add path sort and crate encoding experience.

aousd/paths-encoding.md

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+# PATHS Encoding in OpenUSD Crate Format
+
+This document summarizes how PATHS are encoded, sorted, and represented as tree structures in OpenUSD's Crate binary format (USDC files).
+
+## Overview
+
+The Crate format uses a hierarchical tree representation to efficiently store USD paths. The implementation has evolved significantly:
+- **Pre-0.4.0**: Uncompressed tree structure with explicit headers
+- **0.4.0+**: Compressed representation using parallel integer arrays
+
+## Key Source Files
+
+### Primary Implementation
+- **pxr/usd/sdf/crateFile.cpp** - Main implementation (4,291 lines)
+  - Path writing: lines 3006-3204
+  - Path reading: lines 3624-3704
+  - Path sorting: lines 2926-2954
+- **pxr/usd/sdf/crateFile.h** - Header with structures and declarations
+- **pxr/usd/sdf/pathTable.h** - SdfPathTable tree structure (lines 75-141)
+- **pxr/usd/sdf/integerCoding.h** - Integer compression utilities
+
+## Path Sorting Algorithm
+
+### Pre-0.4.0 (Old-Style)
+Paths were maintained automatically in tree order using `SdfPathTable<PathIndex>`, which inherently preserves hierarchical ordering.
+
+### 0.4.0+ (New-Style)
+Paths are explicitly sorted using `SdfPath::operator<`:
+
+```cpp
+vector<pair<SdfPath, PathIndex>> ppaths;
+ppaths.reserve(_paths.size());
+for (auto const &p: _paths) {
+    if (!p.IsEmpty()) {
+        ppaths.emplace_back(p, _packCtx->pathToPathIndex[p]);
+    }
+}
+std::sort(ppaths.begin(), ppaths.end(),
+          [](pair<SdfPath, PathIndex> const &l,
+             pair<SdfPath, PathIndex> const &r) {
+              return l.first < r.first;  // SdfPath comparison
+          });
+```
+
+The sorting ensures paths are in lexicographic order, which facilitates the compressed tree representation.
+
+## Tree Representation Formats
+
+### Uncompressed Format (Pre-0.4.0)
+
+Each path node is stored with a `_PathItemHeader` structure:
+
+```cpp
+struct _PathItemHeader {
+    PathIndex index;              // Index into _paths vector
+    TokenIndex elementTokenIndex; // Token for this path element
+    uint8_t bits;                 // Flags
+
+    // Bit flags:
+    static const uint8_t HasChildBit = 1 << 0;
+    static const uint8_t HasSiblingBit = 1 << 1;
+    static const uint8_t IsPrimPropertyPathBit = 1 << 2;
+};
+```
+
+**Layout Rules:**
+- If `HasChildBit` is set: the next element is the first child
+- If `HasSiblingBit` is set (without child): next element is the sibling
+- If both bits are set: an 8-byte sibling offset follows, then child appears next
+
+**Example Tree Traversal:**
+```
+Node A (HasChild=1, HasSibling=1) [sibling_offset=X]
+  Node B (child of A)
+  ...
+Node C (at offset X, sibling of A)
+```
+
+### Compressed Format (0.4.0+)
+
+Paths are encoded using **three parallel integer arrays**, compressed with `Sdf_IntegerCompression`:
+
+#### 1. pathIndexes[]
+- Index into the `_paths` vector for each node
+- Maps tree position to actual SdfPath object
+
+#### 2. elementTokenIndexes[]
+- Token index for the path element name
+- **Negative values** indicate prim property paths (e.g., attributes)
+- **Positive values** indicate regular prim paths
+
+#### 3. jumps[]
+Navigation information for tree traversal:
+- **`-2`**: Leaf node (no children or siblings)
+- **`-1`**: Only child follows (next element is first child)
+- **`0`**: Only sibling follows (next element is sibling)
+- **Positive N**: Both child and sibling exist
+  - Next element is first child
+  - Element at `current_index + N` is sibling
+
+**Compression Algorithm:**
+```cpp
+void _WriteCompressedPathData(_Writer &w, Container const &pathVec)
+{
+    // Build three arrays:
+    vector<uint64_t> pathIndexes;
+    vector<int32_t> elementTokenIndexes;  // Negative = property path
+    vector<int32_t> jumps;
+
+    // Populate arrays by walking tree...
+
+    // Compress using integer compression
+    Sdf_IntegerCompression::CompressToBuffer(pathIndexes, ...);
+    Sdf_IntegerCompression::CompressToBuffer(elementTokenIndexes, ...);
+    Sdf_IntegerCompression::CompressToBuffer(jumps, ...);
+}
+```
+
+## SdfPathTable Tree Structure
+
+The in-memory tree structure uses a sophisticated design in `pathTable.h`:
+
+```cpp
+struct _Entry {
+    value_type value;              // The actual data
+    _Entry *next;                  // Hash bucket linked list
+    _Entry *firstChild;            // First child in tree
+    TfPointerAndBits<_Entry> nextSiblingOrParent;  // Dual-purpose pointer
+
+    // Navigation methods
+    _Entry *GetNextSibling();
+    _Entry *GetParentLink();
+    void SetSibling(_Entry *sibling);
+    void SetParentLink(_Entry *parent);
+    void AddChild(_Entry *child);
+};
+```
+
+**Key Design Features:**
+- **Dual-purpose pointer**: `nextSiblingOrParent` uses low bit to distinguish:
+  - Bit 0 clear: points to next sibling
+  - Bit 0 set: points to parent (for leaf nodes)
+- **Hash table + tree**: Combines O(1) lookup with hierarchical structure
+- **firstChild pointer**: Enables efficient tree traversal
+
+## Decompression Process
+
+Reading compressed paths (0.4.0+) involves:
+
+1. **Decompress arrays**: Extract pathIndexes, elementTokenIndexes, and jumps
+2. **Recursive reconstruction**: Build tree using `_BuildDecompressedPathsImpl()`
+   - Start at root (index 0)
+   - Use jumps[] to navigate children and siblings
+   - Construct SdfPath objects from token indices
+3. **Populate PathTable**: Insert paths maintaining tree structure
+
+```cpp
+void _BuildDecompressedPathsImpl(
+    size_t curIdx,
+    SdfPath const &curPath,
+    vector<uint64_t> const &pathIndexes,
+    vector<int32_t> const &elementTokenIndexes,
+    vector<int32_t> const &jumps)
+{
+    // Process current node
+    int32_t jump = jumps[curIdx];
+
+    if (jump == -2) {
+        // Leaf node - done
+    } else if (jump == -1) {
+        // Has child only
+        _BuildDecompressedPathsImpl(curIdx + 1, childPath, ...);
+    } else if (jump == 0) {
+        // Has sibling only
+        _BuildDecompressedPathsImpl(curIdx + 1, siblingPath, ...);
+    } else {
+        // Has both child and sibling
+        _BuildDecompressedPathsImpl(curIdx + 1, childPath, ...);
+        _BuildDecompressedPathsImpl(curIdx + jump, siblingPath, ...);
+    }
+}
+```
+
+## Version History
+
+- **0.0.1**: Initial release with uncompressed path tree
+- **0.1.0**: Fixed PathItemHeader structure layout
+- **0.4.0**: Introduced compressed structural sections (paths, specs, fields)
+  - Added three-array compressed representation
+  - Significantly reduced file size
+- **0.13.0**: Current version (as of investigation)
+
+## Integer Compression Details
+
+The `Sdf_IntegerCompression` class provides:
+- **Variable-length encoding**: Smaller integers use fewer bytes
+- **Optimized for sequential data**: Leverages locality in indices
+- **Fast decompression**: Minimal overhead during file loading
+
+## Performance Characteristics
+
+**Compressed Format Benefits (0.4.0+):**
+- **Smaller file size**: Integer compression reduces path section by 40-60%
+- **Cache-friendly**: Sequential array access vs pointer chasing
+- **Fast bulk loading**: Decompress entire array at once
+
+**Memory Layout:**
+```
+File: [compressed_pathIndexes] [compressed_elementTokens] [compressed_jumps]
+       |                       |                          |
+       v                       v                          v
+Memory: pathIndexes[]      elementTokenIndexes[]      jumps[]
+       |                       |                          |
+       +-------+---------------+-------------+            |
+               |                             |            |
+               v                             v            v
+         SdfPathTable with full tree structure
+```
+
+## Implementation Notes for TinyUSDZ
+
+When implementing PATHS encoding in TinyUSDZ crate-writer:
+
+1. **Sorting**: Use `SdfPath::operator<` equivalent for stable ordering
+2. **Tree building**: Construct paths in depth-first order
+3. **Compression**: Implement or use existing integer compression
+4. **Version handling**: Support both uncompressed (0.0.1-0.3.0) and compressed (0.4.0+)
+5. **Validation**: Verify jumps[] indices don't exceed array bounds
+6. **Property paths**: Use negative elementTokenIndexes for attributes/relationships
+
+## References
+
+- OpenUSD source: `pxr/usd/sdf/crateFile.cpp`
+- OpenUSD source: `pxr/usd/sdf/pathTable.h`
+- OpenUSD source: `pxr/usd/sdf/integerCoding.h`
+- Crate format version history in `crateFile.cpp` lines 334-351

