diff --git a/spec/jsonata-suite/baseline.lua b/spec/jsonata-suite/baseline.lua
index 490934e..e473789 100644
--- a/spec/jsonata-suite/baseline.lua
+++ b/spec/jsonata-suite/baseline.lua
@@ -112,7 +112,11 @@ return {
   ["comparison-operators/deep-equals/7"] = true,
   ["comparison-operators/deep-equals/8"] = true,
   ["comparison-operators/deep-equals/9"] = true,
+  ["conditionals/case000"] = true,
+  ["conditionals/case001"] = true,
   ["conditionals/case002"] = true,
+  ["conditionals/case003"] = true,
+  ["conditionals/case004"] = true,
   ["conditionals/case005"] = true,
   ["conditionals/case006"] = true,
   ["conditionals/case007"] = true,
@@ -435,6 +439,10 @@ return {
   ["function-join/case011"] = true,
   ["function-keys/case000"] = true,
   ["function-keys/case001"] = true,
+  ["function-keys/case002"] = true,
+  ["function-keys/case004"] = true,
+  ["function-keys/case005"] = true,
+  ["function-keys/case006"] = true,
   ["function-length/case000"] = true,
   ["function-length/case001"] = true,
   ["function-length/case002"] = true,
@@ -454,6 +462,7 @@ return {
   ["function-lookup/case000"] = true,
   ["function-lookup/case001"] = true,
   ["function-lookup/case002"] = true,
+  ["function-lookup/case003"] = true,
   ["function-lowercase/case000"] = true,
   ["function-lowercase/case001"] = true,
   ["function-max/case000"] = true,
@@ -645,8 +654,10 @@ return {
   ["function-split/case016"] = true,
   ["function-split/case017"] = true,
   ["function-split/case018"] = true,
+  ["function-spread/case000"] = true,
   ["function-spread/case001"] = true,
   ["function-spread/case002"] = true,
+  ["function-spread/case003"] = true,
   ["function-sqrt/case000"] = true,
   ["function-sqrt/case001"] = true,
   ["function-sqrt/case002"] = true,
@@ -830,6 +841,7 @@ return {
   ["missing-paths/case001"] = true,
   ["missing-paths/case002"] = true,
   ["missing-paths/case003"] = true,
+  ["missing-paths/case004"] = true,
   ["missing-paths/case005"] = true,
   ["multiple-array-selectors/case000"] = true,
   ["multiple-array-selectors/case001"] = true,
@@ -853,7 +865,10 @@ return {
   ["numeric-operators/case009"] = true,
   ["numeric-operators/case010"] = true,
   ["numeric-operators/case011"] = true,
+  ["numeric-operators/case012"] = true,
+  ["numeric-operators/case013"] = true,
   ["numeric-operators/case015"] = true,
+  ["numeric-operators/case016"] = true,
   ["numeric-operators/case017"] = true,
   ["numeric-operators/case018"] = true,
   ["object-constructor/case000"] = true,
@@ -868,12 +883,15 @@ return {
   ["object-constructor/case011"] = true,
   ["object-constructor/case012"] = true,
   ["object-constructor/case013"] = true,
+  ["object-constructor/case014"] = true,
   ["object-constructor/case015"] = true,
   ["object-constructor/case016"] = true,
   ["object-constructor/case017"] = true,
   ["object-constructor/case018"] = true,
   ["object-constructor/case021"] = true,
   ["object-constructor/case022"] = true,
+  ["object-constructor/case023"] = true,
+  ["object-constructor/case024"] = true,
   ["object-constructor/case025"] = true,
   ["object-constructor/case026"] = true,
   ["parent-operator/errors/0"] = true,
@@ -929,6 +947,7 @@ return {
   ["partial-application/case002"] = true,
   ["partial-application/case003"] = true,
   ["partial-application/case004"] = true,
+  ["performance/case000"] = true,
   ["predicates/case000"] = true,
   ["predicates/case001"] = true,
   ["predicates/case002"] = true,
@@ -976,6 +995,7 @@ return {
   ["simple-array-selectors/case011"] = true,
   ["simple-array-selectors/case012"] = true,
   ["simple-array-selectors/case013"] = true,
+  ["simple-array-selectors/case014"] = true,
   ["simple-array-selectors/case015"] = true,
   ["simple-array-selectors/case016"] = true,
   ["simple-array-selectors/case017"] = true,
@@ -1151,6 +1171,7 @@ return {
   ["wildcards/case004"] = true,
   ["wildcards/case005"] = true,
   ["wildcards/case006"] = true,
+  ["wildcards/case008"] = true,
   ["wildcards/case009"] = true,
   ["wildcards/case010/0"] = true,
   ["wildcards/case010/1"] = true,
diff --git a/spec/m6a_spec.lua b/spec/m6a_spec.lua
new file mode 100644
index 0000000..fa3ab9f
--- /dev/null
+++ b/spec/m6a_spec.lua
