strausforge

Strausforge is an experimental computational laboratory for the Erdős–Straus conjecture.

The conjecture asks whether every integer n ≥ 2 admits a decomposition

4/n = 1/x + 1/y + 1/z

in positive integers x, y, z.

Rather than relying purely on brute-force search, this project studies the conjecture through discovering, verifying, and measuring residue-class identities — explicit parametric constructions that solve infinite families of integers at once.

The guiding idea is simple:

turn numerical verification into structural evidence.

Strausforge treats solutions not as isolated computations, but as mathematical objects that can be mined, classified, stress-tested, and reproduced.

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Current experimental coverage (v0.3.x)

Deterministic hardness runs have been executed in 2M windows through:

n ≤ 30,000,000   (windowed runs)

Observed structural behavior:

• Escalation pressure is sparse.
• Expanded cases concentrate overwhelmingly in residues
  1 and 25 mod 48.
• A large majority of expanded cases are prime inputs.
• The prime-or-square-window heuristic dramatically reduces expanded exports relative to --proc-heuristic off.

These results convert large computational ranges into analyzable structural data.

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What this project actually does

Strausforge combines three perspectives.

1. Exact computation

• deterministic search for solutions
• exact rational verification
• reproducible certificate generation
• fully auditable solver paths

2. Identity discovery

• detects congruence-class structure
• fits parametric solution families
• mines residue-class lemmas from verified data
• performs empirical and symbolic validation

3. Experimental number theory

• measures where identities succeed or struggle
• studies structurally “hard” integers
• profiles solver pressure across ranges of n
• visualizes escalation / expansion behavior (often concentrated on primes and squares)

The system functions as a computational microscope for the Erdős–Straus equation.

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Reproducibility contract

Strausforge enforces the following guarantees:

• All solver paths are deterministic.
• All certificates include exact rational verification.
• Hardness metrics are derived from reproducible pipeline stages.
• Expanded-case JSONL exports can be summarized without loading entire files in memory.
• CLI and GUI share the same evaluation engine.

Re-running the same command with the same identity file produces identical outputs.

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Installation

Core CLI install:

python -m pip install -e .

Developer install (tests + lint):

python -m pip install -e '.[dev]'

GUI install:

pip install -e ".[gui]"

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Basic usage

python -m strausforge --help

Hardness run example:

strausforge hardness \
  --identity data/identities.jsonl \
  --n-min 2 \
  --n-max 2000000 \
  --bin-size 5000 \
  --out hardness.csv \
  --progress

Summarize expanded exports:

strausforge expanded-stats --in expanded.jsonl --mod 48 --top 20

# Export structural tags for expanded cases during hardness evaluation.
strausforge hardness \
  --identity data/identities.jsonl \
  --n-min 2 \
  --n-max 2000000 \
  --export-expanded-meta expanded_meta.jsonl \
  --expanded-factor-bound 5000

--export-expanded-meta attaches bounded factor metadata (res48, spf, cofactor, semiprime_kind, semiprime_triggered, spf_bound_used) to expanded cases only, enabling large-range research runs without separate profiling scans. --expanded-factor-bound controls the SPF trial-divisor bound (also capped by isqrt(n)) and defaults to 5000, which provides full coverage for expanded semiprime witnesses in the observed 22M–23M window.

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Window reporting pipeline

Recommended modern workflow for semiprime enrichment stats:

1. Run strausforge hardness with --export-expanded-meta expanded_meta.jsonl.
2. Run tools/window_report_meta.ps1 directly on the expanded meta JSONL.
3. Optionally run tools/analyze_witnesses.py for deeper witness-level analysis.

Example:

pwsh tools/window_report_meta.ps1 `
  -NMin 28000001 `
  -NMax 30000000 `
  -MetaJsonl .\expanded_off_meta_28M_30M.jsonl `
  -Step 97

The legacy CSV-based tools/window_report.ps1 remains supported. Witness CSV generation is now optional for high-level expanded/baseline semiprime reporting.

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Identity mining

Mine identities from certified solutions:

strausforge mine \
  --in certs.jsonl \
  --out data/identities.jsonl \
  --max-identities 50

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Procedural heuristics

Example:

--proc-heuristic semiprime-window

The semiprime-window heuristic captures residual semiprime pressure after the prime-window family eliminates most prime expansion. It deterministically triggers only when:

• n % 48 is in {1, 25}
• bounded SPF discovery finds a factor (spf > 0)

When triggered, the initial procedural search window is widened (currently 8 -> 128) for that n; otherwise behavior is unchanged.

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What this project is (and is not)

Strausforge is:

• a reproducible experimental framework
• a residue-class identity explorer
• a computational number theory laboratory

Strausforge is not:

• a claimed proof of the Erdős–Straus conjecture
• a heuristic black box
• a machine learning system

All results remain deterministic and auditable.

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Philosophy

Large conjectures often resist direct proof but expose structural regularities under systematic measurement.

Strausforge treats computation as structured evidence, not as brute-force confirmation.

The project is released openly so mathematicians and experimenters can extend its structural exploration further.