| ---
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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: perplexity-ai/pplx-decider-v1.2
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| pipeline_tag: feature-extraction
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| library_name: safetensors
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| model_name: pplx_decider_27b_PMTP_polydim_einsof
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| ---
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|
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| # pplx_decider_27b_PMTP_polydim_einsof
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| ### SOTA Stiefel Manifold Adapter & PMTP Zero-Token Reasoning Engine
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|
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| > **Initiative:** POLYDIM-EINSOF | EinsofOS Sovereign Research
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| > **Author & Lead Researcher:** [Ariel García Traba](https://github.com/AGT1973) (Independent Research / EinsofOS)
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| > **Official Codebase:** [github.com/AGT1973/POLYDIM_EinSof](https://github.com/AGT1973/POLYDIM_EinSof)
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| > **Theoretical Foundation & Papers:** [github.com/AGT1973/POLYDIM-THEORICAL](https://github.com/AGT1973/POLYDIM-THEORICAL)
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| > **Mathematical Manifold:** Compact Stiefel Subspace $\mathrm{St}(2048, 5120) \subset S^{2048-1}$
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| > **Silicon Verification:** Exit Code 0 | Max Orthogonality Defect: `1.89e-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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| ---
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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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| * **Codebase & Kernels:** [https://github.com/AGT1973/POLYDIM_EinSof](https://github.com/AGT1973/POLYDIM_EinSof)
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| * **Formal Theory, Theses & Papers:** [https://github.com/AGT1973/POLYDIM-THEORICAL](https://github.com/AGT1973/POLYDIM-THEORICAL)
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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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| `pplx_decider_27b_PMTP_polydim_einsof` is the certified SOTA adapter for **perplexity-ai/pplx-decider-v1.2**, specialized in **Multi-Model Dialectical Arbitrator & Gatekeeper**, projecting hidden activations from dimension $5120$ into the canonical $2048$-dimensional Riemannian Stiefel manifold.
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|
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| ---
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|
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| ## 2. Theoretical Breakthrough & Mathematical Foundations
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|
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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 $d_{\text{in}} = 5120$ into the canonical latent space $d_{\text{out}} = 2048$ through an isometric projection matrix $W \in \mathbb{R}^{2048 \times 5120}$ 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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| ---
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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 (`pplx_decider_27b_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) | **44.73 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) | **`1.89e-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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| ---
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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. | `44.73 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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| ---
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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/pplx_decider_27b_PMTP_polydim_einsof"
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| weights_file = hf_hub_download(repo_id=repo_id, filename="adapter_weights.safetensors")
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|
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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: (2048, 5120)
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| # 3. Project continuous latent activation x (shape: [batch, 5120])
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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, 2048]
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|
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| # 4. Verify Stiefel condition: W @ W^T ≈ I_2048
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| gram = np.matmul(W, W.T)
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| eye = np.eye(2048, 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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| ---
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|
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| ## 6. Official Resources & Repositories
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|
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| * **Primary Codebase:** [https://github.com/AGT1973/POLYDIM_EinSof](https://github.com/AGT1973/POLYDIM_EinSof)
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| * **Theoretical Framework & Scientific Preprints:** [https://github.com/AGT1973/POLYDIM-THEORICAL](https://github.com/AGT1973/POLYDIM-THEORICAL)
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| * **Hugging Face Organization:** [https://huggingface.co/Polydim-Einsof](https://huggingface.co/Polydim-Einsof)
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|
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| ---
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|
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| ## 7. 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/pplx_decider_27b_PMTP_polydim_einsof}},
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| note = {Code: \url{https://github.com/AGT1973/POLYDIM_EinSof} | Theory: \url{https://github.com/AGT1973/POLYDIM-THEORICAL}}
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| }
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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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|
|
