Every calculation here comes from a book, and the book is named.

The ledger above is a list: thirteen texts, what each engine takes from them, what it declines to take, and where in the code each claim lives. A list can be checked, but it cannot show a rule being applied. This long read takes one birth and follows it through the rules named above - the sloka, the function, the result - so that a label such as Ch. 29, Sl. 1-5 becomes arithmetic you can redo on paper.

It also covers what the ledger has no room for: how the line count is produced, where two books disagree, the four reasons behind the refusals, what comes from no book at all, and which sourced results change when a birth time is a few minutes out. Every figure below was produced by running the server's own engines and then re-derived by hand from the cited rule. How the planetary positions themselves are computed is set out on the methodology page and is not repeated here.

Two shelves, kept apart

The thirteen entries fall into two shelves that the code never mixes. Six are astrology texts and feed the chart engines. Seven are numerology books, and each has an engine file of its own because each teaches its own system with its own tables.

The numerology shelf is different in kind. None of the seven is an old text; they are modern books and course notes, and they do not describe one shared system. Advanced Vedic Numerology has a grid, a dasha and a gochar of its own. Life With Number Magick teaches Chaldean name numbers, the Kua number and the Sepharial grid. Power of Numbers is built round an inverted-triangle chart, and the other four each add numbers the rest do not have. The code mirrors that with one engine file per system, so a result can always be traced to a single author and never to a blend nobody published.

What the line count measures, and what it does not

Each title above carries a figure for the lines that reference it. It is a count, not an estimate. Every .js file under the server's source folder is read line by line. A line counts for a text when it matches that text's pattern - the names the code itself uses for the book: its title, its abbreviation, or an author name that no other entry shares. The match is case-sensitive, which keeps ordinary prose from colliding with a title. Several mentions on one line count once.

The unit is lines and not citations because nobody agrees on what one citation is, while anybody can re-run a line count. The cost is known: a reference that wraps over two comment lines may count twice, and a sentence the server ships in three languages counts three times. The API test suite recomputes every figure the same way and fails by name when a typed number disagrees. The fix is to correct the number, never to adjust the pattern until it agrees.

What the figure does not measure is importance or correctness. Daivajna Vallabha is named on a handful of lines and still supplies the whole method behind the Prashna calculator and the Prashna feature. Read the figure as how often the code names the book, and nothing more.

The file-and-line references work on the same principle. Each row stores a short verbatim fragment of the line it points at, and a test checks that the fragment is still on that line, because a bare line number goes stale the moment someone edits the file above it. This long read names functions where the ledger prints line numbers, because a function name survives an edit.

From sloka to function: one birth, followed through

The birth used below is 15 May 1990, 10:30 IST, Mumbai. It is not a real person; it is the worked example the engine's own header carries for the 12th from the Karakamsa. You can reproduce it with thebirth chart calculator. The engine places the ten points as follows.

A divisional chart: the rule is in Ch. 6, the use in Ch. 7

BPHS Ch. 6, Sl. 2-4 names sixteen divisions of a sign. Sl. 10-11 gives the Saptamsa rule: the sign is cut into seven equal parts, and the count of signs begins from the sign itself when it is odd and from the seventh sign when it is even. Ch. 7, Sl. 1-8 then says what each division is consulted for - children and grandchildren from the Saptamsa, the spouse from the Navamsa, power and position from the Dashamsa, parents from the Dwadasamsa. The ledger cites Ch. 7 because the function header records the use; the arithmetic is Ch. 6.

Seven parts of a 30° sign are about 4°17' each. The Sun is at 0.40° of Taurus, the second sign and therefore even: the count starts from the seventh sign, Scorpio, and the first part stays there. The Moon is at 29.84° of Sagittarius, the ninth sign and odd: the count starts from Sagittarius itself, and the seventh part falls six signs on, in Gemini. The Lagna at 2.42° of Cancer, an even sign, starts from Capricorn and stays there. computeSaptamsa returns exactly these - Sun in Scorpio, Moon in Gemini, Lagna in Capricorn - and the Saptamsa calculator returns the same placements for your own birth. The Navamsa, Dashamsa and Dwadasamsa use the same shape of rule with a different number of parts and a different starting sign.

