A Computational Framework for Vedic Charts: Swiss Ephemeris and True Pushya Paksha Ayanamsa

1. Why the Substrate Matters

A Vedic chart is a state vector. Nine planetary positions, twelve houses, twenty-seven nakshatras, the lagna at the eastern horizon, and the divisional charts that fan out from those primary coordinates. Every claim a practitioner makes from a chart, whether classical interpretation or modern statistical analysis, depends on the chart being computed the same way the next practitioner would compute it. If the substrate drifts, the claim drifts with it.

The classical Indian sources are explicit about precision. Texts in the Brihat Parashara Hora Shastra and Brihat Samhita lineages name the degree, the nakshatra and the dasha period to which a reading attaches. The Sanskrit numbering systems for arc carry to thirds of an arc-minute. The astronomers who refined the tables, from Aryabhata through to Bhaskara II, worked to a precision that medieval European observatories did not match for centuries. The methodological discipline was already there. What changed in the modern era is the substrate on which the same computations now run.

Today the same chart can be produced from any of a handful of ephemeris engines combined with any of a handful of ayanamsa conventions. Without an explicit declaration of which substrate the chart was computed against, two practitioners can read the same person, the same country or the same market and disagree about the chart itself. The disagreement is not interpretive. It is a substrate-level mismatch. This is the problem this note sets out to eliminate from any Tempora claim.

2. The Two Independent Decisions

Every chart computation begins with two choices, made independently of each other, that together produce the chart.

The first is the ephemeris. The ephemeris is the table of planetary positions over time. Given a moment, the ephemeris returns the longitude and latitude of every body the chart depends on. Modern ephemeris engines work from numerical integration of orbital mechanics combined with observational corrections fitted to the historical record. The output is deterministic, machine-readable, and consistent across modern engines to a fraction of an arcsecond. The question for a Vedic research firm is which engine to use as the canonical source.

The second is the ayanamsa. The ayanamsa is the angular correction that converts the tropical zodiac of contemporary astronomy into the sidereal frame the classical Vedic sources use. The tropical zodiac measures angles against the vernal equinox, which itself precesses against the fixed stars at roughly 50 arcseconds per year. The sidereal zodiac fixes the reference point against a defined position in the sky, typically a named nakshatra or a specific fixed star. The ayanamsa is the angular offset between the two frames at any given moment. Different ayanamsas pick different reference points and produce different offsets that drift apart slowly over time.

Both choices are necessary. Both are independent. A chart is not the same chart unless both are explicit. Tempora's convention is Swiss Ephemeris for the planetary positions and True Pushya Paksha for the ayanamsa. Sections 3, 4 and 5 of this note take each of those choices in turn.

3. Swiss Ephemeris: Planetary Positions to Sub-Arcsecond

Swiss Ephemeris is a numerical ephemeris developed by Astrodienst, based on the JPL DE431 long-arc integration of planetary motion. It returns positions for the Sun, Moon, the visible planets, the lunar nodes, the major asteroids and a wide set of computed points, across roughly six thousand years on either side of the present. The accuracy at any given moment is fitted to be within a fraction of an arcsecond of the JPL reference integration, which is itself the gold standard used by mission planners and observatories.

For a Vedic research firm, three properties of Swiss Ephemeris matter.

The first is reproducibility. Two researchers running independent stacks against Swiss Ephemeris for the same moment compute the same planetary positions to the same precision. The engine is deterministic and machine-readable, with no observation-quality variation across runs. The same is true of any modern numerical ephemeris (the NASA JPL Horizons system, the Astropy ephemeris bindings, several commercial alternatives), but Swiss Ephemeris is the broadest agreement-point across the Vedic and academic communities, and it is the cleanest fit for the research register Tempora publishes in.

The second is range. Vedic research engages with national charts from the eighteenth century forward and at times with chronology stretching to classical antiquity. Swiss Ephemeris covers both ends of that range without seams. There is no period where the engine's output becomes a coarser approximation. The same machinery computes Saturn's position on 4 July 1776 and Saturn's position on 23 May 2027 to the same arcsecond-level precision.

