Bibliographic record
Abstract
This thesis is concerned with the development of tools and techniques for solving systems of simultaneous congruences—the congruential sieve problem—in both one- and two-dimensions. Though many problems in number theory can be reduced to an instance of the congruential sieve problem, one problem in particular—that of primality proving—will be examined in detail. In previous work [WW06] this author provided numerical evidence for a conjecture that primality may be proved with complexity (logN) 3+o(1) using quantities known as pseudosquares and pseudocubes. This thesis examines an alternate definition of pseudocube—the Eisenstein pseudocube—which leads to a more efficient primality proving method for primes p ≡ 1 (mod 3). In particular, in this thesis, we: (1) develop the notion of an Eisenstein pseudocube, and an associated primality proving algorithm; (2) reduce the problem of finding Eisenstein pseudocubes to an instance of the two-dimensional sieve problem; (3) extend the Calgary Scalable Sieve (CASSIE) toolkit to solve instances of a two-dimensional sieve problem; (4) develop a general-purpose hardware framework for implementing custom computing devices on Xilinx Field Programmable Gate Array (FPGA) devices; (5) design and implement FPGA-based sieve device using this framework; (6) evaluate the performance of the prototype hardware for solving two-dimensional sieve problems; and (7) enumerate Eisenstein pseudocubes using these tools.
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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".