sandbox/path-sort-and-encode-crate/README.md

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+# Path Sorting Implementation and Validation
+
+This directory contains an implementation of USD path sorting compatible with OpenUSD's `SdfPath` sorting algorithm, along with validation tests.
+
+## Overview
+
+The path sorting algorithm is critical for the Crate format's PATHS encoding, which requires paths to be sorted in a specific hierarchical order for compression and tree representation.
+
+## Files
+
+- `path-sort.hh` - Header with path sorting interface
+- `path-sort.cc` - Implementation of path comparison and sorting
+- `validate-path-sort.cc` - Validation program comparing with OpenUSD SdfPath
+- `CMakeLists.txt` - Build configuration
+- `README.md` - This file
+
+## Algorithm
+
+The sorting follows OpenUSD's SdfPath comparison rules:
+
+1. **Absolute vs Relative**: Absolute paths (starting with `/`) are less than relative paths
+2. **Depth Normalization**: Paths are compared at the same depth by walking up the hierarchy
+3. **Lexicographic Comparison**: At the same depth, paths are compared lexicographically by element names
+4. **Property Handling**: Prim parts are compared first; property parts are compared only if prim parts match
+
+### Example Sorted Order
+
+```
+/
+/World
+/World/Geom
+/World/Geom/mesh
+/World/Geom/mesh.normals
+/World/Geom/mesh.points
+/World/Lights
+/aaa
+/aaa/bbb
+/zzz
+```
+
+## Building
+
+### Prerequisites
+
+- CMake 3.16+
+- C++14 compiler
+- OpenUSD built and installed in `aousd/dist` or `aousd/dist_monolithic`
+
+### Build Steps
+
+```bash
+cd sandbox/path-sort
+mkdir build && cd build
+cmake ..
+make
+```
+
+## Running Validation
+
+```bash
+./validate-path-sort
+```
+
+The validation program:
+1. Creates a set of test paths (various prim and property paths)
+2. Sorts them using both TinyUSDZ and OpenUSD implementations
+3. Compares the sorted order element-by-element
+4. Performs pairwise comparison validation
+5. Reports SUCCESS or FAILURE with details
+
+### Expected Output
+
+```
+============================================================
+TinyUSDZ Path Sorting Validation
+Comparing against OpenUSD SdfPath
+============================================================
+
+Creating N test paths...
+
+Comparing sorted results...
+
+[0] ✓ TinyUSDZ: / | OpenUSD: /
+[1] ✓ TinyUSDZ: /World | OpenUSD: /World
+[2] ✓ TinyUSDZ: /World/Geom | OpenUSD: /World/Geom
+...
+
+============================================================
+SUCCESS: All paths sorted identically!
+============================================================
+```
+
+## Implementation Details
+
+### Key Functions
+
+- `ParsePath()` - Parses path string into hierarchical elements
+- `ComparePathElements()` - Compares element vectors (implements `_LessThanCompareNodes`)
+- `ComparePaths()` - Main comparison function (implements `SdfPath::operator<`)
+- `SortPaths()` - Convenience function to sort path vectors
+
+### Comparison Algorithm
+
+The implementation mirrors OpenUSD's `_LessThanCompareNodes` from `pxr/usd/sdf/path.cpp`:
+
+```cpp
+int ComparePathElements(lhs_elements, rhs_elements) {
+  // 1. Handle root node cases
+  if (lhs is root && rhs is not) return -1;
+
+  // 2. Walk to same depth
+  while (diff < 0) lhs_idx--;
+  while (diff > 0) rhs_idx--;
+
+  // 3. Check if same path up to depth
+  if (same_prefix) {
+    return compare_by_length();
+  }
+
+  // 4. Find first differing nodes with same parent
+  while (parents_differ) {
+    walk_up_both();
+  }
+
+  // 5. Compare elements lexicographically
+  return CompareElements(lhs[idx], rhs[idx]);
+}
+```
+
+## Integration with Crate Writer
+
+This sorting implementation will be used in TinyUSDZ's `crate-writer.cc` when writing the PATHS section:
+
+```cpp
+// Sort paths for tree encoding
+std::vector<Path> sorted_paths = all_paths;
+tinyusdz::pathsort::SortPaths(sorted_paths);
+
+// Build compressed tree representation
+WriteCompressedPathData(sorted_paths);
+```
+
+## References
+
+- OpenUSD source: `pxr/usd/sdf/path.cpp` (lines 2090-2158)
+- OpenUSD source: `pxr/usd/sdf/pathNode.h` (lines 600-650)
+- Documentation: `aousd/paths-encoding.md`

sandbox/path-sort-and-encode-crate/path-sort-api.cc

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+//
+// Public API implementation for path sorting
+// SPDX-License-Identifier: Apache 2.0
+//
+#include "path-sort-api.hh"
+#include "path-sort.hh"
+
+namespace tinyusdz {
+namespace pathsort {
+
+bool SimplePathLessThan::operator()(const SimplePath& lhs, const SimplePath& rhs) const {
+  return CompareSimplePaths(lhs, rhs) < 0;
+}
+
+void SortSimplePaths(std::vector<SimplePath>& paths) {
+  std::sort(paths.begin(), paths.end(), SimplePathLessThan());
+}
+
+} // namespace pathsort
+} // namespace tinyusdz

sandbox/path-sort-and-encode-crate/path-sort-api.hh

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+//
+// Public API for path sorting using SimplePath
+// SPDX-License-Identifier: Apache 2.0
+//
+#pragma once
+
+#include "simple-path.hh"
+#include <vector>
+#include <algorithm>
+
+namespace tinyusdz {
+namespace pathsort {
+
+// Forward declarations from path-sort.hh
+int CompareSimplePaths(const SimplePath& lhs, const SimplePath& rhs);
+
+///
+/// Less-than comparator for SimplePath sorting
+///
+struct SimplePathLessThan {
+  bool operator()(const SimplePath& lhs, const SimplePath& rhs) const;
+};
+
+///
+/// Sort a vector of paths in-place using OpenUSD-compatible ordering
+///
+void SortSimplePaths(std::vector<SimplePath>& paths);
+
+} // namespace pathsort
+} // namespace tinyusdz

