dimensions_status
plain-language theorem explainer
The definition supplies a concatenated status string confirming setup of dimensional signatures for physical quantities in Recognition Science. Module maintainers would reference it during verification to ensure [L, T, M] tracking for constants like c, ℏ, G is complete. It is implemented as a direct string literal definition with an embedded evaluation command.
Claim. The module status report is the string ``✓ Dimension structure [L, T, M] defined ✓ Physical constant dimensions (c, ℏ, G) specified ✓ Planck unit dimensions documented ✓ τ₀ dimension documented as [T] ✓ DimensionedQuantity algebra defined''.
background
Recognition Science tracks physical quantities via dimensional signatures [L^a, T^b, M^c]. The Dimension structure encodes these as integer exponents for length, time, and mass. DimensionedQuantity pairs a real value with such a signature, supporting consistent algebra for derived constants.
proof idea
Direct definition that concatenates five fixed verification messages into a single string, terminated by an #eval directive.
why it matters
This definition checkpoints the dimensional infrastructure that supports self-consistent derivation of constants from τ₀, ℓ₀ = c τ₀, and φ. It aligns with the framework's goal of expressing G = λ_rec² c³ / (π ℏ) and related quantities without external units, feeding the steps toward D = 3 and the alpha band.
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