The third is open methodology. Swiss Ephemeris ships as code. Its precision, its assumptions, the fitted corrections and the orbital model are all public. Independent researchers can audit the engine, validate its outputs against alternative ephemerides, and re-derive a Tempora chart from the same starting inputs. This is the property the classical tradition's manuscript record lacked. Today it is recovered, not as theology, as numerical method.

4. The Ayanamsa Question: Tropical Versus Sidereal

The ayanamsa is the most technical of the substrate choices and the one with the broadest interpretive consequence. A primer is in order.

The contemporary astronomy of the European observational tradition measures planetary longitude against the vernal equinox, the moment at which the Sun's apparent path crosses the celestial equator each spring. This is the tropical zodiac. The vernal equinox is itself not fixed against the stars. The Earth's rotational axis precesses against the celestial sphere at a period of roughly twenty-six thousand years, dragging the vernal equinox westward against the fixed stars at approximately 50 arcseconds per year. Across two thousand years the tropical and sidereal frames drift apart by roughly 24 degrees.

The classical Indian astronomical tradition measures planetary longitude against a fixed reference in the sky, typically defined by a named nakshatra or by a specific bright star whose longitude is held constant against the rotating frame of precession. This is the sidereal zodiac. The classical sources read planetary positions, nakshatra placements and house cusps against this sidereal frame. The reading does not work in the tropical frame because the classical signification of each sign is anchored to the fixed stars, not to the seasonally-defined equinox.

The ayanamsa is the angular offset between the two frames at a given moment. Different conventions pick different reference points and yield offsets that differ by a fraction of a degree to several degrees depending on the date. The Lahiri ayanamsa, adopted by the Government of India's Calendar Reform Committee in 1955, fixes the reference at the star Chitra (Spica). The Krishnamurti ayanamsa modifies Lahiri by a small constant. The Raman ayanamsa places the reference earlier. Yukteshwar derives a reference from a different cosmological calculation. Each yields a slightly different chart for the same moment.

The question for any Vedic research firm is not which ayanamsa is correct in the abstract. The question is which ayanamsa, applied across the corpus of classical readings and tested against the historical record, produces charts whose readings correspond most closely to the events the tradition claims they describe. This is an empirical question. It is also one of the under-investigated questions in modern Vedic research. Tempora's convention, True Pushya Paksha, is the result of working this question through and is documented in the next section.

5. True Pushya Paksha: The Lineage and the Empirical Basis

True Pushya Paksha locates the fixed reference of the zodiac at the nakshatra Pushya, the lunar mansion roughly opposite the celestial position of the star Spica in the classical reckoning. The convention is associated with the south Indian Vedic lineages that informed the classical astronomical tradition and is preserved in the working notes of mid-twentieth-century practitioners in that lineage. The reference point itself is calibrated against a defined epoch, with the precession correction applied to date-shifted charts via the orbital mechanics in the ephemeris layer.

Two properties of True Pushya Paksha matter for a research firm.

The first is lineage continuity. The convention threads back through working practitioners who computed charts against this reference and read them against documented life events. The accumulated working record establishes the convention as a discipline that has been applied at scale, not a fresh proposal. For a research firm publishing dated forward calls and inviting reconciliation, the lineage matters. Reading against an ayanamsa that has not been applied at scale risks producing readings whose track record cannot be audited.

The second is empirical fit. The classical claim is that certain nakshatra placements, certain planetary aspects on specific natal positions and certain dasha-period activations correlate with specific event categories. The empirical fit of an ayanamsa is the rate at which charts computed against it support those classical correlations. Tempora's working convention is the result of comparing computed charts against documented events on national and personal charts and selecting the substrate that produces the closest fit. The full empirical comparison is the subject of a later note in this series. The summary point is that True Pushya Paksha is the convention Tempora has been able to defend against the historical record at the resolution required for forward-test publication.

