diff --git a/Kanban/Storage/Ranks.swift b/Kanban/Storage/Ranks.swift
new file mode 100644
index 0000000..7a2d6a0
--- /dev/null
+++ b/Kanban/Storage/Ranks.swift
@@ -0,0 +1,87 @@
+import Foundation
+
+/// Pure gapped-fractional-ordering math: append, insert, midpoint, and the
+/// renumber target, plus the display-order tie-break rule shared by the
+/// loader and the writer. No filesystem or model dependency — see
+/// DESIGN/01-storage-format.md § Ordering, Deletion.
+enum Ranks: Sendable {
+
+    /// Gap between successive ranks on append/head-insert, and the multiple
+    /// used by `renumbered(count:)`.
+    private static let gap: Double = 1024
+
+    // MARK: - Append / insert
+
+    /// Rank for a new item appended after all visible siblings.
+    /// An empty lane's first item lands at `1024` (the board convention).
+    static func append(toVisible orders: some Sequence<Double>) -> Double {
+        (orders.max() ?? 0) + gap
+    }
+
+    /// Rank for a new item inserted before all visible siblings.
+    /// An empty lane's first item lands at `1024` (the board convention).
+    static func insertAtHead(ofVisible orders: some Sequence<Double>) -> Double {
+        guard let minOrder = orders.min() else { return gap }
+        return minOrder - gap
+    }
+
+    /// Rank strictly between `a` and `b`, or `nil` if no `Double` is
+    /// representable between them — including when `a == b` (a duplicate
+    /// order, the tie case). Never returns a value ≤ min(a, b) or
+    /// ≥ max(a, b).
+    static func midpoint(between a: Double, and b: Double) -> Double? {
+        let lower = min(a, b)
+        let upper = max(a, b)
+        guard lower < upper else { return nil }
+        let mid = lower + (upper - lower) / 2
+        guard mid > lower, mid < upper else { return nil }
+        return mid
+    }
+
+    /// `count` fresh ranks, whole multiples of 1024 in ascending order
+    /// (1024, 2048, …) — the renumber target when midpoint precision is
+    /// exhausted. Deterministic by construction; the writer applies these,
+    /// in order, to the current visible siblings in display order.
+    static func renumbered(count: Int) -> [Double] {
+        guard count > 0 else { return [] }
+        return (1...count).map { Double($0) * gap }
+    }
+
+    // MARK: - Display order
+
+    /// Ascending display order: primary key `order`, ties broken by folder
+    /// name (lexicographic) for deterministic rendering. Shared by the
+    /// loader and the writer so both apply the same tie-break rule.
+    static func isOrderedForDisplay<T>(
+        _ lhs: T, before rhs: T,
+        order: (T) -> Double, name: (T) -> String
+    ) -> Bool {
+        let lhsOrder = order(lhs)
+        let rhsOrder = order(rhs)
+        return lhsOrder != rhsOrder ? lhsOrder < rhsOrder : name(lhs) < name(rhs)
+    }
+
+    /// Sorts siblings into display order — ascending `order`, ties broken by
+    /// folder name.
+    static func sortedForDisplay<T>(
+        _ items: [T],
+        order: (T) -> Double,
+        name: (T) -> String
+    ) -> [T] {
+        items.sorted { isOrderedForDisplay($0, before: $1, order: order, name: name) }
+    }
+
+    // MARK: - Tombstone exclusion
+
+    /// `append(toVisible:)`, ignoring tombstoned siblings. Tombstones are
+    /// inert to ordering — appends operate on visible siblings only.
+    static func append(toVisible items: some Sequence<(order: Double, isDeleted: Bool)>) -> Double {
+        append(toVisible: items.filter { !$0.isDeleted }.map { $0.order })
+    }
+
+    /// `insertAtHead(ofVisible:)`, ignoring tombstoned siblings. Tombstones
+    /// are inert to ordering — inserts operate on visible siblings only.
+    static func insertAtHead(ofVisible items: some Sequence<(order: Double, isDeleted: Bool)>) -> Double {
+        insertAtHead(ofVisible: items.filter { !$0.isDeleted }.map { $0.order })
+    }
+}
diff --git a/KanbanTests/RanksTests.swift b/KanbanTests/RanksTests.swift
new file mode 100644
index 0000000..544d4a1
--- /dev/null
+++ b/KanbanTests/RanksTests.swift
@@ -0,0 +1,158 @@
+import Testing
+@testable import Kanban
+
+struct RanksTests {
+
+    // MARK: - Append
+
+    @Test func appendOnEmptyLaneReturnsBoardConvention() {
+        #expect(Ranks.append(toVisible: [Double]()) == 1024)
+    }
+
+    @Test func appendReturnsMaxPlusGap() {
+        #expect(Ranks.append(toVisible: [1024, 2048, 512]) == 3072)
+    }
+
+    // MARK: - Insert at head
+
+    @Test func insertAtHeadOnEmptyLaneReturnsBoardConvention() {
+        #expect(Ranks.insertAtHead(ofVisible: [Double]()) == 1024)
+    }
+
+    @Test func insertAtHeadReturnsMinMinusGap() {
+        #expect(Ranks.insertAtHead(ofVisible: [1024, 2048, 512]) == -512)
+    }
+
+    // MARK: - Midpoint
+
+    @Test func midpointBetweenDistinctValuesIsStrictlyBetween() throws {
+        let mid = try #require(Ranks.midpoint(between: 1024, and: 2048))
+        #expect(mid == 1536)
+        #expect(mid > 1024 && mid < 2048)
+    }
+
+    @Test func midpointIsOrderIndependent() {
+        let forward = Ranks.midpoint(between: 1024, and: 2048)
+        let reversed = Ranks.midpoint(between: 2048, and: 1024)
+        #expect(forward == reversed)
+    }
+
+    @Test func midpointBetweenEqualValuesReturnsNil() {
+        #expect(Ranks.midpoint(between: 42, and: 42) == nil)
+    }
+
+    @Test func midpointNeverEscapesTheOpenInterval() {
+        // Values close enough that a naive (a+b)/2 could round to one of the
+        // endpoints; the result (if any) must stay strictly inside.
