-- M007: FAMM Nanofield Kernel Module
-- Source: famm_frustration_v2 (2-Search-Space/FAMM)
-- Kernel Function: ResourceBalancer
--
-- Frustrated Antiferromagnetic Manifold for resource allocation.
-- Frustration field guides load balancing decisions.
-- Truth Seal: [ SSS-ENE-FAMM-2026-05-03 ]

module M007_FAMMNanofield where

import BaseTypes
import Semantics.Q16_16

structure FAMMSite where
  id        : SiteID
  position  : Vec3
  spin      : Q16_16          -- -1 to 1 (antiferromagnetic)
  energy    : Q16_16          -- Local field energy
  resources : ResourceState   -- CPU, memory, IO capacity
  
structure FAMMBond where
  source    : SiteID
  target    : SiteID
  coupling  : Q16_16          -- Bond strength J
  distance  : Q16_16
  
def frustrationEnergy (sites : Array FAMMSite) (bonds : Array FAMMBond) : Q16_16 :=
  bonds.foldl (\acc bond =>
    let s_i := sites.find (\s => s.id == bond.source)
    let s_j := sites.find (\s => s.id == bond.target)
    let J := bond.coupling
    -- E = -J * s_i * s_j (antiferromagnetic: J > 0, spins anti-align for min energy)
    acc - J * s_i.spin * s_j.spin
  ) Q16_16.zero

-- Monte Carlo step: flip spins to minimize frustration
def mcStep (sites : Array FAMMSite) (bonds : Array FAMMBond) (temperature : Q16_16) : Array FAMMSite :=
  sites.map (\site =>
    let E_before := localEnergy site bonds
    let spin_flipped := { site with spin := Q16_16.neg site.spin }
    let E_after := localEnergy spin_flipped bonds
    
    let deltaE := E_after - E_before
    if deltaE < Q16_16.zero then
      spin_flipped  -- Accept: lowers energy
    else if randomQ16_16 < exp (Q16_16.neg deltaE / temperature) then
      spin_flipped  -- Accept with Boltzmann probability
    else
      site  -- Reject
  )

-- Kernel interface: balance load via FAMM relaxation
def syscallBalanceLoad (requests : Array ResourceRequest) : IO LoadBalance := do
  let sites ← getCurrentFAMMSites
  let bonds ← getCurrentFAMMBonds
  
  -- Relax FAMM to low-frustration state
  let relaxed := iterate 100 (\s => mcStep s bonds TEMPERATURE) sites
  
  -- Assign requests to sites with lowest energy (most available resources)
  let assignments := requests.map (\req =>
    let bestSite := relaxed.minBy (\s => s.energy)
    { request := req, site := bestSite.id, expectedLatency := s.energy }
  )
  
  return { assignments := assignments, finalFrustration := frustrationEnergy relaxed bonds }

end M007_FAMMNanofield