Appendices

Appendix T: Tier Audit Table

This appendix provides the per-claim audit of every primary result, constant, and mechanism in Geometric Consciousness Theory, classified under the Epistemic Tier System defined in 01_Epistemic_Tier_System.md. The table below is the single source of truth for tier assignments; Appendix G (Decision Tree) and the tier examples in the Global Frontmatter cite this table rather than restating its content.

T.1 Audit Table

Claim	Tier	Derivation / Evidence	Notes
Wheeler–DeWitt Constraint ( $\hat{H}\Psi=0$ )	Tier 1	Conservation of Nullity, derived from Axiom 2 (Intelligibility)	—
Lattice Action Postulate ( $\hat{\hbar}=1$ )	Tier 1	Postulated discrete unit of action	—
Photon Masslessness ( $m_\gamma=0$ )	Tier 1	Kinematic Agency / phase freedom in the supersolid vacuum	—
Dimensionality ( $D=3$ )	Tier 1	Knot-Theoretic Bound for persistent identity	—
Icosahedral Projection ( $E_8 \to \mathbb{Z}^6 \to H_3$ )	Tier 1/2	Lemma III, App U §U.6.1 (Schur multipliers) + §U.6.2 (Atiyah–Hirzebruch $w_2$ )	Two independent uniqueness proofs cover all quasicrystalline competitors
6D Parent Lattice ( $\mathbb{Z}^6$ )	Tier 1/2	Theorem T-McKay, App U §U.7 ( $2I \to E_8 \to \mathbb{Z}^6$ ); modular reduction with four of five forcing lemmata closed at Tier 1 (T-McK.1a, T-McK.2, T-McK.3, T-McK.4)	Single bounded gap: Lemma T-McK.1b (App U §U.7.6.3) — finite APS spectral-flow computation of the icosahedral $\eta$ -invariant on $\partial \mathcal{M}_{RT}$ ; closure would elevate the chain to Tier 1
$\phi$ -Selection (Slope)	Tier 1/2	Elser–Sloane projector eigenvalue structure on $H_4$	Inherits the tier of the icosahedral projection
$D=18$ Stiffness Integer	Tier 2	$H_3$ Shephard-Todd invariant-degree sum $\{2,6,10\}$ gives $D=18$	Integer anchor only; the physical RG-running map is separate
$K_\perp/K_\parallel=\phi^{-D}$ RG-running connection and $c$ from $K_\perp/K_\parallel$	Tier 3 conditional	Phason stiffness ratio under the metric reduction; RG-running identification tracked at O.15(b)	The integer $D=18$ is Tier 2; the physical-link claim that the stiffness ratio runs specifically as $\phi^{-D}$ awaits the O.15(b) derivation
Newton's $G$	Tier 2 thermodynamic mechanism + Tier 4 Planck-link conjecture (inherits O.14) + Tier 3 dimensional anchor	Newtonian limit of the phason acoustic metric plus Jacobson thermodynamic chain; 2274 ppm postdiction	O.14
Gauge Group ( $\mathrm{SU}(3) \times \mathrm{SU}(2) \times \mathrm{U}(1)$ )	Tier 2 mechanism + Tier 3 physical SM identification	Holonomy structure of the icosahedral fiber bundle; full spectral-triple identification conditional on O.32	—
Gluon Count ( $N=8$ )	Tier 2	Rank reduction of the ten three-fold RT axes	—
Spin-Statistics Theorem	Tier 2	WZW evaluation on the tethered ribbon (App C §C.4); algebraic-topology step (normalization of $H^3(SU(2);\mathbb{Z})$ generator) closed at Tier 1	Tier 1 elevation reduced to a single bounded analytic step: Lemma T-McK.1b (App U §U.7.6.3) — finite APS spectral-flow computation of the icosahedral $\eta$ -invariant on $\partial \mathcal{M}_{RT}$ closing the defect-index identification ( $n_{\mathrm{def}} = -107$ )
