peer-review surface · cc by 4.0 · agpl · refutation invited

अनुसन्धानम्Research

Bharat Ephemeris is a research artifact with a seeker-facing surface — not the reverse. Everything is reviewable: the substrate paper and reproducible proof scripts in the published Zenodo deposit, quarterly residual reports, machine-checked propositions. Scholars are invited to refute us.

01

संख्याःThe numbers

machine-verified · zero failures
230propositions published · DOI v3
83 / 83machine-checked · published suite
890internal catalog · publication pending
805 / 805machine-checked · internal suite
9 / 9sovereign grahas · 0 foreign
200 yrresidual-audit span

Published: DOI 10.5281/zenodo.20024273 (v3 · 230 propositions · 83/83 machine-checked · 2026-05-04). Current internal catalog: 890 propositions · 805/805 machine-checked — APEX v5/v6, publication pending. The internal numbers are not yet covered by the cited DOI and are stated here only as work-in-progress.

Two separate claims, two separate proofs. The ephemeris accuracy claim — Sun 0.13′ p95 / 0.21′ max, Moon 0.51′ p95 / 1.0′ max, all nine grahas ≤ 3.3′ max across 1,000 samples spanning 2000–2050 — is an empirical measurement of Sūrya-Siddhānta + Kerala-school + dṛk computation against NASA/JPL Horizons, reproducible via scripts/audit/. The (R, g, k) substrate is a separate algebraic research program in number theory with its own DOI. Planetary longitudes do not derive from modular arithmetic, and this site does not claim they do.

02

प्रमाणानिArtifacts

cite these
Citable artifacts · DOI-anchored · open licences
artifactdetailtieraccess
साधार-दत्तम्(R, g, k) algebraic substrate — published recordDOI 10.5281/zenodo.20024273 (v3 · 230 propositions · 83/83 machine-checked · 2026-05-04)Tier-Sdoi.org →
मूल-लिपिःProof scripts — bundled in the same Zenodo depositReproducible proof scripts archived inside DOI 10.5281/zenodo.20024273 · CC BY 4.0Tier-Sdoi.org →
तुलना-दर्शनम्Accuracy audit — Bharat vs NASA/JPL Horizons1,000-date × 9-graha bake-off · 50-year span · Tier-S/W per grahaTier-S/accuracy →
तुलनम्Compare table — 38 platforms · 4 ground-truth observatoriesStructural rigour vs prediction-shaped · feature parity auditTier-W/compare →
Tier-S = falsifiable algebra · machine-verifiableTier-W = witness / provenance · explicit boundary
03

पूर्वताPriority

who wrote it first · cited

The mathematics this engine runs on was not borrowed late. It was written down in Bhārata first — in some cases by a margin of centuries, in one case by a margin of millennia. Each row below is a claim about surviving documents, and each carries a citation you can pull from any research library.

Documented priority · Bhāratīya locus vs the European statement usually credited
resultBhāratīya locususually creditedlead
मात्रा-मेरुःThe Fibonacci recursionPiṅgala, Chandaḥśāstra — enumeration of mātrā metres · c. 300–200 BCE (dating debated); the recursion is stated explicitly by Virahāṅka (c. 600–800 CE) and Hemacandra (1150 CE)1,2Leonardo of Pisa (Fibonacci), Liber Abaci · 1202 CE≈ 1,400 yr
मेरु-प्रस्तारःThe binomial trianglePiṅgala's prastāra (combinatorial enumeration of metres); the triangle itself set out in Halāyudha's Mṛtasañjīvanī commentary · 10th c. CE2Pascal, Traité du triangle arithmétique · 1665 CE≈ 700 yr
अनन्त-श्रेणीInfinite series for π, sine and cosineMādhava of Saṅgamagrāma (c. 1340–1425), transmitted through Nīlakaṇṭha's Tantrasaṅgraha (1501) and Jyeṣṭhadeva's Yuktibhāṣā (c. 1530) — with error terms and convergence accelerators3,4,5Newton (c. 1669) · Gregory (1671) · Leibniz (1673)≈ 250–300 yr
अष्टाध्यायीFormal generative grammar with metarulesPāṇini, Aṣṭādhyāyī · c. 5th c. BCE — ~4,000 ordered sūtras, a technical metalanguage, paribhāṣā metarules, and explicit conflict resolution (vipratiṣedha, 1.4.2)6,7Backus–Naur Form · 1959–1963 CE≈ 2,400 yr
आर्यभटीयम्Diurnal rotation · sine table · decimal place-valueĀryabhaṭa, Āryabhaṭīya · 499 CE — the earth's rotation producing the apparent westward motion of the stars (Gola 9), a 24-entry jyā table in steps of 3°45′ (Gaṇita 12), π ≈ 3.1416 explicitly labelled āsanna, “approaching” (Gaṇita 10), all inside a fully positional decimal framework8Rotation: Copernicus · 1543 CE. Place-value into Europe: Liber Abaci · 1202 CE≈ 700–1,000 yr
तात्कालिक-गतिःInstantaneous rate of changeBhāskara II, Siddhānta-Śiromaṇi · 1150 CE — tātkālika-gati distinguished from mean motion, the sine differential, and the observation that the instantaneous rate vanishes where the planet is stationary (a Rolle-type statement)9,10Rolle · 1691 CE; Newton and Leibniz · c. 1665–1675 CE≈ 500 yr

