GIGI Builds — book cover: Bee Davis with Bird, title over an illustrated portrait
First edition · ISBN 9798181715820

Companion site to the book

GIGI Builds

The fiber-bundle database: a working engineer’s guide from schema to shard — eighteen chapters, every one of them ending in an experiment you can run tonight.

by Bee Rosa Davis · Davis Geometric · 2026

“The engine carries the whole tuple in memory on every operation; the rows are a shadow it casts.”
Get the book Clone the engine

The book

An afternoon to read. Under a minute to run.

In 1970 we flattened data into tables and spent fifty years bolting the shape back on with sidecars — a search service for the proximity we discarded, a graph database for the adjacency, a vector store for the geometry, a lineage tool for the provenance. GIGI Builds is the ask to look under the table: your data has a literal shape — curvature you can measure, holes you can count, loops that remember — and a database that stores the shape alongside the rows.

The phone book and the moon. A phone book is an index with stuff at each name — that’s every relational database ever shipped. Now imagine the index isn’t a flat list but the surface of the moon: terrain under every point, craters, and the strange fact that walking a closed loop can leave you facing a new direction. GIGI treats your database like the moon. The rows are still there — every query returns what Postgres would — but every response also carries the geometry, free, because the substrate computed it on the way through.

Seven parts climb the generator G = (M, g, J, ∇, B, Γ) one piece at a time — from the O(1) address to gauge encryption to running the engine in production. Chapters end with exercises. Claims end with receipts.

The builds

Seven parts. Eighteen chapters. Every one runs.

Each chapter is a build: the prose walks the idea, the code is in the repo, and the exercises reproduce the receipts. Here is the full map — and all 126 exercises are online.

I

The Shape of Data

chapters 1–3 · +1 web extra
Chapter 1

The Phone Book and the Moon

Sixteen operations, side by side: the stack you already run against the moon you could be standing on — and the bill, including what GIGI will not do for you.

side-by-side ops
 Chapter 2

Sections, Not Rows

A record is a section of a bundle. Three dividends follow — starting with migration without ceremony and ending with questions about shape becoming well-posed.

definitions 1.1–1.4
 Chapter 3

The Address Is a Coordinate Chart

Thirty lines of mixer, three gates, one birthday bound: the O(1) address that doesn’t grow, and the claim that matters at 3 a.m.

O(1) hashing
 Web extra

The Mesh That Audits Itself

A tetrahedral mesh as a fibered object: every tet carries certified shape data, so adaptive refinement leaves a queryable audit trail. Not in the printed book — more bonus chapters will land here.

interactive demospec & harness on GitHub
II

The Engine Room

chapters 4–7 · +1 web extra
Chapter 4

Anatomy of a BundleStore

The insert path step by step, the accumulators that replace your cron job, and the epoch counter that makes caching honest.

Welford stats
 Chapter 5

Durability: WAL, mmap & CoW Snapshots

The logbook and the chart room — plus war stories from the commit log, including the record that was counted twice, twice.

war stories
 Chapter 6

DHOOM: The Wire Format That Knows the Zero Section

A stenographer who knows the speaker: eight sigils, interned pools, and elision machinery that only sends departures from the schema.

wire format
 Chapter 7

GQL: A Language Where Geometry Determines Complexity

Seven principles, a verbatim session, the complexity contract with its one load-bearing word — and the table that confesses.

query language
 Web extra

Chemical Space Has a Shape

2,200 molecules as sections of a bundle, flown through in 3D. κ prices the weird ones without being told, and a one-line COVER carves a glowing slab out of property space.

interactive 3D
III

The Signals That Run While You Sleep

chapters 8–10 · +1 web extra
Chapter 8

The Engine’s Opinion: Interoception

Curvature κ in three voices; the map from κ to confidence; the price of having an opinion — and when that opinion is gameable.

anomaly detection
 Chapter 9

Spectra and Communities

The spectral gap in three voices, Cheeger’s bridge over the Maine, Ollivier–Ricci — and expander honesty when the spectrum is a wall of noise.

clustering, free
 Chapter 10

The Brain on the Wire

Eleven brain verbs — SAMPLE, FORECAST, DREAM, RECONSTRUCT, INPAINT, PREDICT, ATTEND, EPISODIC, SEMANTIC, EXPLAIN — and CONFIDENCE, the verb that refuses.

brain verbs
 Web extra

The Spectrum Finds the Rooms

A graph drawn at its own Laplacian eigenvectors, recomputed live. Cut the bridges and watch λ₁ fall while the three communities physically tear apart — the layout is the math.

interactive 3D
IV

What the Loop Remembers

chapters 11–12 · +1 web extra
Chapter 11

Holonomy: What the Loop Remembers

Carry meaning around a closed loop and watch it come back rotated. Gauss–Bonnet on a discrete loop, holonomy debt, and an audit ledger the geometry agrees with.