Born Rule ( $P=\lvert\psi\rvert^2$ )	Tier 2 manuscript theorem assertion; engine non-executable	Gleason's Theorem on the GCT lattice Hilbert space (App D)	Engine records `MANUSCRIPT-THEOREM-ASSERTION`: non-negativity, normalization, non-contextuality, and Gleason applicability are manuscript-level claims pending an executable verifier
Lepton Mass Ratios ( $\phi^{11}, \phi^{17}$ )	Tier 2	Dodecahedral defect resonance via $F_{12}=144$	—
Electron Exponent ( $\phi^{-107}$ )	Tier 2 K-theoretic framework support + Tier 3 specific integer anchor + Tier 4 physical-interpretation chain (per O.14)	6D phase-space suppression and the 1D Identity Tether	—
Electron Mass ( $m_e = M_P \phi^{-107}(1-5\alpha)$ )	Tier 2 framework + Tier 3 integer anchor + Tier 4 K-theoretic physical-link conjecture	Absolute 6D scaling; K-theoretic gap-labeling framework (Bellissard + Connes-Moscovici + Pimsner-Voiculescu, Ch07 §7.2.2) is Tier 2 rigorous. Integer $\\|n\\|=107 = \sum m_i^2(H_3)$ Tier 2 group-theoretic (engine `protocol_o14_coxeter_exponent_squares.py`). The structural-link chain from the $V$ -side Coxeter invariant to the 6D trace-image projection $\tau_*(K_0(\mathcal{A}))$ is Tier 4 conjectural pending Open Problem O.14	—
Muon Drag Coefficient ( $+5\alpha$ )	Tier 2 mechanism + Tier 3 coefficient normalization	$A_5$ phason-channel multiplicity is Tier 2; converting the count into equal-weight pole-mass self-energy units of $\alpha$ is Tier 3 pending O.5	Non-perturbative GCT self-energy / Hessian evaluation deferred (App H O.5, App R)
Tau Screening Coefficient ( $-3.6\alpha$ )	Tier 2 mechanism + Tier 2 integer-pair $(D=18, N=5)$ + Tier 3 combination rule $c = -D/N$ pending O.26b — headline coefficient is Tier 3	$D = 18$ from the $H_3$ Shephard-Todd invariant-degree sum $\{2,6,10\}$ (Anchor A, load-bearing; uniquely $H_3$ among rank-3 Coxeter groups). The 2D-RT-face-in-6D tangent-bundle decomposition $6+6+6 = 18$ is a 6D-ambient consistency cross-check (Anchor B), not a second independent icosahedral anchor (every 6D-ambient theory with this triple-decomposition yields 18 regardless of icosahedral structure; see App H O.26). $N = 5$ from RT pentagonal vertex enumeration. Combination rule $c = -D/N$ pairing the integers as a ratio is Tier 3 pending O.26b	Non-perturbative Hessian evaluation deferred
Muon Second-Order Correction ( $+\phi^8\alpha^2$ )	Exponent arithmetic Tier 2; absolute 21 ppm Tier 3 conditional	The exponent identity $11-3=8$ fixes the displayed $\phi^8\alpha^2$ arithmetic; pole-mass precision assumes SM-equivalent radiative-discipline ansatz	Absolute 21 ppm residual is conditional on unmodeled GCT higher loops matching the SM-equivalent higher-loop contribution at the scored pole-mass precision
Proton Holonomy Correction ( $+\phi^{-1}$ )	Tier 2 mechanism + Tier 3 sheet/exponent handle	Berry phase $\pi$ limit on the SU(2) weak holonomy; coherent two-sheet contribution pending AKN-action derivation	O.5 / AKN-action closure
Proton Mass Exponent ( $15+\phi^{-1}$ )	Tier 2 mechanism + Tier 3 sheet/exponent handle	Baryonic-triad closure $3 \times 5 = 15$ plus weak-holonomy correction; current ~0.015% tree-level residual is not full hadron-sector closure from the current postulate set, and ppm display is suppressed for this offset-fitted handle	O.5 / AKN-action closure
