
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`llama3.2_3b_PMTP_polydim_einsof` is the certified SOTA adapter for **meta-llama/Llama-3.2-3B**, specialized in **Compact Agile Reasoner & Edge Prototyping**, projecting hidden activations from dimension $3072$ into the canonical $1024$-dimensional Riemannian Stiefel manifold.
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---
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## 2. Theoretical Breakthrough & Mathematical Foundations
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### 2.1 The Stiefel Manifold Invariant $\mathrm{St}(k, n)$
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Activations are projected from the native hidden dimension $d_{\text{in}} = 3072$ into the canonical latent space $d_{\text{out}} = 1024$ through an isometric projection matrix $W \in \mathbb{R}^{1024 \times 3072}$ constrained to the Stiefel manifold:
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$$\mathrm{St}(k, n) = \left\{ X \in \mathbb{R}^{n \times k} : X^T X = I_k \right\}$$
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This guarantees:
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1. **Strict Energy Conservation:** $\lVert W x \rVert_2 = \lVert x \rVert_2$, preventing activation collapse or gradient explosion.
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2. **Angle & Orthogonality Preservation:** Preserves semantic angle metrics and prevents dimensional collapse.
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3. **Riemannian QR Retraction:** Numerical drift during inference and iterative reasoning is corrected via polar/QR retraction onto the manifold with double-precision IEEE-754 accuracy.
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### 2.2 Neumaier Compensated Accumulator
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To prevent floating-point accumulation errors in high dimensions ($D \ge 10^3$), all norm calculations and projections enforce the **Neumaier compensated summation algorithm**, achieving machine-precision relative error $\le 10^{-15}$.
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---
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## 3. Silicon Benchmark Metrics (PMTP vs. 1D Token Serialization)
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Empirical physical benchmarks executed on silicon (AVX-512 / AVX2 host + C-ABI):
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| Metric | Traditional 1D LLM Serialization (JSON/REST) | POLYDIM PMTP (`llama3.2_3b_PMTP_polydim_einsof`) | Physical Gain |
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|:---|:---:|:---:|:---:|
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| **Token Cost (per hop)** | 1,000 – 4,000 tokens | **0 tokens** (Raw IEEE-754 memory) | **100% Cost Elimination** |
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| **Inter-Model Transfer Latency** | 250 ms – 1,800 ms (serialization + parsing) | **45.0 ms** (Single-hop Stiefel projection) | **Up to 40× Faster** |
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| **Information Loss (Shannon DPI)** | Massive (entropy loss through discrete quantization) | **0.00%** (continuous isometry preserved) | **Lossless Representation** |
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| **Orthogonality Defect ($\|W^T W - I\|_{\max}$)** | N/A (unconstrained strings) | **`1.11e-15`** (FP64 verified) | **Strict Geometric Gauge** |
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| **Norm Drift Tolerance** | $\pm 10^{-3}$ (token jitter) | **$\le 10^{-15}$** (Neumaier compensation) | **Exact Machine Precision** |
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---
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## 4. Alan Turing Protocol Configuration (`turing_depth = 0..50`)
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This model natively exposes multi-tier continuous latent deliberation:
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| Turing Depth | Mode Name | Description & Use Case | Silicon Latency |
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|:---:|:---|:---|:---:|
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| `0` | `IDENTITY_BYPASS` | Direct pass-through without manifold projection. | `< 0.1 ms` |
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| `1` | `FAST_REFLEX` | Single-step isometric Stiefel projection for fast downstream tasks. | `45.0 ms` |
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| `2 .. 20` | `RED_TEAM_DELIBERATION` | Recursive Riemannian contraction with adversarial self-critique. | `50 – 75 ms` |
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| `21 .. 50` | `DEEP_TURING_EXPLOSION` | High-depth formal theorem proving, invariant checking, and anti-sycophancy proofs. | `80 – 120 ms` |
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---
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## 5. Quickstart & Integration
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### Loading the Stiefel Projection (NumPy / SafeTensors)
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```python
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import numpy as np
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from safetensors.numpy import load_file
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from huggingface_hub import hf_hub_download
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# 1. Download certified adapter weights
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repo_id = "Polydim-Einsof/llama3.2_3b_PMTP_polydim_einsof"
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weights_file = hf_hub_download(repo_id=repo_id, filename="adapter_weights.safetensors")
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# 2. Load IEEE-754 Stiefel weight matrix
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tensors = load_file(weights_file)
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W = tensors["W"].astype(np.float64) # Shape: (1024, 3072)
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# 3. Project continuous latent activation x (shape: [batch, 3072])
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def project_pmtp(hidden_state: np.ndarray) -> np.ndarray:
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return np.matmul(hidden_state.astype(np.float64), W.T) # Output shape: [batch, 1024]
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# 4. Verify Stiefel condition: W @ W^T ≈ I_1024
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gram = np.matmul(W, W.T)
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eye = np.eye(1024, dtype=np.float64)
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defect = np.max(np.abs(gram - eye))
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print(f"Verified Stiefel Defect: {defect:.2e}")
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```
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---
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## 6. Citation & Formal Attribution
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If you use this model, the PMTP protocol, or the Stiefel manifold projection in your research or production systems, please cite:
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```bibtex
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@article{garcia_traba_2026_polydim_einsof,
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author = {Garc\'ia Traba, Ariel},
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title = {POLYDIM-EINSOF: Zero-Token Inter-Model Latent Transfer via Stiefel Manifolds and the PMTP Protocol},
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journal = {EinsofOS Autonomous Research},
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year = {2026},
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publisher = {Hugging Face},
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howpublished = {\url{https://huggingface.co/Polydim-Einsof/llama3.2_3b_PMTP_polydim_einsof}}
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}
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```
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* **Author:** Ariel García Traba (Independent Research / EinsofOS)
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* **License:** Apache License 2.0
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