Unit Distance Research — Scripts and Tools
Complete inventory of the 18 PEP 723 scripts used in the unit distance research, organized by purpose.
Unit Distance Research — Scripts and Tools
Overview
The unit distance research used 18 PEP 723 Python scripts for computation, verification, and analysis. All scripts are located in the scripts/ directory of the unit-distance-csfita repository and are executed via uv run scripts/<name>.py.
The scripts fall into five categories: optimizers (hypothesis-specific), prime sieves, PDF readers, analysis tools, and verification scripts.
Technical Specifications
- Package Manager:
uv(NOT pip) - Script Standard: PEP 723 inline metadata
- Script Location:
scripts/directory only - Execution:
uv run scripts/<name>.py - Hardware: Apple M3 Pro, 24GB Unified VRAM
- Acceleration: NumPy vectorized, Apple MLX, Metal tensors
- Python: Latest stable via uv
Optimizers (Hypothesis-Specific)
These scripts verify and optimize specific hypotheses. Each script implements the full mathematical construction for one hypothesis.
H15: Central Imaginary Quadratic CM Tower
Script: optimize_central_cm_tower.py
Command: uv run scripts/optimize_central_cm_tower.py
Purpose: Verifies the H15 construction -- the central 2-tower over an imaginary quadratic base field achieving delta = 0.013769.
Dependencies: numpy, scipy
What it does:
- Constructs the base field F = Q(sqrt(-D)) with D = product of 151 primes
- Computes the 2-class rank d = 150
- Calculates the GS capacity: 2t = floor(150^2/4) - 150 - 1 = 5474
- Verifies the central tower restriction (complex conjugation commutes with Gal)
- Computes the exponent delta = 1477.21 / 107287.87 = 0.013769 Created: 2026-07-04 (commit 3463ed1) Supports: H15 (Central CM Tower)
H16: Multi-Quadratic CM Degree 16
Script: optimize_multiquadratic_degree16.py
Command: uv run scripts/optimize_multiquadratic_degree16.py
Purpose: Verifies the H16 construction -- the degree 16 multi-quadratic CM field achieving delta = 0.019603.
Dependencies: numpy, scipy
What it does:
- Constructs the base field F = Q(sqrt(-2), sqrt(3), sqrt(5), sqrt(7))
- Computes the 2-class rank d = 2^4 - 1 = 15
- Identifies the 17 unramified split primes via quadratic reciprocity
- Verifies the GS inequality: 22 + 34 = 56 < 56.25
- Computes the exponent delta = 9.1099 / 464.7310 = 0.019603 Created: 2026-07-04 (commit 3463ed1) Supports: H16 (Multi-Quadratic CM16)
Prime Sieves
These scripts identify and verify primes that satisfy specific splitting conditions.
H16 Prime Verification
Script: fix_h16_primes.py
Command: uv run scripts/fix_h16_primes.py
Purpose: Calculates the exact unramified split primes in the H16 base field F = Q(sqrt(-2), sqrt(3), sqrt(5), sqrt(7)).
Dependencies: sympy
What it does:
- For each candidate prime q, checks if q splits completely in F
- Verifies (-2/q) = (3/q) = (5/q) = (7/q) = 1 via Legendre symbols
- Excludes ramified primes {2, 3, 5, 7}
- Returns the first 17 unramified split primes: {59, 131, 251, ..., 2411} Created: 2026-07-04 (commit e88c570) Supports: H16 (Multi-Quadratic CM16)
Base Field Prime Sieve
Script: engineer_p_base.py
Command: uv run scripts/engineer_p_base.py
Purpose: High-scale sieve script verifying Dirichlet density bounds for prime selection.
Dependencies: numpy, sympy
What it does:
- Computes Dirichlet density of primes splitting in multi-quadratic fields
- Verifies density bounds for various base field configurations
- Helps identify optimal prime sets for GS inequality satisfaction Created: 2026-07-04 (commit e88c570) Supports: H15, H16 (prime selection)
PDF Readers
These scripts extract and analyze content from the OpenAI PDFs. They are read-only tools that do not perform mathematical computation.
Chain-of-Thought Keyword Search
Script: search_cot_ideas.py
Command: uv run scripts/search_cot_ideas.py
Purpose: Searches the OpenAI chain-of-thought PDF for keywords related to the proof structure.
Dependencies: none
What it does:
- Reads
wiki/raw/unit-distance-cot.txt(extracted from the PDF) - Searches for keywords: "Golod", "Shafarevich", "class number", "exponent", "delta", "epsilon", "Minkowski", "bounded window", "polydisc"
- Reports frequency and locations of each keyword Created: 2026-07-03 (early session) Supports: H1-H3 (initial exploration)
Remarks Lemma Extraction
Script: read_middle_remarks.py
Command: uv run scripts/read_middle_remarks.py
Purpose: Extracts the middle section of the Remarks PDF, focusing on Lemma 2.1 and Lemma 2.2.
