Formal ledger
Each card holds one construction at its formal address and follows its relation through witness, use, field instance, and lineage.
Five offices
A.01 · Address
Ev : P* → (N>0, ×)
Ordered prime words carry a distinct address through commutative evaluation.
Status
Exact monoid relation.
Certified dependents
V8 word-versus-winding witness; V10 receipt-state implementation; Memory Return.
Native instance
The verifier reads Ev(2,3)=Ev(3,2)=6 while preserving their distinct ordered words.
Lineage
Euclid · Brahmagupta · Fibonacci · Turing
G.01 · Gate
K₈ = (V₈, E₈); |V₈| = 8; |E₈| = 28
Eight addresses generate twenty-eight pairwise relations. Seven perfect matchings partition the complete relation set.
C.01 · Carrier
G = [[−2,1],[1,2]]; G² = 5I
The root carrier has split signature and a stated null-coordinate normal form.
Status
Exact two-by-two algebra.
Certified dependents
V1 root-carrier identity; V2 null-coordinate congruence; V3 signature distinction.
Native instance
The Structure of Survival places the metric carrier beside the native proper-time and null-signal read used by GPS.
Lineage
B.01 · Boundary
K̂ = K ∪ {F}
The historical record and an incoming occurrence keep distinct addresses at admission.
Status
Declared admission structure.
Certified dependents
V10 receipt-state implementation; checksum ledger; versioned audit record.
Native instance
Paper, source, verifier, passing output, and file-identity receipt form one publicly inspectable occurrence record.
Lineage
Π.01 · Contact
G_embodied = e; Π(e, ℓ) = c = (e, ℓ, w, r)
Embodied carrier, light, ordered address, and receipt form one contact record.
I.01 · Inputs
I₂ extension; t = Φ²; admission policy
Each supplied structure enters at its named interface with its own stated office.
Derived cards
C.02 · Carrier distinction
inertia(Q ⊗ Q) = (2,2); inertia(G ⊕ I₂) = (3,1)
The tensor carrier and the supplied Lorentzian extension occupy distinct signature classes.
Status
Exact signature calculation.
Certified dependents
V3 spectrum and signatures; V4 rejected diagonal transition; V5 pp-wave relation.
Native instance
The pp-wave interface carries its own metric, source, and curvature data through the supplied Lorentzian extension.
Lineage
L.01 · Lift
q² = −I; q⁴ = I
A returned visible form can carry a central difference in its lift.
Record route
Named source coordinates and their paper relations.
Nineteen source and dependency maps held beside the paper shelf.
Formal editions, visual plates, sources, and current audit materials.