I'm a litigation & digital economy attorney in Ukraine who also writes cryptographic tooling on Linux. In courtroom and cross-border legal workflows, I kept running into a structural gap: visual PDF watermarks/stamps are purely decorative (trivially stripped or forged), while cryptographic signatures (PAdES / CAdES) live in detached or invisible ASN.1 streams that don't bind to the visible vector geometry on the page.
I built Marma-Crypto (v1.2.1, Apache 2.0) to experiment with binding a cryptographic signature directly into the coordinates of a visible vector figure—specifically the canonical 9-triangle Sri Yantra (Nava-Cakra).
How it works mathematically:
1. Nonlinear Planimetry (Kulaichev 1984 / Huet 2002): The 9 interlocking triangles of the Sri Yantra form an overdetermined nonlinear system generating 43 sub-triangles and 54 triple concurrency points ("marmas") governed by det[A_i, B_i, C_i] = 0. Solving it in IEEE-754 float64 yields a baseline residual of ~6.13e-11 rad.
2. Binary Field Elliptic Curve Binding: We hash the normalized document text (GOST 34.311-95, DSTU 7564:2014 Kupyna-256, and SHA-256) and compute a deterministic (RFC 6979) elliptic curve signature (r, s) under the Ukrainian national standard DSTU 4145-2002 over the polynomial-basis binary Galois field GF(2^257) = F_2[t]/(t^257 + t^12 + 1), alongside a PAdES-B-LTA / RFC 3161 TSP timestamp.
3. 24-Bit Quantized Sub-Micron Perturbation: We take SHA-256(r || "::" || s), slice the first 216 bits into nine 24-bit integers u_k in [0, 16777215], and apply a deterministic micro-perturbation |delta_k| <= 10^-5 to each of the 9 triangles while preserving exact bilateral symmetry (lx_k + rx_k = 2*cx, so Delta_sym = 0).
To try it in the browser verifier linked above: Click the red button "Simulate Attack (0.001)" on the left panel. It shifts a single vertex of triangle U2 by 0.001 units and shows how the concurrency matrix immediately flags the exact tampered layer.
Links for those who want to dig into the code or paper: - Source code (Python + zero-dependency JS verifier): https://github.com/YaroslavBaienko/marma-crypto-protocol - Whitepaper (EN & UA PDFs, self-sealed with PAdES-B-LTA) on CERN Zenodo: https://doi.org/10.5281/zenodo.23436152 - Debian/Ubuntu APT repo (`sudo apt install qes-tools marma-crypto-watermark`): https://yaroslavbaienko.github.io/legaltech/
Happy to answer any questions about the Sri Yantra concurrency math, GF(2^257) arithmetic, or Ukrainian QES/eIDAS infrastructure on Linux!