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Sample Structural Analysis Report
The Maypole–Lattice Framework
A Sharp Threshold for Diagonal Dominance in Prime Dirichlet Polynomial Moments
Matthew J. Goss, Jr. · v8.2.2 · July 2026 · 4,276 lines · 15 sections
Classification
NEW CLAIMS
Claims Extracted
39
Fabric Strands
1,721
Corpus Roots
37
What This Report Shows

MathLab parsed this .tex file, extracted every formal environment (theorems, lemmas, propositions, conjectures, corollaries, computations), decomposed them into individual claims, and mapped each claim against a verified corpus of mathematical results. The structural analysis below shows how this paper connects to established mathematics — and where it stands alone.

Novel Research Detected
All 39 extracted claims are classified as new — they do not duplicate existing results in the corpus. This is the expected outcome for original research. The paper introduces new definitions (Maypole constant), proves new theorems (sharp threshold, equidistribution floor), and formulates new conjectures (bounded minimiser, hybrid anti-correlation). The structural analysis maps the surrounding mathematical fabric, not the paper's own novelty.
Extraction Summary
Theorems
6
Propositions
7
Conjectures
6
Corollaries
6
Computations
25
Proofs
17
Remarks
41
Sections
15
Extracted Claims
39 formal claims decomposed from the .tex source
IDClaimDomain
S3221Gram–Schmidt Structure of Approximation Latticealgebra
S3222Equidistribution Floor Theoremnumber-theory
S3223Quantitative Equidistribution Floor Boundnumber-theory
S3224Growth Condition for Equidistribution Floornumber-theory
S3225Bounded Minimiser Conjecturenumber-theory
S3226Constant Maypole Floor from Bounded Minimisernumber-theory
S3227Khintchine–Cassels Transference Lemmanumber-theory
S3228Sharp Threshold for Diagonal Dominancenumber-theory
S3229Single-Zero Invisibility Propositionmath-physics
S3230Clean Destruction and Monotone Memory Theoremanalysis
S3231No Memory Corruption (Ratchet Property)number-theory
S3232Density Decrement for Bad Setsnumber-theory
S3233Logarithmic Growth of Bad Set Cardinalitynumber-theory
S3234Asymptotic Density Vanishingnumber-theory
S3235Finiteness of Bad Set at Fixed Knumber-theory
S3236Independence Breakdown at Higher Momentsmath-physics
S3237Universal 3/5-Exponent Bottlenecknumber-theory
S3238CFKRS Leading-Order Identitynumber-theory
S3239Hybrid Maypole–Hadamard Anti-Correlation Conjecturenumber-theory
S3240Structural Origin of Anti-Correlationnumber-theory
S3241Gaussian Model Discrepancynumber-theory
S3242Gaussian Model for Anti-Correlationmath-physics
S3243Zero-Driven Mechanism for Anti-Correlationnumber-theory
S3244Function Field Anti-Correlationalgebra
S3245Function Field Mechanism and Number Field Gapnumber-theory
S3246Conditional Hybrid Moment Transfer Theoremnumber-theory
S3247Fixed-Parameter Reduction to Decorrelationnumber-theory
S3248Maypole-Scale Subtletynumber-theory
S3249Conditional Transfer at Fixed Parametersnumber-theory
S3250Gaussian Bootstrap for Moment Anti-correlation Hierarchynumber-theory
S3251Asymptotic Decorrelation at Maypole Scalenumber-theory
S3252Finite-Temperature Anti-correlation at First Momentnumber-theory
S3253K-Monotonicity of Second-moment Anti-correlationnumber-theory
S3254Universal Diagonal Positivity for Subleading Indicesnumber-theory
S3255Kurtosis Scaling with Euler Factor Repartitioningmath-physics
S3256Kurtosis-Variance Scaling Invariantmath-physics
S3257Duality Mismatch Between Euler-Hadamard and Keating-Snaithmath-physics
S3258Non-Extendability of n=1 Proof to n≥2math-physics
S3259Sparse Möbius Large Deviations and Zero-Tail Suppressionmath-physics
Fabric Analysis
Structural context from 1,721 verified mathematical strands
Total Strands
1,721
verified corpus
Root Pillars
37
foundational results
Max Depth
11
dependency levels
Connectivity
100%
0 islands
Blast Points
10
high-impact nodes
Domains
12
mathematical fields
Blast Radius
If these strands were invalidated, this percentage of the fabric would be affected
31.0%
S355 — 534 downstream, 12 domains
22.4%
S372 — 385 downstream, 11 domains
22.4%
S582 — 385 downstream, 10 domains
20.7%
S351 — 356 downstream, 8 domains
18.4%
S413 — 317 downstream, 10 domains
Root Pillars
The foundational results that anchor the surrounding fabric
S355
534 downstream · 31.0% of fabric · 12 domains
S372
385 downstream · 22.4% of fabric · 11 domains
S582
385 downstream · 22.4% of fabric · 10 domains
S351
356 downstream · 20.7% of fabric · 8 domains
S413
317 downstream · 18.4% of fabric · 10 domains
What Happens Next

This sample shows the structural analysis — the first stage of a MathLab session. In a full session, the War Room's four agents (Analyst, Critic, Verifier, Synthesizer) independently evaluate each claim across up to 10 rounds, producing per-theorem confidence scores, dependency maps, and an exportable dossier.

Pro subscribers also access the Forge repair engine, which identifies specific structural gaps and drafts candidate fixes — each validated by an independent court verdict before being offered to the author.

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Analysis generated from a live MathLab session · Paper: v8.2.2 (July 2026) · Corpus: Crystal Farmer (1,721 strands, 14 domains)