The engine estimates the sun's degree on the 360° zodiac circle with a standard shortcut formula, then finds which 5° slice — quinance — that degree falls in; the angel of that slice presides (360 ÷ 5 = 72). The progress bar is literally the sun's position inside the window, and "days left" divides the remaining degrees by the sun's average daily motion. The formula is good to about a degree, so within a day of a boundary the named angel can be off by one.

The names come from the Shem HaMephorash tradition of medieval Kabbalah — 72 three-letter names read out of three 72-letter verses of Exodus. Tying each name to five degrees of the zodiac is a later layer worked out by Renaissance and nineteenth-century European occultists, and each angel's function and "invoke for" line follows the lists passed down with those correspondences. Previous / Next are simply the neighbouring slices on the circle.

The engine counts which day of the year it is and deals it around the 22 letters in order, starting over from Aleph each time it runs out — and again every January 1, since 365 days do not divide evenly by 22. The letter's name, element and Tree of Life path are traditional attributions in the line of Sefer Yetzirah and later Kabbalah; the frequency, gate capacity, bio analogy and Magnum Opus function beside them are the author's own correspondences from the corpus.

The 4D card walks the same day-count around the corpus's 24 motion operators and the seven seed syllables of the chakras — LAM through AUM, syllables that are tantric tradition, though the daily pairing is not. The matrix ID and the base / transformed function lines are fill-in-the-blank phrases assembled from those two lookups. What the daily count means at a deeper level, the corpus leaves open.

The corpus divides a life into six hand-defined age bands — Spark (0–1), Root Formation (1–13), Identity Arc (13–34), Mastery Spiral (34–55), Elder Arc (55–89), Transcendence (89–144) — with nodes at the Fibonacci ages 0, 1, 2, 3, 5, 8, 13, 21, 34, 55 and 89. Loop progress is simply how far through your band you are, and "node in" is the next Fibonacci age minus your age. Mapping a life onto these numbers is the author's own instrument, not an older tradition.

The three copies of that band table, measured. The bands are written out in three separate places — the engine, the spiral drawing beside this text, and the fractal timeline in the section below. Their edges agree exactly: all three cut at 0, 1, 13, 34, 55 and 89. What differs is where they stop. Only the engine carries the sixth band, Transcendence, ages 89–144. Both drawings end at 89 and neither draws it.

That has a consequence worth stating plainly rather than calling it a mismatch. Past age 89 the engine still answers correctly — it puts you in loop 6 — but no ring on the spiral carries loop 6, so nothing lights up; and the fractal timeline scales its axis to a maximum age of 89, so a marker for age 95 is placed past the right-hand end of the picture, outside the drawing. A reader over 89 gets a correct number and two blank pictures. It is a narrow case and it is not patched here, because redrawing the two figures to 144 changes what the author drew.

The spiral’s ring sizes (1, 13, 21, 34, 55) are a separate thing again — they are the Fibonacci numbers used as radii, so the picture grows the way the sequence does. They are not band edges and were never meant to match them; earlier notes on this page read as though they were.