Symbolic Hygiene in Scaling Claims: A Checkable Protocol and a Small Benchmark

This work introduces the Symbolic Hygiene Protocol (SHP), a conservative, checkable framework designed to prevent category errors in scaling and normalization claims. SHP addresses a recurrent failure mode in technical discourse: the unintended elevation of representational artifacts—such as base-dependent encodings, metaphors, mnemonics, or narrative analogies—into governing mathematical structure.

SHP enforces a strict two-layer separation between a Governing layer (definitions, identities, types and units, base or model assumptions, objectives, metrics, and reproducible procedures) and a Commentary layer (metaphor, intuition, and narrative framing). Reverse influence is explicitly forbidden: commentary may annotate governing claims but must not amend them. The protocol incorporates a minimal type discipline, explicit handling of representation versus value, and hygiene requirements for logarithms, bases, norms, and models.

To operationalize the protocol, SHP provides a deterministic checklist that returns PASS or FAIL(SHP-*) with explicit reason codes and evidence pointers. A reusable taxonomy of common failure modes—such as identity-breaking substitutions, base slippage, norm/model slippage, and constant matching without mapping—is paired with corrected statement forms. A small, reproducible benchmark using √10 as a controlled case study demonstrates how SHP separates representation from structure without asserting novelty in the underlying arithmetic.

SHP is intentionally conservative: it does not judge interpretive content as correct or incorrect, only whether it is being used as if it were governing structure. The protocol is intended as a practical tool for authors, reviewers, and researchers seeking clearer, more reproducible scaling and normalization claims.