argumentcomputer
diff --git a/‎Cargo.lock‎
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diff --git a/‎Cargo.toml‎
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diff --git a/‎Ix.lean‎
Lines changed: 2 additions & 0 deletions b/‎Ix.lean‎
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diff --git a/‎Ix/AssumptionTree.lean‎
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@@ -19,6 +19,7 @@ rayon = "1"
 rustc-hash = "2"
 tiny-keccak = { version = "2", features = ["keccak"] }
 dashmap = { version = "6.1.0", features = ["rayon"] }
+memmap2 = "0.9"
 sha2 = "0.10"
 # Iroh dependencies
 bytes = { version = "1.10.1", optional = true }
 
@@ -12,6 +12,8 @@ public import Ix.CompileM
 public import Ix.DecompileM
 public import Ix.KernelCheck
 public import Ix.Claim
+public import Ix.Merkle
+public import Ix.AssumptionTree
 public import Ix.Commit
 public import Ix.Benchmark.Bench
 public import Ix.Aiur
 
@@ -0,0 +1,193 @@
+/-
+  # AssumptionTree: serializable merkle tree over `Address` leaves
+
+  Used to recover the leaf set committed to by a conditional claim's
+  `assumptions` root. The root alone tells the verifier *which* set
+  was assumed; the AssumptionTree carries the actual leaves so the
+  verifier can inspect them.
+
+  Two construction modes — both produce the same `node`-shaped trees,
+  differ only in how leaves are arranged:
+
+  - `canonical leaves` builds the same shape that `Ix.Merkle.merkleRootCanonical`
+    hashes, with `padding` nodes wherever odd-leaf padding occurs.
+  - `join l r` is free-form O(1) composition; result root matches
+    `Ix.Merkle.merkleJoin`.
+
+  ## Serialization
+
+  Tag4 size 2 under flag 0xE:
+
+  ```text
+  [Tag4(0xE, 2) = 0xE2] [body]
+
+  body recursive:
+    leaf(addr):  [0x00] [addr:32]
+    padding:     [0x01]
+    node(l, r):  [0x02] [body l] [body r]
+  ```
+
+  `padding` represents the zero-sentinel slot used by the canonical
+  builder to even out odd levels; its root is exactly `zeroAddress`,
+  matching the bare 32-byte zero that `Ix.Merkle` mixes into odd-level
+  hashing. Splitting it from `leaf` keeps `leaves` clean (returns only
+  real leaves, not synthetic padding addresses).
+-/
+
+module
+public import Ix.Address
+public import Ix.Merkle
+public import Ix.Ixon
+
+public section
+
+namespace Ix
+
+open Ixon
+open Ix.Merkle (leafHash nodeHash zeroAddress merkleJoin)
+
+/-- A merkle tree over `Address` leaves with explicit shape. -/
+inductive AssumptionTree where
+  | leaf (addr : Address)
+  | padding
+  | node (left right : AssumptionTree)
+  deriving BEq, Repr, Inhabited
+
+namespace AssumptionTree
+
+/-- Recursively compute the root hash. -/
+partial def root : AssumptionTree → Address
+  | .leaf addr => leafHash addr
+  | .padding => zeroAddress
+  | .node l r => nodeHash l.root r.root
+
+/-- In-order traversal of real leaves (skips `padding`). Iterative
+    stack-based walk to avoid stack overflow on deep trees. -/
+partial def leaves (t : AssumptionTree) : Array Address := Id.run do
+  let mut acc : Array Address := #[]
+  let mut stack : Array AssumptionTree := #[t]
+  while !stack.isEmpty do
+    let top := stack.back!
+    stack := stack.pop
+    match top with
+    | .leaf a => acc := acc.push a
+    | .padding => continue
+    | .node l r =>
+      -- Push right first so left is processed first (in-order via LIFO).
+      stack := stack.push r
+      stack := stack.push l
+  return acc
+
+/-- True iff `target` appears as a `leaf` somewhere in the tree. -/
+partial def contains (t : AssumptionTree) (target : Address) : Bool :=
+  match t with
+  | .leaf a => a == target
+  | .padding => false
+  | .node l r => l.contains target || r.contains target
+
+/-- Build the canonical sorted+padded merkle tree over a leaf set.