Arudha Lagna: count to the lord, then count again

BPHS Ch. 29, Sl. 1-3 gives the method in one sentence: see how many signs the lord of the Lagna is away from the Lagna, then count the same number again from the lord. Here the Lagna is Cancer and its lord, the Moon, is in Sagittarius, the 6th sign from Cancer. The 6th from Sagittarius is Taurus, which is the 11th house of this chart. computeArudhaLagna returns Taurus, 11th house.

Sl. 4-5 add two exceptions: a pada may not fall in its own house or in the 7th from it. If the count lands back on the house itself, the 10th from it is taken; if it lands on the 7th, the 4th is taken. Neither applies to this Lagna, but one applies a step later. The Upa Pad of Ch. 30, Sl. 1-6 is the pada of the house beside the Lagna. The translator's note there records more than two views on which house is meant and settles on the 12th for an odd rising sign and the 2nd for an even one; the engine follows that note. Cancer is even, so the 2nd house, Leo, is taken. Its lord, the Sun, is in Taurus, the 10th from Leo, and the 10th from Taurus is Aquarius - the 7th from Leo, which is not allowed. The 4th from Leo, Scorpio, replaces it, and Scorpio is what computeUpaPad returns. The Arudha Lagna and Bhava Padas calculators give the first of these and the pada of every house.

Char Karakas: a ranking, and a choice the text leaves open

BPHS Ch. 32, Sl. 3-8 defines the Atma Karaka as the graha that has travelled furthest through its sign, with minutes and then seconds of arc settling a tie. Sl. 13-17 names the roles that follow in descending order. computeCharKarakas is one descending sort on the degree in sign; the degree is held as a decimal, so the tie-break needs no code of its own.

Sl. 1-2 of the same chapter record a disagreement: some bring Rahu in only when two grahas tie, others always rank eight grahas including Rahu. The engine ranks the seven from the Sun to Saturn and fills seven roles, Atma Karaka to Gnati Karaka; the eighth name in the sloka's list, Stri Karaka, is not assigned. That choice is written in the header, and the Char Karakas calculator shows the ranking it produces.

Ch. 33, Sl. 1 defines the Karakamsa as the Navamsa sign the Atma Karaka occupies. The Moon at 29.84° of Sagittarius is in the ninth Navamsa of a dual sign, which counts from the fifth sign, Aries, and so ends in Sagittarius again. The 12th from it is Scorpio, which holds no graha in either the Navamsa or the birth chart, so of the clauses in Sl. 63-74 only the one for an empty sign applies and no worship clause fires. The Karakamsa and 12th from Karakamsa calculators return the same, and the essay on ishta devata and the Karakamsa is the longer treatment of that passage.

Dignity: two kinds of friendship, combined

A graha in a sign it neither owns nor is exalted or debilitated in is judged by its relationship with the lord of that sign, and the relationship has two halves. The natural half is a fixed table (Kannan Ch. III, Table B). The temporary half is read from the chart: BPHS Ch. 3, Sl. 56 makes a graha in the 2nd, 3rd, 4th, 10th, 11th or 12th from another its friend for that chart and its enemy otherwise, and Saravali Ch. 4, Sl. 30 gives the same six positions. Sl. 57-58 combine the halves into five grades. Kannan p. 24 turns the grade into a strength: full for exaltation or Moolatrikona, three quarters for own sign, five eighths for a friend's sign, half for a neutral's, nothing for an enemy's sign or debilitation.

The header of this function records a correction. An earlier version counted the temporary half from a graha's Moolatrikona sign, citing a page of Kannan that on re-reading describes the natural relationship. It now follows the BPHS sloka, with Saravali as the second witness. The engine uses this figure as the positional strength in its Shad Bala working.

