Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
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Examination of the elementary estimates
elementary_grade_reasoning: Grading reproduction of the elementary examination's existing keepers, with exact witnesses, parameter losses and restricted consumer interfaces.
grade: Independent whole-contract grade of the elementary examination, preserving the literal sieve refutation and the exact surviving conditional scopes.
proof_coverage: Clause-by-clause examination of the block sieve, Section 2 tools, Type I application, and all consumer interfaces of the frozen elementary premise.
report: Independent adversarial examination of the complete elementary premise E, with a literal block-sieve cutoff counterexample, full operative proof coverage, consumer interfaces, and explicit classical-source limitations.
subject_map: Exact frozen mathematical subjects, their native paths, reading depths, and reconstruction instructions for the elementary-estimates examination.
weak_steps: Independent derivations of interval discrepancy, rough-number density transfer, and candidate mass for the frozen elementary estimates.
The examination, subject map, proof coverage and weak-step derivations concern the six estimate pages and their supplied consumer interfaces frozen on 2026-10-15 at 20:36:13.943931 UTC and examined that day. The map identifies all ten retained subject excerpts and the depth of each reading. No mathematical program or cached output supports this written examination.
The literal E1 statement is refuted-as-stated for : its remainder sum omits the empty product. The operative range and E2–E5 received refutation-failed findings at their stated classical-premise boundaries. The independent grade, examined on 2026-10-16 UTC, is PASS for each assertion at these split scopes. Its reproduction account assesses the complete written keepers. It does not accept unrestricted E1, establish P, or accept Problem 824. The weighted E3 consumer consequence retains its additional Type II/P assumption.
The current block-sieve statement expressly assumes and its proof includes the empty-prime case. These statement and proof additions are not the frozen wording examined here. All consumed cutoffs tend to infinity; the report separately examines their restricted range.
The source is OpenAI's unrefereed Weighted dilation graphs, smooth shifted primes and totient fibers, 24 September 2026 release. Its supplied excerpt is retained under Apache-2.0, as identified on the source card. The reconstruction and examination are credited to Plasma AI. Original classical proofs and PDF fidelity were not examined.
Mechanical maintenance consists of relocating the ten subject excerpts to
evidence/assets/elementary_estimates_subject/ with .md.txt suffixes,
updating their links, and restoring two newline-damaged \rm labels in the
report's prime indicator and P-group Euler product. The source excerpts,
mathematical assertions, deductions, scopes and verdicts are unchanged.
Ordinary wiki metadata and navigation are generated from these pages.
Display titles, page separators and wiki metadata are formatting maintenance.
The grade's bootstrap-reading qualification concerns operational settings shown before their identity comparison; the original reviewer's static sources were checked before substantive use. The grader found no material mathematical exposure in those settings. The grading parser's disclosed wrong-directory write was corrected before its successful execution; the initial intended-path invocation failed without executing. The filing check confirmed the permitted configuration-only trust append and retained the exact scripts and primary records. Neither incident introduced excluded mathematical input or requires an exposure waiver.
The grade and its reproduction account have maintained links to the existing canonical subject and keeper files, with ordinary page separators and generated metadata. Their scopes, dates, hypotheses, findings and verdicts are unchanged. The exact original delivery remains preserved separately. The malformed delimiter in the original proof-coverage keeper's principal-error display is restored to the line break before . The grade already used that condition from the surrounding text and the supplied consumer; this is a typesetting repair, not a new inference. The exact original is preserved separately.