+    Returns `none` for an empty (post-dedup) leaf set. Matches the
+    shape committed to by `merkleRootCanonical`. -/
+partial def canonical (leaves : Array Address) : Option AssumptionTree :=
+  let sorted := dedupSorted (leaves.qsort fun a b => compare a b == .lt)
+  if sorted.isEmpty then
+    none
+  else if sorted.size == 1 then
+    some (.leaf sorted[0]!)
+  else
+    some (reduce (sorted.map .leaf))
+  where
+    dedupSorted (xs : Array Address) : Array Address := Id.run do
+      if xs.isEmpty then return #[]
+      let mut acc : Array Address := #[xs[0]!]
+      for i in [1:xs.size] do
+        if !(xs[i]! == xs[i-1]!) then acc := acc.push xs[i]!
+      return acc
+    reduce (level : Array AssumptionTree) : AssumptionTree :=
+      if level.size == 1 then level[0]!
+      else reduce (pairLevel level)
+    pairLevel (level : Array AssumptionTree) : Array AssumptionTree := Id.run do
+      let mut next : Array AssumptionTree := #[]
+      let mut i := 0
+      while i < level.size do
+        let l := level[i]!
+        let r := if i + 1 < level.size then level[i+1]! else .padding
+        next := next.push (.node l r)
+        i := i + 2
+      return next
+
+/-- Combine two existing subtrees into a new free-form node in O(1). -/
+@[inline] def join (l r : AssumptionTree) : AssumptionTree := .node l r
+
+/-- Recursive helper for `merkleProof`. Returns the leaf-to-root path
+    if `target` is present, else `none`. -/
+partial def searchPath (t : AssumptionTree) (target : Address)
+    : Option (Array (Address × Bool)) :=
+  match t with
+  | .leaf a => if a == target then some #[] else none
+  | .padding => none
+  | .node l r =>
+    match l.searchPath target with
+    | some p => some (p.push (r.root, false))
+    | none =>
+      match r.searchPath target with
+      | some p => some (p.push (l.root, true))
+      | none => none
+
+/-- Produce a merkle membership path for `target`. Path is in
+    leaf-to-root order (matches `verifyMerkleProof`). -/
+def merkleProof (t : AssumptionTree) (target : Address)
+    : Option Ix.Merkle.MerklePath := searchPath t target
+
+/-! ## Serialization -/
+
+def FLAG : UInt8 := 0xE
+def VARIANT : UInt64 := 2
+
+def BODY_LEAF    : UInt8 := 0x00
+def BODY_PADDING : UInt8 := 0x01
+def BODY_NODE    : UInt8 := 0x02
+
+partial def putBody : AssumptionTree → PutM Unit
+  | .leaf addr => do
+    putU8 BODY_LEAF
+    Serialize.put addr
+  | .padding => do
+    putU8 BODY_PADDING
+  | .node l r => do
+    putU8 BODY_NODE
+    putBody l
+    putBody r
+
+def put (t : AssumptionTree) : PutM Unit := do
+  putTag4 ⟨FLAG, VARIANT⟩
+  putBody t
+
+partial def getBody : GetM AssumptionTree := do
+  let tag : UInt8 ← getU8
+  if tag == BODY_LEAF then
+    return .leaf (← Serialize.get)
+  else if tag == BODY_PADDING then
+    return .padding
+  else if tag == BODY_NODE then
+    let l ← getBody
+    let r ← getBody
+    return .node l r
+  else
+    throw s!"AssumptionTree.getBody: invalid body tag {tag.toNat}"
+
+def get : GetM AssumptionTree := do
+  let tag ← getTag4
+  if tag.flag != FLAG || tag.size != VARIANT then
+    throw s!"AssumptionTree.get: expected Tag4 0xE/2, got {tag.flag.toNat}/{tag.size}"
+  getBody
+
+def ser (t : AssumptionTree) : ByteArray := runPut (put t)
+def de (bytes : ByteArray) : Except String AssumptionTree :=
+  runGet get bytes
+
+end AssumptionTree
+
+end Ix
+
+end