04-EFT.WP.Core.Metrology v1.0 | Chapter 1 — Metrology System and Unit Baselines

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Chapter 1 — Metrology System and Unit Baselines

I. Chapter Objectives and Deliverables

• Establish the minimal postulates and the base dimension set for the EFT metrology system, and fix the DimStr syntax and equivalence rules.
• Provide a unified convention for unit registration and derivation logic, bound to implementation interface I40 1.
• Outputs of this chapter: postulates P90-1…P90-3, the DimStr syntax card, a unit-registration list (≥30 entries), and a cross-volume example (dimensional verification of arrival time T_arr).

II. Dimension Set and Dimensional Postulates (P90-1…P90-3)

• P90-1 Dimension Closure: any physical expression is representable via closed operations on a power set of dimensions. With base dimensions { [L], [T], [M], [Qe], [Temp] }, a dimension can be written as "[L]^a [T]^b [M]^c [Qe]^d [Temp]^e", where a,b,c,d,e ∈ ℤ; omit empty exponents.
• P90-2 Unit Invariance: any two units sharing the same dimension are related by a unique affine transform v_to = a * v_from + b, where b != 0 is permitted only for unit families with an offset zero (e.g., degC ↔ K).
• P90-3 Dimensional Consistency: measurement equations must satisfy dim(lhs) = dim(rhs); the system interface check_dim(expr) is a mandatory gate—expressions that fail must not enter computation or reporting pipelines.

III. DimStr Syntax and Equivalence Rules

1. Syntax
   • Product of factors: DimStr := Factor_1 * Factor_2 * ... * Factor_k。
   • Factor: Factor := "[" Base "]" "^n", Base ∈ { L, T, M, Qe, Temp }, n ∈ ℤ; omit the exponent when n = 1。
2. Equivalence
   • Commutative/associative: factor order is irrelevant; exponents of identical base dimensions add and may be merged。
   • Dimensionless: denote as "[1]" or empty; e.g., radian, ratios, probabilities。
   • Legality: unregistered base-dimension tags are forbidden; fractional exponents are forbidden。

IV. Unit Registration Strategy and Interface Binding (I40 1)

1. Register units via register_unit(name:str, symbol:str, dim:str, factor_to_SI:float, offset_to_SI:float=0.0)。
2. Define derived units via define_derived_unit(symbol:str, expr:str), where expr is composed from registered units and integer powers。
3. Constraints
   • dim(symbol) must be consistent with its conversion chain to SI。
   • Units with offsets must declare offset_to_SI explicitly。
   • Aliases are handled by a separate alias interface and are not redefined here。

V. SI Baselines and Common Derivations — Unit Registration List (≥30 examples)

• register_unit("meter", "m", "[L]", 1.0)
• register_unit("kilometer", "km", "[L]", 1.0e3)
• register_unit("centimeter", "cm", "[L]", 1.0e-2)
• register_unit("millimeter", "mm", "[L]", 1.0e-3)
• register_unit("micrometer", "um", "[L]", 1.0e-6)
• register_unit("nanometer", "nm", "[L]", 1.0e-9)
• register_unit("second", "s", "[T]", 1.0)
• register_unit("millisecond", "ms", "[T]", 1.0e-3)
• register_unit("microsecond", "us", "[T]", 1.0e-6)
• register_unit("minute", "min", "[T]", 60.0)
• register_unit("hour", "h", "[T]", 3600.0)
• register_unit("kilogram", "kg", "[M]", 1.0)
• register_unit("gram", "g", "[M]", 1.0e-3)
• register_unit("milligram", "mg", "[M]", 1.0e-6)
• register_unit("kelvin", "K", "[Temp]", 1.0)
• register_unit("degC", "degC", "[Temp]", 1.0, 273.15)
• register_unit("coulomb", "C", "[Qe]", 1.0)
• register_unit("ampere", "A", "[Qe][T]^-1", 1.0)
• register_unit("milliampere", "mA", "[Qe][T]^-1", 1.0e-3)
• define_derived_unit("Hz", "s^-1")
• define_derived_unit("m_per_s", "m*s^-1")
• define_derived_unit("m_per_s2", "m*s^-2")
• define_derived_unit("N", "kg*m*s^-2")
• define_derived_unit("Pa", "N*m^-2")
• define_derived_unit("J", "N*m")
• define_derived_unit("W", "J*s^-1")
• register_unit("bar", "bar", "[M][L]^-1[T]^-2", 1.0e5)
• define_derived_unit("V", "W*A^-1")
• define_derived_unit("ohm", "V*A^-1")
• define_derived_unit("F", "C*V^-1")
• define_derived_unit("H", "ohm*s")
• register_unit("eV", "eV", "[M][L]^2[T]^-2", 1.602176634e-19)
• register_unit("rad", "rad", "[1]", 1.0)
• define_derived_unit("sr", "rad^2")
• define_derived_unit("S", "ohm^-1")
• define_derived_unit("T", "Wb*m^-2") （requires implementation to resolve Wb = V*s first）
• define_derived_unit("Wb", "V*s")

VI. Compound Units and Writing Conventions

• Express products/quotients with powers, prefer parentheses: ( m*s^-1 ), ( kg*m*s^-2 )。
• Linear combinations or affine transforms apply only between units of identical dimension, e.g., temperature scale: K = ( 1 ) * degC + 273.15。
• Dimensionless quantities (angles, ratios) are denoted "[1]", but reports should still state unit symbols (e.g., rad, %)。

VII. Cross-Volume Example: Dimensional Verification of Arrival Time T_arr

• Constant-factored convention: T_arr = ( 1 / c_ref ) * ( ∫_gamma n_eff d ell )。
  If dim(c_ref) = "[L][T]^-1", dim(n_eff) = "[1]", dim(d ell) = "[L]", then the integrand has dimension "[L]", and the overall dimension is "[T]"。
• General convention: T_arr = ( ∫_gamma ( n_eff / c_ref ) d ell )。
  The integrand dimension is ( "[1]" / "[L][T]^-1" ) * "[L]" = "[T]", so the integral still yields "[T]"。
• Under the convention t0 def= L0 / c_ref, one may write
  T_arr / t0 = ( ∫_gamma ( n_eff / c_ref ) d ell ) / ( L0 / c_ref ) = ∫_gamma ( n_eff ) d bar_ell，where d bar_ell = d ell / L0; the right-hand side is dimensionless, satisfying P90-3 and the reporting convention。

VIII. Chapter Checks and Deliverable List

• Dimensional postulate card: P90-1…P90-3。
• DimStr syntax card: composition rules and legality for DimStr。
• Unit registration list: see §V (exportable via export_units("yaml"))。
• Cross-volume consistency example: the two T_arr conventions’ dimensional-conservation proof, usable directly as a pre-check for bind_to_equation(S20-*, "strict")。