the ledger
 Chapter 12

Torsion: The Asymmetric Carry

Cartan 1922, the connection that refuses to commute, the four (or five) homonyms of τ — and the empirical receipt Marcella carries.

open slot, named
 Web extra

The Loop That Remembers

Honest parallel transport on a curved 3D terrain: drag the loop, carry the frame, and read a live Gauss–Bonnet receipt — walked deficit vs integrated curvature, computed independently.

interactive 3D
V

The Theorem

chapters 13–14
Chapter 13

The Single-Node Tour, with Theorems

T1–T4 on one node: Betti numbers assembled from per-chart pieces, gauges canceling around closed loops — and a penguin walk through baseline, shard, monodromy.

T1–T4
 Chapter 14

The Navigator’s Honest Map

The universal bound that always holds, the naive bound that fails, distributed Lanczos as the fix — and an engine that abstains rather than lies.

T5–T7, sharding
VI

Gauge Encryption

chapters 15–17 · +1 web extra
Chapter 15

The Geometry Is the Encryption

Five modes, not six — the honest correction. The equivariance theorem, the affine invariant ring, and the Curvature-MAC.

five modes
 Chapter 16

The Verifier Without Decryption

Carol holds no key and audits the bundle anyway: the verifier API, canonical fingerprint order, and the three anchor tests.

0-decrypt audit
 Chapter 17

Delegation, Forward Secrecy & What’s Not PQ-Safe Yet

Four seals from Aff(R) to lattice K-of-N threshold, the RG-flow ratchet for per-write forward secrecy — and the honest limit, stated plainly.

ML-KEM-768
 Web extra

Noise to Everyone Else

GIGI spelled in point-cloud fibers, each letter scrambled by its own SO(3) gauge. Ratchet the epochs, revoke your own key, and watch Carol verify the wire without ever reading it.

interactive 3D
VII

Running the Engine

chapter 18 + appendices · +1 web extra
Chapter 18

Bring-Up, Watch, and the Edge of the Public Story

One process, five binaries, one verb. The 503 contract, cold-start self-heal, the geometric column no other logbook has — and Marcella as the headline live customer.

production
Appendices A–D

Every Verb in One Room

The full HTTP API, a glossary mapping geometric terms to engine analogues, the citation index — and the math companion: one generator, eight constructions, three open problems.

reference
Web extra

The Weather on a Sphere That Notices

480 stations streaming onto a globe with no monitoring job anywhere — every insert priced at the door by its own station’s history. Break one and watch it bloom.

interactive 3D

GIGI, the database

A conventional database stores rows. GIGI stores the geometry rows live on.

GIGI (Geometric Intrinsic Global Index) is a fiber-bundle database engine, written in Rust, free for noncommercial use. Curvature, spectral connectivity, holonomy, and confidence update incrementally on every insert and ride along on every query — no sidecar services, no quarterly batch job.

Day one, side by side
You want to…Conventional stackGIGI
Look up by keyB-tree, O(log N)SECTION b AT (id='X') — O(1), response carries κ + confidence
Detect anomaliesStreaming pipeline + outlier modelCurvature κ already updated per insert — outliers are where κ spikes
“How clustered is my data?”Run k-means offlineSPECTRAL b — Fiedler value λ₁, cached, incrementally refreshed
Join two tablesHash joinPULLBACK orders ALONG customers — a pullback of bundles
Encrypt analytics columnsColumn encryption breaks the indexesGauge encryption preserves κ, λ₁, anomaly scores at native speed
 
# clone tonight — the book's standing offer
git clone https://github.com/nurdymuny/gigi
cd gigi && cargo build --release
PORT=3142 ./target/release/gigi-stream

# or just poke the public instance
curl https://gigi-stream.fly.dev/v1/health

Free to read, run & teach

The engine and the book ship under PolyForm Noncommercial 1.0.0: personal use, research, teaching, and running every experiment in every chapter are all permitted purposes. Commercial licensing is reserved.

“I make money off of the people who make money; everyone else reads, runs the experiments, and teaches.”

The author

Bee Rosa Davis

Founder of Davis Geometric, an independent research lab applying differential geometry, fiber-bundle theory, and spectral methods to AI interpretability, plasma physics, pharmacokinetics, agriculture, financial reconciliation, and national security. Brown University alum, NASA engineer, holder of the patents this book cites by number — and author of The Geometry of Flight, the substrate story underneath this one.

“Every receipt this book prints is a receipt the reader can produce.”
Bee reaching for a book with Bird perched on the shelf
Portrait of Bee with Bird on her head
Bee holding a cup of coffee in the park with Bird on her shoulder