The cost of the convention is that it is less standard than Lahiri in contemporary published Vedic literature. Many computational tools default to Lahiri. Conversions are not trivial, since the offset between Lahiri and True Pushya Paksha varies slightly across dates. Any chart in the Tempora corpus is computed against True Pushya Paksha, and readers consulting another stack must convert to compare. The chart is the chart. The substrate is named.

6. Lagna and the House System

The lagna is the ascendant, the degree of the sidereal zodiac rising at the eastern horizon at the birth moment and location. The lagna anchors the house system. A house in the chart is reckoned from the lagna. The first house begins at the lagna degree and continues through thirty degrees of the zodiac. The remaining eleven houses follow in sequence. Planets in the chart sit in specific houses based on where their longitudes fall relative to the lagna.

Computation of the lagna depends on three inputs: the precise moment of the event (date, time, time zone), the precise location of the event (latitude, longitude), and the same ayanamsa applied to the rest of the chart. Sub-minute precision in the birth time matters. A four-minute error in birth time shifts the lagna by approximately one degree at temperate latitudes. A one-degree shift in the lagna can move a planet that sits near a house cusp between houses. The reading that follows from the chart changes accordingly.

Tempora's convention on the house system is whole-sign houses for the primary D1 chart, where the lagna sign becomes the first house and each subsequent sign becomes the next house in sequence. This is the convention the classical Indian sources use as the default reading. The whole-sign convention has the property that house cusps coincide with sign boundaries, which keeps the chart structurally simple and is the working frame the BPHS and similar texts assume. Other conventions (Placidus, Koch, Equal-from-lagna with cusps mid-sign) exist and have their advocates. The whole-sign convention is the cleanest fit for classical readings and the convention Tempora reads charts against.

Beyond the primary chart, the divisional charts (D9 Navamsa, D10 Dashamsha, D60 Shashtiamsha and the rest of the harmonic divisions) compute against the same substrate. Each divisional chart partitions the zodiac into a smaller harmonic and assigns each partition to a sign in the divisional frame. The classical applications of each division (D9 for marriage and dharma, D10 for career, D60 for fine-grained karmic reading) are part of the chart-level reading and are computed deterministically from the primary chart. The substrate decisions documented above propagate to every divisional layer without further choice points.

7. Reproducibility as Audit

A research note that does not let a third party reproduce the work is not a research note. It is an assertion. Reproducibility is the property that distinguishes a published method from a personal practice. For chart-based work, reproducibility means that the inputs (date, time, latitude, longitude, ephemeris, ayanamsa) plus the chart-computation logic plus the divisional configuration produce the same chart on any compatible machine.

The inputs are deterministic and machine-readable. The ephemeris is open and audit-able. The ayanamsa is named and the angular offset for any date is computable. The chart logic is the classical whole-sign convention. There is no proprietary input at the chart-computation layer.

What follows the chart, the rule application, the period state, the historical comparison, the published reading, is where Tempora's research method enters. The rule layer is the subject of subsequent notes in this series. The chart layer is documented here so that any subsequent claim Tempora makes can be traced back to a chart any reader can independently reproduce. This is the property the classical tradition's manuscript record could not preserve. The modern numerical substrate restores it.

The discipline this note documents is small. It is the precondition for every larger claim that follows. Without an explicit substrate declaration, no chart-based research is reproducible. With it, the chart is a fixed point that two researchers can agree on before they disagree about anything else.

8. Limitations

Three limitations are worth naming explicitly.

First, the birth-time precision problem. Sub-minute birth-time precision matters for the lagna and for the dasha-period sequence. Most birth records, especially historical ones, carry birth times accurate to the nearest five or fifteen minutes at best. The chart that follows is precise as a function of the recorded birth time, but the recorded birth time itself carries an irreducible noise floor that the substrate cannot eliminate. Tempora's working convention is to publish chart-time noise transparently and to note when a forward call depends on a chart whose birth-time precision is below the threshold required for the claim. The substrate does not solve the input-data problem.

Second, the ayanamsa empirical-fit problem. True Pushya Paksha is the convention this paper documents. The full empirical defence against alternative ayanamsas is the subject of a separate study. Readers who object to True Pushya Paksha on first principles are welcome to recompute a chart against their preferred ayanamsa and compare. The reading that follows will differ at the resolution of the offset between the two ayanamsas at the date in question. The point of this note is to declare the substrate openly, not to argue the convention is the only defensible one.

