Every source this work relies on, refuses, or could not find — and, where the source makes a geometric claim, what happened when we tested it.
Listing the literature is easy. What is almost never done is to take a paper’s published figure, run it through an engine, and report what closes and what does not. Thirteen of the 27 entries below carry that measurement.
The first modern treatment. A seven-by-seven grid construction, drawable by hand. Their framing — how many points remain free once the largest triangles are set — is the question everyone since has answered.
Their construction misses concurrency by 0.2229% of the construction square’s side: about ten times more accurate than the traditional method, and not exact.
Straightedge-and-compass construction for concurrent Śrī Yantras; the problem reduces to the Apollonius circle–line–point problem. Independently derives four degrees of freedom. The most important paper in this field, and almost nobody cites it. Note his phrasing is careful — the spherical hypothesis *would have been reinforced* by plane impossibility; he does not claim the spherical form is false.
His four degrees of freedom agree with Huet’s count and with ours: imposing concurrency and concentricity on five parameters leaves three free.
The theorem: an under-determined problem with four real parameters admitting an infinity of solutions. Candid that his remaining parameters were fixed by aesthetic judgment. His bibliographic reconstruction — through Zimmer, Woodroffe, Campbell, Jung, Daniélou, Pott, Rawson and Renou — is the best scholarship in the field, and everyone since depends on it.
Solving his fifth parameter from concurrency alone reproduces his published value to 7 × 10⁻⁵ — independent confirmation of his algebra. But his figure satisfies concurrency and nothing else: its concentricity residual is 4.19 × 10⁻², the largest of any figure in this library. The innermost triangle sits visibly off centre.
Huet 1990 / 2002 — concurrency 1.38e-7, concentricity 4.19e-2, 43 chambers.
An eighth-degree polynomial, and the error metric this book adopts throughout — displacement at critical intersections as a percentage of R. Widely reported as having derived spherical equations. He has none, and says so himself, calling a polynomial description “doubtful”. His spherical argument is philological and dimensional, not geometric.
His root y_A = 0.279461220858 is reproduced exactly. His inference that the figure cannot be constructed in the plane fails on a conflation of *constructible* with *solvable in radicals* — Chiodo later constructs it.
Kulaichev 1984 — concurrency -3.58e-7, concentricity 1.18e-7, 43 chambers.
The source of the five-variable parameterisation b, c, d, e, g used throughout the modern literature **without attribution**. His spherical formulation in six variables is the only complete one in existence. Under-credited to the point of invisibility.
All seven of his Table 3 parameter sets satisfy our equations at 10⁻⁷. Two of them already satisfy the three “optimal” criteria — eight years before those criteria were proposed. One correction: his reported global optimum as h → π/2 does not survive checking; the traditional data minimises at r ≈ 20°.
Rao 1998 — plane optimum — concurrency -2.28e-7, concentricity 1.20e-7, 43 chambers.
The source of the kuṇḍāṃśa hypothesis — that the nine apex angles are multiples of 360°/81 — which appears nowhere else and is the most interesting untested claim in the archive. Anonymous: no author, no publisher, closes with a hymn rather than a colophon, and its distinctive phrasing returns nothing on search. Its file properties name “Sri Chakra Hari_16 Dec 2012.docx”, but Hari there is Saundaryalaharī, not a person. Cannot be cited as authority; can be tested, which is what Chapter 7 does.
The kuṇḍāṃśa claim is put to the engine in Chapter 7 rather than repeated. Its other uses are quotation only, on points that are independently checkable. One use is indirect and flagged: at Chapter 12 it relays a comparison of C. S. Rao’s that has not been read in the original.
An architect’s framing: previous work treats the diagram as occult or as abstract sacred geometry, and nobody has asked what functional objective the construction serves. Notes the requirement of 24 triple intersections.
The 24 triple intersections are confirmed and counted by the engine.
Do not cite as evidence. Reproduces 60, 43 and 40 consecutive words from Tiwari as its own prose; carries Huet’s parameters and theorem under the caption “Kulaichev method”; and inherits an OCR corruption of Huet’s “that one *too*” as “that one *two*”, which establishes the direction of copying.
Reports no parameters, no residuals and no geometry. Its algorithm calls undefined primitives and its performance analysis measures milliseconds instead of accuracy, so there is nothing here to test.
The parts list: four Śrīkaṇṭhas, five Śivayuvatīs, nine mūlaprakṛti, forty-three, eight petals, sixteen kalās, three circles, three lines. Names the nine by their **angles** — caraṇakoṇāḥ. Note the trayaś- / catuś- variant, 43 against 44.
The accompanying figure reverses the apex directions and contradicts the commentary’s own text — an engraving error that has propagated widely.
Gives the erasures as fractions of each chord: 1/16, 5/48, 1/3, 3/8, 1/3, 1/12, 1/16.
