PST VERIFICATION COMPUTATIONS
=============================

This directory holds the numerical and symbolic computations referenced
throughout "Precausal Substrate Theory" by number ("Computation N", or
"Comp N"). Each computation_NN.py is a self-contained, runnable check of one
claim in the paper. The per-computation descriptions and the rendered source
are also published at https://meelker.nl/pst-computations, and the paper's
Appendix C/D computation log maps each main-text claim to its script.


ENVIRONMENT
-----------
  - Python 3.9+
  - numpy        (the core dependency; used by ~80 of the scripts)
  - scipy, sympy (each needed by only two scripts -- special-function and
                  symbolic checks; everything else uses the standard library:
                  math, itertools, functools, collections, cmath)

  python3 -m venv venv && source venv/bin/activate
  pip install numpy scipy sympy


RUNNING A COMPUTATION
---------------------
Each script prints its verification block to standard output. Run from inside
this directory (a few scripts import shared helpers such as computation_59,
which resolves only when the working directory is computations/):

  cd computations
  python3 computation_100.py     # substrate cutoff f = e^{-x}; Z_H -> e^{-1}
  python3 computation_121.py     # Fisher-Neyman sufficiency; Z_Gamma4 = 1
  python3 computation_120.py     # full-SM extension of M_* settled negative

No script takes command-line arguments.


DETERMINISM / SEEDS
-------------------
The checks are deterministic. Scripts that use randomness fix the seed
explicitly (numpy.random.default_rng(<seed>) or numpy.random.seed(...)), so
repeated runs reproduce the printed values bit-for-bit. The large-D and
finite-size checks converge monotonically and print the rate, so the limit is
visible from the table even at modest D.


KEY CHECKS AND EXPECTED OUTPUT (a sample)
-----------------------------------------
  computation_100.py
      Bernoulli product structure forces the cutoff f(x) = e^{-x}; the
      normalised action converges to e^{-1}.
      -> "Z_H -> 0.3679..." (= e^{-1}) as D grows.

  computation_109.py
      Doublet convention: C_H = 6*lambda_PST = 3/2, hence
      M_* = 4 pi m_h sqrt(2/3).
      -> C_H = 3/2, M_* ~= 1285 GeV.

  computation_120.py
      Veltman bracket at M_* and the absent top-partner sector.
      -> bracket ~= -3.5; "settled in the negative".

  computation_121.py
      Exact sufficiency factorisation
      Z[Phi] = sum_k C(D,k) 2^-D e^{-Phi(k/D)}; vertex Z_Gamma4 = 1.
      -> factorisation agreement ~1e-15; vertex probe ~3e-16;
         transverse-coupled control gap ~0.30.

  computation_122.py
      What the substrate side needs of F8 linearity (decoupling = symmetry;
      value = vacuum normalisation).
      -> nonlinear g with g(1/2)=1/2 all -> e^{-1}; (diff * D) -> const.

A script "passes" when its printed residuals are at the machine-precision /
stated-O(1/D) level and its assessment block reports the closure it claims.


PROVENANCE
----------
Withdrawn or superseded computations carry a STATUS / UPDATE banner in their
docstring pointing to the successor (for example, Comp 118's Morse-Bott lemma
notes that it is subsumed by Comp 121's exact sufficiency closure). The website
descriptions and the paper's computation log are kept in parity with these
docstrings.