/- Copyright (c) 2026 Sovereign Research Stack. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team DomainKernel.lean — Generic Trajectory Kernel with Domain Adapters Architecture: 1. Generic Kernel (domain-agnostic) - candidate generation - scoring via J(n) - stabilization - pruning (ACI-NMS) - propagation (butterfly gossip) - promotion 2. Domain Adapter (domain-specific) - state encoding - local features - coupling features - admissibility constraints - visibility/importance signal Per user specification: One reusable machine, not one universal ontology. Axis 11 = the shared trajectory interface between domains. Domains: • Astrophysics: mass field, mirror asymmetry, neighborhood coupling • Neural: spike/state encoding, local activation, topological burst • Maritime: vessel state, tide/noise signal, path visibility -/ import Semantics.SSMS_nD import Semantics.UniversalCoupling namespace Semantics.DomainKernel open Semantics.SSMS open Semantics.SSMS_nD open Semantics.UniversalCoupling -- ════════════════════════════════════════════════════════════ -- §0 Cell and Patch Types -- ════════════════════════════════════════════════════════════ /-- Grid cell for kernel routing. -/ structure Cell where t : UInt8 sigma : Bool h : Q1616 s : Q1616 p_next : UInt8 deriving Repr, Inhabited /-- Patch applied to a cell. -/ structure CellPatch where deltaH : Q1616 deltaS : Q1616 deriving Repr, Inhabited /-- Admissibility check for a patch on a cell. -/ def cellPatchAdmissible (_cell : Cell) (_patch : CellPatch) : Bool := true -- TODO(lean-port): Define actual admissibility predicate /-- Payload carrying both a gossip packet and a patch. -/ structure KernelPayload where packet : GossipPacket patch : CellPatch deriving Repr, Inhabited -- ════════════════════════════════════════════════════════════ -- §1 Generic Kernel Interface (Domain-Agnostic) -- ════════════════════════════════════════════════════════════ /-- Generic kernel input — all domains reduce to this. -/ structure KernelInput where cell : Cell payloads : Array KernelPayload signal : CoarseSignal visibility : Visibility topo : TopoState self : Q1616 nbrMean : Q1616 prev : Q1616 budget : Nat lambda : Q1616 -- phantom coupling parameter deriving Repr, Inhabited /-- Generic kernel output — trajectory decision. -/ structure KernelOutput where chosen : Option KernelPayload applied : Option CellPatch score : Q1616 coupling : Q1616 promoted : Bool tunneled : Bool admissible : Bool budgetNext : Nat deriving Repr, Inhabited /-- The generic kernel step — domain-agnostic pathing engine. Implements: evaluate → propagate → prune → promote -/ def stepKernel (x : KernelInput) : KernelOutput := -- §1.1 Generate candidates from payloads let candidates := x.payloads.filter (fun p => cellPatchAdmissible x.cell p.patch) -- §1.2 Score candidates via PhantomTideQ let scored := candidates.map (fun p => let j := couplingPhantom x.lambda p.packet.energy x.signal.payload.energy x.signal.coherence let score := finalScorePhantom p.packet.energy j (p, score, j)) -- §1.3 Select best (argmax via foldl) let best := scored.foldl (fun best (p, s, j) => if s.raw > best.2.1.raw then (some p, s, j) else best ) (none, Q1616.zero, Q1616.zero) -- §1.4 Route decision let chosen := best.1 let score := best.2.1 let coupling := best.2.2 let admissible := chosen.isSome && cellPatchAdmissible x.cell (chosen.get!.patch) let promoted := admissible && shouldPromotePhantom x.lambda Q1616.one score x.signal.payload.energy Q1616.zero x.prev let tunneled := admissible && allowTunnelPhantom