Base64 length is 4 ceil(n/3): byte lengths 0,1,2,3 produce 0,4,4,4 characters. Parent JSON size already includes children; summing both double-counts. Bytes are not model tokens.
Shared code, English mathematical explanation and key multilingual numeric passages reviewed. This is not a full translation proofread.
Mechanism map: follow the transformations from top to bottom.
Before running: predict a boundary case
Base64 length is 4 ceil(n/3): byte lengths 0,1,2,3 produce 0,4,4,4 characters. Parent JSON size already includes children; summing both double-counts. Bytes are not model tokens.
Hint: isolate the assumption
Keep the baseline input fixed, change one parameter or boundary, and compare both the numerical result and the claimed units. A passing example verifies this fixture only.
Minimal executable example
Save the example and linked modules in one folder. Use Node.js 22 or newer, then run node base64-ai-payload-inspector.mjs. No third-party runtime dependencies.
Base64 length is 4 ceil(n/3): byte lengths 0,1,2,3 produce 0,4,4,4 characters. Parent JSON size already includes children; summing both double-counts. Bytes are not model tokens.
Record input, code version, expected result and observed result in the notebook below. Then construct a counterexample that violates the assumption above and explain why the original conclusion no longer follows.
Before revealing an answer, predict one result. After the exercise, record the discrepancy and a transfer test. Saved locally across language editions.
The mathematical review scope is recorded per lesson. It does not establish empirical paper reproduction; report suspected errors in your notes. Review scope