Third, the divisional-chart precision problem. Higher-harmonic divisional charts (D60, D108 and the others) magnify any error in the underlying birth time. A chart computed against a birth time precise to the minute produces a stable D9 but a noisier D60. The classical sources are explicit about this: the higher divisions are taken seriously only when the birth time is verified through corroborating evidence (rectification against documented life events). The substrate documented here is precise enough to support divisional analysis when the underlying birth-time input warrants it.

9. Implications for Research

The substrate decisions documented here have three downstream consequences worth naming.

The first is for the forward-call architecture. Every dated call on the Tempora public tracker depends on a chart, and every chart depends on the substrate this note documents. The reconciliation discipline (each call carries the condition under which it is wrong, the window inside which the test resolves, and the verdict logged when the window closes) presupposes that the chart the call rests on can be recomputed by any third party. With the substrate explicit, the reconciliation is not just a Tempora claim. It is independently checkable.

The second is for the personal-imprint product. The Kaal imprint capture computes a chart from four user-supplied fields (name, date of birth, time of birth, city of birth) against the same substrate documented here. The imprint that follows is reproducible by the user against any independent stack that computes against Swiss Ephemeris and True Pushya Paksha. The imprint is not a black box. It is a deterministic output of a deterministic stack the user can inspect.

The third is for cross-research comparability. A Vedic research firm publishing against a documented substrate creates a common ground with any academic, statistical or classical researcher who reads the same substrate. Disagreements after that are interpretive, not substrate-level. The classical tradition's working record, dispersed across manuscripts and lineages, gave its readers no shared ground from which to compare. The modern substrate restores that ground.

10. What This Note Establishes

The chart-computation layer Tempora publishes against is deterministic, open and reproducible. Planetary positions are computed against Swiss Ephemeris. Sidereal correction is applied via True Pushya Paksha. Lagna and house computation use the whole-sign convention. Divisional charts derive deterministically from the primary chart. Birth-time precision is the principal input-data limitation; the substrate itself is precise.

Every subsequent Tempora claim about a chart rests on this layer. The rule applications, the period-state readings, the forward-test discipline and the published research notes that follow this one each take the substrate documented here as their input. With the substrate declared openly, the rest of the framework can be evaluated on its own terms.

11. Worked Example: The USA 1776 Chart Under Two Ayanamsas

This section illustrates the substrate decisions on a concrete chart. The chart is the United States 1776 founding chart, cast for the moment the Declaration of Independence was signed in Philadelphia at the conventional Sibly timing of 17:10 LMT. The chart is widely cited in mundane research and the natal positions are not proprietary. The illustration that follows shows how the choice between True Pushya Paksha and Lahiri ayanamsa shifts the sidereal positions of the chart's planets, and where that shift carries interpretive consequence.

Step 1: Compute the planetary positions

Swiss Ephemeris produces the tropical (geocentric ecliptic) longitudes of the planets at the chart moment to sub-arcsecond accuracy. These tropical positions are independent of the ayanamsa choice. They are the same on any independent stack that runs Swiss Ephemeris against the same date, time and location.

The same chart computation, applied with True Pushya Paksha as the ayanamsa, produces the following sidereal positions:

Step 2: The ayanamsa offset on the chart date

The chart moment is 4 July 1776 at approximately 22:17 UT (17:10 Philadelphia local mean time). Swiss Ephemeris with True Pushya Paksha returns an ayanamsa of 19.594° on that moment. The same engine with Lahiri returns 20.737°. The offset between the two ayanamsas on the chart date is therefore 1.143°, or roughly 68.58 arcminutes.

Applying the offset, the Lahiri chart for the same moment puts every planet 1.14° earlier in the zodiac than the True Pushya Paksha chart shows. The Sun under Lahiri sits at Gemini 22.58° rather than Gemini 23.72°. The Moon under Lahiri sits at Aquarius 6.42° rather than 7.56°. Each planet's position shifts by the same angular amount.

