riemann

evidence/v124/g2_schur_directional/

Manuscript v1.16 — CERTIFICATE bundle: the directional infinite-complement certificate at lambda=3 (complete fixed-window positivity), even and odd, at 768 and 896 bits, with frozen witnesses (schur_witness_*.json.gz, up to 29 MB), Arb Weil-sequence enclosures, finite-output pilots (no remote-tail bound, per pilot_schur.py) and the weighted prime-tail certificate.

The files here are byte-identical to evidence/v126/g2_schur_directional/.

Start here: G2_v116_Research_and_Reproduction.md, fixed_window_certificate_report.md, adversarial_schur_report.md

Files

• G2_v116_Research_and_Reproduction.md (5 KB) — Reproducing complete fixed-window positivity — manuscript v1.16
• adversarial_schur_report.md (11 KB) — Adversarial Schur assessment and a stronger certified tail
• assembly.py (3 KB) — Exact lambda=3 Weil sequences; Arb enclosures and reusable parity blocks. Fixed first-slot-linear convention; unshifted normalized Fourier basis.
• assembly_independent_overlap.json (211 B) — (no description in file)
• certify_infinite_schur.py (7 KB) — Directional infinite-complement certificate at lambda=3. All arithmetic enclosures use Arb.
• certify_weighted_prime_tail.py (3 KB) — Arb certificate of a positive-weight Schur bound for lambda=3 prime shifts. Only scalar exact rational coefficient comparisons and analytic tail constants are certified.
• checkpoint_entry.md (10 KB) — Current research checkpoint: September 21, 2026 — v1.16 complete fixed-window positivity
• directional_schur_insert.tex (6 KB) — A directional certificate for the entire Fourier complement
• directional_tail_derivation.md (12 KB) — A moment-preserving PSD enclosure of the infinite remote Weil residual

• directional_tail_gram.py (3 KB) — Certified real-matrix remote Gram majorants for the actual Weil commutator. Conditional inputs: exact matrices are enclosed by G and b; B bounds

  b_n

  for all n; optional…

• finish_checkpoint.py (10 KB) — (no description in file)
• fixed_window_certificate_report.md (8 KB) — Complete fixed-window Weil positivity certificate at lambda=3
• fixed_window_insert.tex (5 KB) — A certificate for the complete fixed-window form
• infinite_schur_N256_M512_J1024_r128_even_b768.json (1 KB) — (no description in file)
• infinite_schur_N256_M512_J4096_r80_even_b768.json (1 KB) — (no description in file)
• infinite_schur_N256_M512_J4096_r80_even_b768_diagonal.json (24 KB) — (no description in file)
• infinite_schur_N256_M512_J4096_r80_even_b896_diagonal.json (24 KB) — (no description in file)
• infinite_schur_N256_M512_J4096_r80_odd_b768_diagonal.json (1 KB) — (no description in file)
• infinite_schur_N512_M1024_J2048_r128_odd_b768.json (1 KB) — (no description in file)
• infinite_schur_N512_M1024_J4096_r100_odd_b768_diagonal.json (46 KB) — (no description in file)
• infinite_schur_N512_M1024_J4096_r100_odd_b896_diagonal.json (46 KB) — (no description in file)
• integrate_v116.py (7 KB) — (no description in file)
• pilot_N256_M512_J1024_even.json (943 B) — (no description in file)
• pilot_N256_M512_J1024_odd.json (935 B) — (no description in file)
• pilot_N512_M1024_J2048_odd.json (940 B) — (no description in file)
• pilot_gamma_sensitivity_odd.json (953 B) — (no description in file)
• pilot_improved_gamma_odd.json (743 B) — (no description in file)
• pilot_schur.py (4 KB) — Finite-output pilot for the residual Schur certificate. No remote-tail bound. An adverse sign here invalidates this particular Gamma-only budget, not W.
• schur_pilot_report.md (7 KB) — Directional Schur pilots at the exact window lambda = 3
• schur_witness_N256_M512_even_b768.json.gz (7.0 MB) — (no description in file)
• schur_witness_N512_M1024_odd_b768.json.gz (27.9 MB) — (no description in file)
• weighted_prime_inverse_insert.tex (7 KB) — A positive weight for the prime shifts and a diagonal inverse bound
• weighted_prime_tail_certificate.json (7 KB) — (no description in file)
• weil_sequences_n1024_b768_k128.json (498 KB) — (no description in file)
• weil_sequences_n2048_b768_k128.json (995 KB) — (no description in file)
• weil_sequences_n4096_b768_k128.json (1.9 MB) — (no description in file)
• weil_sequences_n4096_b896_k128.json (2.1 MB) — (no description in file)

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