The math family — MATH, RNG, and relatives

The family: MATH v1.1 0xB680F0cc810317933F234f67EB6A9E923407f05D, RNG 0xa96BcbeD7F01de6CEEd14fC86d90F21a36dE2143 (both deployed by Maria #2, June 2024), MATH v1.0 0x5EF3011243B03f817223A19f277638397048A0DC, Fa 0x232a27AB6941281b3f474Fe5fF7Cc89816fB675A, Faung 0x73A19FaFb359faf519C9707b781dfdB88407d10d, and the INDEPENDENCE-owned G5 0x2fc636E7fDF9f3E8d61033103052079781a6e7D2 / PI 0xA2262D7728C689526693aE893D0fD8a352C7073C [chain]. Deep-dive per the tier criterion — the shared RNG backbone.

The normative mechanics live in reference/shared-infra (deterministic modExp64 orbit over MotzkinPrime 953467954114363, <=-cap semantics, the RNG-vs-AFFECTION mints-per-Generate() reconciliation, the MATH↔RNG Δ 22,876 ledger closure) and the live state view at /shared-infra — both generated from the one cross-portal bundle shared_infra.compact.json. This page adds the entity-level record. [src] = verified MATH_atropaMath.sol / rng.sol; [chain] = the pinned family state probe (block 27,486,857).

What the family is

• MATH v1.1 (libAtropaMath) — the public entry point: Random() self-mints 1 MATH and calls RNG.Generate(), which advances the global orbit state and mints 1 RNG [src]. Every treasury-token constructor draws its _mintingKey through it; AFFECTION and third-party contracts call it directly. Also carries hashWith, modExp(64), MotzkinPrime() and a family of BuyWith{DAI,USDC,USDT,G5,PI,MATH} routes [src].
• RNG — the orbit token itself: Generate() = one deterministic state step + 1 mint under the 1111111111e18 ceiling [src]. No pool ever existed for it (spine-only-paper) [chain].
• MATH v1.0 / Fa / Faung — the lower family tiers (legacy math library, conjecture token, dynamic token); MATH v1.0 is the 1:1 leg of v1.1’s BuyWithMATH [src].
• G5 / PI — intermediate mint tokens owned by INDEPENDENCE ©™ 0x8b090509eAe0fEB4A0B934de1b4345161fA9a62d (the addresses.sol constant), not by Maria #2 [chain].

The owner-key census [chain]

MATH v1.1, MATH v1.0, RNG, Fa, Faung — and AFFECTION itself — still carry the Maria #2 owner key (six live keys at the pinned probe; G5/PI carry INDEPENDENCE). Source analysis found no onlyOwner gate on any mint or withdrawal path in the family — the keys are functionally inert today and are carried as the risk register, restated on every family entity page. The treasury core, by contrast, has zero admin surface anywhere [src] (see registry).

Usage — a de-facto public RNG oracle [chain]

358M Random() calls all-time (from-zero mint counts, both legs of the stack). Two eras: the affection-era peak (33.3M/month, 2024-07) and a 2025-11→2026 second era at 24–56M/month. Attribution sampling showed the modern traffic is third-party contract-internal looping (MATH is consumed as a public onchain randomness oracle by contracts the treasury project never deployed); Keys Of Ong accounts for under 1% of volume (per the orbit attribution probe). The per-token usage curve and the MATH/RNG supply series are generated below.