Method · Technical note Y-1

On the Calculation of a Yantrika from a Wish, a Touch, a Moment and the Sky

Yantrika Laboratory · yantrika.shop
Revision 1.0 · 26 October 2026

Abstract We describe the deterministic procedure by which a Yantrika is computed. Six independent observables are sampled at a single instant t₀: the wish as written, the hoped-for horizon, the micro-dynamics of a fingertip held on glass, the civil time to the millisecond, the observer’s geographic position, and the apparent geocentric ecliptic longitudes of the Sun, the Moon and the five classical planets. These are quantised, serialised and compressed by a 128-bit avalanche hash into a seed s ∈ {0,1}¹²⁸. The seed selects one of sixty canonical forms (ten intentional classes × six structures), sets its personal parameters, orients its sky ring to the true Sun, engraves the inputs as micro-text, and fixes a 3 to 7-day intention cycle. The probability that two Yantrikas share a seed is of order 10⁻³⁸.

§1The observation vector

Every Yantrika begins as a single vector of observations, all taken within the same tap.

x = (w, h, t_{0}, φ, λ, τ, Σ)

\in U^{*} \times H \times ℤ \times S^{2} \times ℝ^{6} \times 𝕋^{8}

(1.1)

w: the wish, a Unicode string normalised by whitespace collapse
h: the horizon of hope, h ∈ 𝓗 = {now, month, year, cosmos}
t₀: the instant the touch completes, in integer milliseconds since 1970-01-01T00:00:00Z
(φ, λ): geodetic latitude and longitude, when the observer consents; otherwise the IANA time zone stands in
τ: the touch tensor: contact ellipse, pressure, tremor, hold duration and sample count
Σ: the sky state: seven ecliptic longitudes and the lunar elongation

§2Temporal anchoring

Civil time is converted to the continuous Julian Date, then to Terrestrial Time by adding ΔT, the slowly drifting difference between atomic time and the rotation of the Earth.

JD = \frac{t_{0}}{86 400 000} + 2 440 587.5

{JD}_{TT} = JD + \frac{Δ T}{86 400}

(2.1)

All periodic series below are evaluated in Julian millennia τ and centuries T from the standard epoch J2000.0:

T = \frac{{JD}_{TT} - 2 451 545.0}{36 525}

τ = \frac{T}{10}

(2.2)

The local apparent sidereal time, which binds the sky to the observer’s meridian, follows from the Earth rotation angle θ, small precession terms, the equation of the equinoxes and the observer’s longitude:

θ = 2 π (0.779 057 273 264 + 1.002 737 811 911 354 48 D_{U})

θ_{L} \approx θ + Δ ψ \cos ε + λ

(2.3)

§3Ephemeris of the sky

The heliocentric coordinates of each planet are summed from the VSOP87 planetary theory of Bretagnon and Francou: thousands of periodic terms, each an amplitude, a phase and a frequency.

L (τ) = \sum_{α = 0}^{5} τ^{α} \sum_{k} A_{α k} \cos (B_{α k} + C_{α k} τ)

(3.1)

The geocentric vector is the difference of two heliocentric vectors, evaluated at the retarded time t − ρ/c so that each body is placed where its light left it, then corrected for the aberration of light caused by the Earth’s own velocity v⊕:

ρ = r_{b} (t - \frac{| ρ |}{c}) - r_{\oplus} (t)

ρ^{'} \approx ρ + \frac{| ρ |}{c} v_{\oplus}

(3.2)

The vector is precessed and nutated from the J2000 frame onto the true ecliptic of date, where the apparent ecliptic longitude is read:

λ_{b} = atan2 (y_{ecl}, x_{ecl}) \mod 360 °

r_{ecl} = R_{1} (ε) N (T) P (T) ρ_{J2000}

(3.3)

The Moon follows an analytic lunar theory. Its elongation from the Sun gives the phase angle ψ, and the illuminated fraction k is engraved as the small disc on the sky ring, drawn with the true terminator:

ψ = (λ_{☽} - λ_{☉}) \mod 360 °

k = \frac{1 + \cos i}{2}

waxing \Leftrightarrow ψ < 180 °

(3.4)

When the observer’s position is known, each body’s altitude above the local horizon is computed from its declination δ and hour angle H = θ_L − α. Bodies above the horizon are drawn brighter:

\sin a = \sin φ \sin δ + \cos φ \cos δ \cos H

(3.5)

Agreement with standard ephemerides is within about one arcminute. The sky is never still: the Moon alone advances by

{\dot{λ}}_{☽} \approx 13.176 ° d^{- 1} \approx 0.549 ″ s^{- 1}

(3.6)

so no two moments, and no two Yantrikas, share the same sky.

