The full manuscript is at the archive root. Extract the complete cumulative ZIP before running these commands; the current scripts use the retained sibling directories g2_schur_directional, g2_certificate and g2_source_certificate.
Dependencies: Python 3, python-flint 0.9.0 (FLINT 3.6.0 used for the recorded runs); LaTeX/latexmk for the PDF. All decisive certificate arithmetic is outward Arb arithmetic. No floating-point eigenvalue is an input to the proof.
From g2_ground_order/:
python3 certify_shifted_inertia.py --N 256 --M 512 --J 4096 --r 80 --parity even --bits 768 --diagonal --shift 1e-34 --witness ../g2_schur_directional/schur_witness_N256_M512_even_b768.json.gz
python3 certify_shifted_inertia.py --N 512 --M 1024 --J 4096 --r 100 --parity odd --bits 768 --diagonal --shift 1e-36 --witness ../g2_schur_directional/schur_witness_N512_M1024_odd_b768.json.gz
Repeat each command with --bits 896, retaining its same --witness path. The results must have status inertia_certified, 257 even pivots with exactly one negative (index24), and 512 positive odd pivots. Every pivot must exclude zero. The script recomputes all middle residual rows and bounds every remote row. The returned inertia is that of a lower Schur form; a negative pivot alone is not an actual negative Weil direction.
Then run:
python3 certify_trial_reuse.py
python3 certify_ground_overlap_constants.py
These verify the exact finite-supported Rayleigh quotient, the improved trial energy, exact projected-source normalization and the conservative angular constants. Their overlap outputs are explicitly conditional on the separately proved complete even threshold and global ordering. The manuscript combines these ingredients with the earlier full positivity theorem. The exact candidate SHA256 is 6d326cafbe715752f89b90cd92eb1d5a68ab0b78befb6afe074e797372b1a18e.
The archive includes the failed odd shift1e-34 report for research continuity; it is not a proof input. Duplicate witness files are not added: their original files and hashes remain under g2_schur_directional/. Cached coefficient enclosures and the analytic series remainder construction are preserved there. To recalculate coefficient caches, move aside the matching weil_sequences_n4096_b*_k128.json before running; each is regenerated by assembly.py.
The established conclusion is only for lambda3: a simple even ground with 0<mu0<3.644e-38, full next level greater than1e-36, and exact normalized P64-source ground-angle sine below.01931. Endpoint and growing-window statements require new arguments. G2 and RH are not proved.
To build the whole paper, run latexmk -pdf -interaction=nonstopmode -halt-on-error fixed_space_prime_action_v1.tex from the archive root.