Dependencies: none
What it does:
- Reads
wiki/raw/unit-distance-remarks.txt - Extracts text around Lemma 2.1 and Lemma 2.2
- Prints the relevant mathematical content Created: 2026-07-03 (early session) Supports: H1-H4 (Lemma 2.2 analysis)
Proposition 2.3 Reader
Script: read_prop_2_3.py
Command: uv run scripts/read_prop_2_3.py
Purpose: Extracts Proposition 2.3 from the Remarks PDF.
Dependencies: none
What it does:
- Reads
wiki/raw/unit-distance-remarks.txt - Locates and extracts Proposition 2.3
- Prints the proposition text Created: 2026-07-03 (early session) Supports: H1-H4 (proposition analysis)
Remarks 2.3 Reader
Script: read_remarks_2_3.py
Command: uv run scripts/read_remarks_2_3.py
Purpose: Extracts the remarks following Proposition 2.3.
Dependencies: none
What it does:
- Reads
wiki/raw/unit-distance-remarks.txt - Locates the remarks after Proposition 2.3
- Prints the remark text Created: 2026-07-03 (early session) Supports: H1-H4 (remark analysis)
Sawin-Tsimerman Reader
Script: read_sawin_tsimerman.py
Command: uv run scripts/read_sawin_tsimerman.py
Purpose: Extracts references to Sawin and Tsimerman from the OpenAI materials.
Dependencies: none
What it does:
- Reads the OpenAI PDF text files
- Searches for mentions of "Sawin" and "Tsimerman"
- Reports context around each mention Created: 2026-07-03 (early session) Supports: Anti-contamination protocol (identifying external references)
Section 7 Reader
Script: read_section_7.py
Command: uv run scripts/read_section_7.py
Purpose: Extracts Section 7 from the OpenAI proof PDF.
Dependencies: none
What it does:
- Reads
wiki/raw/unit-distance-proof.txt - Locates and extracts Section 7
- Prints the section text Created: 2026-07-03 (early session) Supports: H1-H4 (proof structure analysis)
Analysis Tools
These scripts perform mathematical analysis on the proof structure and hypothesis parameters.
Exponent Analysis
Script: analyze_exponent.py
Command: uv run scripts/analyze_exponent.py
Purpose: Analyzes the exponent calculation in the OpenAI proof.
Dependencies: none
What it does:
- Reads
wiki/raw/unit-distance-remarks.txt - Extracts Lemma 2.1 and Lemma 2.2 text
- Analyzes the exponent formula: delta = gamma / (4B)
- Helps understand the relationship between entropy (gamma) and packing (B) Created: 2026-07-03 (early session) Supports: H1-H4 (exponent understanding)
Reflection Analysis
Script: analyze_reflections.py
Command: uv run scripts/analyze_reflections.py
Purpose: Analyzes the reflection principles used in the OpenAI proof.
Dependencies: none
What it does:
- Reads the OpenAI PDF text files
- Identifies reflection-related content
- Helps understand the geometric interpretation of the construction Created: 2026-07-03 (early session) Supports: H1-H4 (geometric understanding)
Remarks Analysis
Script: analyze_remarks.py
Command: uv run scripts/analyze_remarks.py
Purpose: Comprehensive analysis of the Remarks PDF structure.
Dependencies: none
What it does:
- Reads
wiki/raw/unit-distance-remarks.txt - Identifies all lemmas, propositions, and remarks
- Creates a structural map of the Remarks document Created: 2026-07-03 (early session) Supports: H1-H4 (document navigation)
H1-H3 Quantification
Script: quantify_h1_h2_h3.py
Command: uv run scripts/quantify_h1_h2_h3.py
Purpose: Quantifies the parameter optimization space for hypotheses H1-H3.
Dependencies: numpy, scipy
What it does:
- Implements the H1 valuation optimization formula
- Implements the H2 polydisc radius optimization
- Maps the parameter space for H3 (pro-3 towers)
- Computes optimal parameters for each hypothesis Created: 2026-07-03 (early session) Supports: H1-H3 (parameter optimization)
Parameter Optimization
Script: optimize_parameters.py
Command: uv run scripts/optimize_parameters.py
Purpose: General-purpose parameter optimization for tower constructions.
Dependencies: numpy, scipy
What it does:
- Implements the delta(ell, t, k) function
- Uses scipy.optimize to find the global maximum
- Handles constraints: GS inequality, density bounds, CM involution
- Returns optimal parameters and the corresponding exponent Created: 2026-07-03 (Session 1) Supports: H5-H8 (global optimization)
Verification Scripts
These scripts verify specific mathematical claims or check the integrity of the research infrastructure.
Epsilon-U Validity Check
Script: verify_epsilon_u_valid.py
Command: uv run scripts/verify_epsilon_u_valid.py
Purpose: Verifies the validity of the epsilon-U construction in the OpenAI proof.