§4The touch tensor

While the fingertip rests on the glass for T_h = 2.5 s, the screen’s digitiser reports positions p_i = (x_i, y_i), contact axes (a_i, b_i) and normal pressure π_i, sampled at the display rate and between frames. No human finger is perfectly still; the physiological tremor of the hand is measured as the root-mean-square excursion about the centroid:

\bar{p} = \frac{1}{N} \sum_{i = 1}^{N} p_{i}

σ_{τ} = \sqrt{\frac{1}{N} \sum_{i = 1}^{N} {‖ p_{i} - \bar{p} ‖}^{2}}

(4.1)

τ = (\bar{a}, \bar{b}, \bar{π}, σ_{τ}, T_{h}, N)

(4.2)

Where a device does not report contact geometry or pressure, those components are declared absent rather than invented, and the signature shows “—”.

§5Quantisation and the canonical record

Each real-valued observable is quantised to two decimal places by q(x) = ⌊100x + ½⌋ / 100. For position this is a deliberate privacy bound: a hundredth of a degree of latitude spans

Δ s = R_{\oplus} \cdot 0.01 ° \cdot \frac{π}{180}

\approx 6 371 km \times 1.745 \times 10^{- 4} \approx 1.11 km

(5.1)

so no Yantrika ever carries a home address. The quantised vector is serialised in a fixed key order into a canonical string C(x), so that identical observations always yield identical bytes.

§6The seed

C is absorbed by four interleaved 32-bit lanes. Each code unit c is mixed into every lane through multiplication by a large odd constant modulo 2³², and each lane feeds the next:

h_{j} \leftarrow h_{j + 1} \oplus [(h_{j} \oplus c) \cdot m_{j} \mod 2^{32}]

m = (\begin{matrix} 597 399 067 & 2 869 860 233 \\ 951 274 213 & 2 716 044 179 \end{matrix})

(6.1)

A final avalanche pass, with shifts of 18, 22, 17 and 19 bits, ensures that changing a single input bit flips on average half of the 128 output bits:

s = (s_{0}, s_{1}, s_{2}, s_{3}) \in {(ℤ_{2^{32}})}^{4}

\Pr [s_{k} (x) \neq s_{k} (x \oplus e_{i})] \approx \frac{1}{2}

(6.2)

With 2¹²⁸ ≈ 3.4 × 10³⁸ possible seeds, the birthday bound gives the chance that any two of n Yantrikas collide:

P_{coll} (n) \approx 1 - e^{- n^{2} / 2^{129}}

\Rightarrow P_{coll} (10^{9}) \approx 1.5 \times 10^{- 21}

(6.3)

The seed is shown on the calculation screen as it forms: each frame hashes a longer prefix of C until every observation has been absorbed.

§7Intentional class and form

The wish is tokenised and lightly stemmed, then scored against ten intentional classes Θ = {home, love, career, abundance, wellbeing, adventure, courage, creativity, learning, hope}. Phrases weigh 3, words 1, weak relational words 0.2; ties fall to the class named first:

θ^{*} = \underset{θ \in Θ}{arg max} \sum_{κ \in K_{θ} \cap stem (w)} ω_{κ}

(7.1)

Each class holds six canonical forms. Writing P_θ for the forms of class θ not yet shown on this device, the form is

f^{*} = P_{θ^{*}} [s_{0} \mod | P_{θ^{*}} |]

P_{θ} \leftarrow F_{θ} when P_{θ} = \emptyset

(7.2)

Form	Triangles	Inner / outer petals	Enclosure
Shri	4 ▲ + 5 ▼ interlocking	8 / 16	bhūpura, three walls
Shatkona	{6/2} hexagram ×2	12 / 24	triple circle, 12 nodes
Ashta	{8/2} + {8/3} octagram	8 / —	double octagon
Pancha	{5/2} pentagram	10 / 20	bhūpura, two walls
Shikhara	3 nested ▲ + 1 ▼	16 / 32	bhūpura, three walls
Padma	{6/2} hexagram	6 / 12	24-petal corona

§8Geometry

All geometry lives in a unit frame whose radius 1 meets the outermost wall. In the Shri form, each triangle’s base vertices lie on the circle of radius R = 0.43, so a base at height y_b has half-width

x_{b} = \pm \sqrt{R^{2} - y_{b}^{2}}

y_{apex} = \mp R (1 - 0.62 u + ξ)

(8.1)

the construction of the classical Śrī Yantra, whose geometry was analysed mathematically by Kulaichev. Lotus petals are quadratic Bézier arcs between base points P₀, P₂ on the petal circle, pulled through a control point P₁:

B (u) = {(1 - u)}^{2} P_{0} + 2 (1 - u) u P_{1} + u^{2} P_{2}

u \in [0, 1]

(8.2)

The personal parameters are bound to the observations: petal curvature to the tremor, gate width to the millisecond, the sky ring’s orientation to the true Sun.

