Model specification: Finite ledger template

A proposed selection package must address the following entries.

1. Operational class and access. Name the process class, data assignment, admissible instruments, observations, and equivalences. State every class restriction. Default status here: $\mathsf{DECL}$ as a required interface, with actual selection $\mathsf{OPEN}$.

2. Order formation. Name the relation extracted and prove that ${⪯}_D$ is a partial order on the claimed carrier. If it is obtained from influence by closure, restriction, or quotient, justify that operation. Default status: $\mathsf{OPEN}$.

3. H-faithful-generation. Construct the representation and prove (eq:faithfulness)–(eq:generation), with properness and a declared fixed dimension $m\ge 3$. A conditional theorem may explicitly assume that the proposed extraction returns such a representation. It must then state that construction and admission remain conditional. Default status: $\mathsf{OPEN}$.

4. H-homogeneity. For

   $$\mathrm{Aut}(K_D)=\{A\in \mathrm{GL}(V_D):A(K_D)=K_D\},$$

   require

   $$\forall u,v\in \mathrm{int}{K}_D\exists A\in \mathrm{Aut}(K_D):Au=v.$$

   Either prove this from the declared operational premises or mark it $\mathsf{ASSUMED}$. Default status: $\mathsf{OPEN}$.

5. H-strict-convexity. Require

   $$u,v\in K_D\setminus \{0\},u,v\text{non-proportional}⟹u+v\in \mathrm{int}{K}_D.$$

   Either prove it or mark it $\mathsf{ASSUMED}$. Default status: $\mathsf{OPEN}$.

6. H-continuum or extension. If used, specify the refinement or completion, comparison maps, topology, compatibility conditions, and convergence theorem. State separately whether uniqueness is claimed. Default status: $\mathsf{OPEN}$, or explicitly not applicable to a construction using no such step.

7. Operational equivalence and extraction invariance. Prove that equivalent data and permitted relabellings produce affinely isomorphic representations, with an invertible linear map on the cone differences. Do not hide an independently supplied Lorentz cone in the extraction choices. Default status: $\mathsf{OPEN}$.

8. Exactness, tolerance, and evidence. Distinguish exact signalling guards from tolerance guards. If statistical or implemented data are used, give the applicable coverage, calibration, and complete-channel allowances. Default status: $\mathsf{OPEN}$, with exact mathematical-data branches identified separately.