These are **identical** to Lakṣmīdhara’s integers once the unit is recognised as twenty-fourths of the chord — which dissolves a century-old charge that the two commentators disagree.
Erasures as absolute units: 3, 5, —, 16, 18, 16, —, 4, 3. Also the antarbhāva triad: meru = the sixteen Nityās, kailāsa = the Mātṛkās, bhū = the Vaśinīs — with **no word about elevation**.
The four Meru elevation profiles, each with its phala. The printed viviкramāt is corrupt; read tri-trikramāt with the Saubhāgyaratnākara p. 46.
All four profiles are implemented and selectable. None of them fixes a height: the tradition prescribes the elevation ordinally and never metrically.
Distinguishes bhauma and mairava prastāra. States plainly that **the innermost enclosure is the highest** — against the widely-copied web accounts, which have it backwards.
The triad bhū / ūrdhva / meru as a distinction of **relief**: incised below, raised but level, progressively raised. This is the passage Gopinatha Rao inverts.
The Kāśmīra construction method, and the 96-unit total scale giving 4 : 9 : 11 : 48.
The 4 : 9 : 11 : 48 proportions are the default ornament scale in the studio.
Diameter 48; chords at 6, 12, 17, 20, 23, 27, 30, 36, 42; erasures 3, 4, 0, 16, 19, 16, 0, 4, 3; and the complete apex topology.
The apex topology is verified against the algebra for all nine triangles. The twenty-seven numbers are mutually inconsistent at 2.675% of R — the tradition’s own noise floor, and the standard against which every reconstruction in this library is judged.
The Tradition — 12 : 6 : 7 : 11 : 3 in twenty-fourths — concurrency 2.21e-2, concentricity -3.63e-3, 43 chambers.
Names the Tantrarāja and the Gaurīyāmala as sanctioning the meruprastāra.
Cited by Bhāskararāya for the Meru and by Gupta for the kūrma. Not found in any digitised form. **The single highest-value missing source for this work** — it may settle the elevation, the kūrma, or both.
Listed among the nine Nityā-tantras by the Manoramā on Tantrarāja 1.2. A construction manual of exactly the right name. Does not survive.
Use with care. The locus for the Meru’s plan being the plane figure, and for the Meru / Kailāsa / Bhū triad. But he **inverts bhū**, which in the Lakṣaṇasāgara is the flat incised form; omits Lakṣmīdhara’s meru = the sixteen Nityās; and cites no source. Huet quotes the passage verbatim, which is how the error entered Western scholarship.
His Plate XCVIII — a photograph of the Śṛṅgeri metal plate — is the closest thing to a physical exemplar in the literature, and the best candidate for rectified photogrammetry.
The frontispiece added by the translators is a *correct* figure; the book’s own diagrams are not, and they disagree with it. A source of much subsequent error.
The cover carries the **false Śrī Yantra**, with floating apexes — triangles whose vertices do not meet. Propagated through Campbell and, inverted, through Jung.
Settles the orientation: five downward and four upward. His accompanying figure 28 is nonetheless a false Śrī Yantra.
Collates the entire modern literature on three-dimensional Śrīcakra typology, and **reports no proportions from any author**. The word yojana does not occur in the volume. Much of the negative result — that no text gives a Meru height — rests on this collation.
The Purāṇic inverted-cone problem. Has never met the Śrīvidyā literature, and vice versa — a connection never yet made.
Mount Meru at 84,000 yojanas high, 32,000 at the summit, 16,000 at the base — wider at the top. Wilson’s note calls it “an inverted cone”. **Incompatible with a yantra narrowing to a bindu**, and applied by nobody.
The name traces to a 2009 parody post; the site’s articles are unsigned and written in the first person plural. The site itself is real and still sells the source application. Treat the authorship as unverified.
Six questions this work leaves open, and where an answer would have to come from. They are listed because a study that reports only what it settled is not reporting honestly.
| question | where the answer lies |
|---|---|
| The third, fourth and fifth conditions | Rectified photogrammetry of an old metal plate — Gopinatha Rao’s Plate XCVIII is the candidate. |
| The Kundāṃśa hypothesis | Test on exact figures and on the base angles. |
| Chord 5 — erasure 18 or 19? | Manuscripts of the Kaivalyāśrama tradition. |
| Is the kūrma real or decorative? | Ellipse fits to type-III base arcs; one r, or nine. |
| Meru tier heights | Photograph a dozen historical Merus in elevation, with a scale. |
| All of the above, possibly | The Gaurīyāmala. |
This page links to sources; it does not reproduce them. Where a paper is genuinely open access the link goes to the publisher’s own copy. Where it is not, you will find the citation and our reading of it, and nothing else — the annotation is ours to give away, the paper is not.