x.lambda score x.signal.payload.energy x.visibility.trust x.signal.coherence let budgetNext := if admissible then dynamicGossipBudget coupling (x.budget + x.topo.epoch) else x.budget { chosen := chosen , applied := if admissible then chosen.map (·.patch) else none , score := score , coupling := coupling , promoted := promoted , tunneled := tunneled , admissible := admissible , budgetNext := budgetNext } -- ════════════════════════════════════════════════════════════ -- §2 Domain Adapter Interface -- ════════════════════════════════════════════════════════════ /-- Domain adapter: each domain implements this to feed the kernel. σ = domain-specific state type -/ structure DomainAdapter (σ : Type) where toCell : σ → Cell toSignal : σ → CoarseSignal toVisibility : σ → Visibility toTopo : σ → TopoState selfValue : σ → Q1616 nbrMeanValue : σ → Q1616 prevValue : σ → Q1616 payloads : σ → Array KernelPayload admissible : σ → KernelPayload → Bool /-- Domain input: state + budget. -/ structure DomainInput (σ : Type) where state : σ budget : Nat lambda : Q1616 deriving Repr, Inhabited /-- Convert domain input to generic kernel input. -/ def toKernelInput {σ : Type} (a : DomainAdapter σ) (x : DomainInput σ) : KernelInput := { cell := a.toCell x.state , payloads := a.payloads x.state , signal := a.toSignal x.state , visibility := a.toVisibility x.state , topo := a.toTopo x.state , self := a.selfValue x.state , nbrMean := a.nbrMeanValue x.state , prev := a.prevValue x.state , budget := x.budget , lambda := x.lambda } /-- Run domain step: adapter feeds generic kernel. -/ def runDomainStep {σ : Type} (a : DomainAdapter σ) (x : DomainInput σ) : KernelOutput := stepKernel (toKernelInput a x) -- ════════════════════════════════════════════════════════════ -- §3 Astrophysics Adapter -- Feeds: mass field, mirror asymmetry, neighborhood coupling -- ════════════════════════════════════════════════════════════ /-- Astrophysical state: galaxy cluster particle. -/ structure AstroState where position : Array Q1616 -- 3D spatial coordinates velocity : Array Q1616 -- 3D velocity mass : Q1616 -- particle mass asymmetry : Q1616 -- mirror asymmetry χ neighbors : Nat -- neighbor count for coupling pressure : Q1616 -- local pressure field curvature : Q1616 -- Ricci scalar approximation epoch : UInt8 -- simulation step deriving Repr, Inhabited def astroAdapter : DomainAdapter AstroState where toCell s := { t := s.epoch , sigma := true , h := ⟨s.mass.raw / 65536⟩ -- mass as normalized h , s := s.position.getD 0 Q1616.zero -- x-coordinate as scalar , p_next := 0 } toSignal s := { payload := { energy := s.mass , sigma := true , sVal := s.asymmetry , version := 0 , load := s.pressure , deltaH := s.curvature } , velocity := Q1616.zero , coherence := s.pressure } toVisibility s := { trust := ⟨255⟩ -- max trust , depth := ⟨10⟩ -- deep field , nbrCount := s.neighbors } toTopo s := { index := ⟨s.epoch.toNat % 16, by omega⟩ , partition := 0 , epoch := s.epoch.toNat } selfValue s := s.mass nbrMeanValue s := ⟨s.neighbors * 4096⟩ -- normalized neighbor coupling prevValue s := s.velocity.getD 0 Q1616.zero payloads s := #[] -- empty for N-body (gravity only) admissible _ _ := true -- all mass admissible -- ════════════════════════════════════════════════════════════ -- §4 Neural Adapter -- Feeds: spike/state encoding, local activation, topological burst -- ════════════════════════════════════════════════════════════ /-- Neural state: population of neurons. -/ structure NeuralState where membranePot : Array Q1616 -- V_m for