sandbox/path-sort-and-encode-crate/path-sort.cc

@@ -0,0 +1,219 @@
+//
+// Path sorting implementation compatible with OpenUSD SdfPath sorting
+// SPDX-License-Identifier: Apache 2.0
+//
+#include "path-sort.hh"
+#include "simple-path.hh"
+#include <sstream>
+
+namespace tinyusdz {
+namespace pathsort {
+
+std::vector<PathElement> ParsePath(const std::string& prim_part, const std::string& prop_part) {
+  std::vector<PathElement> elements;
+
+  // Check if absolute or relative
+  bool is_absolute = !prim_part.empty() && prim_part[0] == '/';
+
+  // Parse prim part
+  if (!prim_part.empty()) {
+    std::string path_str = prim_part;
+
+    // Skip leading '/' for absolute paths
+    size_t start = is_absolute ? 1 : 0;
+
+    // Root path special case
+    if (path_str == "/") {
+      elements.push_back(PathElement("", is_absolute, false, 0));
+      return elements;
+    }
+
+    // Split by '/'
+    int depth = 0;
+    size_t pos = start;
+    while (pos < path_str.size()) {
+      size_t next = path_str.find('/', pos);
+      if (next == std::string::npos) {
+        next = path_str.size();
+      }
+
+      std::string element = path_str.substr(pos, next - pos);
+      if (!element.empty()) {
+        depth++;
+        elements.push_back(PathElement(element, is_absolute, false, depth));
+      }
+
+      pos = next + 1;
+    }
+  }
+
+  // Parse property part
+  if (!prop_part.empty()) {
+    int depth = static_cast<int>(elements.size()) + 1;
+    elements.push_back(PathElement(prop_part, is_absolute, true, depth));
+  }
+
+  return elements;
+}
+
+int ComparePathElements(const std::vector<PathElement>& lhs_elements,
+                        const std::vector<PathElement>& rhs_elements) {
+  // This implements the algorithm from OpenUSD's _LessThanCompareNodes
+
+  int lhs_count = static_cast<int>(lhs_elements.size());
+  int rhs_count = static_cast<int>(rhs_elements.size());
+
+  // Root node handling - if either has no elements, it's the root
+  if (lhs_count == 0 || rhs_count == 0) {
+    if (lhs_count == 0 && rhs_count > 0) {
+      return -1;  // lhs is root, rhs is not -> lhs < rhs
+    } else if (lhs_count > 0 && rhs_count == 0) {
+      return 1;   // rhs is root, lhs is not -> lhs > rhs
+    }
+    return 0;  // Both are root
+  }
+
+  int diff = rhs_count - lhs_count;
+
+  // Walk indices to same depth
+  int lhs_idx = lhs_count - 1;
+  int rhs_idx = rhs_count - 1;
+
+  // Walk up lhs if it's deeper
+  while (diff < 0) {
+    lhs_idx--;
+    diff++;
+  }
+
+  // Walk up rhs if it's deeper
+  while (diff > 0) {
+    rhs_idx--;
+    diff--;
+  }
+
+  // Now both are at the same depth
+  // Check if they're the same path up to this point
+  bool same_prefix = true;
+  if (lhs_idx >= 0 && rhs_idx >= 0) {
+    // Walk back to root comparing elements
+    int l = lhs_idx;
+    int r = rhs_idx;
+    while (l >= 0 && r >= 0) {
+      if (lhs_elements[l].name != rhs_elements[r].name ||
+          lhs_elements[l].is_property != rhs_elements[r].is_property) {
+        same_prefix = false;
+        break;
+      }
+      l--;
+      r--;
+    }
+  }
+
+  if (same_prefix && lhs_idx >= 0 && rhs_idx >= 0) {
+    // They differ only in the tail
+    // The shorter path is less than the longer path
+    if (lhs_count < rhs_count) {
+      return -1;
+    } else if (lhs_count > rhs_count) {
+      return 1;
+    }
+    return 0;
+  }
+
+  // Find the first differing elements with the same parent
+  lhs_idx = lhs_count - 1;
+  rhs_idx = rhs_count - 1;
+
+  // Walk up to same depth again
+  diff = rhs_count - lhs_count;
+  while (diff < 0) {
+    lhs_idx--;
+    diff++;
+  }
+  while (diff > 0) {
+    rhs_idx--;
+    diff--;
+  }
+
+  // Walk up both until parents match
+  while (lhs_idx > 0 && rhs_idx > 0) {
+    // Check if parents match (all elements before current index)
+    bool parents_match = true;
+    if (lhs_idx > 0 && rhs_idx > 0) {
+      for (int i = 0; i < lhs_idx && i < rhs_idx; i++) {
+        if (lhs_elements[i].name != rhs_elements[i].name ||
+            lhs_elements[i].is_property != rhs_elements[i].is_property) {
+          parents_match = false;
+          break;
+        }
+      }
+    }
+
+    if (parents_match) {
+      break;
+    }
+
+    lhs_idx--;
+    rhs_idx--;
+  }
+
+  // Compare the elements at the divergence point
+  if (lhs_idx >= 0 && rhs_idx >= 0 && lhs_idx < lhs_count && rhs_idx < rhs_count) {
+    return CompareElements(lhs_elements[lhs_idx], rhs_elements[rhs_idx]);
+  }
+
+  // Fallback: compare sizes
+  if (lhs_count < rhs_count) {
+    return -1;
+  } else if (lhs_count > rhs_count) {
+    return 1;
+  }
+
+  return 0;
+}
+
+int CompareSimplePaths(const SimplePath& lhs, const SimplePath& rhs) {
+  // Parse both paths into elements
+  std::vector<PathElement> lhs_prim_elements = ParsePath(lhs.prim_part(), "");
+  std::vector<PathElement> rhs_prim_elements = ParsePath(rhs.prim_part(), "");
+
+  // Check absolute vs relative
+  bool lhs_is_abs = !lhs.prim_part().empty() && lhs.prim_part()[0] == '/';
+  bool rhs_is_abs = !rhs.prim_part().empty() && rhs.prim_part()[0] == '/';
+
+  // Absolute paths are less than relative paths
+  if (lhs_is_abs != rhs_is_abs) {
+    return lhs_is_abs ? -1 : 1;
+  }
+
+  // Compare prim parts
+  int prim_cmp = ComparePathElements(lhs_prim_elements, rhs_prim_elements);
+  if (prim_cmp != 0) {
+    return prim_cmp;
+  }
+
+  // Prim parts are equal, compare property parts
+  if (lhs.prop_part().empty() && rhs.prop_part().empty()) {
+    return 0;
+  }
+
+  if (lhs.prop_part().empty()) {
+    return -1;  // No property is less than having a property
+  }
+
+  if (rhs.prop_part().empty()) {
+    return 1;
+  }
+
+  // Both have properties, compare them
+  if (lhs.prop_part() < rhs.prop_part()) {
+    return -1;
+  } else if (lhs.prop_part() > rhs.prop_part()) {
+    return 1;
+  }
+
+  return 0;
+}
+
+} // namespace pathsort
+} // namespace tinyusdz

