Research foundation · the floor · 239 propositions · 92/92 machine-checked

The substrate is algebraic, public, and refutable.

Every reading rests on the same floor — three Zenodo DOIs, one IJHS submission, one IBM Heron r2 hardware run. The floor is not the reading; it is what the reading is checked against.

i · master equation

Ψ(n) = 2ⁿ mod 9

Multiplication by 2 in the cyclic group ℤ/9ℤ has order six. The orbit {1, 2, 4, 8, 7, 5} is a closed loop. Every Vedic period — daśā, antar-daśā, transit — projects onto this orbit. The orbit is the spine of the year.

ii · structural triple

(R, g, k)

Read: R = ℤ/3ᵏℤ, g = 2, k ∈ {1, 2, 3, ...}. The 3-adic tower. Every chart carries a k-signature — the minimal k for which Ψ resolves the chart's known facts. Lower k is sharper.

02 / four invariants What does not change Across charts

Four invariants, independent of birth-data noise.

iΣ

Orbit sum

1+2+4+8+7+5 = 27 = 3³. Closure under multiplication implies a 3-tower.

Z369 / Tesla
ii∂

Phase transition

Daśā transitions are discontinuous on the orbit; transits are continuous.

BPHS · 47.4
iiiα

α-time

The substrate-cert at the moment of birth. α = 1.000 is the rare unforked instant.

Engine
03 · open propositions

239 propositions, 0 fail at last verification.

10.5281 / zenodo.20024273 Trikoṇa Algebra · 33 theorems on the (R, g, k) substrate Zenodo · CC-BY 4.0 · 2025-11-09
10.5281 / zenodo.20107412 α-time · the substrate-cert protocol for Vedic computation Zenodo · 2026-01-22
10.5281 / zenodo.20221855 IBM Heron r2 · 15-anchor R²=0.9995 hardware validation Zenodo · 2026-03-04

A submission is open at the Indian Journal of History of Science. The text is on Zenodo before the journal accepts. We do not gate publication on review.