Bottom-Quark Coefficient ( $5/4$ )	Tier 2	$A_5$ representation-dimension ratio $\dim(5E)/\dim(4D)$	—
Light-Quark Masses (rational-exponent: $m_u, m_s, m_t$ )	Tier 2	Mixed-Harmonic Area Law ( $\phi^2$ ); integer or $\mathbb{Z}[\phi]$ -integer exponents	—
Light-Quark Masses (FK-determinant: $m_d, m_c$ ; CKM $s_{23}, s_{13}$ )	Tier 3	Fuglede–Kadison determinant on the finite cage; continuum limit deferred	5–20% discretization residuals disclosed; see Open Problem O.5 (Ch10)
Fine-Structure Constant ( $\alpha^{-1}_{bare} = 360\phi^{-2}$ )	Tier 2 mechanism + Tier 3 specific multiplier	600-cell gauge edge-count mechanism; selection of the 360 multiplier and anti-screening magnitude remain O.19/O.5 closure targets	3442 ppm bare residual; phason anti-screening pathway deferred (App Z §Z.5–§Z.6)
Higgs VEV ( $v \approx 246$ GeV)	Tier 2 mechanism + Tier 3 calibrated integer factor + Tier 3 numerical residual	Absolute Pipeline $v = m_\mu \times 1440 \times \phi$ , with $1440 = N_{\rm cage} \times N_{C_3} = 144 \times 10$ the canonical muon-defect-saturation pathway (V3 Ch05 §5.2.1); App H O.20 supplies enumeration-level closure, records that 1440 is non-unique in factorisation, and treats the three independent icosahedral cross-check factorisations $(120 \times 12)$ , $(24 \times 60)$ , $(15 \times 96)$ as dimensional cross-checks	The structural derivation is geometric; quantitative agreement with the experimental value is reported in App R
Weinberg Angle (bare) ( $\sin^2\theta_W = \phi^{-3}$ )	Tier 1 algebraic value + Tier 2 physical identification	Volume ratio $V_\perp / V_\parallel = \phi^{-3}$ (Ch04 §4.3.1); uniqueness of $\phi^{-3}$ among rational $\phi^n$ powers given the substrate-invariant inputs T1.a–T1.c is proved in App U §U.9 Theorem U.9; coupling-to-volume identification ( $SU(2)_L \propto V_\parallel$ , $U(1)_Y \propto V_\perp$ ) is the Tier 2 framework postulate	—
Weinberg Gram Boundary Scalar (GUT) ( $\rho_G = \phi^{-2}$ ; normalized Cartan share $=0.276393$ )	Tier 1	Gram projection theorem on $SU(2) \leftrightarrow E_\parallel$ , $U(1) \leftrightarrow E_\perp$ (Ch04 §4.3.2)	Physical Weinberg-angle input remains the separate volume-coupling value $\sin^2\theta_W^{\rm bare}=\phi^{-3}$
Weinberg Angle ( $M_Z$ ) ( $\sin^2\theta_W(M_Z) = 0.23122$ )	Tier 3 (Observational)	Z-pole measurement; used as the RGE endpoint	Not a prediction — the running matches observation by construction
Right-Handed Hypercharges ( $Y_R = 2Q$ )	Tier 2	Topological proof on the internal phase space	—
CP Violation ( $\delta_{CP} = 360°\phi^{-1}$ )	Tier 3	PMNS-sector phase ansatz; $222.49^\circ$ sits above the current normal-ordering global-fit central region; Jarlskog geometry remains O.7	O.7
Cabibbo Angle	Tier 2 bare + Tier 3 transfer	Bare $\phi^{-3}$ face-tunneling is Tier 2; $(1-5\alpha)$ lepton-to-hadron transfer pending O.5	—
PMNS Mixing Angles ( $\theta_{23}$ and remaining)	Tier 3	Icosahedral 3-fold symmetry; structural ansatz pending FK closure	$4.09\sigma$ tension on $\theta_{23}$ documented; Ch09 §9.4.2
Phason Anti-Screening	Tier 2	6D lattice action at one loop	Sign requirement (+); magnitude approximately 0.34%; QLQCD-1L evaluation deferred (App M §M.7; App Z §Z.6)