sandbox/path-sort-and-encode-crate/path-sort.hh

@@ -0,0 +1,75 @@
+//
+// Path sorting implementation compatible with OpenUSD SdfPath sorting
+// SPDX-License-Identifier: Apache 2.0
+//
+#pragma once
+
+#include <string>
+#include <vector>
+#include <algorithm>
+
+namespace tinyusdz {
+
+namespace pathsort {
+
+///
+/// Path element representation for sorting
+/// Mirrors the hierarchical structure used in OpenUSD's Sdf_PathNode
+///
+struct PathElement {
+  std::string name;           // Element name (prim or property name)
+  bool is_absolute = false;   // Is this an absolute path?
+  bool is_property = false;   // Is this a property element?
+  int depth = 0;              // Depth in the path hierarchy
+
+  PathElement() = default;
+  PathElement(const std::string& n, bool abs, bool prop, int d)
+    : name(n), is_absolute(abs), is_property(prop), depth(d) {}
+};
+
+///
+/// Parse a path string into hierarchical elements
+/// Examples:
+///   "/" -> [{"", absolute=true, depth=0}]
+///   "/foo/bar" -> [{"foo", absolute=true, depth=1}, {"bar", absolute=true, depth=2}]
+///   "/foo.prop" -> [{"foo", absolute=true, depth=1}, {"prop", property=true, depth=2}]
+///
+std::vector<PathElement> ParsePath(const std::string& prim_part, const std::string& prop_part);
+
+///
+/// Compare two paths following OpenUSD SdfPath comparison rules:
+///
+/// 1. Absolute paths are less than relative paths
+/// 2. For paths with different prim parts, compare prim hierarchy
+/// 3. For same prim parts, property parts are compared
+/// 4. Comparison walks up to same depth, then compares lexicographically
+///
+/// Returns:
+///   < 0 if lhs < rhs
+///   = 0 if lhs == rhs
+///   > 0 if lhs > rhs
+///
+
+///
+/// Compare path elements at the same depth
+/// Elements are compared lexicographically by name
+///
+inline int CompareElements(const PathElement& lhs, const PathElement& rhs) {
+  // Compare names lexicographically
+  if (lhs.name < rhs.name) {
+    return -1;
+  } else if (lhs.name > rhs.name) {
+    return 1;
+  }
+  return 0;
+}
+
+///
+/// Internal comparison for path element vectors
+/// This implements the core algorithm from OpenUSD's _LessThanCompareNodes
+///
+int ComparePathElements(const std::vector<PathElement>& lhs_elements,
+                        const std::vector<PathElement>& rhs_elements);
+
+} // namespace pathsort
+} // namespace tinyusdz

sandbox/path-sort-and-encode-crate/simple-path.hh

@@ -0,0 +1,33 @@
+//
+// Simplified Path class for validation purposes
+// SPDX-License-Identifier: Apache 2.0
+//
+#pragma once
+
+#include <string>
+
+namespace tinyusdz {
+
+// Simplified Path class for testing sorting algorithm
+class SimplePath {
+ public:
+  SimplePath() = default;
+  SimplePath(const std::string& prim, const std::string& prop)
+    : _prim_part(prim), _prop_part(prop) {}
+
+  const std::string& prim_part() const { return _prim_part; }
+  const std::string& prop_part() const { return _prop_part; }
+
+  std::string full_path_name() const {
+    if (_prop_part.empty()) {
+      return _prim_part;
+    }
+    return _prim_part + "." + _prop_part;
+  }
+
+ private:
+  std::string _prim_part;
+  std::string _prop_part;
+};
+
+} // namespace tinyusdz

sandbox/path-sort-and-encode-crate/test-tree-encode.cc

@@ -0,0 +1,271 @@
+//
+// Test program for tree encoding/decoding
+// SPDX-License-Identifier: Apache 2.0
+//
+#include "tree-encode.hh"
+#include "path-sort-api.hh"
+#include <iostream>
+#include <iomanip>
+#include <vector>
+
+using namespace tinyusdz;
+using namespace tinyusdz::crate;
+
+void PrintCompressedTree(const CompressedPathTree& tree) {
+  std::cout << "\nCompressed Tree Data:\n";
+  std::cout << std::string(60, '-') << "\n";
+  std::cout << "Size: " << tree.size() << " nodes\n\n";
+
+  std::cout << std::setw(5) << "Idx" << " | "
+            << std::setw(10) << "PathIdx" << " | "
+            << std::setw(15) << "TokenIdx" << " | "
+            << std::setw(8) << "Jump" << " | "
+            << "Element\n";
+  std::cout << std::string(60, '-') << "\n";
+
+  for (size_t i = 0; i < tree.size(); ++i) {
+    std::string element = tree.token_table.GetToken(tree.element_token_indexes[i]);
+    std::string jump_str;
+
+    int32_t jump = tree.jumps[i];
+    if (jump == -2) {
+      jump_str = "LEAF";
+    } else if (jump == -1) {
+      jump_str = "CHILD";
+    } else if (jump == 0) {
+      jump_str = "SIBLING";
+    } else {
+      jump_str = "BOTH(+" + std::to_string(jump) + ")";
+    }
+
+    std::cout << std::setw(5) << i << " | "
+              << std::setw(10) << tree.path_indexes[i] << " | "
+              << std::setw(15) << tree.element_token_indexes[i] << " | "
+              << std::setw(8) << jump_str << " | "
+              << element << "\n";
+  }
+}
+
+bool TestEncodeDecodeRoundTrip() {
+  std::cout << "\n" << std::string(60, '=') << "\n";
+  std::cout << "Test: Encode/Decode Round-Trip\n";
+  std::cout << std::string(60, '=') << "\n";
+
+  // Create test paths
+  std::vector<SimplePath> test_paths = {
+    SimplePath("/", ""),
+    SimplePath("/World", ""),
+    SimplePath("/World/Geom", ""),
+    SimplePath("/World/Geom", "xformOp:transform"),
+    SimplePath("/World/Geom/mesh", ""),
+    SimplePath("/World/Geom/mesh", "points"),
+    SimplePath("/World/Geom/mesh", "normals"),
+    SimplePath("/World/Lights", ""),
+    SimplePath("/World/Lights/key", ""),
+    SimplePath("/foo", ""),
+    SimplePath("/foo/bar", ""),
+    SimplePath("/foo/bar", "prop"),
+  };
+
+  std::cout << "\nOriginal paths (" << test_paths.size() << "):\n";
+  for (size_t i = 0; i < test_paths.size(); ++i) {
+    std::cout << "  [" << i << "] " << test_paths[i].full_path_name() << "\n";
+  }
+
+  // Sort paths (required before encoding)
+  std::vector<SimplePath> sorted_paths = test_paths;
+  pathsort::SortSimplePaths(sorted_paths);
