{"_meta": {"description": "Shared RNG/math infrastructure \u2014 single source of truth for both portals (KB v2 plan section 6)", "provenance": "[chain] state probe at pinned block; [src] verified sources rng.sol / MATH_atropaMath.sol / affection docs sources", "state_block": 27486857, "usage_note": "1 from-zero self-mint per call under cap; buckets = 200k-block windows"}, "family": {"0xB680F0cc810317933F234f67EB6A9E923407f05D": {"label": "MATH v1.1", "address": "0xB680F0cc810317933F234f67EB6A9E923407f05D", "owner": "0x7a20189b297343cf26d8548764b04891f37f3414", "owner_is_maria2": true, "owner_is_zero": false, "totalSupply": 362812654999999999999999999, "totalSupply_units": 362812655.0}, "0x5EF3011243B03f817223A19f277638397048A0DC": {"label": "MATH v1.0", "address": "0x5EF3011243B03f817223A19f277638397048A0DC", "owner": "0x7a20189b297343cf26d8548764b04891f37f3414", "owner_is_maria2": true, "owner_is_zero": false, "totalSupply": 16512000000000000000000, "totalSupply_units": 16512.0}, "0xa96BcbeD7F01de6CEEd14fC86d90F21a36dE2143": {"label": "RNG", "address": "0xa96BcbeD7F01de6CEEd14fC86d90F21a36dE2143", "owner": "0x7a20189b297343cf26d8548764b04891f37f3414", "owner_is_maria2": true, "owner_is_zero": false, "totalSupply": 362835531000000000000000000, "totalSupply_units": 362835531.0}, "0x232a27AB6941281b3f474Fe5fF7Cc89816fB675A": {"label": "Fa", "address": "0x232a27AB6941281b3f474Fe5fF7Cc89816fB675A", "owner": "0x7a20189b297343cf26d8548764b04891f37f3414", "owner_is_maria2": true, "owner_is_zero": false, "totalSupply": 2846000000000000000000, "totalSupply_units": 2846.0}, "0x73A19FaFb359faf519C9707b781dfdB88407d10d": {"label": "Faung", "address": "0x73A19FaFb359faf519C9707b781dfdB88407d10d", "owner": "0x7a20189b297343cf26d8548764b04891f37f3414", "owner_is_maria2": true, "owner_is_zero": false, "totalSupply": 3000000000000000000, "totalSupply_units": 3.0}, "0x2fc636E7fDF9f3E8d61033103052079781a6e7D2": {"label": "G5", "address": "0x2fc636E7fDF9f3E8d61033103052079781a6e7D2", "owner": "0x8b090509eae0feb4a0b934de1b4345161fa9a62d", "owner_is_maria2": false, "owner_is_zero": false, "totalSupply": 1200034000000000000000000, "totalSupply_units": 1200034.0}, "0xA2262D7728C689526693aE893D0fD8a352C7073C": {"label": "PI", "address": "0xA2262D7728C689526693aE893D0fD8a352C7073C", "owner": "0x8b090509eae0feb4a0b934de1b4345161fa9a62d", "owner_is_maria2": false, "owner_is_zero": false, "totalSupply": 95927999999999999999000, "totalSupply_units": 95928.0}, "0x24F0154C1dCe548AdF15da2098Fdd8B8A3B8151D": {"label": "AFFECTION", "address": "0x24F0154C1dCe548AdF15da2098Fdd8B8A3B8151D", "owner": "0x7a20189b297343cf26d8548764b04891f37f3414", "owner_is_maria2": true, "owner_is_zero": false, "totalSupply": 389194905400000000001572863, "totalSupply_units": 389194905.4}}, "cap_semantics": {"ceiling_units": 1111111111, "conditional": "if (totalSupply() <= 1111111111e18) _mint(address(this), 1e18)", "note": "<= ceiling lets supply touch cap+1; burns re-open headroom (bounds concurrent supply, not lifetime issuance)", "applies_to": ["MATH v1.1 Random()", "RNG Generate()", "AFFECTION Generate()/_mintToCap()", "Fa", "Faung"]}, "orbit": {"deterministic": true, "mechanism": "modExp64 transforms over MotzkinPrime 953467954114363 on the global Mu (Faung) state; zero onchain entropy; one step per call", "sources": ["docs/solidity/verified/MATH_atropaMath.sol", "docs/affection_docs/sources/rng.sol", "docs/affection_docs/sources/fa.sol", "docs/affection_docs/sources/faung.sol"]}, "usage_curve": {"MATH": {"address": "0xb680f0cc810317933f234f67eb6a9e923407f05d", "mints_total": 