Method and formulas

The five phases as a cyclic group

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.

1. The sexagenary cycle is derived, not arbitrary

Astronomy and calendarSixty pairs = solutions of two congruences

x \equiv a (mod 10), x \equiv b (mod 12) solvable ⟺ a \equiv b (mod g cd (10, 12) = 2)

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

Fixed classical ruleYear pillar = two residue phases

n_{stem} = (y - 4) mod 10, n_{branch} = (y - 4) mod 12

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

2. Solar terms and true solar time (measurable astronomy)

Astronomy and calendarTwenty-four terms = ecliptic marks

24 = \frac{36 0 ^{\circ}}{1 5 ^{\circ}}, start of spring = 31 5^{\circ}

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

Astronomy and calendarEquation of time

E o T = 9.87 sin 2 B - 7.53 cos B - 1.5 sin B, B = \frac{36 0 ^{\circ} ( N - 81 )}{364}

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

Our own modelTrue solar time (hour pillar only)

t_{⊙} = t_{std} + \frac{λ _{local} - λ _{zone}}{1 5 ^{\circ} / h} + \frac{E o T}{60}

Longitude offset plus the equation of time. We correct the hour pillar only: year, month and day pillars stay as given, and we never apply a second timezone conversion on top.

Stored as clock time plus longitude, converted on the fly

3. Five phases and ten gods (algebra)

Astronomy and calendarFive phases = a five-element cyclic group

phases ≅ Z /5 Z, generates : + 1, controls : + 2 (mod 5)

The five phases are not five parallel nouns but a cyclic group of order five. One step around the ring generates, two steps controls; both relations are just step sizes, and enumerating five elements verifies all of them.

Same structure as the ring diagram above

Fixed classical ruleTen gods = 5 × 2

5 relations \times 2 (same or opposite polarity) = 10

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

4. Scoring: how the above becomes numbers

Our own modelBalance = normalised Shannon entropy

H (w) = - i = 1 \sum 5 w_{i} lo g_{5} w_{i}, w_{i} = \frac{s _{i}}{\sum _{j} s _{j}}

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

Our own modelStrength of the day master: a soft threshold

P (strong) = \frac{1}{1 + e ^{- (S - θ) / τ}}

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

Fixed classical ruleStart of the luck cycle: three days to a year

start age = \frac{days from birth to the solar term}{3}

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

Our own modelPillar stepping: ten places per decade

n_{k} = (n_{0} + 10 k) mod 60

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

Our own modelAnnual phase

φ (y) = \frac{2 π (( y - 4 ) mod 60 )}{60}

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

Our own modelDomain score: position weighting

S_{d} = j \sum W_{j} f_{j} (\cdot), W_{month} > W_{day branch} > W_{hour} > W_{year}

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

Two commitments about this material:

The calendar skeleton (solar terms, stem-branch cycle, true solar time) is astronomy and number theory, independently verifiable, and we compute it exactly
Scores and projections are model output: formula, substituted values and result are all shown. We do not vouch for the conclusions and we make no fortune-telling claim

Thirteen formulas, all in the open

The five phases as a cyclic group

1. The sexagenary cycle is derived, not arbitrary

2. Solar terms and true solar time (measurable astronomy)

3. Five phases and ten gods (algebra)

4. Scoring: how the above becomes numbers