{
  "abstract": "Reading Planck energy as a completed modular-charge budget\n\nVersion: 3.9\n\nConcept DOI: 10.5281/zenodo.19975260\n\nAuthor: Ali Attar\n\nWebsite: quantumtraction.org\n\n\\[ \\boxed{ E_P=m_Pc^2=\\hbar\\omega_P =\\rho_A^{(4)}\\!\\left(4\\pi\\ell_A^4\\right) =\\frac{\\hbar c}{2\\pi\\ell_A}Q_P, \\qquad Q_P=2\\pi. } \\]\n\nThe paper reads mass, frequency, completed-event four-capacity, and A7-saturated modular capacity as faces of one endpoint budget. Version 3.8 makes the fourth face auditable rather than merely dimensionally recognizable:\n\n\\[ \\boxed{ \\Delta V_A^{(4)}=24\\left(\\frac{\\pi}{6}\\ell_A^3\\right)\\ell_A=4\\pi\\ell_A^4, \\qquad |\\mathcal O_3^+|=24. } \\]\n\nThe external standard ingredients are the ball volume and the proper orientation count. The QTT-native object is the completed address-event product measure and its fourth-face role. The fifth face then uses the separately declared A7 modular saturation \\(Q_P=2\\pi\\); the release does not reclassify ordinary low-energy Landauer erasure as the same object.\n\nPublic anchors\n\nQuantum Traction Theory: Main Book\n\nCompleted-Event Four-Capacity Theorem\n\nQTT Lexicon\n\nQTT Derivation Atlas\n\nThe release package exposes one PDF preview. Source, verification material, metadata, and a SHA-256 manifest are bundled in the reconstruction ZIP.\n\nRelated work and the distinct source construction\n\nConrad Ranzan's The Fundamental Process of Energy--Part I (2014), Sections 5-6, already identifies mass-energy with substrate absorption. His Dynamic Aether Theory of Gravity (2025), Sections 1.1 and 6.1, connects continuing supply with existence and explicitly describes discrete units. His 2014 text also rejects gravitons. These broad ideas are credited as related work rather than claimed as exclusive QTT distinctions.\n\nThe additional QTT structure is the declared completed-event product capacity, A7 modular normalization and common funded-operator energy/endurance construction. An induced density is not counted as a second independent value prediction. A bare substrate unit is distinguished from a completed energy-valued event. The comparison is bounded to the two examined works; it assigns no new observational significance and changes none of the inherited theorem or access-map statuses.\n\nPrimary references: Ranzan's 2014 primary reprint; Ranzan's 2025 gravity paper.",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher, Colombes, France"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Ali Attar",
      "orcid": "0009-0008-9931-2691"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e0ad1yet9m6gn.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23543381",
  "fulltext_url": null,
  "id": "e0ad1yet9m6gn",
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  "landing_url": "https://zenodo.org/records/23543381",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
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  "pdf_url": "https://zenodo.org/api/records/23543381/files/00_qtt_fifth_face_v3_9.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e0ad1yet9m6gn.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T12:20:57Z",
      "native_id": "23543381",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23543381"
    }
  ],
  "subjects": [],
  "title": "A modular-charge fifth face of the Unified Equilibrium Law in Quantum Traction Theory: E_P = (ℏc/2πℓ_P) Q_P at A7 saturation",
  "title_text": "A modular-charge fifth face of the Unified Equilibrium Law in Quantum Traction Theory: E_P = (ℏc/2πℓ_P) Q_P at A7 saturation",
  "type": "preprint",
  "updated_at": "2026-11-04T12:20:57Z",
  "url": "https://research.draconitic.com/paper/e0ad1yet9m6gn",
  "venue": "Zenodo",
  "versions": []
}