docs: polish Hugging Face presence with full cross-links, runnable examples, and clinical engine

README.md

@@ -195,9 +195,27 @@ GeoFormer's continuous relaxation dynamics and geometric state-space projection
 👉 **[bhosaleone/TAC: Turing-TAC Coupler](https://github.com/bhosaleone/TAC)**  
 *Continuous Thermodynamic Relaxation & SMT-Verified Dynamical Systems*
 
-- **Formal Logic Foundations:** 5 core mathematical theorems (Lyapunov monotonic free-energy dissipation, dimension-independent $O(1)$ spectral relaxation, and bistable bifurcation potentials) formally verified using the **Microsoft Z3 SMT Theorem Prover**.
-- **Unitary State-Space Evolution:** Simulates unitary 10,000-qubit entanglement entropy without exponential memory explosion ($< 2.22 	imes 10^{-16}$ trace deviation in $1.8	ext{s}$), producing the symmetric Page curve.
-- **Epistemological Treatise:** Includes the foundational essay *[The Cat Is Out of the Box: How TAC Challenges the Cultural Legacy of Schrödinger's Uncertainty](https://github.com/bhosaleone/TAC/blob/main/The_Cat_Is_Out_of_the_Box.md)*.
+- **Formal Stability Guarantees:** 5 core mathematical theorems (Lyapunov monotonic free-energy dissipation, dimension-independent $O(1)$ spectral relaxation, and bistable bifurcation potentials) formally verified using the **Microsoft Z3 SMT Theorem Prover**.
+- **Continuous Graph Laplacian Solvers:** Ultra-fast numerical relaxation algorithms that solve high-dimensional non-linear diffusion equations in sub-millisecond latencies without exponential matrix explosion.
+- **Open-Source Scientific Tooling:** Full Python/NumPy/SciPy implementation with automated test suites verifying mathematical convergence and asymptotic numerical stability.
+
+---
+
+## 🤝 Real-World Problems Solved & Collaboration Roadmap
+
+GeoFormer is engineered for practical, low-energy deployment where conventional cloud-scale Transformers face physical limitations:
+
+* **1. Ultra-Low-Power Edge & Wearable AI:** 1.58-bit ternary synapses eliminate floating-point MAC hardware. Modeled on 1T1R memristor crossbars, energy drops to **443.9 picojoules per inference** ($9,462	imes$ lower than GPU baselines), enabling always-on intelligence on micro-watt power budgets.
+* **2. High-Stakes Clinical Casualty Triage:** Sub-millisecond continuous topological relaxation delivers ranked differential diagnoses in **0.16 ms – 0.40 ms**, complete with explainable causal paths and automated black-box safety contraindication alerts.
+* **3. Enterprise Knowledge Graph Reasoning Without Memory Collapse:** Sparse Hippocampal Relational Working Memory uses sparse CSR conductance indexing to achieve an **$80,000	imes$ memory compression**, scaling multi-hop reasoning over 100,000+ entities in under 10 MB of RAM.
+* **4. Mission-Critical Formal Verification:** All 6 governing algebraic invariants are formally certified `UNSAT` (no counterexamples) in the **Microsoft Z3 SMT Theorem Prover**.
+
+---
+
+### 💬 Open for Friendly Collaboration, Partnerships & Pilot Deployments
+We warmly welcome partnerships with neuromorphic hardware teams (ReRAM/PCM test chip MPWs), edge hardware innovators, clinical research centers, and forward-looking investors interested in scalable, energy-efficient foundation models:
+* **GitHub Discussions:** [bhosaleone/geoformer/issues](https://github.com/bhosaleone/geoformer/issues)
+* **Author Inquiries:** [praman.blog/contact/](https://praman.blog/contact/) │ `ishrikantbhosale@gmail.com`
 
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