Consistency of Execution Counts across Different Kernel Versions

Reconciliation of Execution Counts

There is no documented behavior for "reconciling" execution counts across different kernel versions because execution counts are not synchronized with the kernel's internal state. The counts displayed in a notebook are purely cosmetic metadata stored within the .ipynb JSON file; they are not a reflection of the kernel's current memory or a validation of the execution sequence.

The Protocol and State Gap

The Jupyter messaging protocol (ZeroMQ) operates as a one-way update for these integers: when a cell finishes executing, the kernel sends an incremented integer to the frontend, which then updates the notebook metadata. However, the protocol provides no mechanism to validate if the current kernel state matches the recorded sequence.

When you open a notebook in a new environment or a different kernel version:

• Metadata Persistence: The recorded execution counts remain visible in the UI as a historical record of the previous session.
• Kernel State: The new kernel starts with a clean memory state and its own internal counter (typically starting at 1), regardless of what the notebook metadata claims.
• Execution Logic: The kernel does not use the recorded counts to determine the order of operations; it only executes cells in the order they are triggered by the user or a "Run All" command.

Verification of Behavior

To verify that execution counts are decoupled from the kernel state, you can perform the following steps:

1. Execute several cells in a notebook to generate counts (e.g., [1], [2], [3]).
2. Save the notebook and restart the kernel (or open the file in a different kernel version).
3. Observe that the counts [1], [2], and [3] persist in the UI, but any variable defined in those cells is now missing from memory.
4. Run a cell; the kernel will assign it the next number in its current session sequence, regardless of the numbers already present in the file.

Assumptions and Constraints

This behavior is consistent across standard Jupyter kernels (IPython) and the ZeroMQ protocol. However, different frontend implementations (such as VS Code, JupyterLab, or Google Colab) may vary in how they visually handle or reset these counts upon session start. To provide a more specific recommendation, please clarify if you are using a standard Jupyter frontend or a third-party IDE integration.