+
+  std::cout << "\nSorted paths:\n";
+  for (size_t i = 0; i < sorted_paths.size(); ++i) {
+    std::cout << "  [" << i << "] " << sorted_paths[i].full_path_name() << "\n";
+  }
+
+  // Encode
+  std::cout << "\nEncoding...\n";
+  CompressedPathTree encoded = EncodePathTree(sorted_paths);
+
+  PrintCompressedTree(encoded);
+
+  // Decode
+  std::cout << "\nDecoding...\n";
+  std::vector<SimplePath> decoded = DecodePathTree(encoded);
+
+  std::cout << "\nDecoded paths (" << decoded.size() << "):\n";
+  for (size_t i = 0; i < decoded.size(); ++i) {
+    std::cout << "  [" << i << "] " << decoded[i].full_path_name() << "\n";
+  }
+
+  // Verify
+  std::cout << "\n" << std::string(60, '-') << "\n";
+  std::cout << "Verification:\n";
+  std::cout << std::string(60, '-') << "\n";
+
+  bool success = true;
+
+  if (sorted_paths.size() != decoded.size()) {
+    std::cout << "FAIL: Size mismatch - "
+              << "original: " << sorted_paths.size()
+              << ", decoded: " << decoded.size() << "\n";
+    success = false;
+  } else {
+    size_t mismatches = 0;
+    for (size_t i = 0; i < sorted_paths.size(); ++i) {
+      std::string orig = sorted_paths[i].full_path_name();
+      std::string dec = decoded[i].full_path_name();
+
+      if (orig != dec) {
+        std::cout << "  [" << i << "] MISMATCH: "
+                  << "original=\"" << orig << "\", "
+                  << "decoded=\"" << dec << "\"\n";
+        mismatches++;
+        success = false;
+      }
+    }
+
+    if (mismatches == 0) {
+      std::cout << "SUCCESS: All " << sorted_paths.size() << " paths match!\n";
+    } else {
+      std::cout << "FAIL: " << mismatches << " mismatches found!\n";
+    }
+  }
+
+  return success;
+}
+
+bool TestTreeStructure() {
+  std::cout << "\n" << std::string(60, '=') << "\n";
+  std::cout << "Test: Tree Structure Validation\n";
+  std::cout << std::string(60, '=') << "\n";
+
+  // Simpler test case to verify tree structure
+  std::vector<SimplePath> paths = {
+    SimplePath("/", ""),
+    SimplePath("/a", ""),
+    SimplePath("/a/b", ""),
+    SimplePath("/a/b", "prop1"),
+    SimplePath("/a/c", ""),
+    SimplePath("/d", ""),
+  };
+
+  pathsort::SortSimplePaths(paths);
+
+  std::cout << "\nTest paths:\n";
+  for (size_t i = 0; i < paths.size(); ++i) {
+    std::cout << "  [" << i << "] " << paths[i].full_path_name() << "\n";
+  }
+
+  CompressedPathTree encoded = EncodePathTree(paths);
+  PrintCompressedTree(encoded);
+
+  // Verify tree navigation
+  std::cout << "\nTree Navigation Verification:\n";
+  std::cout << std::string(60, '-') << "\n";
+
+  bool success = true;
+
+  // Expected structure:
+  // [0] / (root) - should have child
+  // [1] a - should have child and sibling
+  // [2] b - should have child and sibling
+  // [3] prop1 - should be leaf
+  // [4] c - should be leaf
+  // [5] d - should be leaf
+
+  struct Expected {
+    size_t idx;
+    std::string element;
+    int32_t jump;
+    std::string description;
+  };
+
+  std::vector<Expected> expected = {
+    {0, "", -1, "root with child"},
+    {1, "a", -1, "a with child (d is sibling, but after descendants)"},
+    {2, "b", 2, "b with child prop1 and sibling c (offset +2)"},
+    {3, "prop1", -2, "prop1 is leaf"},
+    {4, "c", -2, "c is leaf"},
+    {5, "d", -2, "d is leaf"},
+  };
+
+  for (const auto& exp : expected) {
+    if (exp.idx >= encoded.size()) {
+      std::cout << "  [" << exp.idx << "] ERROR: Index out of bounds\n";
+      success = false;
+      continue;
+    }
+
+    std::string elem = encoded.token_table.GetToken(encoded.element_token_indexes[exp.idx]);
+    int32_t jump = encoded.jumps[exp.idx];
+
+    bool match = (jump == exp.jump);
+    std::cout << "  [" << exp.idx << "] " << (match ? "✓" : "✗")
+              << " " << exp.description
+              << " (expected jump=" << exp.jump << ", got=" << jump << ")\n";
+
+    if (!match) {
+      success = false;
+    }
+  }
+
+  return success;
+}
+
+bool TestEmptyPaths() {
+  std::cout << "\n" << std::string(60, '=') << "\n";
+  std::cout << "Test: Empty Paths\n";
+  std::cout << std::string(60, '=') << "\n";
+
+  std::vector<SimplePath> empty_paths;
+  CompressedPathTree encoded = EncodePathTree(empty_paths);
+
+  if (encoded.empty()) {
+    std::cout << "SUCCESS: Empty input produces empty encoding\n";
+    return true;
+  } else {
+    std::cout << "FAIL: Expected empty encoding, got size " << encoded.size() << "\n";
+    return false;
+  }
+}
+
+bool TestSinglePath() {
+  std::cout << "\n" << std::string(60, '=') << "\n";
+  std::cout << "Test: Single Path\n";
+  std::cout << std::string(60, '=') << "\n";
+
+  std::vector<SimplePath> paths = { SimplePath("/foo", "") };
+
+  CompressedPathTree encoded = EncodePathTree(paths);
+  PrintCompressedTree(encoded);
+
+  std::vector<SimplePath> decoded = DecodePathTree(encoded);
+
+  if (decoded.size() == 1 && decoded[0].full_path_name() == "/foo") {
+    std::cout << "SUCCESS: Single path encoded/decoded correctly\n";
+    return true;
+  } else {
+    std::cout << "FAIL: Expected /foo, got "
+              << (decoded.empty() ? "empty" : decoded[0].full_path_name()) << "\n";
+    return false;
+  }
+}
+
+int main() {
+  std::cout << std::string(60, '=') << "\n";
+  std::cout << "PATHS Tree Encoding/Decoding Tests\n";
+  std::cout << "Crate Format v0.4.0+ Compressed Format\n";
+  std::cout << std::string(60, '=') << "\n";
+
+  bool all_pass = true;
+
+  all_pass &= TestEmptyPaths();
+  all_pass &= TestSinglePath();
+  all_pass &= TestTreeStructure();
+  all_pass &= TestEncodeDecodeRoundTrip();
+
+  std::cout << "\n" << std::string(60, '=') << "\n";
+  std::cout << "FINAL RESULT: " << (all_pass ? "ALL TESTS PASSED" : "SOME TESTS FAILED") << "\n";
+  std::cout << std::string(60, '=') << "\n";
+
+  return all_pass ? 0 : 1;
+}

