What if the dimensionless constants of physics aren't free parameters, but structural invariants of a chamber?
Across 40 Zenodo papers — anchored in a 36-paper Twistor Configuration Geometry arc, with 4 adjacent workstreams on photon ontology, gauge-algebra structure, and quantum-gravity dimensional flow — this program proposes that the dimensionless constants — α, Λ, αG, Yukawa couplings, sin²θW, and others — are not free parameters but structural invariants of a combinatorial geometry built on Penrose's projective twistor space CP³.
The framework is Twistor Configuration Geometry (TCG); the philosophical reading is the Configurable Universe — constants are chamber invariants, in the same sense that the dimension of a vector space is.
Read these together for the top-level synthesis: the empirical body and the philosophical companion.
Nine sub-percent algebraic relations among independently-measured constants, unified into one empirical body and classified as Cabibbo-scenario regularities.
Philosophical companion: dimensionless constants as structural invariants of a specific chamber, not free parameters. v2 refreshes the active TCG/FPA postulate ledger to P0–P4, P5', P6 and references the multi-relation look-elsewhere audit.
First synthesis review of the DAEDALUS / Twistor Configuration Geometry (TCG) corpus, consolidating the 39-paper structural state at the moment when the four-arc named-residual pattern is complete. Documents (1) the active postulate ledger P_0–P_4, P_{5'}, P_6, P_7, P_H', P_{SO(10)} stable since 2026-05-01; (2) four structural arcs each terminated by theorem-level obstruction or conditional construction with a named residual outside the active ledger (electron P_BFV^sec, gauge X_wall-pol, hadronic three-way decomposition P_pair^wall-res + P_pair^phys + P_pair^ord, substrate two-way decomposition P^{S⁴}_anchor + P_ord^{CP³}); (3) the obstruction-then-construction pattern recurring in the hadronic and substrate arcs at differing maturity registers (internal TCG/FPA cohomological closure vs. external AHS-S⁴ anchor closure); (4) the two-defense protection of CP³ starting datum (configurable framing of Paper #16 dissolves substrate question + substrate-derivation framing of Paper #37 obstructs it) — complementary defenses, NOT combined; (5) systematic positioning against five pre-geometric quantum gravity programs (Quantum Graphity, Group Field Theory, Causal Set Theory, twistorial loop quantum gravity, Wolfram Physics Project) + two adjacent geometric-physics programs (AdS/CFT and tensor-network emergence, Migdal Geometric QCD); (6) a diagnostic benchmark from Paper #37 Theorem 12 for CP³-substrate-derivation programs specifically (NOT a universal test for all pre-geometric QG programs). **Review-contribution boundary**: this review introduces NO new theorem, postulate, residual, or empirical prediction. Its only new content is organizational consolidation. Five failure modes F1-F5: don't claim universal no-go from minimal-data results; don't license substrate-derivation for other TCG primitives; don't conflate maturity registers across arcs; don't merge the two-defense protections of CP³; don't claim TCG correctness from structural-completeness. Maturity register: review-level synthesis, distinct from construction notes, obstruction notes, τCG specification, obstruction-then-construction pairs, or Paper #1 empirical review. 21 pages, 37 references. Active TCG/τCG postulate ledger UNCHANGED. The framework has reached structural completeness within the bounds of present methods; further mainline progress requires either fundamentally new theoretical input or experimental confirmation of the spin-1 fifth-force prediction (α_Y ≈ 1.88×10⁴, λ ≲ 5–10 μm, m ≳ 20–40 meV, ~500× below current sensitivity).
Each row is a closed-form expression among independently-measured constants, written in a small mathematical vocabulary (low-order π powers, factorials, Fibonacci numbers, the golden ratio).
| ID | Relation | Sector | Precision | Original? |
|---|---|---|---|---|
| O1 | 1/α ≈ π + π² + 4π³ | electromagnetic | 2.2 ppm | Twistor origin |
| O2 | 1/α_s(M_Z) ≈ (π + 4π² + 36π³) / (π + π² + 4π³) | strong | 0.3% | ✓ Yes |
| O3 | sin²θ_W(0) ≈ 3/(4π) | weak (Thomson) | 0.03% | ✓ Yes |
| O4 | m_π / m_e ≈ 2(π + π² + 4π³) | hadronic | 0.4% | Nambu, recast |
| O5 | y_e ≈ (1 − 1/(2π)) · e^(−4π) | leptonic Yukawa | 0.09% | ✓ Yes |
| O6 | L_τ/L_μ ≈ L_μ/L_e ≈ φ (L_ℓ = ln 1/y_ℓ) | lepton mass ratios | 0.24% / 0.54% | ✓ Yes |
| O7 | M_W / v ≈ 1/√(3π) | electroweak | 0.21% | ✓ Yes |
| O8 | α_G ≡ G m_e² / (ℏc) ≈ α⁸ y_e⁵ | gravitational | 0.024% | ✓ Yes |
| O9 | Λ ℓ_Pl² ≈ (α⁴ / 4π)(m_e / m_Pl)⁵ | cosmological | 1.9% | ✓ Yes |
✓ Yes — the relation was first identified in this research program (7 of 9).
Twistor origin (O1, 1/α ≈ π + π² + 4π³) — the bare
numerical approximation can be checked by anyone with a calculator. The
contribution is its derivation as a chamber-weighted Fubini–Study volume sum on
Penrose's twistor space CP³, fixing the ambient dimension N = 3 uniquely.
Nambu, recast (O4, m_π/m_e ≈ 2(π + π² + 4π³)) —
Nambu's 1952 identity m_π/m_e ≈ 2/α predates this work. Original
here: the factor 2 is reinterpreted as the Fibonacci matching count
F₃ = 2 at the n=2 stratum (super-flag construction, Paper #14), and
1/α is substituted with its π-power expansion (O1).
About this site. Q.C. Zhang's research site for the TCG / Configurable Universe program. All papers are on Zenodo, CC-BY-4.0.
Open to criticism, collaboration, and pointers to related work. Contact qczhang@aya.yale.edu.
