Rigorous Proof that 196 is a Lychrel Number: Modular Obstructions and Computational Certification
Bibliographic record
Abstract
AbstractThis research presents a rigorous mathematical proof that 196 is a Lychrel number.The work combines modular obstruction theory and computational certification to demonstrate that the number 196 — and its entire symmetry class — cannot converge to a palindrome under the reverse-and-add process. Main Results• Modular obstruction rigorously established via Hensel’s Lemma, proving no valid lift modulo 2k2^k2k for any kkk.• Definition and persistence of a robust algebraic invariant A(robust)A^{(\mathrm{robust})}A(robust).• 289,292 exhaustive computational trajectories verified with zero failures. Included Materials– Complete LaTeX source and compiled PDF of the proof– Python verification scripts and computational certificates Author: Stéphane Lavoie — Independent Researcher (Canada), 2025License: CC BY 4.0
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.002 | 0.000 |
| Scholarly communication | 0.002 | 0.000 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".