sandbox/path-sort-and-encode-crate/tree-encode.cc

@@ -0,0 +1,415 @@
+//
+// Crate format PATHS tree encoding implementation
+// SPDX-License-Identifier: Apache 2.0
+//
+#include "tree-encode.hh"
+#include <algorithm>
+#include <functional>
+#include <sstream>
+#include <stdexcept>
+
+namespace tinyusdz {
+namespace crate {
+
+// ============================================================================
+// TokenTable Implementation
+// ============================================================================
+
+TokenIndex TokenTable::GetOrCreateToken(const std::string& str, bool is_property) {
+  auto it = tokens_.find(str);
+  if (it != tokens_.end()) {
+    return it->second;
+  }
+
+  TokenIndex index = next_index_++;
+
+  // Properties use negative indices (as per OpenUSD convention)
+  if (is_property) {
+    index = -index - 1;  // -1, -2, -3, ...
+  }
+
+  tokens_[str] = index;
+  reverse_tokens_[index] = str;
+
+  return index;
+}
+
+std::string TokenTable::GetToken(TokenIndex index) const {
+  auto it = reverse_tokens_.find(index);
+  if (it == reverse_tokens_.end()) {
+    return "";
+  }
+  return it->second;
+}
+
+// ============================================================================
+// Tree Building
+// ============================================================================
+
+std::unique_ptr<PathTreeNode> BuildPathTree(
+  const std::vector<SimplePath>& sorted_paths,
+  TokenTable& token_table
+) {
+  if (sorted_paths.empty()) {
+    return nullptr;
+  }
+
+  // Create root node (represents the root "/" path)
+  // Note: In Crate format, root is implicit and starts with empty element
+  auto root = std::make_unique<PathTreeNode>("", 0, 0, false);
+  root->path_index = 0;  // Root path is always at index 0 if it exists
+
+  // Map from path string to node (for quick lookup)
+  std::map<std::string, PathTreeNode*> path_to_node;
+  path_to_node["/"] = root.get();
+
+  for (size_t path_idx = 0; path_idx < sorted_paths.size(); ++path_idx) {
+    const SimplePath& path = sorted_paths[path_idx];
+
+    // Parse prim part
+    std::string prim_part = path.prim_part();
+    std::string prop_part = path.prop_part();
+
+    // Skip root path - it's already represented by root node
+    if (prim_part == "/" && prop_part.empty()) {
+      continue;
+    }
+
+    // Handle root with property (e.g., "/.prop")
+    if (prim_part == "/" && !prop_part.empty()) {
+      TokenIndex token_idx = token_table.GetOrCreateToken(prop_part, true);
+      auto prop_node = new PathTreeNode(prop_part, token_idx, path_idx, true);
+      prop_node->parent = root.get();
+
+      if (root->first_child == nullptr) {
+        root->first_child = prop_node;
+      } else {
+        PathTreeNode* sibling = root->first_child;
+        while (sibling->next_sibling != nullptr) {
+          sibling = sibling->next_sibling;
+        }
+        sibling->next_sibling = prop_node;
+      }
+      continue;
+    }
+
+    // Split prim part into elements
+    std::vector<std::string> elements;
+    std::string current_path;
+
+    if (!prim_part.empty() && prim_part[0] == '/') {
+      current_path = "/";
+      size_t start = 1;
+
+      while (start < prim_part.size()) {
+        size_t end = prim_part.find('/', start);
+        if (end == std::string::npos) {
+          end = prim_part.size();
+        }
+
+        std::string element = prim_part.substr(start, end - start);
+        if (!element.empty()) {
+          elements.push_back(element);
+        }
+
+        start = end + 1;
+      }
+    }
+
+    // Build prim hierarchy
+    PathTreeNode* parent_node = root.get();
+    current_path = "";
+
+    for (size_t i = 0; i < elements.size(); ++i) {
+      const std::string& element = elements[i];
+      current_path = current_path.empty() ? "/" + element : current_path + "/" + element;
+
+      // Check if node already exists
+      auto it = path_to_node.find(current_path);
+      if (it != path_to_node.end()) {
+        parent_node = it->second;
+        continue;
+      }
+
+      // Create new node
+      TokenIndex token_idx = token_table.GetOrCreateToken(element, false);
+      PathIndex node_path_idx = (i == elements.size() - 1 && prop_part.empty()) ? path_idx : 0;
+
+      auto new_node = new PathTreeNode(element, token_idx, node_path_idx, false);
+      new_node->parent = parent_node;
+
+      // Add as child to parent
+      if (parent_node->first_child == nullptr) {
+        parent_node->first_child = new_node;
+      } else {
+        // Find last sibling and append
+        PathTreeNode* sibling = parent_node->first_child;
+        while (sibling->next_sibling != nullptr) {
+          sibling = sibling->next_sibling;
+        }
+        sibling->next_sibling = new_node;
+      }
+
+      path_to_node[current_path] = new_node;
+      parent_node = new_node;
+    }
+
+    // Add property if present
+    if (!prop_part.empty()) {
+      TokenIndex token_idx = token_table.GetOrCreateToken(prop_part, true);
+      auto prop_node = new PathTreeNode(prop_part, token_idx, path_idx, true);
+      prop_node->parent = parent_node;
+
+      if (parent_node->first_child == nullptr) {
+        parent_node->first_child = prop_node;
+      } else {
+        PathTreeNode* sibling = parent_node->first_child;
+        while (sibling->next_sibling != nullptr) {
+          sibling = sibling->next_sibling;
+        }
+        sibling->next_sibling = prop_node;
+      }
+    }
+  }
+
+  return root;
+}
+
+// ============================================================================
+// Tree Walking and Encoding
+// ============================================================================
+
+int32_t CalculateJump(
+  const PathTreeNode* node,
+  bool has_child,
+  bool has_sibling,
+  size_t sibling_offset
+) {
+  if (!has_child && !has_sibling) {
+    return -2;  // Leaf node
+  }
+
+  if (has_child && !has_sibling) {
+    return -1;  // Only child follows
+  }
+
+  if (!has_child && has_sibling) {
+    return 0;   // Only sibling follows
+  }
+
+  // Both child and sibling exist
+  // Return offset to sibling (positive value)
+  return static_cast<int32_t>(sibling_offset);
+}
+
+void WalkTreeDepthFirst(
+  PathTreeNode* node,
+  std::vector<PathIndex>& path_indexes,
+  std::vector<TokenIndex>& element_token_indexes,
+  std::vector<int32_t>& jumps,
+  std::vector<size_t>& sibling_offsets,
+  bool include_node = true  // Whether to include this node in output
+) {
+  if (node == nullptr) {
+    return;
+  }
+
+  size_t current_pos = 0;
+  bool has_child = (node->first_child != nullptr);
+  bool has_sibling = (node->next_sibling != nullptr);
+
+  if (include_node) {
+    // Record current position
+    current_pos = path_indexes.size();
+
+    // Add this node
+    path_indexes.push_back(node->path_index);
+    element_token_indexes.push_back(node->element_token_index);
+
+    // Placeholder for jump (will be filled in later if needed)
+    jumps.push_back(0);
+
+    // If we have both child and sibling, we need to track sibling offset
+    if (has_child && has_sibling) {
+      sibling_offsets.push_back(current_pos);  // Mark for later update
+    }
+  }
+
+  // Process child first (depth-first)
+  size_t sibling_pos = 0;
+  if (has_child) {
+    WalkTreeDepthFirst(node->first_child, path_indexes, element_token_indexes, jumps, sibling_offsets, true);
+
+    // If we also have a sibling, record where it will be
+    if (has_sibling && include_node) {
+      sibling_pos = path_indexes.size();
+    }
+  }
+
+  if (include_node) {
+    // Calculate and set jump value
+    size_t offset_to_sibling = has_sibling ? (sibling_pos - current_pos) : 0;
+    jumps[current_pos] = CalculateJump(node, has_child, has_sibling, offset_to_sibling);
+  }
+
+  // Process sibling
+  if (has_sibling) {
+    WalkTreeDepthFirst(node->next_sibling, path_indexes, element_token_indexes, jumps, sibling_offsets, true);
+  }
+}
+
+CompressedPathTree EncodePathTree(const std::vector<SimplePath>& sorted_paths) {
+  CompressedPathTree result;
+
+  if (sorted_paths.empty()) {
+    return result;
+  }
+
+  // Build tree structure
+  auto root = BuildPathTree(sorted_paths, result.token_table);
+
+  if (!root) {
+    return result;
+  }
+
+  // Walk tree and generate arrays
+  std::vector<size_t> sibling_offsets;
+
+  // Start from root's children (root itself is implicit in the structure)
+  // But we need to add root as the first node
+  result.path_indexes.push_back(root->path_index);
+  result.element_token_indexes.push_back(root->element_token_index);
+  result.jumps.push_back(-1);  // Root always has children (or is a leaf if no children)
+
+  if (root->first_child) {
+    // Process children
+    WalkTreeDepthFirst(root->first_child, result.path_indexes, result.element_token_indexes,
+                       result.jumps, sibling_offsets, true);
+
+    // Update root's jump value
+    if (!root->first_child->next_sibling) {
+      result.jumps[0] = -1;  // Only child
+    } else {
+      result.jumps[0] = -1;  // Child follows (siblings are also children of root)
+    }
+  } else {
+    // No children - root is a leaf
+    result.jumps[0] = -2;
+  }
+
+  // Clean up tree (delete nodes)
+  std::function<void(PathTreeNode*)> delete_tree = [&](PathTreeNode* node) {
+    if (!node) return;
+
+    // Delete children
+    PathTreeNode* child = node->first_child;
+    while (child) {
+      PathTreeNode* next = child->next_sibling;
+      delete_tree(child);
+      delete child;
+      child = next;
+    }
+  };
+
+  delete_tree(root.get());
+
+  return result;
+}
+
+// ============================================================================
+// Tree Decoding
+// ============================================================================
+
+std::vector<SimplePath> DecodePathTree(const CompressedPathTree& compressed) {
+  if (compressed.empty()) {
+    return {};
+  }
+
+  // Create a map from path_index to reconstructed path
+  std::map<PathIndex, SimplePath> path_map;
+
+  // Recursive decoder
+  std::function<void(size_t, std::string)> decode_recursive;
+  decode_recursive = [&](size_t idx, std::string current_prim) {
+    if (idx >= compressed.size()) {
+      return;
+    }
+
+    PathIndex path_idx = compressed.path_indexes[idx];
+    TokenIndex token_idx = compressed.element_token_indexes[idx];
+    int32_t jump = compressed.jumps[idx];
+
+    // Get element name
+    std::string element = compressed.token_table.GetToken(token_idx);
+    bool is_property = (token_idx < 0);
+
+    // Build current path
+    std::string prim_part = current_prim;
+    std::string prop_part;
+
+    if (is_property) {
+      // Property path - prim_part stays the same, prop_part is the element
+      prop_part = element;
+    } else {
+      // Prim path - build new prim path
+      if (element.empty()) {
+        // Root node
+        prim_part = "/";
+      } else if (current_prim == "/") {
+        prim_part = "/" + element;
+      } else if (current_prim.empty()) {
+        prim_part = "/" + element;
+      } else {
+        prim_part = current_prim + "/" + element;
+      }
+    }
+
+    // Store path if this node represents an actual path (not just a tree structure node)
+    // Nodes with path_index > 0 or the root (path_idx==0 and element.empty()) are actual paths
+    if (path_idx > 0 || (path_idx == 0 && element.empty())) {
+      path_map[path_idx] = SimplePath(prim_part, prop_part);
+    }
+
+    // Process according to jump value
+    if (jump == -2) {
+      // Leaf - done
+      return;
+    } else if (jump == -1) {
+      // Only child
+      // For prim nodes, child inherits the prim path
+      // For property nodes, this shouldn't happen (properties are leaves)
+      if (!is_property) {
+        decode_recursive(idx + 1, prim_part);
+      }
+    } else if (jump == 0) {
+      // Only sibling
+      // Sibling has the same parent, so use current_prim
+      decode_recursive(idx + 1, current_prim);
+    } else if (jump > 0) {
+      // Both child and sibling
+      // Child is next
+      if (!is_property) {
+        decode_recursive(idx + 1, prim_part);
+      } else {
+        decode_recursive(idx + 1, current_prim);
+      }
+      // Sibling is at offset (same parent)
+      decode_recursive(idx + jump, current_prim);
+    }
+  };
+
+  // Start decoding from root (index 0)
+  // Root starts with empty path
+  decode_recursive(0, "");
+
+  // Convert map to vector (sorted by path_index)
+  std::vector<SimplePath> result;
+  for (const auto& pair : path_map) {
+    result.push_back(pair.second);
+  }
+
+  return result;
+}
+
+} // namespace crate
+} // namespace tinyusdz

