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  "slug": "compartment-fragmentation-phase-classification",
  "title": "Critical nonexplosion and phase transitions in finite-catalyst compartment systems",
  "shortTitle": "The exact boundary between fragmentation and explosion",
  "url": "https://evidencepress.org/releases/compartment-fragmentation-phase-classification/",
  "oneLine": "A complete phase diagram identifies when a finite-catalyst compartment population is conservative and when infinitely many events occur in finite time.",
  "abstract": "This research candidate classifies explosion for a stochastic population of noninteracting compartments with finitely many conserved catalysts, superlinear substrate production and content-dependent fragmentation. For production b+alpha(e)(s)_m and fragmentation kappa s^gamma, fragmentation prevents explosion when gamma>m-1 and, at the critical power gamma=m-1, exactly when alpha is at most kappa log(1/p). All other catalyst-containing finite states explode almost surely, whereas catalyst-free states remain conservative. The proof controls the complete descendant population rather than only an active lineage and proves the source conjecture. Extensions cover real exponents, logarithmic second-order boundaries, moment-controlled kernels and fresh random retained fractions Q, where the critical logarithmic loss becomes E[-log Q]. Equal mean retention need not determine the same phase. Explosive regimes also admit uniform exponential lifetime bounds at bounded catalyst count. Exact finite checks support selected algebra; the universal conclusions rest on the written proofs.",
  "datePublished": "2026-10-20",
  "dateModified": "2026-10-20",
  "version": "1.0.0-candidate",
  "doi": "10.5281/zenodo.23505123",
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  "authors": [
    "Anonymous"
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  "keywords": [
    "compartment systems",
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    "fragmentation",
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    "random retention"
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    "For gamma>m-1 the process is conservative; for gamma<m-1 every finite catalyst-containing state explodes almost surely.",
    "At gamma=m-1 the exact threshold is alpha <= kappa log(1/p), including equality.",
    "With fresh random retention Q, the threshold uses E[-log Q] under one finite inverse moment and uniform conditional moment bounds."
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    {
      "citation": "Anderson, Howells and Rojas La Luz (2026), source compartment model and Conjecture 3.14.",
      "url": "https://arxiv.org/abs/2601.11083",
      "doi": "10.48550/arXiv.2601.11083"
    },
    {
      "citation": "Brockwell, Gani and Resnick (1982), birth processes with population-dependent catastrophes.",
      "url": "https://doi.org/10.1017/S0021900200034622",
      "doi": "10.1017/S0021900200034622"
    },
    {
      "citation": "Menshikov and Petritis (2014), explosion, implosion and moments for continuous-time Markov chains.",
      "url": "https://doi.org/10.1017/CBO9781107415324",
      "doi": "10.1017/CBO9781107415324"
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