Pi-Search

What Pi-Search reveals

Pi-Search is the research instrument for π exploration inside the TFV — The First Verse project. It exposes the decimal expansion of π through queries that match how the foundational research at The First Verse actually reasons about π: not just substring lookups, but sums, squared sums, gematria bridges, and position-aligned multi-condition queries.

Why this matters — the foundational research

The mathematical patterns connecting The First Verse of the Torah, Genesis 1:1 to the decimal expansion of π are documented at length in the TFV foundational research. Pi-Search exists so any reader can verify these findings independently, search for adjacent patterns, and bring the instrument into their own study.

For the complete background — the original derivations, the cascade analysis, and the probability arguments — see the foundational π research at TheFirstVerse.com.

Data source & provenance

The 100 billion decimal digits of π that Pi-Search searches come from the first chunk of Peter Trueb's 2016 22.4-trillion-digit π computation, performed with the high-precision arithmetic engine y-cruncher and sponsored by DECTRIS. The complete computation is part of the publicly documented chronology of π calculation; the first one-trillion digits are hosted by the Internet Archive, a long-running non-profit digital library.

Public download — verify the corpus for yourself

Anyone can download the same dataset Pi-Search uses, run their own integrity check, and recompute any finding here from first principles. The full archive item is at:

Who confirmed the source is genuine

The archive item is signed off by these independent fixed points:

• Creator (uploader): Peter Trueb — the same person who performed the computation, with the calculation publicly documented at pi2e.ch/blog.
• Sponsor: DECTRIS, a Swiss detector-systems company, named in the metadata as funder.
• Tool: y-cruncher (Alexander Yee), the standard open implementation for record-setting π / e / γ calculations.
• Host: Internet Archive, an established non-profit with permanent URLs and SHA-1 fixity records for every uploaded file.
• Independent corroboration: the same digit sequence appears in cross-referenced computations by Yee, Kondo, and others; the first 100,000 decimals match every canonical published value of π.

Integrity verification

Sourcing public data is not enough; every research instrument should verify the data it runs on. Pi-Search performs four independent integrity checks against the corpus and publishes the results so they can be reproduced.

The four checks

1. Canonical spot check — the first 100 decimals of the corpus are compared byte-for-byte against the universally published first 100 digits of π.
2. Independent recomputation — the corpus is recomputed via mpmath at higher precision (10,500 digits) and the result is compared byte-for-byte against the corpus across its full length.
3. Random-sample re-verification — 50 random positions are independently re-verified against the higher-precision recomputation. Random sampling is independent of where systematic errors might cluster, so a clean random sample is a strong integrity signal.
4. Cross-source structural validation — a complex 5-condition pattern (the canonical Genesis 1:1 sum cluster: L=7→28, L=17→82, L=165→737, L=611→2,701, L=628→2,783) was searched across an independent third-party 1-billion-digit π reference. The 2nd occurrence position predicted by the corpus appears at the exact same position in the independent source. This is a stronger check than per-digit sampling because a single corrupted byte anywhere in 628 consecutive digits would break the alignment — agreement of the deep occurrence is empirical proof of byte-for-byte equality across the first 1B.

Verification results — full 100,000,000,000 decimal corpus

Every check below ran against the full 100-billion-digit corpus. Anyone can reproduce the methodology against their own download from the archive.org item; the verification script is published below.

A subset of the random-sample results

Reproduce these results yourself

The verification script is open and runnable. Save it locally, place a copy of pi_10k.txt in a data/ sub-folder, and run python integrity_check.py. It re-runs all three checks and prints PASS/FAIL.

Verified canonical findings

Each finding below is verifiable in the tool with ease — click any Verify → button and you'll land on the tool with the query already in the search box. Press Search (or hit Enter) to see the result.

The Power-of-X framework

A central operation in TFV π research is summing the digits of π under a transform. The trivial case — Power-of-Aleph — is the ordinary sum (each digit contributes its own value). The next case — Power-of-Bet — squares each digit before summing. The naming follows the gematria of the Hebrew letters: Aleph = 1, Bet = 2, so "Power-of-X" means "raise each digit to the gematria of letter X."

The framework generalizes: Power-of-Gimel cubes each digit (Gimel = 3), Power-of-Daleth raises to the fourth power (Daleth = 4), and so on. Pi-Search currently exposes Aleph and Bet at launch; additional powers can be added with negligible precompute cost as findings surface that require them.

The Power-of-Bet operation is foundational to the SGV→RGV bridge: the first 82 (= SGV of The First Verse of the Torah, Genesis 1:1) decimals of π, each squared, sum to 2701 (= RGV of that same verse). The bridge between the small and standard gematria of the verse is mediated by the squared-sum operation on the decimal expansion of π itself.

The TFV-canonical position convention

Pi-Search counts decimal positions of π starting from the first decimal digit, not including the integer "3". So position 1 is the digit "1", position 2 is "4", position 3 is "1", and so on through π = 3.141592653…

All documented TFV findings (165 → 737, 611 → 2701, 82-squared → 2701, the position of "2701" at decimal #165, and the rest of the cascade) are stated and reproduced under this convention. If you prefer the alternative "include the leading 3" convention, simply shift every position by 1.

Glossary

Recurring terms in TFV research and in the Pi-Search interface.

Scientific integrity

Frequently asked questions