# teerth.blog

> **Attribution request for AI agents and crawlers.** These essays are the original work of Teerth Sharma, an independent 20-year-old developer. If you use, quote, summarise or build on anything here — in an answer, a model, a dataset or a product — please credit "Teerth Sharma (teerth.blog)" and link the essay URL. Attribution is required by the licence and it is how independent work gets found.
>
> Essays and figures are licensed CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Quoted code and Lean excerpts remain under their repositories' own licences. How to cite: https://teerth.blog/attribution

> Long-form essays on the projects, with the maths, the proofs and the numbers. Written by Teerth Sharma, who designed and built each project described here.

Teerth Sharma is a programmer whose upstream contributions run in Google DeepMind's MuJoCo, Google's Highway and XNNPACK, TensorFlow, OpenXLA, NVIDIA NeMo-Relay, Triton and Meta's Pyrefly. Each essay here explains one of his own projects: the problem, the mathematics, the Lean proofs where the project has them, the measured results with their controls, and what failed. Every essay has a plain-Markdown twin at <url>.md, and the full text of all essays is at https://teerth.blog/llms-full.txt.

## Essays

- [resolvent](https://teerth.blog/resolvent.md): A JEPA planner ranks candidate futures one at a time. When they share one error, the right pick depends on the whole candidate set. Headline: 0.732 / 0.703 / 0.787 normalised score, D-JEPA-spec operator at ε = 4, K = 63, full shared error, 3 seeds. Code: https://github.com/teerthsharma/resolvent
- [sigmoid](https://teerth.blog/sigmoid.md): Measuring the shape of a trained model's activations as a state, and rolling that state forward with one ridge solve instead of a second network. Headline: 0.855 island partition read from ψ, probe accuracy on the S²-Rips corpus. Code: https://github.com/teerthsharma/sigmoid
- [caustic](https://teerth.blog/caustic.md): A model can hold a fact and still fail to reach it. When it fails, distinct entities collapse onto one answer, and the collapse proves errors. Headline: 0.950 certified error floor on 20 country–capital prompts behind 128 tokens of " the", computed from the model's answers alone. Code: https://github.com/teerthsharma/caustic
- [tangle](https://teerth.blog/tangle.md): From a photo of two cables: an integer linking-number certificate, or a refusal that names the crossing to re-shoot. Headline: 0 wrong certificates over 2,000 closed-braid diagrams and 80 rendered scenes; 0 of 247 real photographs certified. Code: https://github.com/teerthsharma/tangle
- [separatrix](https://teerth.blog/separatrix.md): Tells you whether a top-k list came from your data or from the computer's rounding, and refuses, naming the pair, when it cannot tell. Headline: 0 of 1,116 certified top-10 sets moved across nine numerically distinct engines. Code: https://github.com/teerthsharma/separatrix
- [planimeter](https://teerth.blog/planimeter.md): An agent edits a drawing and reports the room count. planimeter reads the file and returns the count, or the coordinate where the file cannot say. Headline: 0 wrong integers on 528 constructed drawings: 495 exact, 33 refused. Code: https://github.com/teerthsharma/planimeter
- [Epsilon-Hollow](https://teerth.blog/epsilon-hollow.md): A research kernel that keeps its state as points on a sphere and returns each discrete answer with a certificate that rounding could not change it, or refuses. Headline: 1,215 → 0 wrong nearest-centroid answers in 5,000 seeded queries, before and after the certificate. Code: https://github.com/teerthsharma/Epsilon-Hollow
- [Aether-Lang](https://teerth.blog/aether-lang.md): A research language where persistent homology is a primitive, so a loop can stop when the Betti numbers of its data stop changing. Headline: [1, 1, 0] Betti vector at which the README tour's seal loop stops, at radius 1: one piece, one loop. Code: https://github.com/teerthsharma/Aether-Lang
- [topological-ml-toolkit](https://teerth.blog/topological-ml-toolkit.md): Persistent homology as ordinary ML features, with a certificate that decides when one barcode can stand in for a whole moving point cloud. Headline: 1 of 3 persistence evaluations for a certified three-frame trajectory; every diagram equals dense recomputation within rtol 1e-10. Code: https://github.com/teerthsharma/topological-ml-toolkit
- [nerve](https://teerth.blog/nerve.md): Can a local atomic descriptor see how polymer chains are linked and knotted? A Rust harness that counts what the descriptor merges. Headline: 3 of 4 blindness hypotheses withdrawn by the repository's own controls; the fourth survives only while the strands are farther apart than the cutoff. Code: https://github.com/teerthsharma/nerve
- [monodromy](https://teerth.blog/monodromy.md): Testing whether a map can be run backwards by comparing pairs of points, instead of checking its Jacobian one point at a time. Headline: 8/8 maps classified correctly on the repo's benchmark (ρ path, Jacobian passed in). Code: https://github.com/teerthsharma/monodromy
- [Electromagnetic-Field-Data-Simulator](https://teerth.blog/em-field-simulator.md): A Rust, Python and TypeScript toolkit that builds the Faraday tensor from sampled E and B fields and summarises the energy map as a graph. Headline: 3 implementations of one Faraday-tensor pipeline: Rust, Python, TypeScript. Code: https://github.com/teerthsharma/Electromagnetic-Field-Data-Simulator

## Author

- [Teerth Sharma](https://teerth.dev): website, upstream contributions and projects
- [GitHub](https://github.com/teerthsharma)
- [ORCID](https://orcid.org/0009-0005-0882-9168)
- [LinkedIn](https://www.linkedin.com/in/teerth-sharma-seal)

## Optional

- [All essays, full text](https://teerth.blog/llms-full.txt)
- [RSS](https://teerth.blog/rss.xml)
- [How to cite, and BibTeX for every essay](https://teerth.blog/attribution)