@@ -0,0 +1,116 @@
+local jsonata = require("jsonata")
+local function run(src, input)
+  return jsonata.compile(src):evaluate(input)
+end
+
+describe("M6a C-1: $$ root context", function()
+  it("$$ resolves to the root input", function()
+    assert.are.same({ a = 1 }, run("$$", { a = 1 }))
+  end)
+  it("$$ reaches root from a nested path step", function()
+    assert.are.same({ a = { b = 2 } }, run("a.$$", { a = { b = 2 } }))
+  end)
+  it("$$.field indexes the root", function()
+    assert.are.equal(1, run("$$.a", { a = 1 }))
+  end)
+  it("$ (current context) still works", function()
+    assert.are.equal(5, run("a.$", { a = 5 }))
+    assert.are.same({ x = 1 }, run("$", { x = 1 }))
+  end)
+end)
+
+describe("M6a B-3: $keys/$spread empty & scalar", function()
+  it("$keys of an empty result is undefined, not []", function()
+    assert.is_nil(run("$keys(5)"))
+    assert.is_nil(run("$keys({})"))
+  end)
+  it("$keys still returns the keys of an object", function()
+    assert.are.same({ "a", "b" }, run('$keys({"a":1, "b":2})'))
+  end)
+  it("$spread echoes a scalar argument", function()
+    assert.are.equal(5, run("$spread(5)"))
+    assert.is_true(run("$spread(true)"))
+  end)
+  it("$spread still spreads an object", function()
+    assert.are.same({ { a = 1 } }, run('$spread({"a":1})'))
+  end)
+end)
+
+describe("M6a C-4a: undefined-operand arithmetic", function()
+  local function code(src, input)
+    local ok, err = pcall(run, src, input)
+    assert.is_false(ok)
+    return err.code
+  end
+  it("arithmetic with an undefined operand is undefined", function()
+    assert.is_nil(run("5 + nope", {}))
+    assert.is_nil(run("nope - 1", {}))
+    assert.is_nil(run("nope * 2", {}))
+    assert.is_nil(run("10 / nope", {}))
+    assert.is_nil(run("-nope", {}))
+  end)
+  it("normal arithmetic still works", function()
+    assert.are.equal(7, run("5 + 2"))
+    assert.are.equal(-3, run("-(1 + 2)"))
+  end)
+  it("a genuine non-number operand still raises a type error", function()
+    assert.are.equal("T2001", code("'x' + 5"))
+    assert.are.equal("T2002", code("5 + 'x'"))
+  end)
+  it("matches jsonata operand ordering (type error before undefined short-circuit)", function()
+    assert.are.equal("T2002", code("nope + 'x'", {})) -- undefined LHS, defined non-number RHS -> T2002
+    assert.are.equal("T2001", code("'x' + nope", {})) -- defined non-number LHS -> T2001
+    assert.is_nil(run("nope + 5", {})) -- undefined LHS, number RHS -> undefined
+    assert.is_nil(run("5 + nope", {})) -- number LHS, undefined RHS -> undefined
+    assert.are.equal("T2001", code("false + nope", {})) -- defined non-number LHS (case018) -> T2001
+  end)
+end)
+
+describe("M6a C-3: object-literal key rules", function()
+  local function code(src, input)
+    local ok, err = pcall(run, src, input)
+    assert.is_false(ok)
+    return err.code
+  end
+  it("an undefined key skips the whole pair", function()
+    assert.are.same({}, run("{nope: 1}", {}))
+  end)
+  it("an undefined value omits the pair", function()
+    assert.are.same({}, run('{"a": nope}', {}))
+  end)
+  it("a non-string key raises T1003", function()
+    assert.are.equal("T1003", code('{1: "x"}'))
+  end)
+  it("a duplicate key raises D1009", function()
+    assert.are.equal("D1009", code('{"a":1, "a":2}'))
+  end)
+  it("a normal object literal still builds correctly", function()
+    assert.are.equal(2, run('{"a":1, "b":2}.b', {}))
+  end)
+end)
+
+describe("M6a adversarial fixes", function()
+  local function code(src, input)
+    local ok, err = pcall(run, src, input)
+    assert.is_false(ok)
+    return err.code
+  end
+
+  it("$spread of an empty object/array is undefined", function()
+    assert.is_nil(run("$spread({})"))
+    assert.is_nil(run("$spread([])"))
+  end)
+
+  it("a duplicate object key with an undefined value still raises D1009", function()
+    assert.are.equal("D1009", code('{"a":1, "a":nope}', {}))
+    assert.are.equal("D1009", code('{"a":nope, "a":2}', {}))
+    assert.are.equal("D1009", code('{"a":nope, "a":nope}', {}))
+  end)
+
+  it("unary minus on a non-number raises D1002", function()
+    assert.are.equal("D1002", code("-'x'"))