κ = 0.16 + \min (0.45, \frac{σ_{τ}}{4} + \frac{s_{2} \mod 100}{1000})

g = 0.08 + 0.06 \frac{t_{0} \mod 1000}{1000}

θ_{0} = λ_{☉}

(8.3)

Each body b is placed on the sky ring at the polar angle

ϑ_{b} = - \frac{π}{2} - (λ_{b} - λ_{☉})

r_{b} = 0.783 (\cos ϑ_{b}, \sin ϑ_{b})

(8.4)

so that today’s Sun stands at the zenith of every Yantrika and the planets keep their true angular separations.

§9The ten-second cycle

The living Yantrika is a closed loop of period P = 10 s. For a petal ring of order n, the rotation over one period is exactly one petal, 2π/n. Because the ring has cyclic symmetry C_n, the last frame maps onto the first and the loop has no seam:

α (t) = \pm \frac{2 π}{n} \cdot \frac{t \mod P}{P}

R_{α (P)} (L) = L \forall L \in Fix (C_{n})

(9.1)

The luminance breathes once per period, g(t) = 0.65 + 0.35 cos(2π t / P), and the Clip is the same loop captured at 30 frames per second.

§10The intention cycle

The cycle length N is drawn from the seed within an interval set by the horizon of hope, and its days are counted from the observer’s local date:

N = ℓ_{h} + (s_{3} \mod (u_{h} - ℓ_{h} + 1))

[ℓ_{h}, u_{h}] \in {[3, 4], [4, 6], [5, 7], [3, 7]}

(10.1)

§11Engraving and scale

The observations are engraved as micro-text on three rings: the wish at r = 0.458, the full signature at r = 0.7545 and the seed around the central seal at r = 0.162. Glyph height is 0.0062 units. On a phone the Yantrika’s radius is a few hundred device pixels, so the text is one to two pixels tall and reads as a fine dotted ring. The renderer switches to letterforms only when a glyph exceeds 2.6 device pixels:

legible \Leftrightarrow 0.0062 \cdot ρ_{px} \cdot z \geq 2.6

\Rightarrow z \geq \frac{2.6}{0.0062 ρ_{px}}

(11.1)

where ρ_px is the Yantrika’s radius in device pixels and z the zoom; on most phones the words appear between 2× and 6×. The 3000-pixel image carries the micro-text at about 8.6 px, so it survives zooming in any photo viewer and on a printed poster.

§12The symbolic vocabulary

The geometry follows the traditional grammar of the yantra as described in the Tantric literature. The bindu, the central point, is the unmanifest origin from which form proceeds. The trikoṇa, the triangles, pair the upward and downward principles, often read as Śiva and Śakti. The padma, the lotus petals, mark the unfolding of the inner circuit. The bhūpura, the square enclosure with four gates, is the earth plane through which one enters. Contemplation traditionally moves from the gates inward to the bindu, and then out again. The practice that accompanies each Yantrika follows that path.

What this calculation is, and is not. Every number on the calculation screen is real and reproducible: the same observations always give the same Yantrika. The sky positions are real astronomy, not astrology. The method determines the form of your Yantrika. It does not predict or guarantee outcomes. Yantrika is an object for contemplation and intention.

§13References

Bretagnon, P. & Francou, G. (1988). Planetary theories in rectangular and spherical variables: VSOP87 solutions. Astronomy & Astrophysics, 202, 309–315.
Meeus, J. (1998). Astronomical Algorithms, 2nd ed. Willmann-Bell.
Montenbruck, O. & Pfleger, T. (2000). Astronomy on the Personal Computer, 4th ed. Springer.
Cross, D. (2019–2023). Astronomy Engine, MIT-licensed ephemeris library. github.com/cosinekitty/astronomy
Kulaichev, A. P. (1984). Śrīyantra and its mathematical properties. Indian Journal of History of Science, 19(3).
Khanna, M. (1979). Yantra: The Tantric Symbol of Cosmic Unity. Thames & Hudson.

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