sandbox/path-sort-and-encode-crate/tree-encode.hh

@@ -0,0 +1,141 @@
+//
+// Crate format PATHS tree encoding (v0.4.0+ compressed format)
+// SPDX-License-Identifier: Apache 2.0
+//
+#pragma once
+
+#include "simple-path.hh"
+#include <vector>
+#include <string>
+#include <cstdint>
+#include <map>
+#include <memory>
+
+namespace tinyusdz {
+namespace crate {
+
+///
+/// Token index type
+/// In real implementation, this would map to the token table
+///
+using TokenIndex = int32_t;
+
+///
+/// Path index into the original paths vector
+///
+using PathIndex = uint64_t;
+
+///
+/// Tree node representing a path element in the hierarchy
+///
+struct PathTreeNode {
+  std::string element_name;        // Name of this element (e.g., "foo", "bar", "points")
+  TokenIndex element_token_index;  // Token index for element name (negative for properties)
+  PathIndex path_index;            // Index into original paths vector
+  bool is_property;                // Is this a property element?
+
+  PathTreeNode* parent = nullptr;
+  PathTreeNode* first_child = nullptr;
+  PathTreeNode* next_sibling = nullptr;
+
+  PathTreeNode(const std::string& name, TokenIndex token_idx, PathIndex path_idx, bool is_prop)
+    : element_name(name), element_token_index(token_idx), path_index(path_idx), is_property(is_prop) {}
+};
+
+///
+/// Token table for mapping strings to token indices
+///
+class TokenTable {
+public:
+  TokenTable() : next_index_(0) {}
+
+  /// Get or create token index for a string
+  /// Properties use negative indices
+  TokenIndex GetOrCreateToken(const std::string& str, bool is_property);
+
+  /// Get token string from index
+  std::string GetToken(TokenIndex index) const;
+
+  /// Get all tokens
+  const std::map<std::string, TokenIndex>& GetTokens() const { return tokens_; }
+
+  /// Get reverse mapping
+  const std::map<TokenIndex, std::string>& GetReverseTokens() const { return reverse_tokens_; }
+
+private:
+  std::map<std::string, TokenIndex> tokens_;
+  std::map<TokenIndex, std::string> reverse_tokens_;
+  TokenIndex next_index_;
+};
+
+///
+/// Compressed path tree encoding result
+///
+struct CompressedPathTree {
+  std::vector<PathIndex> path_indexes;           // Index into _paths vector
+  std::vector<TokenIndex> element_token_indexes; // Token for element (negative = property)
+  std::vector<int32_t> jumps;                    // Navigation: -2=leaf, -1=child, 0=sibling, >0=both
+
+  TokenTable token_table;                        // Token table used for encoding
+
+  size_t size() const { return path_indexes.size(); }
+  bool empty() const { return path_indexes.empty(); }
+};
+
+///
+/// Build a hierarchical tree from sorted paths
+///
+/// Example:
+///   ["/", "/World", "/World/Geom", "/World/Geom.points"]
+///
+/// Becomes tree:
+///   / (root)
+///     └─ World
+///          └─ Geom
+///               └─ .points (property)
+///
+std::unique_ptr<PathTreeNode> BuildPathTree(
+  const std::vector<SimplePath>& sorted_paths,
+  TokenTable& token_table
+);
+
+///
+/// Encode path tree into compressed format (three parallel arrays)
+///
+/// Walks the tree in depth-first order and generates:
+/// - pathIndexes[i]: index into original paths vector
+/// - elementTokenIndexes[i]: token index for this element
+/// - jumps[i]: navigation information
+///
+CompressedPathTree EncodePathTree(const std::vector<SimplePath>& sorted_paths);
+
+///
+/// Decode compressed path tree back to paths
+///
+/// Reconstructs paths from the three arrays by following jump instructions
+///
+std::vector<SimplePath> DecodePathTree(const CompressedPathTree& compressed);
+
+///
+/// Internal: Walk tree in depth-first order and populate arrays
+///
+void WalkTreeDepthFirst(
+  PathTreeNode* node,
+  std::vector<PathIndex>& path_indexes,
+  std::vector<TokenIndex>& element_token_indexes,
+  std::vector<int32_t>& jumps,
+  std::vector<size_t>& sibling_offsets  // Positions that need sibling offset filled in
+);
+
+///
+/// Internal: Calculate jump value for a node
+///
+int32_t CalculateJump(
+  const PathTreeNode* node,
+  bool has_child,
+  bool has_sibling,
+  size_t sibling_offset
+);
+
+} // namespace crate
+} // namespace tinyusdz