+    assert.are.equal("D1002", code("-true"))
+    assert.is_nil(run("-nope", {})) -- undefined still propagates
+    assert.are.equal(-5, run("-5")) -- normal still works
+  end)
+end)
diff --git a/src/jsonata/errors.lua b/src/jsonata/errors.lua
index 27aecdc..25731db 100644
--- a/src/jsonata/errors.lua
+++ b/src/jsonata/errors.lua
@@ -29,6 +29,7 @@ local MESSAGES = {
   T2012 = "The delete clause of the transform expression must evaluate to an array of strings",
   -- Dynamic / runtime errors
   D1001 = "Number out of range to be formatted",
+  D1002 = "Cannot negate a non-numeric value: {{value}}",
   D1009 = "Multiple key definitions evaluate to same key: {{value}}",
   D2014 = "The size of the sequence allocated by the range operator (..) must not exceed 1e7.  Attempted to allocate {{value}}.",
   D3001 = "Unsupported in M1",
diff --git a/src/jsonata/evaluator.lua b/src/jsonata/evaluator.lua
index 0aabf96..3eb81e6 100644
--- a/src/jsonata/evaluator.lua
+++ b/src/jsonata/evaluator.lua
@@ -59,8 +59,17 @@ local function eval_binary(node, input, env)
   end
 
   if op == "+" or op == "-" or op == "*" or op == "/" or op == "%" then
-    local a = as_number(lhs, "T2001")
-    local b = as_number(rhs, "T2002")
+    if not V.is_nothing(lhs) and V.typeof(lhs) ~= "number" then
+      errors.raise("T2001", { value = lhs })
+    end
+    if not V.is_nothing(rhs) and V.typeof(rhs) ~= "number" then
+      errors.raise("T2002", { value = rhs })
+    end
+    if V.is_nothing(lhs) or V.is_nothing(rhs) then
+      return V.NOTHING
+    end
+    local a = lhs
+    local b = rhs
     if op == "+" then
       return a + b
     elseif op == "-" then
@@ -696,7 +705,14 @@ local function _evaluate(node, input, env)
     return V.NULL
   elseif t == "unary" then
     if node.value == "-" then
-      return -as_number(evaluate(node.expression, input, env), "T2001")
+      local v = evaluate(node.expression, input, env)
+      if V.is_nothing(v) then
+        return V.NOTHING
+      end
+      if V.typeof(v) ~= "number" then
+        errors.raise("D1002", { value = v })
+      end
+      return -v
     end
     errors.raise("S0211", { token = node.value })
   elseif t == "binary" then
@@ -765,11 +781,22 @@ local function _evaluate(node, input, env)
     return arr
   elseif t == "object" then
     local obj = V.object()
+    local seen = {}
     for _, pair in ipairs(node.pairs) do
       local k = evaluate(pair[1], input, env)
-      local val = evaluate(pair[2], input, env)
-      local kstr = V.is_nothing(k) and "" or functions.string.impl(k)
-      V.obj_set(obj, kstr, val)
+      if not V.is_nothing(k) then -- undefined key: skip the whole pair
+        if V.typeof(k) ~= "string" then
+          errors.raise("T1003", { value = k })
+        end
+        if seen[k] then -- duplicate key (regardless of value)
+          errors.raise("D1009", { value = k })
+        end
+        seen[k] = true
+        local val = evaluate(pair[2], input, env)
+        if not V.is_nothing(val) then -- undefined value: omit the pair
+          V.obj_set(obj, k, val)
+        end
+      end
     end
     return obj
   elseif t == "function" then
diff --git a/src/jsonata/functions/object.lua b/src/jsonata/functions/object.lua
index 85edee4..f8f5f26 100644
--- a/src/jsonata/functions/object.lua
+++ b/src/jsonata/functions/object.lua
@@ -25,6 +25,9 @@ R.keys = H.def(function(x)
       end
     end
   end
+  if #out == 0 then
+    return V.NOTHING
+  end
   return out
 end, 1, 1, "<x-:a<s>>")
 
@@ -75,6 +78,11 @@ R.spread = H.def(function(x)
         spread_obj(x[i])
       end
     end
+  else
+    return x -- scalar: jsonata functionSpread echoes the argument unchanged
+  end
+  if #out == 0 then
+    return V.NOTHING
   end
   return out
 end, 1, 1, "<x-:a<o>>")
diff --git a/src/jsonata/init.lua b/src/jsonata/init.lua
index 27aed2a..1c646db 100644
--- a/src/jsonata/init.lua
+++ b/src/jsonata/init.lua
@@ -69,6 +69,7 @@ function Expression:evaluate(input, bindings)
     env:bind("__explain_hook", self._explain_hook)
   end
   local internal_input = adapter.from_lua(input)
+  env:bind("$", internal_input)
   local result = Evaluator.evaluate(self.ast, internal_input, env)
   return adapter.to_lua(result)
 end