diff --git a/data/README.md b/data/README.md
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+++ b/data/README.md
@@ -61,6 +61,7 @@
 | datapage_v2_empty_datapage.snappy.parquet | A compressed FLOAT column with DataPageV2, a single row, value is null, the file uses Snappy compression, but there is no data for uncompression (see [related issue](https://github.com/apache/arrow-rs/issues/7388)). The zero bytes must not be attempted to be uncompressed, as this is an invalid Snappy stream. |
 | unknown-logical-type.parquet | A file containing a column annotated with a LogicalType whose identifier has been set to an abitrary high value to check the behaviour of an old reader reading a file written by a new writer containing an unsupported type (see [related issue](https://github.com/apache/arrow/issues/41764)). |
 | int96_from_spark.parquet | Single column of (deprecated) int96 values that originated as Apache Spark microsecond-resolution timestamps. Some values are outside the range typically representable by 64-bit nanosecond-resolution timestamps. See [int96_from_spark.md](int96_from_spark.md) for details. |
+| int96_timestamp_order.parquet | Single `required int96` column written with the `INT96_TIMESTAMP_ORDER` column order ([parquet-format #584](https://github.com/apache/parquet-format/pull/584)). Values are chosen so a byte-wise comparison disagrees with the chronological order, so the min/max statistics (and column index) are only correct for a reader that honors the new order. See [int96_timestamp_order.md](int96_timestamp_order.md) for details. |
 | binary_truncated_min_max.parquet | A file containing six columns with exact, fully-truncated and partially-truncated max and min statistics and with the expected is_{min/max}_value_exact.  (see [note](Binary-truncated-min-and-max-statistics)).|
 
 TODO: Document what each file is in the table above.
diff --git a/data/int96_timestamp_order.md b/data/int96_timestamp_order.md
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+<!--
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+  ~ regarding copyright ownership.  The ASF licenses this file
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+  ~ "License"); you may not use this file except in compliance
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+  ~   http://www.apache.org/licenses/LICENSE-2.0
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+  ~ under the License.
+  -->
+
+# `int96_timestamp_order.parquet`
+
+A single `required int96` column written with the `INT96_TIMESTAMP_ORDER` column order added in
+[parquet-format #584](https://github.com/apache/parquet-format/pull/584). It exercises a reader's
+ability to honor the new order: the column carries min/max statistics and a column index, and the
+footer's `column_orders[0]` is set to `INT96_TIMESTAMP_ORDER` (union field 3) rather than
+`TYPE_ORDER`.
+
+INT96 timestamps are 12 little-endian bytes: an 8-byte nanoseconds-within-the-day followed by a
+4-byte Julian day. The defined order compares the Julian day (as a signed int32) first, then the
+nanoseconds (as a signed int64) — i.e. chronological order.
+
+## Why this file is non-trivial
+
+The values are deliberately chosen so that a **byte-wise (lexicographic) comparison disagrees with
+the chronological order**. Because the low-order nanosecond bytes come first in the little-endian
+layout, a reader that compares the raw 12 bytes (or that ignores the new order) computes the wrong
+min/max. A reader must implement the chronological comparison to pass.
+
+| Value          | Julian day | nanos-of-day      | Timestamp                          | first byte |
+|----------------|------------|-------------------|------------------------------------|------------|
+| EARLY          | 2440000    | 123               | 1968-05-23 00:00:00.000000123      | `0x7B`     |
+| SAME_DAY_EARLY | 2440588    | 1000              | 1970-01-01 00:00:00.000001000      | `0xE8`     |
+| LATE_IN_DAY    | 2440588    | 86399999999999    | 1970-01-01 23:59:59.999999999      | `0xFF`     |
+| NEXT_DAY       | 2440589    | 0                 | 1970-01-02 00:00:00.000000000      | `0x00`     |
+
+Values are written to the file out of order: `LATE_IN_DAY, NEXT_DAY, EARLY, SAME_DAY_EARLY` (so that
+the correct min/max are also neither the first nor the last value).
+
+- Correct (`INT96_TIMESTAMP_ORDER`) min/max: **EARLY / NEXT_DAY**
+- Byte-wise (incorrect) min/max would be: **NEXT_DAY / LATE_IN_DAY** (ordered by the leading
+  nanosecond byte `0x00 < 0x7B < 0xE8 < 0xFF`)
+
+The min/max written to the statistics (and the column index) are therefore:
+
+```
+min = 0x 7B 00 00 00 00 00 00 00 40 3B 25 00   (EARLY:    nanos 123,  Julian day 2440000)
+max = 0x 00 00 00 00 00 00 00 00 8D 3D 25 00   (NEXT_DAY:  nanos 0,    Julian day 2440589)
+```
+
+## How it was generated
+
+Written by parquet-java (parquet-mr 1.18.0-SNAPSHOT) via the
+`TestInt96TimestampStatistics#writeInt96TimestampOrderInteropFile` test:
+
+```
+mvn -pl parquet-hadoop test \
+  -Dtest='TestInt96TimestampStatistics#writeInt96TimestampOrderInteropFile' \
+  -Dparquet.testing.data.dir=<parquet-testing>/data
+```
+
+## Schema
+
+```
+message int96_timestamp_order {
+  required int96 ts;
+}
+```
diff --git a/data/int96_timestamp_order.parquet b/data/int96_timestamp_order.parquet
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