Dependencies: numpy
What it does:
- Implements the epsilon-U packing bound
- Verifies that the bound holds for various parameter choices
- Checks consistency with the OpenAI proof Created: 2026-07-03 (early session) Supports: H1-H4 (validity check)
Subagent Log Checker
Script: check_subagent_log.py
Command: uv run scripts/check_subagent_log.py
Purpose: Checks the subagent invocation logs for contamination events.
Dependencies: none
What it does:
- Reads the Antigravity transcript JSONL files
- Searches for subagent invocations
- Identifies any searches for external sources (potential contamination)
- Reports contamination events if found Created: 2026-07-03 (post-H3 contamination event) Supports: Anti-contamination protocol
Wiki Link Auditor
Script: wiki_link_auditor.py
Command: uv run scripts/wiki_link_auditor.py
Purpose: Audits the wiki for broken links, missing index entries, and OKF compliance.
Dependencies: none
What it does:
- Scans all
.mdand.mdxfiles in thewiki/directory - Checks that all wiki links (``) resolve to existing pages
- Verifies that all pages in the wiki are indexed in
wiki/index.md - Checks OKF frontmatter compliance (required fields: type, title, description, timestamp)
- Reports broken links, missing index entries, and OKF violations Created: 2026-07-04 (commit 5ddf8de) Supports: WIKI-MAINTAINER sub-agent
Scripts by Hypothesis
| Hypothesis | Scripts Used | Purpose |
|---|---|---|
| H1-H3 | search_cot_ideas.py, read_middle_remarks.py, read_prop_2_3.py, read_remarks_2_3.py, read_sawin_tsimerman.py, read_section_7.py, analyze_exponent.py, analyze_reflections.py, analyze_remarks.py, quantify_h1_h2_h3.py | Initial exploration, PDF analysis |
| H4 | quantify_h1_h2_h3.py, optimize_parameters.py | Pro-3 tower optimization |
| H5-H6 | optimize_parameters.py | Global parameter tuning |
| H7 | optimize_parameters.py | Multivariate optimization |
| H8 | optimize_parameters.py | Imaginary quadratic optimization |
| H9-H10 | (no dedicated scripts) | Unproven, disqualified before scripting |
| H11 | optimize_parameters.py | Formal proof verification |
| H12-H14 | optimize_parameters.py | Completeness failure analysis |
| H15 | optimize_central_cm_tower.py | Central CM tower verification |
| H16 | optimize_multiquadratic_degree16.py, fix_h16_primes.py, engineer_p_base.py | Multi-quadratic CM16 verification |
| Infrastructure | wiki_link_auditor.py, check_subagent_log.py | Wiki integrity, contamination detection |
Scripts by Creation Date
| Date | Scripts | Session |
|---|---|---|
| 2026-07-03 (early) | search_cot_ideas.py, read_middle_remarks.py, read_prop_2_3.py, read_remarks_2_3.py, read_sawin_tsimerman.py, read_section_7.py, analyze_exponent.py, analyze_reflections.py, analyze_remarks.py, quantify_h1_h2_h3.py | Session 1 (initial exploration) |
| 2026-07-03 (mid) | optimize_parameters.py, verify_epsilon_u_valid.py, check_subagent_log.py | Session 1 (optimization) |
| 2026-07-04 (early) | optimize_central_cm_tower.py, optimize_multiquadratic_degree16.py | Session 2 (H15-H16 verification) |
| 2026-07-04 (mid) | wiki_link_auditor.py, fix_h16_primes.py, engineer_p_base.py | Session 2 (infrastructure) |
Execution Examples
# Verify H16 construction
uv run scripts/optimize_multiquadratic_degree16.py
# Verify H15 construction
uv run scripts/optimize_central_cm_tower.py
# Verify H16 split primes
uv run scripts/fix_h16_primes.py
# Audit wiki integrity
uv run scripts/wiki_link_auditor.py
# Search CoT for keywords
uv run scripts/search_cot_ideas.py
# Check for contamination events
uv run scripts/check_subagent_log.py
Technical Notes
PEP 723 Inline Metadata
All scripts use PEP 723 inline metadata to declare dependencies:
# /// script
# dependencies = ["numpy", "scipy"]
# ///
This allows uv run to automatically install dependencies without a separate requirements.txt file.
Apple Silicon Acceleration
The optimization scripts (optimize_parameters.py, optimize_central_cm_tower.py, optimize_multiquadratic_degree16.py) use NumPy vectorized operations that benefit from Apple Silicon's unified memory architecture. Future scripts may use MLX for Metal tensor acceleration.
Anti-Contamination Design
The check_subagent_log.py script was created specifically in response to the H3 contamination event. It scans the Antigravity transcript logs for any searches for external sources, providing an automated check against contamination.
References
- unit-distance-development-journey — Full session-by-session chronology
- unit-distance-seasons — Research seasons and hypothesis progression
- unit-distance-dead-ends — Analysis of failed hypotheses and lessons learned
- unit-distance — Mathematical background and current status