Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
Updated
Frozen subject and reconstruction map
The report examines the following neutral excerpts frozen on
2026-10-15 at 20:36:13.943931 UTC. Examination date: 2026-10-15.
The copies linked below preserve the delivered mathematical text with the
mechanical maintenance listed on the record index, including
the preparer's [cut] markers. Those markers exclude standing, prior-review
material, and source sections outside the commission. A marker is not an
assertion that the omitted material was examined.
Every line locator in the report and keepers refers to these copies. Native paths identify the mathematical pages from which the extraction was prepared; they were not opened as live pages. The whole delivered text of each listed file was read. The scope column distinguishes proof examination from reading for a consumer interface.
| Retained excerpt | Native repository-relative path | Lines and examination scope |
|---|---|---|
| estimates.md | wiki/research/smooth_successor_estimates/_index.md | 1–125; all E1–E5 assertions, choice order, classical boundary and conditional consequences |
| block_sieve.md | wiki/research/smooth_successor_estimates/block_sieve.md | 1–189; entire statement and proof, all five instances |
| proxy_discrepancy.md | wiki/research/smooth_successor_estimates/proxy_discrepancy.md | 1–264; entire proposition and harmonic-character lemma, every character and interval case |
| proxy_densities.md | wiki/research/smooth_successor_estimates/proxy_densities.md | 1–282; entire density construction, counts, identity, bound and mesh deduction |
| candidate_mass.md | wiki/research/smooth_successor_estimates/candidate_mass.md | 1–208; all six assertions, sampling proof, slot uniformity and micro-band comparison |
| classical_inputs.md | wiki/research/smooth_successor_estimates/classical_inputs.md | 1–207; exact classical statements as supplied, all derived inputs and the complete Type I application |
| consumer_combined.md | wiki/research/smooth_successor_primes/_index.md | 1–181; full reading; premise boundaries, E interfaces and conditional consequence audit |
| consumer_signed_type_ii.md | wiki/research/smooth_successor_primes/signed_type_ii.md | 1–488; full reading; definitions and exact E5 uses checked; P's truth is excluded |
| consumer_extraction.md | wiki/research/smooth_successor_primes/successor_prime_extraction.md | 1–435; full reading; candidate definitions, Type I and all sieve/proxy/mass interfaces checked |
| source_sections_2_6_definitions_7.md | library/arithmetic_functions/openai_2026_weighted_dilation_graphs_smooth_shifted_primes_totient_fibers/openai_2026_weighted_dilation_graphs_smooth_shifted_primes_totient_fibers.md | 1–603; supplied Section 2, Section 6 definitions and Theorem 6.1 statement, full Section 7 and bibliography read; reconstructed E deductions compared throughout |
The manuscript is OpenAI, Weighted dilation graphs, smooth shifted primes and totient fibers, 24 September 2026 release, an unrefereed manuscript. The source-owned mathematics retains that authorship. The project reconstruction, uniformity accounting and original project reasoning are Plasma AI's. The supplied form is a retained transcription, not an original PDF or page image. No print-fidelity examination was possible. Section 6's source proof and the proof of P in Sections 3–5 were not supplied. Original classical texts were not supplied or opened; their statements and bibliographic locators were read only in these excerpts.
Rebuilding the assessment
Read the exact copies above, then the report's restatements and premise census. Follow proof coverage for E1, E5, all five sieve instances and consumer composition. Follow weak steps for the three independent derivations of E2, E3 and E4. Reproduce the E1 witness by substituting its single-object data into the displayed inequality and support clause. This is a written proof check; no mathematical executable, numerical output, random seed, hidden dataset, or success cache is required.
The assessment can be rebuilt from this package's ordinary files without
accessing any prior context or repository history. Public adoption must retain
the report, both keepers, this map and the ten exact excerpts together, or
mechanically maintain their links when placing the excerpts under the owning
page's evidence/assets/. A private handoff by itself is not a durable native
warrant. Independent grading, public filing and any resulting standing are
separate from this examination.