Quantitative Code Analysis & Mathematical Experiments
Measuring what standard static analysis and heuristic linters miss. Formal algorithmic bounds, compiler optimization mechanics, memory safety invariants, and reproducible benchmark evaluations.
Core Research Hubs
⚡ Quantitative Code Analysis
Empirical evaluation of compiler optimizations, binary guard stripping, sanitizer survivability, and real assembly instruction traces across Clang and GCC.
🔬 Mathematical Experiments
Hypothesis formulation and statistical validation for branch density saturation, differential fuzzing entropy, and invariant preservation proofs.
📊 Computation & Complexity
Benchmarking memory allocation overhead, cache miss latency distributions, and state space divergence across x86_64, AArch64, and RISC-V.
The Riemann Hypothesis as Dimensional Rigidity: Scale-Space Topology, Information Saturation, and Machine-Verified Stability
A structured candidate framework establishing $\operatorname{Re}(s) = 1/2$ as a unique dimensional saturation invariant in scale-space topology. Features Microsoft Z3 formal SMT proofs, numerical verification across 500,000 configurations, Weil positivity across 4,097 bins, and an explicit epistemic gap register.
Additional Research Investigations
Scope Theory: A Geometric Baseline for Information Scaling
The axiomatic mathematical foundation unifying the Reality Manifold $\Omega = (X, T, R, \mu, g)$, the agent 5-tuple (t)$, non-commuting agency interference, Fokker-Planck stochastic SDEs, and Shapley-value Gap Theory with the Youth Opportunity Index (t)$. Serves as the parent theory for our Riemann dimensional rigidity and fundamental shape monographs.
Geometry in Motion: Time, Energy & Living Systems
Deriving trajectories, Euler-Lagrange variational mechanics, Poiseuille flow, Murray’s law r₀³ = r₁³ + r₂³, Turing morphogenesis, and Kleiber’s 3/4 fractal allometry with Z3 SMT proofs.
Fundamental Shapes of Reality & Origin of Φ = 120
Derivation of the 21 stable shapes across dimensions under four ISL closure layers. Explaining the sequence 1, 1, ∞, 5, 6, 3, 3…, the 24-cell anomaly, and α⁻¹ ≈ 137.036.
Fractal Approximations & Dimension Discontinuity
Constructive proof that fractal sequences with constant Hausdorff dimension ≈ 1.2619 converge to smooth circles with dim = 1.0 at rate O(1/n²), proving Hausdorff dimension is not continuous.
Unified Constraint Framework for Plane Curves
The Shape Specification Triplet (SST) unifies conics, Lamé superellipses, Cassini ovals, and lemniscates via 3 drawing oracles, closed-form Gamma area proofs, and Z3 SMT verification.
Code as Geometry: 21 Universal Shapes Projecting to 9 Languages
The GeoCode universal intermediate representation: eliminating syntactic syntax tax with 21 universal shapes and a 3-layer Graph IR projecting cleanly into Python, Rust, and C++.
Formal Invariant Verification: Rust vs C++ Memory Bounds
Evaluating affine type systems against RAII smart pointers via mathematical state invariants, compiler proofs, and Hoare logic preconditions.
The Infinity & Fundamental Constants Trilogy
Resolving mathematical divergences and cosmological catastrophes via dimensional upgrades, scale horizons, and the seven irrational constants.
Infinity as Dimensional Insufficiency
When geometry breaks, upgrade the dimension. Proof of hypersphere volume collapse to zero, QFT dimensional regularization poles, and holographic boundary reduction with Z3 proofs.
Infinity Is a Scale Problem
The Coastline Paradox, Wilsonian Renormalization Group flows, and resolving the 10¹²⁰ vacuum energy discrepancy through the holographic Planck-to-Hubble horizon ratio.
Meditation of the Seven Constants
A journey through π, e, φ, √2, i, 0, and ∞. Hurwitz’s Theorem proving why φ is the most irrational number, the Hippasus proof, and the Weyl ergodic desynchronization engine.
Editorial Rigor & Verification Philosophy
PotatoBullet is curated by Shrikant Bhosale, an independent systems researcher. We believe computer science should be treated as an empirical discipline—grounded in measurable machine execution cycles, memory pages, AST invariant proofs, and concrete counterexamples.
All research is published freely with open methodology. We welcome peer reviews, benchmark reproduction inquiries, and technical corrections.
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