Binding Constraints After Guth-Maynard: A Structural Analysis of the EXPDB Pipeline
A computational analysis of the Analytic Number Theory Exponent Database (EXPDB) pipeline after the Guth-Maynard (2024) large value estimate. We ran the full pipeline (482 hypotheses, scipy-based polytope backend), identified the binding constraints, and performed a complete sensitivity analysis.
Key results:
- The GM result creates a cusp at sigma = 7/10 where Ingham (1940) and GM (2024) meet at A = 30/13, determining theta_PNTALL = 17/30
- Sensitivity: d(theta)/d(||A||) = 169/900. The attack surface is narrow: an epsilon-improvement needs to hold on an interval of width ~0.006 around sigma = 0.70
- The bottleneck is purely in A(sigma) for theta_PNTALL; the energy exponent A*(sigma) only enters at the GAPSQUARE level
- Pipeline completeness verified: no unexploited transformation chain changes the binding value
- Succession landscape: after the cusp, the next bottlenecks migrate rightward through Ivic (2003), Ivic (1980), TTY (2024), and onward to the Density Hypothesis
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| Zero-density envelope with binding constraints | Sensitivity cone at the cusp |
Full paper, figures, and code: PAPERS/EXPDB-Analysis/
Companion papers:
- EXPDB-Skyline: A Polyhedral Reinterpretation - identifies the master polytope P from which all EXPDB outputs descend
- Background analysis - how GM fits into the EXPDB polyhedral framework
The Factor Skyline is a geometric architecture for the integers in which each integer n is represented as a column of width lpf(n) (least prime factor) and height n/lpf(n). The resulting two-dimensional landscape is governed by five emergent concepts (width, height, activation, coverage, and escape), all deriving from the single primitive function lpf. The project develops the Factor Skyline as a unified architectural, statistical, dynamical, and meta-mathematical theory of multiplicative number theory.
The Factor Skyline is one instance of Architectural Distillation (AD), a general methodology for extracting structure from systems composed of interacting mechanisms.
| Part | Title | Theorems |
|---|---|---|
| I | Architectural Foundation | 22 |
| II | Correlations and Randomness | 14 |
| III | Information, Dynamics, and Universality | 17 |
| IV | Meta-Structure | 13 |
| Directory | Purpose |
|---|---|
PAPERS/EXPDB-Analysis/ |
EXPDB binding constraint analysis after Guth-Maynard (2024). Papers, figures, pipeline report. |
PAPERS/EXPBD-Skyline/ |
EXPDB-Skyline polyhedral reinterpretation paper. |
compute/ |
Pipeline code, gap test harness, plotting scripts, and the EXPDB clone with scipy cdd replacement. |
monograph/ |
The unified four-part Factor Skyline monograph. |
PAPERS/ |
All standalone papers (FS Parts I-IV, EXPDB analyses, evaluations). |
modules/ |
18 derivation modules for the Factor Skyline theory. |
reproducibility/ |
Deterministic reproducibility harness for all FS numerical claims. |
maps/ |
Architectural maps of the monograph structure. |
archive/ |
Earlier drafts, preserved for provenance. |
python reproducibility/run_all.py
Deterministic seeding (seed 123456), 20 verification tables, timestamped output, GitHub Actions CI on every push. See reproducibility/README.md.
@misc{proxmire2026factorskyline,
author = {Allen Proxmire},
title = {The Factor Skyline: An Ontological Lookout Over the Integers},
year = {2026},
version = {v1.0},
doi = {10.5281/zenodo.18275273},
url = {https://doi.org/10.5281/zenodo.18275273},
note = {Monograph and supporting materials available at
https://github.com/allen-proxmire/factor-skyline}
}See LICENSE for details.
Questions, feedback, and collaboration inquiries are welcome. Please open an issue or reach out via GitHub Discussions.