Polaron Unity Proposition	Tier 3 conditional for trefoil case and general-prime extension	Trefoil-case Polaron Unity is Tier 3 conditional pending O.18 fixed-slice reduction + finite-quotient meridian trace + represented-progroup direct-product/operator-factor closure; the general-prime extension adds O.18 Anderson-Putnam-to-knot-complement extension + canonicity of K -> A_K + finite-quotient meridian trace construction, plus O.35 trivial-amenable-radical, O.36 primary representation, and O.32 KO-dimension sign verification.	O.18 + O.35 + O.36 + O.32
Neutrino Mass Scale ( $m_e\,\phi^{-36}$ )	Tier 2	Second-order phason coupling limit	—
3.55 keV Line	Tier 2	$m_e/144$ identity audit on the vacuum binding energy	—
PTA Anisotropy ( $\ell=6$ )	Tier 2 harmonic-form mechanism + Tier 3 specific amplitude pending O.15(b)	Icosahedral spherical harmonics; topological-glass mode structure	Specific $\phi^{-18}$ amplitude inherits the O.15(b) RG-map closure target
PTA $\Delta\Gamma_{max}$ Amplitude ( $\approx 1.73 \times 10^{-4} = \phi^{-18}$ )	Tier 2 mechanism + Tier 3 amplitude pending O.15(b)	Phason–graviton linear perturbation formula	Integer $D=18$ is a core integer postulate; $K_\perp/K_\parallel=\phi^{-D}$ RG-running awaits O.15(b)
Phason Vacuum Cosmology ( $w=-1$ )	Tier 2	Frozen phason strain; baseline equation of state	—
Muon $g-2$ HVP arbitration channel ( $\Delta a_\mu \approx 250.65 \times 10^{-11}$ )	Tier 3 fitted/equal-weight $1/5$ coefficient + A3; tension under WP2025	WP2025 leaves a $\sim0.6\sigma$ SM-experiment gap; the GCT correction overshoots the residual by $3.34\sigma$	Not load-bearing empirical support under the current baseline; decisive status requires a future independently reopened R-ratio / lattice-HVP gap
Biogenic Dark Energy — Lagrangian Structure ( $\mathcal{L}_{DE} \propto \dot{\mathcal{I}}$ )	Tier 2	Phason vacuum action at the macroscopic scale (V2 Ch14 §14B.1)	—
Biogenic Dark Energy — Susceptibility ( $\chi \approx 10^{121}$ )	Tier 3	Imported holographic ratio; equals $A_H/(4\ell_P^2)$	—
Biogenic Dark Energy — Magnitude	Tier 4	First-principles magnitude overshoots observation by $10^{220}$	Explicitly quarantined (V2 Ch14 §14B.0)
Biogenic Equation of State ( $w(z) < -1$ )	Tier 3	Phason negative inertia; phantom-phase hypothesis	DESI DR2 sign-opposite tension; sign labelled Tier 3
$\lambda_{bio}$ (Coupling)	Tier 3	Calibrated fit	—
$\chi$ (Holographic Ratio)	Tier 2	Holographic identity $\chi = A_H / (4\ell_P^2)$	—
Phason Mass Gap ( $m_{\rm phason}^{\rm operative}$ )	Tier 3	Operative biogenic-DE quartic mass scale $1.7\times10^{-5}$ eV; not the $M_P\phi^{-147}$ Weinberg-candidate ansatz and not $\hbar H_0$	O.1 / O.37
Biological Phason Freezing ( $E_{bio}$ )	Tier 3	Polaron topological state; self-consistency bound	—
Selection Semantics	Tier 3	Bayesian update via Consistent Histories	Philosophical framework

T.2 Notes on the Audit

Every entry whose tier depends on a deferred computation (the $N=144$ Hessian, the App C APS boundary integral, the QLQCD-1L closure, or the Fuglede–Kadison determinant) carries the explicit dependency in the Notes column. The tier listed is the present standing; any future elevation requires the dependency to close.
