# Ivan Besevic — mathematics and Pandrosion

> Independent research in constructive geometry, numerical analysis and formal verification.

Canonical website: https://ivanbesevic.com/
Author: Ivan Besevic (ORCID: https://orcid.org/0009-0004-4124-1465).

The geometric preprint and the generic Pandrosion 449 solver are distinct works. Lean proofs cover stated mathematical models, not the Python implementation end to end. Numerical benchmarks do not establish universal convergence or superiority.

Public resources below require no login, cookies or JavaScript. Cite the work's version and DOI. Each resource retains its own license.

## Research pages

- [Geometric ideas. Verifiable results.](https://ivanbesevic.com/index.md): Ivan Besevic’s research in constructive geometry, real roots, Lean proofs and Pandrosion 449. Papers, Python code, documented results and interactive animations. HTML: https://ivanbesevic.com/
- [Geometric Root Calculators](https://ivanbesevic.com/publications/geometric-root-calculators/index.md): Positive-root constructions: a fifth-order arc, a nested-radical support of order nine in the cubic case, and real-degree enclosures. HTML: https://ivanbesevic.com/publications/geometric-root-calculators/
- [Pandrosion, the solver.](https://ivanbesevic.com/pandrosion/index.md): A standalone numerical engine for finding roots and least-squares stationary points. Free release: 449. HTML: https://ivanbesevic.com/pandrosion/
- [Results, with their scope.](https://ivanbesevic.com/validation/index.md): Comparison protocols, numerical tests and the precise scope of the formal proofs. HTML: https://ivanbesevic.com/validation/
- [About.](https://ivanbesevic.com/about/index.md): Ivan Besevic: independent research in constructive geometry, numerical analysis and formal verification. Publications, Pandrosion, ORCID and open resources. HTML: https://ivanbesevic.com/about/
- [Privacy and resources.](https://ivanbesevic.com/privacy/index.md): How ivanbesevic.com works, technical logs and consent-based Google analytics. Contact details and cookie choices. HTML: https://ivanbesevic.com/privacy/
- [Mathematics in motion.](https://ivanbesevic.com/animations/index.md): Interactive animations: a geometric cube-root construction, actual Pandrosion 449 runs and stereographic projection onto a sphere. HTML: https://ivanbesevic.com/animations/
- [Pandrosion 455](https://ivanbesevic.com/pandrosion-455/index.md): Optimized standalone solver and complete validation bundle. $49 USD, one payment, MIT license. Direct access for people and AI agents. HTML: https://ivanbesevic.com/pandrosion-455/
- [Pandrosion 601 — robotics solver](https://ivanbesevic.com/pandrosion-601/index.md): Standalone Python solver for robotics with or without AI. Inverse kinematics, Jacobians and target tracking. Complete MIT bundle: $49 USD, one payment. HTML: https://ivanbesevic.com/pandrosion-601/
- [Pandrosion 601 — benchmark protocol and results](https://ivanbesevic.com/pandrosion-601-benchmarks/index.md): Reproducible Pandrosion 601 versus 600 benchmarks: local solving, target tracking, bounded cases and shared callbacks. Methods, results and limitations. HTML: https://ivanbesevic.com/pandrosion-601-benchmarks/
- [Publications](https://ivanbesevic.com/publications/index.md): Research preprints, abstracts and downloadable papers. HTML: https://ivanbesevic.com/publications/

## Direct downloads

- [Geometric Root Calculators: A ninth-order cubic construction and real-degree root solvers](https://ivanbesevic.com/downloads/geometric-root-calculators-27-nr.pdf): version 27-NR; application/pdf; 283449 bytes; DOI: https://doi.org/10.5281/zenodo.23449823; SHA-256: 43fd3919a7983f6cd13f8be9ad4e5e100cbe4cfa42dd9b81e99b17553ccb7ffe.
- [Pandrosion 449 standalone Python solver](https://ivanbesevic.com/downloads/pandrosion_449_standalone.py): version 449; text/plain; 82968 bytes; DOI: https://doi.org/10.5281/zenodo.23839661; SHA-256: 9a358497e3bdafadf4e119511d3d031a6984ee012cd402aa9caad7c0bb6b2b74.
- [Pandrosion 449 validation report](https://ivanbesevic.com/downloads/validation-449.txt): version 449; text/plain; 6158 bytes; DOI: https://doi.org/10.5281/zenodo.23839661; SHA-256: 3961460f019dca6ae9d5c809c7ff72c492ac007f3471b7b2fbe84af4ab76f8b2.
- [Pandrosion 449 mathematical models and proofs](https://ivanbesevic.com/downloads/Pandrosion449.lean): version 449; text/plain; 46638 bytes; DOI: https://doi.org/10.5281/zenodo.23839661; SHA-256: b1079c684082489804ed61f619c02be1d1a392e70068e26030cc0a3301f79fd9.

## Paid software access

- [Pandrosion 455](https://ivanbesevic.com/pandrosion-455/): complete standalone and validation bundle; 49.00 USD, one payment; MIT license. Payment accepts currently verified liquid assets on Solana and the supported EVM mainnets. The API lists the exact supported network IDs. The crypto amount is quoted for five minutes; network fees are additional.
- [Agent purchase guide](https://ivanbesevic.com/api/payments/agent-guide.md): create an order, retain its secret access token, pay the exact instructions with an authorized wallet, submit the transaction and download after finality. Direct invoice API, plus x402 v2 exact USDC on Base.
- [Purchase API](https://ivanbesevic.com/api/payments/openapi.json): typed OpenAPI 3.1 specification. [x402 availability](https://ivanbesevic.com/api/payments/v1/x402). [Reference Python client](https://ivanbesevic.com/api/payments/agent-client.py). [Product and file hashes](https://ivanbesevic.com/api/payments/v1/products/pandrosion-455).

- [Pandrosion 601 — robotics with or without AI](https://ivanbesevic.com/pandrosion-601/): 49.00 USD, one payment, MIT. Set product_id=pandrosion-601 when ordering. Inverse kinematics, Jacobians, joint bounds and target tracking. Synthetic validation only; no hard real-time guarantee. [601 manifest and hashes](https://ivanbesevic.com/api/payments/v1/products/pandrosion-601).

## Machine-readable access

- [Public research catalog](https://ivanbesevic.com/research.json): JSON with stable download URLs, versions, exact byte counts and SHA-256 hashes.
- [All public page text](https://ivanbesevic.com/llms-full.txt): consolidated Markdown of the public website, not the full manuscript.
- [Sitemap](https://ivanbesevic.com/wp-sitemap.xml): canonical HTML pages.

- [Stripe card checkout](https://ivanbesevic.com/api/payments/v1/stripe): check current availability, create a private order, save its receipt, prepare the Stripe-hosted checkout and use an authorized payer. Card details and required issuer authentication stay at Stripe. Poll the order until paid, then download with its private Bearer token.