Yogas: one settled rule per name

The yoga rules that were taken are each a single condition that two readers would apply the same way. Saravali Ch. 13, Sl. 1 forms Sunapha when a graha other than the Sun sits in the 2nd from the Moon, Anapha in the 12th and Durudhura in both. Saturn is in Capricorn, the 2nd from the Moon's Sagittarius, and Scorpio is empty: Sunapha. Rahu is in Capricorn too, but the chapter never mentions the nodes, so the engine does not count them. Ch. 14, Sl. 1 does the same from the Sun; Jupiter in Gemini is in the 2nd and Mercury in Aries in the 12th, so the chart has Ubhayachari. BPHS Ch. 75, Sl. 1-2 forms a Panchamahapurusha Yoga when Mars, Mercury, Jupiter, Venus or Saturn is in its own or exaltation sign in a kendra from the Lagna; Saturn in Capricorn in the 7th makes Sasa Yoga. detectYogas returns all three for this chart, and theyogas calculator lists the yogas found in your own chart. What a yoga does and does not tell you is the subject of what a yoga in your chart means.

Planetary rays: a choice the text itself reports

Saravali Ch. 36 is one book holding two answers. Sl. 2 gives each graha a different number of rays at exaltation, ten for the Sun down to five for Mars, Mercury and Saturn. Sl. 3-4 report a second school that gives every graha seven, say the majority lean that way, and note that all agree on zero at debilitation. The engine takes the majority view and, following Sl. 6, scales each graha by its distance from its exact debilitation degree. Here Venus, about eight degrees short of its exaltation point, has 6.69 rays; Mercury, about 29 degrees past its debilitation point, has 1.15; the seven total 32.71 of a possible 49. The adjustments in Sl. 7-9 are not applied, and the header says so.

The numerology shelf, worked on the same date

Numerology needs only the date and, for name numbers, the spelling. For 15 May 1990 the day reduces to a Mulank of 6 (1 + 5) and the whole date to a Bhagyank of 3 (the digits total 30). Those two are defined in the app's own rules document and explained in Mulank, Bhagyank and Life Path. The sourced books come in after that.

One name, two letter tables

The app carries two letter-to-number tables, and they are not interchangeable. The Pythagorean table runs the alphabet in order: A to I are 1 to 9, J to R are 1 to 9 again, S to Z are 1 to 8. The Chaldean table, taken from Life With Number Magick (p. 41-99) and checked letter for letter against the one printed in Numerology Made Easy, groups the letters differently and gives no letter the value 9. Take the sample name Meera Joshi.

The same spelling is a 4 under one table and a 7 under the other. Neither is an error. The name number calculator returns the Chaldean profile, and the numerology profile takes its Destiny, Soul Urge and Personality numbers from the Pythagorean table. A name written only in Devanagari has no Latin letters to value, and the engine returns no number for it and does not pick a transliteration, because spelling is exactly what these numbers depend on.

Life Challenges: subtraction, not addition

Numerology Made Easy (Ch. 8, p. 71-77) builds its Challenges by subtracting the reduced parts of the birth date from one another. The month is 5, the day 15 reduces to 6, and the year 1990 reduces through 19 and 10 to 1. First Sub-Challenge: 5 and 6 differ by 1. Second: 6 and 1 differ by 5. Third: 5 and 1 differ by 4. Main Challenge: the first two differ by 4, and it stays for life. The first window runs to age 36 less the Life Path - 33 here - and the next two are 27 years each, so the windows are 0-33, 34-60 and 61-87. calculateLifeChallenges returns 1, 5 and 4 with a Main Challenge of 4 and those windows.

Two sets of arrows on two different grids

The digits of the date are 1, 5, 0, 5, 1, 9, 9, 0, so the grid holds two 1s, two 5s and two 9s and nothing else. On the layout printed in Numerology: Metaphysical Secrets (Ch. 5, p. 85-89), with 1-2-3 up the left column and 7-8-9 up the right, the cells 1, 5 and 9 form a diagonal, and detectArrowsOfPythagoras reports that one line. The book gives it two names, Determination and Resignation, for the same three cells and no rule for choosing between them; the engine returns both. The Vedic grid of Advanced Vedic Numerology arranges the digits as 3-1-9, 6-7-5, 2-8-4, so its lines are made of different triples and mean different things. The Vedic grid and the Sepharial grid have calculators of their own, and the essay on missing numbers in the Lo Shu grid covers the grid itself.

