ZeqID — your identity is an equation
On most systems your identity is a row in someone's database. Here it's a mathematical object. You choose an equation, and your identity — your ZeqID — is derived from it. The framework never stores the equation itself; it stores only what it needs to recognise that you can reproduce it. Your identity is something you know how to compute, not something a server holds on your behalf.
From equation to ZeqID
When you register, the equation is hashed — PBKDF2-SHA256, 210,000 iterations, with a random salt — and your ZeqID is derived deterministically from that hash:
The result looks like ZEQ7G8K2…. Because it's a pure function of the equation, two properties
follow that make ZeqID unusual:
Deterministic
The same equation produces the same ZeqID on every node in the lattice. You are the same identity everywhere, with no central registry syncing anything.
Zero-knowledge
The raw equation crosses the wire zero times and is never stored. Login recomputes the hash from what you type and compares — the secret stays with you.
Yours to reproduce
Because identity is derived, not issued, no one can revoke or reset it. Whoever can reproduce the equation is the account — which is exactly why the recovery file matters.
Simple-tier accounts can start from a memorable phrase (the framework turns the phrase into an equation); Expert-tier accounts supply the equation directly. Either way the derivation is the same, and the tiers are covered in identity tiers; the login handshake in the account equation.
Saving your equation
Because there is no password reset — nothing to email you, no support desk that can let you back in — you keep your own way back. Creating an account must show you this before anything else: signing up never silently logs you in, because if you lose the equation, the account is genuinely gone. So the framework hands you the credential — your equation and its salt, sealed with HITE encryption under a PIN you choose — and lets you store it in whatever form survives your life best:
A .ZEQ recovery file
The sealed credential written to a file you download and keep. The plain, portable form — the one artifact that lets you back in.
Hidden inside a photo
Carry the sealed credential inside an ordinary image. The photo still opens normally everywhere, with no visible trace that anything is in it.
Inside a PDF or as ciphertext
The same carrier works in a PDF, or you can copy the credential as encrypted text — never the readable equation.
Hiding your equation in an image
The HITE Carrier embeds your sealed credential into a host photo or PDF while keeping the host a completely valid, normally-openable file. It doesn't crudely staple bytes to the end — it tucks the payload where every decoder already knows to ignore it:
| Host | Where the credential rides | Why it's invisible |
|---|---|---|
| JPEG | an APP15 (0xFFEF) marker segment after the start-of-image | every JPEG decoder skips unknown APPn segments |
| PNG | a private ancillary chunk (zeQc) before IEND | every PNG decoder ignores ancillary chunks |
| PDF / other | appended in a tolerated trailer | readers ignore trailing bytes |
The image displays identically in Preview, a browser, a phone, an editor — it is a real photo. There is no plaintext marker anywhere in it: the only way to confirm the credential is even present is to successfully decrypt it, because what's hidden is the HITE-sealed blob, not the equation. So a picture of your cat can quietly be your recovery key, and anyone who doesn't hold your PIN sees nothing but a picture of your cat.
your equation → hashed (PBKDF2) → ZeqID (ZEQ7…)
your equation → sealed by HITE under your PIN → .ZEQ file · a photo · a PDF (any of them)
Recovery is the reverse: hand back the file — the plain .ZEQ, the photo, or the PDF — enter your PIN,
and the carrier extracts and decrypts the credential to sign you in.
One identity, one orb
Every user ZeqID is paired with a personal-orb ZeqID — a companion identity (a prefix swap on the same derivation) that a machine or agent can act under on your behalf without being you. It inherits the same determinism: the orb is the same everywhere you are.
Read next
- The account equation — the equation-login handshake, step by step.
- Identity tiers — Simple vs Expert, and what each key can do.
- Data sovereignty — because your ZeqID is the same on every node, your data can follow you to any of them.