MAX ID as a mathematical identity

The MAX ID is defined as a universal mathematical identity based on a set of prime numbers generated deterministically through the MAX Prime Theory and aggregated into a Merkle Tree-like structure. Unlike traditional random keys, the primes used are not independent: they are selected so that they share specific modular properties.

Under ordinary conditions, a set of randomly chosen primes shows, with respect to a fixed modulus P, an approximately uniform distribution of residues. In the case of the MAX ID, however, modular filters are applied to the generating function: all primes in the same family produce the same residue r = p % P.

The primes are grouped into two families, labelled N and d, each characterized by a constant modular signature. The combination of these families defines a personal modular signature, which acts as a unique arithmetic fingerprint associated with the MAX ID.

This construction differs substantially from current public-key schemes: RSA relies on two randomly selected primes, ECC on points over elliptic curves, hash-based schemes like SPHINCS⁺ on hash trees, and lattice-based systems on Gaussian vectors. With MAX ID, the identity is not a single element, but hundreds of correlated primes bound by modular constraints and organized in a tree.

From a theoretical perspective, the MAX ID can be interpreted as a prime congruence class organized inside a Merkle Tree of primes with controlled modular signatures. This introduces a new paradigm for defining mathematical identities, based on internal arithmetic relations within the prime sequence rather than on purely random bits.

These modular properties are not hypothetical: they have been formally proven and experimentally verified. All mathematical and computational proofs are published and can be independently replicated.

The papers and public demos below describe in detail the MAX Prime Theory, the sequences of primes generated with and without modular filters, and their use in constructing the MAX ID inside the MAX App. The code repositories on GitHub (when available) allow independent analysis and verification.

• Zenodo • Paper 1
• Zenodo • Paper 2
• Hugging Face • Sequence-A (no filters)
• Hugging Face • Sequence-A (mod 3)
• Hugging Face • Sequence-A (mod 7)
• Hugging Face • Sequence-A (mod 3+7)
• Hugging Face • Sequence-A (3+37, esc=5)
• Hugging Face • MAX-Test

Contact: max@max-russo.com • LinkedIn

To view the prime numbers with the same modular signature associated with your own mathematical identity, you can log in to the reserved area using the MAX App by clicking “Login with MAX” and navigating to the Modular Signatures section.