Formal Notation Basis Gap Tool

Description

Multiply each step by log10 of its base and return secondLogDilution-firstLogDilution.

Serial dilution multiplies retained fractions, so logarithms turn repeated dilution factors into sums. Comparing formal factors does not demonstrate actual chemical composition, manufacturing quality, or a treatment effect.

Multiply each step by log10 of its base and return secondLogDilution-firstLogDilution.

When to use this tool

Use Formal Notation Basis Gap when you need one explicit formal dilution calculation with a stated base and stage convention.

How to use the tool and how it works

Enter firstStep, firstSuppliedBase, secondStep, secondSuppliedBase. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read firstLogDilution, secondLogDilution, logGap. Use the output convention below.

Require nonnegative integer steps and both supplied bases greater than one. Multiply each step by log10 of its base and return secondLogDilution-firstLogDilution.^[1]

Homeopathic notation does not establish treatment efficacy.^[2]

Input field	Meaning and units	Accepted input
firstStep	First Step	Required. Safe integer; minimum 0.
firstSuppliedBase	First Supplied Base	Required. Finite number; strictly above 1.
secondStep	Second Step	Required. Safe integer; minimum 0.
secondSuppliedBase	Second Supplied Base	Required. Finite number; strictly above 1.

Output field	Interpretation	Returned shape
firstLogDilution	First Log Dilution	Required. Finite number.
secondLogDilution	Second Log Dilution	Required. Finite number.
logGap	Log Gap	Required. Finite number.

json

{
  "input": {
    "firstStep": 3,
    "firstSuppliedBase": 10,
    "secondStep": 2,
    "secondSuppliedBase": 100
  },
  "output": {
    "firstLogDilution": 3,
    "secondLogDilution": 4,
    "logGap": 1
  }
}

Limitations and assumptions

The signed gap is in base-ten dilution-log units; source conventions and actual preparation are not verified and no therapeutic equivalence is established.
Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.

Alternative or Complementary methods

Keep formal expectations separate from measured contents and evaluate treatment claims through appropriate clinical evidence.

References

Calculation and input contract: homeopathy/formal-notation-basis-gap — tool.io
Homeopathy: What You Need To Know — National Center for Complementary and Integrative Health

Similar or alternative tools

Homeopathy Label Dilution Log Factor
Return -stages × log10(base) for log10Fraction and the opposite sign for log10Dilution.
Formal Dilution Step Logsum
Require aligned nonnegative logDilutions and repetitions and return their dot product as formalLogDilution.