+        let a = 1.0
+        let b = 1.0.nextUp.nextUp.nextUp
+        if let mid = Ranks.midpoint(between: a, and: b) {
+            #expect(mid > a && mid < b)
+        }
+    }
+
+    // MARK: - Renumbered
+
+    @Test func renumberedProducesWholeMultiplesOf1024() {
+        #expect(Ranks.renumbered(count: 4) == [1024, 2048, 3072, 4096])
+    }
+
+    @Test func renumberedWithZeroCountIsEmpty() {
+        #expect(Ranks.renumbered(count: 0) == [])
+    }
+
+    // MARK: - Display order / tie-break
+
+    @Test func sortedForDisplayOrdersAscendingByRank() {
+        let items: [(order: Double, name: String)] = [
+            (order: 3072, name: "c-card"),
+            (order: 1024, name: "a-card"),
+            (order: 2048, name: "b-card"),
+        ]
+        let sorted = Ranks.sortedForDisplay(items, order: { $0.order }, name: { $0.name })
+        #expect(sorted.map { $0.name } == ["a-card", "b-card", "c-card"])
+    }
+
+    @Test func sortedForDisplayBreaksTiesByFolderName() {
+        let items: [(order: Double, name: String)] = [
+            (order: 1024, name: "zzz-uuid"),
+            (order: 1024, name: "aaa-uuid"),
+            (order: 1024, name: "mmm-uuid"),
+        ]
+        let sorted = Ranks.sortedForDisplay(items, order: { $0.order }, name: { $0.name })
+        #expect(sorted.map { $0.name } == ["aaa-uuid", "mmm-uuid", "zzz-uuid"])
+    }
+
+    @Test func isOrderedForDisplayMatchesSortedForDisplay() {
+        let a: (order: Double, name: String) = (order: 1024, name: "aaa")
+        let b: (order: Double, name: String) = (order: 1024, name: "bbb")
+        #expect(Ranks.isOrderedForDisplay(a, before: b, order: { $0.order }, name: { $0.name }))
+        #expect(!Ranks.isOrderedForDisplay(b, before: a, order: { $0.order }, name: { $0.name }))
+    }
+
+    // MARK: - Tombstone exclusion
+
+    @Test func appendIgnoresTombstonedSiblings() {
+        let items: [(order: Double, isDeleted: Bool)] = [
+            (order: 1024, isDeleted: false),
+            (order: 9999, isDeleted: true),
+            (order: 2048, isDeleted: false),
+        ]
+        #expect(Ranks.append(toVisible: items) == 3072)
+    }
+
+    @Test func insertAtHeadIgnoresTombstonedSiblings() {
+        let items: [(order: Double, isDeleted: Bool)] = [
+            (order: 1024, isDeleted: false),
+            (order: -9999, isDeleted: true),
+            (order: 2048, isDeleted: false),
+        ]
+        #expect(Ranks.insertAtHead(ofVisible: items) == 0)
+    }
+
+    @Test func appendWithAllSiblingsTombstonedReturnsBoardConvention() {
+        let items: [(order: Double, isDeleted: Bool)] = [
+            (order: 1024, isDeleted: true),
+            (order: 2048, isDeleted: true),
+        ]
+        #expect(Ranks.append(toVisible: items) == 1024)
+    }
+
+    @Test func insertAtHeadWithAllSiblingsTombstonedReturnsBoardConvention() {
+        let items: [(order: Double, isDeleted: Bool)] = [
+            (order: 1024, isDeleted: true),
+            (order: 2048, isDeleted: true),
+        ]
+        #expect(Ranks.insertAtHead(ofVisible: items) == 1024)
+    }
+
+    // MARK: - Precision exhaustion → renumber, deterministically
+
+    @Test func precisionExhaustionThenRenumberIsDeterministic() {
+        func runScenario() -> (iterations: Int, renumbered: [Double]) {
+            let lower = 1024.0
+            var upper = 2048.0
+            var iterations = 0
+            let iterationCap = 4000
+            while iterations < iterationCap, let mid = Ranks.midpoint(between: lower, and: upper) {
+                upper = mid
+                iterations += 1
+            }
+            return (iterations, Ranks.renumbered(count: 5))
+        }
+
+        let first = runScenario()
+        let second = runScenario()
+
+        // Precision must actually have been exhausted, not just hit the cap.
+        #expect(first.iterations > 0)
+        #expect(first.iterations < 4000)
+
+        // Same scenario, run twice, must produce bit-identical results.
+        #expect(first.iterations == second.iterations)
+        #expect(first.renumbered == second.renumbered)
+
+        // Renumbering yields clean whole multiples of 1024.
+        #expect(first.renumbered == [1024, 2048, 3072, 4096, 5120])
+    }
+}