# Verification and scope report

Title: Seed Aggregation for Competing First-Passage Percolation

- Five-page English manuscript; author Alper Ferudun, Mercury Software GmbH in a footnote.
- Complete written proof of the scoped existence criterion, with detailed originating-researcher self-audit.
- 336,970 exact finite diagnostic checks agree under ordinary and optimized Python.
- The original and quotient generators are computed separately on 20,790 labelled matchings and 311,850 colour states.
- Exact second-moment identities and rational exponent checks support the elementary calculations.
- Source theorem parameters, configuration-model scope, simplicity conditioning, subsequence necessity and rounded construction are audited explicitly.
- Both the desktop LaTeX compiler and a portable source-only build succeed.
- Every final PDF page has been visually checked; no clipping, overlap, missing symbols or unresolved references.

Accepted scope: For an almost regular configuration-model family obtained by merging k_N slow seeds into q_N hubs, with fixed degree d>=3 and rate ratio r in (0,1), a construction with convergent finite second degree moment and slow-type final density tending to one exists exactly when q_N/N^(1-2r) tends to infinity, assuming q_N=o(N). This includes a sharp one-hub threshold r>1/2 and an explicit construction for every positive rate ratio. The high-probability conclusions transfer to uniform simple graphs.

Theorem scope resolved: yes. Whole original source question resolved: no.
New original-source closures: zero. Growth limits are prior work, credited prominently.
The fixed-iid problem and the critical regime remain unclaimed.
No outside review, proof-assistant formalization or absolute novelty certification.
AI tools assisted derivation, literature search, verification code and exposition.
License: CC BY 4.0.