The Polaron Unity Proposition is classified Tier 3 conditional for the canonical trefoil-knot Identity Polaron case and for the general prime-knot extension under the modular reduction of Appendix Y. The finite-level ambient space is $M_n \cong S^1 \times \mathbb{R}^3$ , so the classical 3-manifold Wirtinger/product argument requires a fixed-slice reduction $H_{Y.1}$ not yet proved by the Ch11 ansatz. Downstream uses inherit this conditional disposition; closure requires O.18 fixed-slice reduction + finite-quotient meridian trace + Anderson-Putnam-to-knot-complement extension, O.35 trivial-amenable-radical, O.36 primary representation, and O.32 KO-dimension sign verification before promotion from Proposition to Theorem.
Theorem T-McKay (App U §U.7) is classified Tier 1/2 under a modular reduction parallel to App Y's treatment of Polaron Unity. Four of the five forcing lemmata are closed at Tier 1 in the published literature (T-McK.1a Schur cover; T-McK.2 McKay correspondence; T-McK.3 Elser–Sloane projection; T-McK.4 $\phi$ from the $H_4$ Cartan/root metric), with explicit bibliographic anchors to McKay 1980, Elser & Sloane 1987, Moody & Patera 1993, and Humphreys' Reflection Groups and Coxeter Groups §3.7. The single remaining open step (Lemma T-McK.1b, App U §U.7.6.3) is the APS spectral-flow computation of the icosahedral $\eta$ -invariant on the boundary $\partial \mathcal{M}_{RT}$ of the rhombic-triacontahedron acceptance window; the reduction to a finite operator-algebra computation follows from Atiyah–Patodi–Singer 1975 + Connes 1994 + Connes–Moscovici 1995. Both the 6D Parent Lattice and Spin-Statistics rows inherit this disposition; closure of U.7.6.3 elevates the entire chain to Tier 1.
The Higgs VEV entry distinguishes the structural derivation (Tier 2) from the comparison with the experimental value (reported in App R). The Tier 2 status refers to the geometric pipeline; experimental agreement is a separate empirical question.
Where a result is reported in two locations of the manuscript with different precision figures (e.g., the tau lepton precision), the canonical figure lives in App R (Precision Scorecard), and every front-matter and chapter abstract cites App R rather than restating the figure.

Appendices

Appendix T: Tier Audit Table

T.1 Audit Table

Claim	Tier	Derivation / Evidence	Notes
Wheeler–DeWitt Constraint ( $\hat{H}\Psi=0$ )	Tier 1	Conservation of Nullity, derived from Axiom 2 (Intelligibility)	—
Lattice Action Postulate ( $\hat{\hbar}=1$ )	Tier 1	Postulated discrete unit of action	—
Photon Masslessness ( $m_\gamma=0$ )	Tier 1	Kinematic Agency / phase freedom in the supersolid vacuum	—
Dimensionality ( $D=3$ )	Tier 1	Knot-Theoretic Bound for persistent identity	—
Icosahedral Projection ( $E_8 \to \mathbb{Z}^6 \to H_3$ )	Tier 1/2	Lemma III, App U §U.6.1 (Schur multipliers) + §U.6.2 (Atiyah–Hirzebruch $w_2$ )	Two independent uniqueness proofs cover all quasicrystalline competitors
6D Parent Lattice ( $\mathbb{Z}^6$ )	Tier 1/2	Theorem T-McKay, App U §U.7 ( $2I \to E_8 \to \mathbb{Z}^6$ ); modular reduction with four of five forcing lemmata closed at Tier 1 (T-McK.1a, T-McK.2, T-McK.3, T-McK.4)	Single bounded gap: Lemma T-McK.1b (App U §U.7.6.3) — finite APS spectral-flow computation of the icosahedral $\eta$ -invariant on $\partial \mathcal{M}_{RT}$ ; closure would elevate the chain to Tier 1
