Research Scientist – Latent Topology & Cryptographic Mapping

Research Scientist – Latent Topology & Cryptographic Mapping Location: Cambridge, UK Type: Full-Time About FactTrace FactTrace builds the foundational infrastructure for Semantic Signal Processing. Moving past traditional, fragile character-level hashing and computationally expensive vector database brute-forcing, we map multi-modal meaning into a continuous, high-density mathematical signature. Our core engine yields a fingerprint perfectly invariant to semantic noise (paraphrasing, translation, compression, formatting changes) yet hyper-sensitive to micro-mutations (corrupted data, altered facts, AI hallucinations). The Role: Objective As a Research Scientist specializing in Latent Topology and Cryptography, your sole focus will be to transform continuous, probabilistic embedding manifolds into deterministic, cryptographically secure, and self-routing semantic signatures. You will join the research track that treats high-dimensional embedding spaces as topological manifolds. Your job is to manipulate these spaces so that semantic invariants (meaning) are mapped to rigid topological properties, which are then encoded using cryptographic primitives. This ensures that our fingerprints are completely robust to (paraphrasing, translation, compression, formatting changes) , yet violently and predictably fracture at $O(1)$ computation when a malicious domain specific mutation occurs. Key Responsibilities Topological Manifold Manipulation: Apply differential geometry, algebraic topology, or geometric deep learning to analyze and restructure the latent spaces of multi-modal embedding models. Cryptographic Primitive Integration: Design and implement cryptographic mapping layers (e.g., drawing from lattice-based cryptography, functional encryption, or vector commitment schemes) directly on top of structured embedding manifolds. Deterministic Fingerprint Architecture: Engineer mathematical guarantees that map "semantic distance" to deterministic cryptographic bounds, eliminating the need for probabilistic nearest-neighbor searches or database brute-forcing. Adversarial Robustness Math: Mathematically prove the collision resistance of our fingerprints against adversarial text/data manipulations that attempt to alter meaning without triggering a fingerprint change. IP and Patent Leadership: Formulate, prove, and document these mathematical breakthroughs to drive the filing of our foundational patent on Topological Semantic Cryptography. Targeted Academic & Research Background We are looking for a highly specialized PhD whose research natively straddles the line between modern machine learning geometry and rigorous information security. Ph.D. in Pure/Applied Mathematics, Theoretical Computer Science, or Mathematical Cryptography with a heavy focus on geometric deep learning or topological data analysis. Specialized Doctoral/Post-Doc Focus: Your thesis or published track record (e.g., Crypto, Eurocrypt, Asiacrypt, ICLR, NeurIPS) must explicitly intersect differential geometry/topology of high-dimensional spaces with cryptographic security/hashing. Key Research Moats of Interest: Geometric Deep Learning: Manifold learning, optimization on Riemannian manifolds, or graph/topological neural networks. Mathematical Cryptography: Lattice-based cryptography (LWE), functional encryption, or locality-sensitive hashing (LSH) frameworks optimized for provable security bounds. Algebraic/Computational Topology: Persistent homology or sheaves applied to representation spaces to extract stable semantic features. Core Engineering & Technical Skills We are not looking for a pure theorist; you must be capable of translating complex topological formulas into production-grade, hyper-optimized code. Advanced Mathematical Programming: Absolute fluency in Python. Native comfort with scientific computing libraries. Manifold Manipulation in Code: Practical experience writing custom loss functions, geodesic distance matrices, and custom layers that constrain or distort latent embedding spaces. Cryptographic Implementation: Hands-on experience prototyping cryptographic algorithms, custom hash families, or low-level mathematical operations with strict security and precision guarantees. Algorithmic Complexity Optimization: Practical execution of $O(1)$ architecture designs, discrete optimization, and space-partitioning algorithms. What We Offer Foundational Impact: The opportunity to build a high-stakes, IP layer for the global computing and AI traffic fabric. Elite Environment: A distraction-free, highly collaborative, co-located research hub in Cambridge alongside top-tier quantitative minds.