Kua number: the one calculation that asks for gender

Life With Number Magick, Part 2 (p. 183-186) reduces the birth year to one digit - 1990 gives 19, then 10, then 1 - and then takes 11 minus the digit for a man and the digit plus 4 for a woman. That is 10, reduced to 1, for a man, and 5 for a woman; the book replaces a 5 with 2 for men and 8 for women, so calculateKuaNumber returns 1 and 8, each with its four directions. A birth before 5 February counts with the previous year, the book's stated edge case. The source has no formula that works without gender, so the Kua number calculator asks for it and returns nothing when it is not given.

Where two books disagree, and what the app does

The closing line of the ledger says the app does not quietly pick a side. These are the cases met above, with what the code does in each.

Disagreement between two books is handled in the open. Disagreement between the code and a book is a bug, and it is fixed. Saravali Ch. 14, Sl. 1 and BPHS Ch. 38, Sl. 1 agree on which side of the Sun makes Vesi and which makes Vasi. The engine once had the two the other way round; the header now records the mistake and the two slokas that settled it. Across the two shelves there is nothing to reconcile, since a chart and a number system are different instruments; when astrology and numerology disagree explains how the app reports both. The six reference dashas are on the alternate dashas calculator, beside the main Vimshottari timeline.

Four kinds of refusal

The copper rows above look alike, but they come from four different reasons.

• The text does not give one rule. General Raja Yoga detection is the clear case: choosing one of many formation rules would be the app's preference presented as the book's. Where a single settled rule exists, it is taken under its own name.
• The data needed is not there. BPHS Ch. 46 Sl. 40-41 gives Shastihayani's lords, years and stars, but its table lists 27 of the 28 stars, with Chitra missing, and the sloka gives no rule for the balance at birth. The engine does not fill either gap with a guess of its own: both are now taken from a cited published reference outside BPHS, Sanjay Rath's Vimsottari and Udu Dasa's (2002, Table 51), and flagged as such on the result. An uncited guess would be silently wrong for some births.
• The content is something this app does not issue. Death timing, lifespan, verdicts on what follows death, caste classifications of people and illness presented as destiny are all present in these texts and all left out, whichever book they come from. This is a product decision, stated as one; it is not a claim that the passages are not there.
• The detail is reduced. Bhrigu Sutras gives long prose for each of 108 placements; the app keeps the structure - a strong dignity lets the matters of the house flourish, a weak one tests them - in 216 short lines of its own wording. A paraphrase is not a transcription, and the ledger says which it is.

One absence runs across every book: remedies. Several of these texts give them at length - the closing chapters of BPHS, from Ch. 84 on, are largely remedial - and none are implemented. The app does not prescribe gemstones, mantras, rituals or donations.

What comes from no book

Three layers of the product are not on the ledger, because no book here supplies them. The first is the astronomy. Positions are computed with standard published algorithms (Meeus, Astronomical Algorithms) and moved to the sidereal zodiac with the Lahiri ayanamsa. This is not Swiss Ephemeris, and the methodology page says so. The app's rules document puts the Moon within roughly 0.1 to 0.3 of a degree, which is enough to resolve a nakshatra but matters at a boundary, as the next section shows. The ayanamsa calculator shows the offset for any date.

The second is place: a birth place is resolved to coordinates from a bundled city list first and a geocoding lookup second, and no coordinates are invented when both fail. The third is the app's own writing - the short paraphrased readings, the bands on a score, the wording of a note. Those are the product's voice, kept within the limits described on the accuracy page, and they are not attributed to a book.

Birth-time sensitivity: which sourced results move

A citation tells you where a rule comes from. It does not make the result robust. The same birth was run again fifteen minutes earlier and twenty-five minutes later.

