Quantum Sphaera Companion: A Structure-First Mathematical Unfolding

Quantum Sphaera Companion v4.8.0 release. v4.8.0 carries the source-only layers recorded after the v4.7.0 release (v4.7.0-r85 to r94) and opens the v4.8.0 line with the Planck-Readout Metric Layer (v4.8.0-r01). Post-v4.7.0 layers: citation repair and unity-theorem scope separation (r85); C5 asymptotic-collar bookkeeping with the threshold function n_min(theta) and the finite-zero exclusion for any multiplicative collar recursion with q > 0 (r86); photon-clock selector-window calibration and its correction (r87, r89); admissibility test for non-collar routes, excluding the subtractive channel and truncation and leaving only a non-collar witness open (r88); an approximate reconstruction of the bound Delta_gamma < 1/5 (r90), sharpened into an exact one: 1/5 is the minimal admissible relative drop over the primary relay chain, attained at chart V3 (r92); execution of the C4 mixed-kernel branch Q4, showing that beta_4 = 1/256 cannot be spent under matter-frame typing (r91); the two-sided tensor typing read as a routing grammar (r93); and the provenance of the C5 contraction factor 3/4, recorded as a declared ledger value whose detector stage n = 20 fixes q only to an interval (r94). v4.8.0-r01 defines a readout-calibrated Planck scale l_eff(R) = l_P lambda_R with an orientation code, recovers the matter-frame Planck scale up to a declared calibration error, identifies the photon-frame Planck length as an instance, and separates the orientation code from the r82 tachyon-frame interval signature. The MM/HC field-equation refactor of this research line is not performed in this release. Scope guard: this is a guarded local/restricted/effective release. Guard and residual vectors are unchanged from v4.7.0. It does not claim exact finite C5 zero closure, exact all-readout terminality, C6/T2 closure, a global photon-clock or Riemann-Hypothesis theorem, global all-readout closure, or a negative physical length. Version DOI: 10.5281/zenodo.23365244Concept DOI: 10.5281/zenodo.19210728Previous version DOI (v4.7.0): 10.5281/zenodo.20232911Previous/baseline DOI (v4.6.0): 10.5281/zenodo.20117361

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-14
DOI
https://doi.org/10.5281/zenodo.23365244
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
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preprint

Quantum Sphaera Companion: A Structure-First Mathematical Unfolding

Marc Brendecke
Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
preprint

Quantum Sphaera Companion: A Structure-First Mathematical Unfolding

Marc Brendecke
preprint en

Abstract

Quantum Sphaera Companion v4.8.0 release. v4.8.0 carries the source-only layers recorded after the v4.7.0 release (v4.7.0-r85 to r94) and opens the v4.8.0 line with the Planck-Readout Metric Layer (v4.8.0-r01). Post-v4.7.0 layers: citation repair and unity-theorem scope separation (r85); C5 asymptotic-collar bookkeeping with the threshold function n_min(theta) and the finite-zero exclusion for any multiplicative collar recursion with q > 0 (r86); photon-clock selector-window calibration and its correction (r87, r89); admissibility test for non-collar routes, excluding the subtractive channel and truncation and leaving only a non-collar witness open (r88); an approximate reconstruction of the bound Delta_gamma < 1/5 (r90), sharpened into an exact one: 1/5 is the minimal admissible relative drop over the primary relay chain, attained at chart V3 (r92); execution of the C4 mixed-kernel branch Q4, showing that beta_4 = 1/256 cannot be spent under matter-frame typing (r91); the two-sided tensor typing read as a routing grammar (r93); and the provenance of the C5 contraction factor 3/4, recorded as a declared ledger value whose detector stage n = 20 fixes q only to an interval (r94). v4.8.0-r01 defines a readout-calibrated Planck scale l_eff(R) = l_P lambda_R with an orientation code, recovers the matter-frame Planck scale up to a declared calibration error, identifies the photon-frame Planck length as an instance, and separates the orientation code from the r82 tachyon-frame interval signature. The MM/HC field-equation refactor of this research line is not performed in this release. Scope guard: this is a guarded local/restricted/effective release. Guard and residual vectors are unchanged from v4.7.0. It does not claim exact finite C5 zero closure, exact all-readout terminality, C6/T2 closure, a global photon-clock or Riemann-Hypothesis theorem, global all-readout closure, or a negative physical length. Version DOI: 10.5281/zenodo.23365244Concept DOI: 10.5281/zenodo.19210728Previous version DOI (v4.7.0): 10.5281/zenodo.20232911Previous/baseline DOI (v4.6.0): 10.5281/zenodo.20117361

Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
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