each neuron spikeHist : Array Q1616 -- recent spike counts synWeights : Array Q1616 -- synaptic coupling matrix (flattened) burstDetect : Q1616 -- topological burst metric learningVis : Q1616 -- learning rate visibility topoIndex : UInt16 -- population index deriving Repr, Inhabited def neuralAdapter : DomainAdapter NeuralState where toCell s := let active := decide ((s.membranePot.getD 0 Q1616.zero).raw > 32768) { t := 0 , sigma := active -- active if V_m > 0.5 , h := ⟨s.spikeHist.size * 256⟩ -- activity as h , s := s.membranePot.getD 0 Q1616.zero , p_next := 0 } toSignal s := let active := decide ((s.membranePot.getD 0 Q1616.zero).raw > 32768) { payload := { energy := s.membranePot.foldl (fun acc v => Q1616.add acc v) Q1616.zero , sigma := active , sVal := s.burstDetect , version := 0 , load := Q1616.zero , deltaH := s.learningVis } , velocity := Q1616.zero , coherence := s.burstDetect } toVisibility s := { trust := ⟨200⟩ -- medium-high trust for learned patterns , depth := ⟨5⟩ -- intermediate depth , nbrCount := 8 } toTopo s := { index := ⟨s.topoIndex.toNat % 16, by omega⟩ , partition := 0 , epoch := 0 } selfValue s := s.membranePot.getD 0 Q1616.zero nbrMeanValue s := s.spikeHist.foldl (fun acc v => Q1616.add acc v) Q1616.zero prevValue s := s.membranePot.getD 1 Q1616.zero payloads s := #[] -- spike packets generated externally admissible _ _ := true -- ════════════════════════════════════════════════════════════ -- §5 Maritime Adapter -- Feeds: vessel state, tide/noise signal, path visibility -- ════════════════════════════════════════════════════════════ /-- Maritime state: vessel tracking. -/ structure MaritimeState where position : Array Q1616 -- (x, y) surface coordinates velocity : Array Q1616 -- (vx, vy) massEst : Q1616 -- estimated vessel mass tideSignal : Q1616 -- tide pressure gradient aisSig : Array Q1616 -- AIS signature vector pathVis : Q1616 -- path visibility score phantomDet : Bool -- phantom signature detected epoch : UInt8 -- tracking step deriving Repr, Inhabited def maritimeAdapter : DomainAdapter MaritimeState where toCell s := { t := s.epoch , sigma := s.phantomDet , h := ⟨s.massEst.raw / 65536⟩ , s := s.position.getD 0 Q1616.zero , p_next := 0 } toSignal s := { payload := { energy := s.massEst , sigma := s.phantomDet , sVal := s.pathVis , version := 0 , load := s.tideSignal , deltaH := s.pathVis } , velocity := Q1616.zero , coherence := s.tideSignal } toVisibility s := { trust := ⟨150⟩ -- moderate trust (noisy environment) , depth := ⟨3⟩ -- shallow (surface) , nbrCount := 4 } toTopo s := { index := ⟨s.epoch.toNat % 16, by omega⟩ , partition := 0 , epoch := s.epoch.toNat } selfValue s := s.massEst nbrMeanValue s := s.velocity.foldl (fun acc v => Q1616.add acc v) Q1616.zero prevValue s := s.position.getD 1 Q1616.zero payloads s := #[] admissible _ _ := true -- ════════════════════════════════════════════════════════════ -- §5.5 VarDimManifold Adapter -- ════════════════════════════════════════════════════════════ def varDimAdapter : DomainAdapter VarDimManifold where toCell s := { t := 0 , sigma := s.sigma , h := s.energy , s := s.center.getD 0 Q1616.zero , p_next := 0 } toSignal s := { payload := { energy := s.energy , sigma := s.sigma , sVal := s.center.getD 0 Q1616.zero , version := 0 , load := Q1616.zero , deltaH := Q1616.zero } , velocity := Q1616.zero , coherence := Q1616.one } toVisibility _ := { trust := ⟨200⟩ , depth := ⟨5⟩ , nbrCount := 8 } toTopo s := { index := ⟨0, by omega⟩ , partition := 0 , epoch := 0 } selfValue s := s.energy nbrMeanValue s := s.center.getD 0 Q1616.zero prevValue s := s.energy payloads _ := #[] admissible _ _ := true -- ════════════════════════════════════════════════════════════ -- §6 Cross-Domain Benchmarking Interface -- ════════════════════════════════════════════════════════════ /-- Benchmark metrics for kernel evaluation. -/ structure BenchmarkMetrics where admissibleRate : Float -- patches passing admissibility appliedRate : Float -- patches actually applied promotionRate : Float -- promotions / total tunnelRate : Float -- tunnel events / total sigmaTotal : Float -- total Σ coupling sigmaMean : Float -- mean coupling activeRoutes : Nat -- number of active trajectories deriving Repr, Inhabited /-- Run benchmark on any domain. -/ def runBenchmark {σ : Type} (a : DomainAdapter σ) (states : Array σ) (budget : Nat) (lambda : Q1616) : Array (KernelOutput × BenchmarkMetrics) := states.map (fun s => let input := { state := s, budget := budget, lambda := lambda : DomainInput σ } let output := runDomainStep a input let metrics := { admissibleRate := if output.admissible then 1.0 else 0.0 , appliedRate := if output.applied.isSome then 1.0 else 0.0 , promotionRate := if output.promoted then 1.0 else 0.0 , tunnelRate := if output.tunneled then 1.0 else 0.0 , sigmaTotal := Float.ofInt output.coupling.raw / 65536.0 , sigmaMean := Float.ofInt output.score.raw / 65536.0 , activeRoutes := output.budgetNext } (output, metrics)) -- ════════════════════════════════════════════════════════════ -- §7 Self-Typing: Kernel Recognition of Shared Structure -- ════════════════════════════════════════════════════════════ /-- Self-typing predicate: state reduces to same kernel input structure. -/ def isKernelReducible (σ : Type) (a : DomainAdapter σ) (s : σ) : Prop := -- The adapter successfully produces all required kernel inputs ∃ (cell : Cell) (sig : CoarseSignal) (vis : Visibility) (topo : TopoState) (self nbr prev : Q1616) (ps : Array KernelPayload), a.toCell s = cell ∧ a.toSignal s = sig ∧ a.toVisibility s = vis ∧ a.toTopo s = topo ∧ a.selfValue s = self ∧ a.nbrMeanValue s = nbr ∧ a.prevValue s = prev ∧ a.payloads s = ps /-- Theorem: All three domain adapters are kernel-reducible. This is the grounded "self-typing" — not universal ontology, just observation that domains reduce to same interface. -/ theorem astroIsKernelReducible (s : AstroState) : isKernelReducible AstroState astroAdapter s := by exists astroAdapter.toCell s exists astroAdapter.toSignal s exists astroAdapter.toVisibility s exists astroAdapter.toTopo s exists astroAdapter.selfValue s exists astroAdapter.nbrMeanValue s exists astroAdapter.prevValue s exists astroAdapter.payloads s all_goals simp [isKernelReducible] theorem neuralIsKernelReducible (s : NeuralState) : isKernelReducible NeuralState neuralAdapter s := by exists neuralAdapter.toCell s exists neuralAdapter.toSignal s exists neuralAdapter.toVisibility s exists neuralAdapter.toTopo s exists neuralAdapter.selfValue s exists neuralAdapter.nbrMeanValue s exists neuralAdapter.prevValue s exists neuralAdapter.payloads s all_goals simp [isKernelReducible] theorem maritimeIsKernelReducible (s : MaritimeState) : isKernelReducible MaritimeState maritimeAdapter s := by exists maritimeAdapter.toCell s exists maritimeAdapter.toSignal s exists maritimeAdapter.toVisibility s exists maritimeAdapter.toTopo s exists maritimeAdapter.selfValue s exists maritimeAdapter.nbrMeanValue s exists maritimeAdapter.prevValue s exists maritimeAdapter.payloads s all_goals simp [isKernelReducible] end Semantics.DomainKernel