परम्पराThis engine stands in that lineage

Not as homage — as usage. The Kerala-school series in the kernel are the same mathematics: Nīlakaṇṭha’s equation-of-centre and śīghra corrections from the Tantrasaṅgraha (1501) are evaluated directly, and Mādhava’s periodic terms are the terms we sum. We did not rediscover this material from a European textbook and then decorate it with Sanskrit names. We compute with the series as the paramparā wrote them, and we measure the result against NASA/JPL Horizons in public.

priority = a claim about documentsaccuracy = a claim about residualsthe two are proved separately

What this section does not claim. (a) That any of these results reached Europe. Independent rediscovery versus transmission is an open historiographical question, and nothing above depends on the answer. (b) That Backus or Naur read Pāṇini — the kinship is structural, and it was later computer scientists who noted it. (c) That historical priority is evidence of this engine’s accuracy. Priority is settled by manuscripts; accuracy is settled by residuals, measured against NASA/JPL Horizons and published on /accuracy.

References

  1. [1] Parmanand Singh, “The So-called Fibonacci Numbers in Ancient and Medieval India”, Historia Mathematica 12:3 (1985), 229–244.
  2. [2] Kim Plofker, Mathematics in India, Princeton University Press, 2009 — ch. 3 (Piṅgala, prastāra, meru-prastāra).
  3. [3] C. M. Whish, “On the Hindú Quadrature of the Circle, and the infinite Series of the proportion of the circumference to the diameter exhibited in the four S’ástras…”, Transactions of the Royal Asiatic Society of Great Britain and Ireland 3:3 (1834), 509–523 — the first report of the Kerala series to European scholarship.
  4. [4] Ranjan Roy, “The Discovery of the Series Formula for π by Leibniz, Gregory and Nīlakaṇṭha”, Mathematics Magazine 63:5 (1990), 291–306.
  5. [5] George Gheverghese Joseph, The Crest of the Peacock: Non-European Roots of Mathematics, 3rd ed., Princeton University Press, 2011.
  6. [6] P. Z. Ingerman, “Pāṇini–Backus Form suggested”, Communications of the ACM 10:3 (1967), 137.
  7. [7] Paul Kiparsky, “On the Architecture of Pāṇini’s Grammar”, in Sanskrit Computational Linguistics, Springer LNCS 5402 (2009), 33–94.
  8. [8] K. S. Shukla & K. V. Sarma (eds. and trans.), Āryabhaṭīya of Āryabhaṭa, Indian National Science Academy, New Delhi, 1976.
  9. [9] Kim Plofker, Mathematics in India, Princeton University Press, 2009 — §6.3 (tātkālika-gati and the vanishing instantaneous rate at a station).
  10. [10] B. Datta & A. N. Singh (revised by K. S. Shukla), “Use of Calculus in Hindu Mathematics”, Indian Journal of History of Science 19:2 (1984), 95–104.
04

सहकार्यम्Collaboration

four tracks · open entry

साक्षात्-तुलनाIndependent residual reproduction

sākṣāt-tulanā

Run the published bench against your own DE441 build. We publish the 1,000-date × 9-graha test set; you publish your residuals. If they reproduce ours within noise, we cite each other.

ग्रन्थ-समीक्षाClassical-text co-citation

grantha-samīkṣā

If you publish on BPHS, Sārāvalī, Phaladīpikā, Jaimini-Sūtra and your edition meets the citation discipline (ISBN + translator + page), we link readers from /library to your publication; you cite the (R, g, k) substrate.

दशा-प्रस्तावRouted-daśā extension

daśā-prastāva

We currently route 12 daśā systems. If your paramparā computes a 13th — a regional Vimśottarī variant, for instance — submit a PR or paper. We bench it, route it, and credit you on the new /dasha/[system] page.

मेघ-गणनम्High-precision Moon · indigenous-series sprint

megha-gaṇanam

Joint sprint to take Candra from the current ~1 arc-minute (p95 0.51′) vs NASA/JPL Horizons toward arc-second precision — by extending the indigenous Kerala-school series (additional Mādhava / Tantrasaṅgraha periodic terms: evection, variation, annual equation), 100% Bhāratīya, zero foreign runtime. Co-publish, named co-authorship, open-source release.

05

सम्पर्कःContact

research@bharatephemeris.com

Propose a collaboration

Send your CV or publication list and the track you want to enter. The verified-academic API tier is ₹0, permanently.

प्रस्तावः Propose →

(R, g, k) = (ℤ/3³³⁷ℤ, 2, k=337) · published: DOI 10.5281/zenodo.20024273 (v3 · 230 propositions · 83/83 machine-checked) · internal catalog: 890 propositions · 805/805 — APEX v5/v6, publication pending