Skip to content

METHOD.md

Latest commit

 

History

History
47 lines (27 loc) · 2.24 KB

METHOD.md

File metadata and controls

47 lines (27 loc) · 2.24 KB
Raw

Method

This document defines the shipped runtime contract for lpp_seed and lpp_refined_predictor.

It is separate from the benchmark-leader summary in CANDIDATE_CATEGORIES.md.

The Lorentz Prime Predictor defines two related objects, and this repository keeps them separate in both prose and measurement.

Official Seed

$$ lpp_seed(n) = r_inverse_seed(n) $$

lpp_seed is now the repository's official deterministic inversion seed. It returns an integer estimate for the $n$th prime for $n \geq 1$.

For the main regime, this is the fixed-step inverse construction defined in FORMULA.md. For the narrow low-index compatibility window below 100, the runtime uses the legacy closed-form path so the public API stays defined on the full declared domain.

This is the correct object for the repo's primary seed contract. The older closed-form path and the other comparison formulas remain available as alternates, not as the shipped default.

Refined Predictor

$$ lpp_refined_predictor(n) = nextPrime(lpp_seed(n) - 1) $$

lpp_refined_predictor starts at the official seed and moves forward deterministically until a prime output is reached, again for $n \geq 1$.

This answers a different question. It measures whether the shipped seed is a useful launch point for a practical prime-returning method, not only whether the seed lands near $p_n$.

Why the Separation Matters

A strong refined predictor does not by itself prove a stronger seed formula. A strong seed formula does not by itself prove the best prime-output stack. The two layers support different claims and must not be merged into one headline result.

For this repository, that means:

  • seed tables report seed accuracy only
  • refined tables report prime-output accuracy only
  • summary language must name which estimand is being discussed
  • refined comparisons are valid only when the refinement rule is shared across predictors

Alternate Seeds

The codebase also exposes:

  • legacy_lpp_seed
  • cipolla_log5_repacked_seed
  • li_inverse_seed
  • r_inverse_seed

r_inverse_seed is the explicit method name for the same construction that now ships as lpp_seed. The other three names are alternate formulas retained for benchmark and research work.