357980586, "buckets": [[20400000, 28336, "2024-05"], [20600000, 6046704, "2024-06"], [20800000, 15251482, "2024-07"], [21000000, 18094232, "2024-07"], [21200000, 17798279, "2024-08"], [21400000, 12507992, "2024-09"], [21600000, 729619, "2024-10"], [21800000, 194165, "2024-10"], [22000000, 154202, "2024-11"], [22200000, 47416, "2024-12"], [22400000, 786154, "2025-01"], [22600000, 200387, "2025-02"], [22800000, 952697, "2025-02"], [23000000, 3092, "2025-03"], [23200000, 10108, "2025-04"], [23400000, 87400, "2025-05"], [23600000, 13404, "2025-05"], [23800000, 271907, "2025-06"], [24000000, 974037, "2025-07"], [24200000, 250770, "2025-08"], [24400000, 201348, "2025-09"], [24600000, 104453, "2025-09"], [24800000, 13598, "2025-10"], [25000000, 3979082, "2025-11"], [25200000, 10030981, "2025-12"], [25400000, 7162944, "2025-12"], [25600000, 25193946, "2026-01"], [25800000, 28741224, "2026-02"], [26000000, 34683768, "2026-03"], [26200000, 32035361, "2026-04"], [26400000, 24209376, "2026-04"], [26600000, 29397982, "2026-05"], [26800000, 33205380, "2026-06"], [27000000, 24029881, "2026-07"], [27200000, 22161986, "2026-08"], [27400000, 8426893, "2026-08"]]}, "RNG": {"address": "0xa96bcbed7f01de6ceed14fc86d90f21a36de2143", "mints_total": 358003462, "buckets": [[20400000, 36027, "2024-05"], [20600000, 6051405, "2024-06"], [20800000, 15251675, "2024-07"], [21000000, 18096932, "2024-07"], [21200000, 17799847, "2024-08"], [21400000, 12509647, "2024-09"], [21600000, 729691, "2024-10"], [21800000, 194166, "2024-10"], [22000000, 154304, "2024-11"], [22200000, 47418, "2024-12"], [22400000, 786507, "2025-01"], [22600000, 200486, "2025-02"], [22800000, 952697, "2025-02"], [23000000, 3092, "2025-03"], [23200000, 10122, "2025-04"], [23400000, 88550, "2025-05"], [23600000, 13404, "2025-05"], [23800000, 271908, "2025-06"], [24000000, 974037, "2025-07"], [24200000, 250772, "2025-08"], [24400000, 201348, "2025-09"], [24600000, 104453, "2025-09"], [24800000, 13604, "2025-10"], [25000000, 3979082, "2025-11"], [25200000, 10030985, "2025-12"], [25400000, 7162947, "2025-12"], [25600000, 25193947, "2026-01"], [25800000, 28741237, "2026-02"], [26000000, 34683837, "2026-03"], [26200000, 32035377, "2026-04"], [26400000, 24209416, "2026-04"], [26600000, 29397999, "2026-05"], [26800000, 33205382, "2026-06"], [27000000, 24029882, "2026-07"], [27200000, 22161986, "2026-08"], [27400000, 8429293, "2026-08"]]}}, "reconciliation_rng_mints_per_generate": {"resolved": true, "summary": "The two readings describe DIFFERENT contracts. RNG token Generate() mints exactly 1 RNG/call (single _mint under the <= cap; no _mintToCap exists in rng.sol). AFFECTION's own Generate() mints 3 A/call (its local React() calls _mintToCap() twice + one final _mintToCap()).", "rng_conditional_src": "docs/affection_docs/sources/rng.sol lines 1369-1370: if (totalSupply() <= (1111111111 * 10 ** decimals())) _mint(address(this), 1 * 10 ** decimals());", "affection_conditional_src": "docs/affection_docs/sources/conjecture.sol _mintToCap; affection.sol Generate() = React x2 + _mintToCap", "math_rng_ledger": {"math_from_zero_mints": 357980586, "rng_from_zero_mints": 358003462, "delta": 22876, "delta_meaning": "Generate() calls that did NOT pass through MATH.Random() (direct RNG calls; both supplies were always far below cap, so no cap-phase divergence; constructor mints cancel)", "current_state_check": {"MATH_supply": 362812655.0, "RNG_supply": 362835531.0, "current_delta": 22876.0}}}}