Method and formulas
Behind the traditional rules there is algebra. These formulas fall into three groups: astronomy and number theory (measurable or provable), fixed classical rules (no editorial licence taken), and our own models (every one in the product). Each card is labelled with which is which.
Place wood, fire, earth, metal and water on a ring. One step around the ring (+1) generates; two steps (+2) controls. So "wood controls earth" is not a memorised saying, it is 2 mod 5: wood(0) to earth(2), fire(1) to metal(3), and so on without exception.
The same structure explains why there are ten gods rather than five: five relations times two polarities, 5 × 2 = 10.
Ten stems and twelve branches allow 120 pairings, but only 60 satisfy both congruences at once; the other 60 cannot exist. 10 × 12 ÷ 2 = 60 is why the cycle is sixty long, not a hundred and twenty.
Number theory: Chinese remainder theorem with non-coprime moduli
A year reduced modulo 10 and modulo 12 gives the two phases that make up its stem-branch pair. Both were zero in 1984, which is why that year was the first pair of the cycle.
Anchored at 4 CE; the year turns at the start of spring
Solar terms mark the sun every 15 degrees of ecliptic longitude. The start of spring sits at 315 degrees and can be computed from an ephemeris rather than estimated. We use it only to fix where the year pillar changes.
Ephemeris-grade astronomy, independently verifiable
The gap between true and mean solar time, swinging within plus or minus 16 minutes over a year. That is wide enough to move an hour pillar: two births fifteen minutes apart can land in different hours.
Standard approximation, error under 30 seconds
Longitude offset plus the equation of time. A correction usually moves only the hour pillar; if it crosses midnight (up to about two hours in the far west) the date moves back with it and the day pillar changes. This is the only correction applied, so nothing is converted twice.
Stored as clock time plus longitude, converted on the fly
We model the five phases as a cyclic structure of order five: one step around the ring generates, two steps controls; in this model both relations are just step sizes, and enumerating five elements checks all of them.
Same structure as the ring diagram above
Same as me, I generate, generates me, controls me, I control. Split each by polarity and you get exactly ten gods. Every domain on the status page names the star that governs it.
Verifiable by exhaustive enumeration
The entropy is 1 when the five phases are perfectly even and 0 when everything piles into one. This is exactly where the balance score comes from: evenness scores higher, and both extremes fall away again.
Our model, base 5 so the result lands in 0 to 1
A sigmoid turns an on or off decision into a probability: near the cut-off the output sits around 0.5 instead of flipping on a 0.1 point difference. Tau sets how wide the transition band is.
Our model; the cut-off and width are fixed and inspectable
The classical conversion, three days to one year, produces a decimal age from which we lay out ten-year luck pillars. No discretionary adjustment is applied.
Fixed classical conversion
Each step advances ten places on the sixty-term cycle, so six steps return to the beginning. That is why the table can be extended indefinitely in ten-year steps.
The table spans birth year plus or minus 100 years
Maps the sixty-year cycle onto a phase angle from 0 to 2 pi, so a given year can be treated as a periodic signal alongside your luck pillar.
Our model
Every life domain is scored separately, weighted by pillar position: the month command carries the most, then the day branch, then the hour, then the year. Each domain has its own governing star rather than one blended verdict.
Our model; each term can be recomputed
Most charts take the useful element from the ordinary strong/weak rule. When the day master has no root and one element dominates, the chart is read as a following structure instead and the useful element follows it. This step decides which element adds to a score and which subtracts, so the conditions and thresholds are printed here rather than tuned case by case.
Classical rule (Ziping Zhenquan) plus our thresholds
Every chart gets three readings that never mix: the base layer depends only on the birth chart and the current period (read-only); the effort layer depends only on what you actually logged; the fusion layer multiplies the two, so a higher base earns more for the same effort. The neutral line is one meaningful entry per day - below it the current score drifts down, above it up, and an empty period is never docked retroactively. Alpha shrinks with the period (0.30 for the current block down to 0.08 for the year).
Our own algorithm; every substituted value is printed on this page
The overall score first drops the top and bottom 20 percent, so one domain cannot swing the whole picture, then docks points for the weakest domain: the further it sits below the mean, the bigger the deduction. There is no 100 cap - long-term effort plus a good period can push it past 100.
Our own algorithm; the 20 percent and 0.35 are engine constants you can re-check
Period effects are weighted by layer; the current two-hour block is reference only and never enters the main score. On top of the layers come interactions: clash, combination, punishment and harm carry fixed values, only the strongest instance of a given relation on a given pillar counts, and a single domain is capped at 10 interaction points. Same-pillar repeats, stem-to-stem clashes and full clashes follow the classical texts; a long step coinciding with its year acts as a multiplier or a hint only.
Our own algorithm; layer weights and interaction values are engine constants
Two commitments about this material: