riemann

evidence/v126/g2_low_schur/

Manuscript v1.20 — CERTIFICATE bundle: the low-mode Schur revision at lambda=4 — certified far-inverse iteration constants (320/384 bits), the actual low-head Schur certificate and a structured inverse bound (768 bits), with frozen witnesses and Arb Weil-sequence enclosures. check_structured_ceiling.py replays exact dyadic counter-witnesses and, per its docstring, “does NOT certify a negative direction”.

Start here: README_schur_revision.md, adversarial_uniform_review.md

Subdirectories

• current/ — manuscript source snapshot

Files

• README_schur_revision.md (2 KB) — v1.20 Schur revision: reproduction and scope
• adversarial_uniform_review.md (19 KB) — Adversarial review: the low Schur correction and growing-window scales
• assembly_general.py (3 KB) — Arb enclosures of the actual Weil Fourier coefficients at integer lambda.
• build_complete_pdf.py (1 KB) — Compile in a fresh directory; install only a closed, parseable full PDF.
• certify_far_inverse.py (2 KB) — Certify the complete far-operator inverse iteration constants at lambda=4. Analytic inputs: the manuscript’s two-sided diagonal bound and commutator norm bound, with the…
• certify_low_schur.py (4 KB) — Actual low-head Schur certificate using the proved complete lambda4 tail metric.
• check_structured_ceiling.py (3 KB) — Replay exact dyadic obstructions to three structured lower-bound candidates. This checks K - V from the saved interval ingredients.
• checkpoint.md (9 KB) — Current research checkpoint: September 21, 2026 — v1.20 low-mode Schur revision
• far_inverse_contraction_b320.json (2 KB) — (no description in file)
• far_inverse_contraction_b384.json (2 KB) — (no description in file)
• far_inverse_insert.tex (4 KB) — (no description in file)
• integrate_v120_schur.py (6 KB) — (no description in file)
• low_matrix_even_M256_b768.json (114 KB) — (no description in file)
• low_schur_even_M256_J2048_r64_b768.json (682 B) — (no description in file)
• low_witness_even_M256_b768.json.gz (368 KB) — (no description in file)
• low_witness_odd_M256_b768.json.gz (364 KB) — (no description in file)
• package_revision.py (4 KB) — (no description in file)
• render_review.py (1 KB) — (no description in file)
• sequences_v3_l4_J2048_b768_k96.json (1.5 MB) — (no description in file)
• sequences_v3_l4_J4096_b768_k96.json (2.9 MB) — (no description in file)
• structured_ceiling_counterwitness.json (2 KB) — (no description in file)
• structured_ceiling_counterwitness_M1024.json (2 KB) — (no description in file)
• structured_ceiling_counterwitness_M512.json (2 KB) — (no description in file)
• structured_even_M1024_J4096_ingredients.json (243 KB) — (no description in file)
• structured_even_M1024_J4096_r64_b768_t0.json (815 B) — (no description in file)
• structured_even_M1024_J4096_r64_b768_t0_matrix.json (121 KB) — (no description in file)
• structured_even_M256_J4096_ingredients.json (243 KB) — (no description in file)
• structured_even_M256_J4096_r64_b768_t0.json (815 B) — (no description in file)
• structured_even_M256_J4096_r64_b768_t0_matrix.json (121 KB) — (no description in file)
• structured_even_M256_J4096_r64_b768_t8.json (723 B) — (no description in file)
• structured_even_M256_J4096_r64_b768_t8_matrix.json (120 KB) — (no description in file)
• structured_even_M256_midpoint_diagnostic.json (1 KB) — (no description in file)
• structured_even_M512_J4096_ingredients.json (243 KB) — (no description in file)
• structured_even_M512_J4096_r64_b768_t0.json (814 B) — (no description in file)
• structured_even_M512_J4096_r64_b768_t0_matrix.json (121 KB) — (no description in file)
• structured_even_M512_midpoint_diagnostic.json (272 B) — (no description in file)
• structured_inverse_insert.tex (12 KB) — Reusing the signed tail certificate in the low-mode correction
• structured_low_schur.py (5 KB) — Structured inverse bound on the actual lambda=4 low-head Schur residual. All arithmetic entering a sign decision is Arb; frozen witnesses are dyadic.

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