Appendix O

Master Index

This appendix provides a comprehensive cross-reference of all TMT results, organised by topic. For each result, the chapter where it is derived, the source Part, and the current status are listed. This index is designed to facilitate independent verification: a reader wishing to check any specific claim can trace it directly to the relevant derivation.

Foundational Results

Table 0.1: Foundational results index
ResultChapterSourceStatus
P1: \(ds_6^{\,2} = 0\)Ch. 2Part 1POSTULATE
Product structure \(M^4 \times S^2\)Ch. 3Part 2PROVEN
\(D = 6\) uniquenessCh. 3Part 2PROVEN
\(S^2\) optimalCh. 4Part 2PROVEN
Temporal momentum \(p_T = mc/\gamma\)Ch. 5Part 1PROVEN
Velocity budget \(v^2 + v_T^2 = c^2\)Ch. 5Part 1PROVEN
Modulus stabilisationCh. 8Part 4PROVEN
Interface scale \(L \approx 81\,\mu\)mCh. 8Part 4PROVEN
\(\mathcal{M}^6 \approx 7296\) GeVCh. 8Part 4PROVEN

Gauge Structure Results

Table 0.2: Gauge structure results index
ResultChapterSourceStatus
SO(3) from \(S^2\) isometryCh. 15Part 3PROVEN
SU(2) as double coverCh. 15Part 3PROVEN
U(1) from monopole bundleCh. 16Part 3PROVEN
SU(3) from monopole harmonicsCh. 17Part 3PROVEN
\(\pi_2(S^2) = \mathbb{Z}\) classificationCh. 16Part 3PROVEN
\(n = 1\) ground stateCh. 16Part 3PROVEN
\(g^2 = 4/(3\pi)\)Ch. 18Part 3PROVEN
\(\sin^2\theta_W = 1/4\) (tree)Ch. 20Part 4PROVEN
\(\theta_{\text{QCD}} = 0\)Ch. 19Part 3PROVEN
Anomaly cancellationCh. 22Part 6CPROVEN

Electroweak and Higgs Results

Table 0.3: Electroweak and Higgs results index
ResultChapterSourceStatus
Higgs doublet from \(S^2\)Ch. 23Part 4PROVEN
\(v = 246\) GeVCh. 24Part 4PROVEN
\(m_H \approx 126\) GeVCh. 25Part 6APROVEN
\(M_W \approx 80.4\) GeVCh. 26Part 4PROVEN
\(M_Z \approx 91.2\) GeVCh. 26Part 4PROVEN
SSB from geometryCh. 24Part 4PROVEN
No additional Higgs bosonsCh. 25Part 4PROVEN

Fermion Results

Table 0.4: Fermion results index
ResultChapterSourceStatus
Three generations from \(\ell_{\max} = 3\)Ch. 29Part 5PROVEN
No fourth generationCh. 29Part 5PROVEN
Fermion mass hierarchyCh. 42Part 6ADERIVED
CKM matrix structureCh. 50Part 6BPROVEN
PMNS matrix structureCh. 55Part 6APROVEN
Neutrino seesaw mechanismCh. 56Part 6APROVEN
Normal neutrino hierarchyCh. 57Part 6ADERIVED
Hypercharge quantisationCh. 22Part 6CPROVEN
\(B - L\) conservationCh. 22Part 6CPROVEN

Gravity and Cosmology Results

Table 0.5: Gravity and cosmology results index
ResultChapterSourceStatus
Newton's law from P1Ch. 60Part 5PROVEN
Modified potential at \(81\,\mu\)mCh. 62Part 5PROVEN
\(H_0 = 73.3\) km/s/MpcCh. 69Part 5PROVEN
Dark energy from vacuumCh. 70Part 5PROVEN
MOND acceleration \(a_0\)Ch. 72Part 8PROVEN
\(c_{\text{gw}} = c\) (exact)Ch. 77Part 9APROVEN
Tensor polarisation onlyCh. 77Part 9APROVEN
Black hole entropyCh. 79Part 9CPROVEN
MOND \(\to\) GR transitionCh. 74Part 9BPROVEN

Inflation Results

Table 0.6: Inflation results index
ResultChapterSourceStatus
Modulus-driven inflationCh. 82Part 10APROVEN
\(r = 0.003 \pm 0.002\)Ch. 83Part 10APROVEN
\(n_s = 0.965\)Ch. 83Part 10APROVEN
\(N_e \approx 60\) e-foldsCh. 82Part 10APROVEN
Reheating mechanismCh. 84Part 10APROVEN
Initial conditions from P1Ch. 85Part 10BDERIVED

Quantum Mechanics Results

Table 0.7: Quantum mechanics results index
ResultChapterSourceStatus
QM emergence from \(S^2\)Ch. 32Part 7PROVEN
\(\hbar\) from geometryCh. 33Part 7PROVEN
Born rule derivationCh. 34Part 7PROVEN
Decoherence \(\tau_0 = 149\) fsCh. 35Part 7PROVEN
\(\sqrt{N}\) scalingCh. 35Part 7PROVEN
Entanglement as \(L\)-conservationCh. 36Part 7DERIVED
Measurement problem resolutionCh. 37Part 7DERIVED

Part XI and XII Results

Table 0.8: Temporal determination and Millennium Prize results index
ResultChapterSourceStatus
Arrow of time from \(T\)-breakingCh. 88Part 11PROVEN
Proton mass \(\approx 937\) MeVCh. 90Part 11PROVEN
Muon \(g-2\) BSM \(< 10^{-14}\)Ch. 87Part 11PROVEN
Navier–Stokes regularityCh. 97Part 12PROVEN
Yang–Mills mass gapCh. 104Part 12PROVEN
NS–YM unificationCh. 111Part 12DERIVED

Falsification Criteria Index

Table 0.9: Complete falsification criteria cross-reference
#TestTMT PredictionExperimentChapter
1Gravity scale\(81\,\mu\)mStanford/IUPUICh. 62
2Gravity signRepulsive correctionTable-topCh. 62
34th generationNoneLHCCh. 29
4Proton decayNoneHyper-KCh. 22
5Neutrino hierarchyNormalDUNE/JUNOCh. 57
6Tensor ratio\(r = 0.003\)LiteBIRDCh. 83
7WIMP DMNoneDirect detectionCh. 72
8Decoherence \(\tau_0\)149 fsAttosecondCh. 35
9\(\sqrt{N}\) scalingConfirmedInterferometryCh. 35
10Muon \(g-2\) BSM\(< 10^{-14}\)FermilabCh. 87
11Arrow of timeIrreversibilityMacroscopicCh. 88
12Proton mass\(937 \pm 5\%\) MeVPDGCh. 90
13Exotic chargesNoneCollidersCh. 22

How to Use This Index

To verify a specific prediction:

    • Find the result in the tables above.
    • Go to the indicated chapter for the full derivation.
    • Trace the derivation chain back to P1 using the chain displayed in each chapter's “Derivation Chain Summary” section.
    • Check each step against the source Part indicated.
    • Consult Appendix F for the complete chain in condensed form.

To check a numerical value:

    • Look up the value in Appendix G (Numerical Results Summary).
    • Follow the chapter reference to the factor origin table.
    • Verify each factor's geometric origin independently.
    • Cross-check against Appendix L (Mathematica Verification).

To understand the interpretive framework:

    • Read Part A (Chapters 112–114) for the scaffolding interpretation.
    • Consult Chapter 116 for philosophical implications.
    • Check Appendix E for notation conventions.
    • Refer to the Glossary (Appendix H) for TMT-specific terminology.