Finite Validation → Loop Quantum Gravity: companion code

Simulation runs supporting the preprint

Physics from Finite Validation: Loop Quantum Gravity from a Validation Network — Spin Networks, the Area Spectrum, and the Immirzi Parameter from the Serial Door (I. Denysov, United Field Initiative, 2026).

Every script is a standalone Python 3 program with its success criteria stated in the header, in the status discipline of the series: reproduced (a known LQG structure recovered from the mechanism), derived (a consequence of the mechanism), selects (a value fixed under a named assumption), predicted (a falsifiable departure), conceptual, or open. The runs are consistency checks within stated models, not measurements of nature.

The one place the recoupling arises independently of the known mathematics is the binor Z₂ sign of 05_signs_binors.py; everything the Ponzano–Regge script checks (07) follows once the door's amplitude equals the Wigner 6j, and is marked as a consistency check rather than an independent confirmation.

Requirements

python >= 3.9
numpy
scipy
sympy      # optional: only 07 uses it, as an independent cross-check of the 6j

Install: pip install numpy scipy sympy

Run

Each script is standalone and prints its result and verdict:

python 01_area_law_and_dictionary.py
python 02_casimir_from_isotropy.py
...
python 09_higher_spin_j1.py

Runtime: seconds each.

File → paper section map

Script	Section	What it shows	Status
01_area_law_and_dictionary.py	§3, §4	Area = channel count gives the area law N ∝ R² (slope 2.09); the Immirzi values 0.127 / 0.23753 / 0.274; the Finite-Validation ↔ LQG dictionary	reproduced / selects
02_casimir_from_isotropy.py	§3	√(j(j+1)) from a finite symmetric isotropic alphabet, exactly for all j; independent binary ticks fail for j ≥ 1 (control)	reproduced (SU(2) repackaged via isotropy)
03_serial_gate.py	§3	The serial gate ("one door") derives the spin ladder (step 1, ±j, half-integer j) and the Casimir for all j; composition matches SU(2) weights	derived
04_intertwiners.py	§5	Node admissibility (triangle + parity) = routing solvability (4913/4913); intertwiner dimensions = intermediate serial tallies (6561 sets); naive routing fails (control)	reproduced
05_signs_binors.py	§6	The order-of-ends Z₂ sign gives real binor recoupling: 2 node states, modulus-squared = quantum, interference not Markov; the one independent source of recoupling	derived
06_immirzi_and_synergy.py	§4, §8	Immirzi selection (0.23753) under the two-state boundary assumption; synergy sift (SU(2) generated; volume valence threshold; silence-dressed vertices ×4.5)	selects / partial / predicted
07_ponzano_regge.py	§7	The door's 6j: orthogonality, tetrahedral symmetry, the Biedenharn–Elliott / Pachner 2–3 identity (triangulation invariance), and the Ponzano–Regge 1/√(12πV) asymptotics ⇒ 3D quantum gravity	reproduced (3D dynamics)
08_hybrid_conclusions.py	§8	Holography as "area in bits" (near-circular); geometric noise at the Planck floor (consistent with the Holometer null, not Hogan's enhanced noise); the extensive-count-vs-rate reading	conceptual / predicted
09_higher_spin_j1.py	§6	Higher-spin spot-check: the serial door (two ticks symmetrised = Jones–Wenzl) reproduces the SU(2) 6j recoupling for j=1; the mechanism does not break at the first higher representation	reproduced (spot-check)

Honest limits (named in the paper)

• The area spectrum √(j(j+1)) is reproduced via an isotropy axiom that repackages SU(2), not removes it; three-axis isotropy is a geometric input, so the Casimir weight is not purely background-independent.
• The Immirzi value is selected under a named assumption (a two-state horizon reading), not derived; the 2 vs (2j+1) seam with the area alphabet is open.
• Higher spins are spot-checked at j=1 (09); a general-j proof is not attempted.
• The 3D dynamics (Ponzano–Regge) is topological — no local degrees of freedom, no graviton. The 4D spin foam (EPRL, 15j) remains a debt.
• The reduction of this combinatorial spin network to the elastic continuum of the Bridge paper is a conjecture, and the priority open debt of the programme.

Cite

I. Denysov, Physics from Finite Validation: Loop Quantum Gravity from a Validation Network, United Field Initiative, 2026.

License

Code: MIT (see LICENSE).