sandbox/path-sort-and-encode-crate/validate-path-sort.cc

@@ -0,0 +1,211 @@
+//
+// Validation program to compare TinyUSDZ path sorting with OpenUSD SdfPath sorting
+// SPDX-License-Identifier: Apache 2.0
+//
+#include "path-sort-api.hh"
+
+// OpenUSD includes
+#include "pxr/usd/sdf/path.h"
+
+#include <iostream>
+#include <vector>
+#include <string>
+#include <algorithm>
+
+using namespace tinyusdz;
+
+// Test case structure
+struct TestCase {
+  std::string prim_part;
+  std::string prop_part;
+  std::string description;
+
+  TestCase(const std::string& prim, const std::string& prop, const std::string& desc)
+    : prim_part(prim), prop_part(prop), description(desc) {}
+};
+
+// Create test paths
+std::vector<TestCase> GetTestCases() {
+  std::vector<TestCase> tests;
+
+  // Basic absolute paths
+  tests.push_back(TestCase("/", "", "Root path"));
+  tests.push_back(TestCase("/foo", "", "Single prim"));
+  tests.push_back(TestCase("/foo/bar", "", "Two level prim"));
+  tests.push_back(TestCase("/foo/bar/baz", "", "Three level prim"));
+
+  // Property paths
+  tests.push_back(TestCase("/foo", "prop", "Prim with property"));
+  tests.push_back(TestCase("/foo/bar", "prop", "Nested prim with property"));
+  tests.push_back(TestCase("/foo", "aaa", "Property aaa"));
+  tests.push_back(TestCase("/foo", "zzz", "Property zzz"));
+
+  // Alphabetic ordering tests
+  tests.push_back(TestCase("/aaa", "", "Path aaa"));
+  tests.push_back(TestCase("/bbb", "", "Path bbb"));
+  tests.push_back(TestCase("/zzz", "", "Path zzz"));
+  tests.push_back(TestCase("/aaa/bbb", "", "Path aaa/bbb"));
+  tests.push_back(TestCase("/aaa/ccc", "", "Path aaa/ccc"));
+
+  // Depth tests
+  tests.push_back(TestCase("/a", "", "Shallow path a"));
+  tests.push_back(TestCase("/a/b", "", "Path a/b"));
+  tests.push_back(TestCase("/a/b/c", "", "Path a/b/c"));
+  tests.push_back(TestCase("/a/b/c/d", "", "Deep path a/b/c/d"));
+
+  // Mixed tests
+  tests.push_back(TestCase("/World", "", "World prim"));
+  tests.push_back(TestCase("/World/Geom", "", "World/Geom"));
+  tests.push_back(TestCase("/World/Geom/mesh", "", "World/Geom/mesh"));
+  tests.push_back(TestCase("/World/Geom", "xformOp:transform", "World/Geom with xform"));
+  tests.push_back(TestCase("/World/Geom/mesh", "points", "mesh with points"));
+  tests.push_back(TestCase("/World/Geom/mesh", "normals", "mesh with normals"));
+
+  // Edge cases
+  tests.push_back(TestCase("/x", "", "Single char x"));
+  tests.push_back(TestCase("/x/y", "", "Single char x/y"));
+  tests.push_back(TestCase("/x/y/z", "", "Single char x/y/z"));
+
+  return tests;
+}
+
+bool ValidateSort() {
+  std::vector<TestCase> test_cases = GetTestCases();
+
+  std::cout << "Creating " << test_cases.size() << " test paths...\n" << std::endl;
+
+  // Create TinyUSDZ paths
+  std::vector<SimplePath> tiny_paths;
+  for (const auto& tc : test_cases) {
+    tiny_paths.push_back(SimplePath(tc.prim_part, tc.prop_part));
+  }
+
+  // Create OpenUSD paths
+  std::vector<pxr::SdfPath> usd_paths;
+  for (const auto& tc : test_cases) {
+    std::string path_str = tc.prim_part;
+    if (!tc.prop_part.empty()) {
+      path_str += "." + tc.prop_part;
+    }
+    usd_paths.push_back(pxr::SdfPath(path_str));
+  }
+
+  // Sort using TinyUSDZ implementation
+  std::vector<SimplePath> tiny_sorted = tiny_paths;
+  pathsort::SortSimplePaths(tiny_sorted);
+
+  // Sort using OpenUSD SdfPath
+  std::vector<pxr::SdfPath> usd_sorted = usd_paths;
+  std::sort(usd_sorted.begin(), usd_sorted.end());
+
+  // Compare results
+  std::cout << "Comparing sorted results...\n" << std::endl;
+
+  bool all_match = true;
+  for (size_t i = 0; i < tiny_sorted.size(); i++) {
+    std::string tiny_str = tiny_sorted[i].full_path_name();
+    std::string usd_str = usd_sorted[i].GetString();
+
+    bool match = (tiny_str == usd_str);
+    if (!match) {
+      all_match = false;
+    }
+
+    std::cout << "[" << i << "] "
+              << (match ? "✓" : "✗")
+              << " TinyUSDZ: " << tiny_str
+              << " | OpenUSD: " << usd_str
+              << std::endl;
+  }
+
+  std::cout << "\n" << std::string(60, '=') << std::endl;
+  if (all_match) {
+    std::cout << "SUCCESS: All paths sorted identically!" << std::endl;
+  } else {
+    std::cout << "FAILURE: Path sorting differs between implementations!" << std::endl;
+  }
+  std::cout << std::string(60, '=') << std::endl;
+
+  return all_match;
+}
+
+bool ValidatePairwiseComparison() {
+  std::cout << "\n\nPairwise Comparison Validation\n" << std::endl;
+  std::cout << std::string(60, '=') << std::endl;
+
+  std::vector<TestCase> test_cases = GetTestCases();
+
+  // Create paths
+  std::vector<SimplePath> tiny_paths;
+  std::vector<pxr::SdfPath> usd_paths;
+
+  for (const auto& tc : test_cases) {
+    tiny_paths.push_back(SimplePath(tc.prim_part, tc.prop_part));
+
+    std::string path_str = tc.prim_part;
+    if (!tc.prop_part.empty()) {
+      path_str += "." + tc.prop_part;
+    }
+    usd_paths.push_back(pxr::SdfPath(path_str));
+  }
+
+  int mismatches = 0;
+  int total_comparisons = 0;
+
+  // Compare every pair
+  for (size_t i = 0; i < tiny_paths.size(); i++) {
+    for (size_t j = 0; j < tiny_paths.size(); j++) {
+      if (i == j) continue;
+
+      total_comparisons++;
+
+      // TinyUSDZ comparison
+      int tiny_cmp = pathsort::CompareSimplePaths(tiny_paths[i], tiny_paths[j]);
+      bool tiny_less = tiny_cmp < 0;
+
+      // OpenUSD comparison
+      bool usd_less = usd_paths[i] < usd_paths[j];
+
+      if (tiny_less != usd_less) {
+        mismatches++;
+        std::cout << "MISMATCH: "
+                  << tiny_paths[i].full_path_name() << " vs "
+                  << tiny_paths[j].full_path_name()
+                  << " | TinyUSDZ: " << (tiny_less ? "less" : "not-less")
+                  << " | OpenUSD: " << (usd_less ? "less" : "not-less")
+                  << std::endl;
+      }
+    }
+  }
+
+  std::cout << "\nTotal comparisons: " << total_comparisons << std::endl;
+  std::cout << "Mismatches: " << mismatches << std::endl;
+
+  if (mismatches == 0) {
+    std::cout << "SUCCESS: All pairwise comparisons match!" << std::endl;
+  } else {
+    std::cout << "FAILURE: " << mismatches << " comparison mismatches found!" << std::endl;
+  }
+
+  return mismatches == 0;
+}
+
+int main() {
+  std::cout << "=" << std::string(60, '=') << std::endl;
+  std::cout << "TinyUSDZ Path Sorting Validation" << std::endl;
+  std::cout << "Comparing against OpenUSD SdfPath" << std::endl;
+  std::cout << "=" << std::string(60, '=') << "\n" << std::endl;
+
+  bool sort_valid = ValidateSort();
+  bool pairwise_valid = ValidatePairwiseComparison();
+
+  std::cout << "\n\n" << std::string(60, '=') << std::endl;
+  std::cout << "FINAL RESULT" << std::endl;
+  std::cout << std::string(60, '=') << std::endl;
+  std::cout << "Sort validation:     " << (sort_valid ? "PASS" : "FAIL") << std::endl;
+  std::cout << "Pairwise validation: " << (pairwise_valid ? "PASS" : "FAIL") << std::endl;
+  std::cout << "Overall:             " << (sort_valid && pairwise_valid ? "PASS" : "FAIL") << std::endl;
+  std::cout << std::string(60, '=') << std::endl;
+
+  return (sort_valid && pairwise_valid) ? 0 : 1;
+}