Step 3: Where the offset matters

An angular offset of 1.14° has three different consequences at three different resolutions of the reading.

At sign resolution (30° per sign), the offset changes a planet's sign only when the planet sits within 1.14° of a sign boundary. None of the USA 1776 planets sit within 1.14° of a sign boundary in this chart, so no planet changes sign between the two ayanamsas. This is the case where the substrate choice has the least visible consequence at the reading level. A chart where a critical planet sits near a sign cusp would behave differently.

At nakshatra resolution (13°20' per nakshatra), the offset shifts the nakshatra of any planet whose position within its nakshatra is within 1.14° of the boundary. Sun at Gemini 23.72° under True Pushya Paksha sits in Punarvasu (which runs from Gemini 20° to Cancer 3°20'). Under Lahiri the Sun at Gemini 22.58° remains in Punarvasu but its position within the nakshatra shifts. Mercury at Cancer 4.60° under True Pushya Paksha sits in Pushya (Cancer 3°20' to Cancer 16°40'). Under Lahiri Mercury at Cancer 3.46° still sits in Pushya. Saturn at Virgo 25.20° sits in Chitra under both ayanamsas. So no planet in this chart crosses a nakshatra boundary between the two ayanamsas. Charts where a planet sits at the edge of a nakshatra would show a different reading on this layer.

At nakshatra-pada resolution (3°20' per pada), the offset is large enough to shift the pada for any planet whose position is within 1.14° of the pada boundary. Sun at Gemini 23.72° under True Pushya Paksha sits in Punarvasu pada 4 (which runs from Gemini 23°20' to Cancer 3°20'). Under Lahiri the Sun at Gemini 22.58° drops back into Punarvasu pada 3 (Gemini 20° to 23°20'). The pada-level reading of the Sun is therefore different between the two ayanamsas. The classical interpretive consequence is non-trivial: Punarvasu pada 4 is associated with the Cancer-flavoured expression of the nakshatra, while pada 3 carries the Sagittarius-flavoured signature. The substrate choice produces two different readings on this layer.

Step 4: The lagna and the house system

The lagna for the USA 1776 chart at the Sibly timing computes to Sagittarius 7.72° under True Pushya Paksha. Under Lahiri the same moment computes to Sagittarius 8.86°. The 1.14° offset operates the same way at the lagna level: same sign, different position within the sign. Houses reckoned by the whole-sign convention assign the first house to the lagna's sign, so the house system is structurally identical under both ayanamsas in this case. A chart whose lagna sits within 1.14° of a sign boundary, however, would have its first house jump signs between the two ayanamsas, with every subsequent house shifting accordingly. The cascade through twelve houses is structurally consequential for the reading.

Step 5: Why the substrate declaration matters

The USA 1776 example shows the offset operating at three resolutions, with different consequences at each. Two different practitioners reading the same Sibly chart under the two different ayanamsas would produce broadly consistent sign-level readings on this particular chart, since no planet crosses a sign boundary at the offset. They would produce different nakshatra-pada readings on the Sun. They would produce different positions within signs throughout. And on a chart where any critical planet sat near a sign or nakshatra boundary, they would produce fundamentally different chart-level readings.

The substrate declaration is the methodological precondition for those differences to be addressable. Without it, two practitioners disagreeing on a chart cannot tell whether the disagreement is interpretive (different reading conventions applied to the same chart) or substrate-level (different charts produced from the same inputs). With it, the disagreement is at a specific layer and can be resolved by comparing the substrate choices.

The reader who wants to verify this worked example independently can do so against any Swiss Ephemeris stack with the named ayanamsa modes (Lahiri available as SIDM_LAHIRI, True Pushya Paksha as SIDM_TRUE_PUSHYA in the standard pyswisseph and similar libraries). The chart inputs are the same Philadelphia coordinates, the same 4 July 1776 date and the same 17:10 LMT timing. The output should match the table above to a fraction of an arcsecond.

11. Frequently asked

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