Research Scientist – Latent Topology & Cryptographic Mapping in Cambridge

Location: Cambridge, UK (hybrid)

Type: Full-Time

About FactTrace

FactTrace is building the Universal Protocol for Digital and Functional Integrity. We engineer cryptographic infrastructure that mathematically separates an Input Data Structure from its Functional Output State. Moving past fragile character-level hashing and computationally expensive vector databases, we aim to map multi-modal traffic (linguistic, audiovisual, quantitative data) into continuous, high-density small mathematical signatures. Our work on algorithms that are invariant to structural/formatting noise, yet violently and predictably fractures upon encountering a mutation that alters the underlying functional meaning.

The Role: Objective

As a Research Scientist specializing in Latent Topology and Cryptography, your focus will be to transform continuous, probabilistic embedding manifolds into deterministic, cryptographically secure, and self-routing invariant signatures. You will join our Cambridge research hub, treating high-dimensional multi-modal embedding spaces as topological manifolds. Your objective is to manipulate these spaces so that functional invariants are mapped to rigid topological properties, encoded using cryptographic primitives. This ensures our fingerprints remain completely stable against identity-preserving noise (paraphrasing, translation, coordinate rotations, formatting), yet fracturing at $O(1)$ computation when a functional or 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 foundational models.
• Cryptographic Primitive Integration: Design and implement cryptographic mapping layers (e.g., lattice-based cryptography, functional encryption, or vector commitment schemes) directly on top of structured embedding manifolds.
• Deterministic Fingerprint Architecture: Engineer mathematical guarantees that map "functional distance" to deterministic cryptographic bounds, completely eliminating the need for probabilistic nearest-neighbour searches or database brute-forcing.
• Adversarial Robustness Math: Mathematically prove the collision resistance of our fingerprints against adversarial manipulations (across text, code, or data) that attempt to alter functional meaning without triggering a fingerprint fracture.
• IP Fulfillment & Proof Generation: Your responsibility is to formulate, prove, and document the rigorous topological mathematics required to execute these frameworks.

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.
• Specialized Doctoral/Post-Doc Focus: Your thesis or published track record (e.g., Crypto, Eurocrypt, Asiacrypt, ICLR, NeurIPS) must explicitly intersect the differential geometry/topology of high-dimensional spaces with cryptographic security/hashing.
• Geometric Deep Learning: Experience with 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, invariant functional features.

Core Engineering & Technical Skills

We are not looking for a pure theorist; you must be capable of prototyping your math to hand off to our Principal Algorithmic Engineer for hardware-ready production.

• 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 Optimisation: Practical execution of $O(1)$ architecture designs, discrete optimisation, and space-partitioning algorithms.

What We Offer

• Foundational Impact: The opportunity to build the baseline cryptographic IP layer for the global computing and data center fabric.
• Elite Environment: A top team, a distraction-free, highly collaborative, co-located research hub in Cambridge. You will focus purely on the math and the algorithms, fully shielded from operational overhead and client deployments.