At 10:15 the Lagna is still in the last degree of Gemini. Everything counted from the Lagna changes with it: the Arudha Lagna, the house the Upa Pad is taken from (the 12th, since Gemini is an odd sign), the Saptamsa Lagna, and the Panchamahapurusha Yoga. Saturn is no longer in a kendra, while Venus, exalted in Pisces, now is, so Sasa gives way to Malavya.

At 10:55 the Moon has crossed from the end of Sagittarius into Capricorn. Its degree in sign drops to 0.06, so it falls from first to last in the Char Karaka ranking, Mars becomes Atma Karaka and the Karakamsa moves to Taurus. The Lagna lord is now in the 7th, so the count for the Arudha Lagna lands back on Cancer and the exception of Sl. 4-5 sends it to the 10th, Aries. A graha near the end of a sign makes this whole layer fragile, and the Moon covers about a degree every two hours.

What did not move: every numerology result above, which needs only the date and the name, and the signs of the slower grahas. When no birth time is given at all, the chart function leaves out the Lagna and the houses, so the rows that depend on them are not returned and nothing is assumed in their place. What to do when the birth time is unknown covers that case, and the Lagna calculator shows how close your own rising degree is to a sign boundary.

Where to go from here

Each rule on this page has a place where you can run it on your own data. The calculators run one calculation at a time without an account. The Kundali feature puts the chart-based ones together and the numerology feature the number-based ones. The essays in the library explain single ideas at length: what a Mahadasha is, the Navamsa as a second chart and why apps disagree on your nakshatra.

Questions about the sources

Why are the code locations plain text and not links?

The source repository is not public, so a link would lead to an error page, and a dead link is worse than a reference. The file and line are printed so that anyone who does have the source can find the rule in one search. They are never translated, because a file name is not English.

Does a higher line count mean a more reliable calculation?

No. The count says how often the code names a book. A text named on a handful of lines can carry an entire feature, and a text named on many can still have a rule read wrongly. Reliability comes from the rule being stated clearly in the text, implemented as stated, and checked against a worked example - which is what the sections above do for one birth.

The book says something about my placement that the app does not show. Why?

Most often because the reading is a paraphrase with part of the source left out on purpose. The planet-in-house lines keep the structure of Bhrigu Sutras and drop its predictions of death, illness as destiny and the like. The nakshatra temperaments drop the caste classification and the physical and marriage predictions in the same chapter.

Another app lists several Raja Yogas in my chart and this one shows one or none. Which is right?

Both may be applying real rules. The primary text gives many ways a Raja Yoga can form, and several depend on systems this app has not built. The app does not run a general detector and reports only rules that are single and settled, each under its own name. A missing label here means that those particular conditions are not met, not that the chart lacks strength. What a yoga in your chart means goes further.

Why do some entries give an edition and year and others do not?

Author lines, editions and dates appear only where the project's own records state them. It would be easy to look up a plausible translator and year for a classical text, and wrong to print one the records cannot support on a page whose whole job is provenance. Where the record is silent, the page is silent.

My name number here differs from the one on another site. Is one of them wrong?

Usually neither. There are two published letter tables, and the same spelling gives different totals under each - 49 and 34 for the sample name above. Check which table the other site uses, and check the spelling: a doubled vowel or a dropped letter changes the total under either table.

What happens when a citation or a rule turns out to be wrong?

It is corrected in the code, and the correction is written into the function header beside the rule with the sloka that settled it. Two examples are described above: the side of the Sun that forms Vesi and Vasi, and the way temporary friendship is counted. Tests then hold the line: one recomputes every line count, and another checks that each code location still points at the line it claims to.

Can I check a result without access to the code?

Yes, for most of it. The rules worked above need only the positions and some counting: seven parts of a sign for the Saptamsa, a count to the lord and back for the Arudha Lagna, a sort by degree for the Char Karakas, a subtraction for the Life Challenges. Take the positions from the birth chart calculator, apply the sloka by hand and compare.