Theoretical audit demonstrates formal proof provenance and verification boundaries in the discrete algebraic corpus, highlighting strict distinctions between discrete and continuous structures.
D2b-C — Evidentiary Companion to D2b: Reproduced Statements, Proof Structures, and Verification Status from the Discrete Corpus D2b-C is the evidentiary reference layer accompanying D2b. Its purpose is to make the logical and documentary status of the claims used in D2b explicit and auditable against the primary discrete corpus. The document separates three orthogonal questions for each relevant claim: Provenance: whether the assertion originates in D1, D2a, D2a-C, the primary discrete corpus, or standard mathematics. Verifiability from D2b-C: whether the assertion can be reconstructed directly from D2b-C or requires consultation of the underlying corpus or computational certificates. Logical role: whether the assertion functions as a premise, construction, conditional bridge, imported mathematical result, reported computation, or conclusion. D2b-C deliberately distinguishes documentary status from verification mode. A corpus-reproduced statement is therefore not automatically presented as an independently reconstructed proof. Reported computations and exhaustive enumerations are identified as such when their certificates are not reproduced. The companion establishes a strict separation between the principal layers of the construction: [MP(III)+CPEΩ_7×_F gTrin,] followed, only under the explicitly stated H6 bridge, by the octonionic and continuous identifications involving (G_2). Particular attention is given to the distinction between the discrete Fano-plane automorphism group and the continuous Lie group (G_2), to the distinction between the skew derivation algebra and the full derivation algebra, and to the separation of the GH and H6 conditional boundaries. D2b-C also records the remaining limitations of the evidentiary layer. In particular, reported finite computations such as the dimension-14 calculation, Killing-form non-degeneracy, and exhaustive classifications are not presented as independently certified when their exact computational certificates are not reproduced. Likewise, simplicity of the discrete algebra is not promoted beyond the evidence actually supplied. The document is therefore not intended to replace the primary corpus or reproduce every underlying computation. Its function is instead to provide a transparent evidentiary map for auditing D2b: what is stated, where it comes from, what is actually reproduced, what remains conditional, and where external mathematical results enter. D2b-C is restricted to the discrete perimeter of D2b and does not retro-import later continuous or cosmological closures into the discrete derivation.
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Fabio Diniz Pinto (2026) studied this question.
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