Physics · Compilers · AI · Topology
teerths57@gmail.com · @teerthsharma · Bangalore, India

Computed from Git history across all repositories. Updated May 14, 2026.

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I build mathematical machines at the intersection of topological physics, compiler theory, and distributed AI systems. My research treats the universe as a topological object: the Big Bang is a phase transition ∅→H₀→H₁→H₂→GOD_FIXED, electromagnetism is a Banach fixed-point on barcodes, and intelligence emerges from persistent homology in high-dimensional weight spaces.

Research focus: Learning physics directly from topological invariants rather than numerical fields. The God Tensor project (faraday) demonstrates a learned operator on E/H field barcodes converges to a true mathematical fixed point at 1.755×10⁻¹⁶ machine epsilon — verified by 50,001 immutable, SHA-256 hash-chained ledger lines.

Systems focus: Rust kernels, sub-20ns I/O prefetch, stochastic resonance for LLM training, and Aether-Lang — a universal topology programming language with 23 theorems and a Lean 4 verified kernel.

Universal Topology Engine · 9 commits

Models cosmological emergence as a sequence of topological phase transitions driven by persistent homology. Betti numbers (b₀, b₁, b₂) serve as fundamental cosmological state variables — counts of connected components, loops, and voids in the Vietoris–Rips filtration of a quantum point cloud.

Phase sequence: ∅ (VACUUM) → H₀ → H₀+H₁ → H₀+H₁+H₂ → GOD_FIXED
Fixed point:    T(x*) = x*    (T = God Tensor, x* = cosmological attractor)
Convergence:    ‖x_{n+1} − x_n‖ < 10⁻¹⁵ at machine epsilon

The GOD_FIXED state is the Banach fixed-point of the God Tensor — where electric and magnetic field coupling reaches equilibrium. Phase transitions are triggered by POVM quantum measurements on the Hilbert space vector.

Key files: src/omni_topos/__init__.py · src/phase_manager.py · src/god_tensor.py

God Tensor (50k burn) + N-Body Extension · 46 combined commits

Learns a reduced-order topological operator on FDFD-derived electromagnetic fingerprints. The pipeline:

Cavity Geometry → FDFD solver → |E| point cloud → Ripser PH
→ Betti-0/1 barcodes → Hilbert series embedding (50D → 16D)
→ Learn T: E-embedding → H-embedding via lstsq
→ Banach iteration → God Tensor x*
→ T(x*) = x* at machine epsilon (verified May 5, 2026)

50,001 epochs, each logged to immutable SHA-256 hash-chained ledger:
  Banach Loss: 1.755e-16  ← ‖T(x_n) − x_n‖ at IEEE 754 machine epsilon
  Betti-1 plateau: 0.00328  ← irreducible topological mismatch (open problem)

Extends the God Tensor to N coupled electromagnetic bodies via tensor product Hilbert space:

𝓗_total = 𝓗_1 ⊗ 𝓗_2 ⊗ ... ⊗ 𝓗_N    (dimension d^N)

The coupling Hamiltonian H ∈ ℝ^(d×d) is learned via outer-product averaging on paired observations. SU(2)/SU(3) gauge theory provides algebraic structure for non-Abelian field coupling. Banach fixed-point iteration in a reduced subspace bypasses the d^N combinatorial explosion.

Key files: faraday/src/faraday/god_tensor.py · hamliton/src/hamilton/

TDA Memory, Visualization, and LLM Integration · 20 combined commits

Persistent homology via ripser + FAISS-backed similarity index. Transforms point clouds into fixed-length Hilbert coefficient vectors. Applications include shape matching, molecular fingerprinting, and LLM context encoding via topological signatures rather than raw token embeddings.

Renders Vietoris–Rips filtration as animated 3D topological landscapes. Supports Betti bar charts, persistence landscape surfaces, VR complex mesh collapse, and barcode-to-GIF export. Computation: ~0.8s for 10k point clouds.

Projects semantic state onto the unit 2-sphere S² via a seeded random linear map. Produces barcode signatures enabling O(P) geometric state transfer (P ≤ 64 payload point budget).

Key files: lambda-topo/lambda_shappire/ · topoflow/src/ · phi-mem/src/

Pure assembly, bare-metal kernels, AVX-512 SIMD · 4 new repos

AVX-512 SIMD implementation of persistent homology on Vietoris–Rips filtrations. Distance matrix construction, simplex enumeration, boundary matrix reduction — all in hand-written x86_64 assembly with cache-blocked 64×64 tiles. Achieves 11.8× speedup over ripser (Python/C++), 3× speedup over GUDHI C++. Numerical correctness verified against reference implementation with < 10⁻¹² bottleneck distance error.

Benchmark (N=10,000 points, d=3, H₁ homology):
  ripser (Python/C++):  48.2s
  GUDHI C++:            14.1s
  topo-asm AVX-512:      4.1s   ← 11.8× faster
  topo-asm 4-thread:     1.1s   ← 43.8× faster

A #![no_std] Rust microkernel exploring persistence landscape distance as the primary scheduling criterion (replacing CFS runqueue priority). I/O fast path runs in pure AVX-512 assembly with sub-3ns decision latency. Includes full x86_64 long-mode boot: GDT, IDT, page tables, interrupt handling. Boot to kernel: ~12ms.

1,247 lines of NASM assembly implementing the complete x86_64 paging subsystem: 4-level page table setup, recursive self-mapping, huge pages (1 GiB + 2 MiB), KPTI trampoline, PCID context switching. Every TLB invalidation is explicit. Serves as a reference implementation and building block for kernels needing fine-grained memory isolation control.

Hand-optimized SIMD kernels for dot product (11.8× over scalar), matrix multiply (35× over naive C), Mandelbrot (687× over Python), and FFT. Demonstrates that compiler auto-vectorization leaves 20–40% performance on the table on memory-bandwidth-bound workloads.

Key files: topo-asm/asm/ · hollow-asm/asm/ · pgtable-asm/asm/ · vec-simd/asm/

Rust toolchain, POVM stochastic resonance, sub-20ns I/O · 27 combined commits

Adaptive noise injection using the POVM (Positive Operator-Valued Measure) formalism. Three POVM operators probe the Bloch sphere representation of training loss dynamics, continuously adapting the measurement basis without trained parameters:

E₁ = cos(θ + φ)   → spatial (LBA velocity / loss gradient alignment)
E₂ = sin(θ/2 − φ) → temporal phase (drives basis rotation)
E₃ = cos(θ · φ)   → spectral (drives fetch sigmoid)

The adaptive gain algorithm grows noise when optimization stagnates, decays it when progress resumes — helping LLMs escape sharp local minima during training.

Rust #![no_std] kernel using quantum-inspired adaptive measurement for storage prefetching. Decision latency ~18.1ns per I/O cycle on x86_64/AArch64/RISC-V. Zero heap allocations, zero network calls.

Telemetry extraction:  ~1.4 ns (O(1), zero-copy DSP)
Decision loop:         ~18.1 ns full cycle
Throughput:           ~55 M ops/sec single-threaded

A universal topology programming language. Rust language runtime for topological ML — manifold embeddings, persistent homology, Lean 4 verified kernel. Zero-sorry proofs. 23 theorems.

• Email: teerths57@gmail.com
• GitHub: @teerthsharma
• Website: teerthsharma.vercel.app

Built with Banach fixed-point convergence and persistent homology. All Git history is publicly verifiable.