NoDataStorage (NDS) — Axiomatic Definition

AXIOM 1 — Identity is Computed

identity := f(secret, payment_proof_bytes)

Identity exists exclusively as the output of a deterministic cryptographic function. Identity is not created by registration, storage, or assignment. Identity is created only by computation.

AXIOM 2 — Identity is Not Stored

∀ identity ∈ NDS:
identity ∉ database

No persistent storage of identity exists within the NDS system.

Prohibited Manufacturer Storage

• identity
• payment_proof_bytes
• identity mappings
• ownership mappings
• identity database entries

AXIOM 3 — Determinism

Given:
  secret = constant
  payment_proof_bytes = constant

Then:
  identity = constant

Formally:
  f(secret, payment_proof_bytes) = deterministic

Repeated computation with identical inputs produces identical identity outputs.

AXIOM 4 — Verifiability Without Storage

Verification requires only the following inputs:

• secret
• payment_proof_bytes
• engraved_identity

Verification does not require:

• database lookup
• identity registry
• ownership registry

verify(identity) :=
  identity == f(secret, payment_proof_bytes)

AXIOM 5 — Epistemic Separation

Knowledge Domains

• Manufacturer knows: secret
• User knows: payment_proof_bytes, engraved_identity
• System stores: NONE

No single party permanently stores all identity derivation components in one location.

AXIOM 6 — Absence of Identity Database

The NDS system contains no identity database, ownership database, customer database, or registry.

∀ identity:
  identity_storage = NONE

AXIOM 7 — Cryptographic Binding

Identity is cryptographically bound to payment_proof_bytes.

• Without payment_proof_bytes, identity cannot be derived.
• Without secret, identity cannot be forged.

identity forgery probability ≈ 2^-160

AXIOM 8 — Statelessness

system_state := NONE

The NDS system has no internal mutable state. Identity derivation does not depend on:

• time
• database
• prior computation
• system memory

AXIOM 9 — External Storage Independence

External systems (e.g., blockchain, banking infrastructure, user-managed storage) may store payment proof. These systems are not part of NDS. Identity derivation remains stateless regardless of external storage.

AXIOM 10 — Identity Ontology

• identity_type: COMPUTED
• identity_storage: NONE
• identity_origin: CRYPTOGRAPHIC_FUNCTION

Identity is not an object; identity is a deterministic function output.

AXIOM 11 — Non-Existence of Stored Identity

stored_identity_count = 0

Identity exists only at computation time. After computation, identity persists only as an engraved representation or as a recomputable value derived from valid inputs.

AXIOM 12 — Canonical Statement

Identity is computed, not stored.

identity := Base64(HMAC-RIPEMD160(secret, payment_proof_bytes))
identity ∉ database