$\phi$ -Selection (Slope)	Tier 1/2	Elser–Sloane projector eigenvalue structure on $H_4$	Inherits the tier of the icosahedral projection
$D=18$ Stiffness Integer	Tier 2	$H_3$ Shephard-Todd invariant-degree sum $\{2,6,10\}$ gives $D=18$	Integer anchor only; the physical RG-running map is separate
$K_\perp/K_\parallel=\phi^{-D}$ RG-running connection and $c$ from $K_\perp/K_\parallel$	Tier 3 conditional	Phason stiffness ratio under the metric reduction; RG-running identification tracked at O.15(b)	The integer $D=18$ is Tier 2; the physical-link claim that the stiffness ratio runs specifically as $\phi^{-D}$ awaits the O.15(b) derivation
Newton's $G$	Tier 2 thermodynamic mechanism + Tier 4 Planck-link conjecture (inherits O.14) + Tier 3 dimensional anchor	Newtonian limit of the phason acoustic metric plus Jacobson thermodynamic chain; 2274 ppm postdiction	O.14
Gauge Group ( $\mathrm{SU}(3) \times \mathrm{SU}(2) \times \mathrm{U}(1)$ )	Tier 2 mechanism + Tier 3 physical SM identification	Holonomy structure of the icosahedral fiber bundle; full spectral-triple identification conditional on O.32	—
Gluon Count ( $N=8$ )	Tier 2	Rank reduction of the ten three-fold RT axes	—
Spin-Statistics Theorem	Tier 2	WZW evaluation on the tethered ribbon (App C §C.4); algebraic-topology step (normalization of $H^3(SU(2);\mathbb{Z})$ generator) closed at Tier 1	Tier 1 elevation reduced to a single bounded analytic step: Lemma T-McK.1b (App U §U.7.6.3) — finite APS spectral-flow computation of the icosahedral $\eta$ -invariant on $\partial \mathcal{M}_{RT}$ closing the defect-index identification ( $n_{\mathrm{def}} = -107$ )
Born Rule ( $P=\lvert\psi\rvert^2$ )	Tier 2 manuscript theorem assertion; engine non-executable	Gleason's Theorem on the GCT lattice Hilbert space (App D)	Engine records `MANUSCRIPT-THEOREM-ASSERTION`: non-negativity, normalization, non-contextuality, and Gleason applicability are manuscript-level claims pending an executable verifier
Lepton Mass Ratios ( $\phi^{11}, \phi^{17}$ )	Tier 2	Dodecahedral defect resonance via $F_{12}=144$	—
Electron Exponent ( $\phi^{-107}$ )	Tier 2 K-theoretic framework support + Tier 3 specific integer anchor + Tier 4 physical-interpretation chain (per O.14)	6D phase-space suppression and the 1D Identity Tether	—
Electron Mass ( $m_e = M_P \phi^{-107}(1-5\alpha)$ )	Tier 2 framework + Tier 3 integer anchor + Tier 4 K-theoretic physical-link conjecture	Absolute 6D scaling; K-theoretic gap-labeling framework (Bellissard + Connes-Moscovici + Pimsner-Voiculescu, Ch07 §7.2.2) is Tier 2 rigorous. Integer $\\|n\\|=107 = \sum m_i^2(H_3)$ Tier 2 group-theoretic (engine `protocol_o14_coxeter_exponent_squares.py`). The structural-link chain from the $V$ -side Coxeter invariant to the 6D trace-image projection $\tau_*(K_0(\mathcal{A}))$ is Tier 4 conjectural pending Open Problem O.14	—
Muon Drag Coefficient ( $+5\alpha$ )	Tier 2 mechanism + Tier 3 coefficient normalization	$A_5$ phason-channel multiplicity is Tier 2; converting the count into equal-weight pole-mass self-energy units of $\alpha$ is Tier 3 pending O.5	Non-perturbative GCT self-energy / Hessian evaluation deferred (App H O.5, App R)
Tau Screening Coefficient ( $-3.6\alpha$ )	Tier 2 mechanism + Tier 2 integer-pair $(D=18, N=5)$ + Tier 3 combination rule $c = -D/N$ pending O.26b — headline coefficient is Tier 3	$D = 18$ from the $H_3$ Shephard-Todd invariant-degree sum $\{2,6,10\}$ (Anchor A, load-bearing; uniquely $H_3$ among rank-3 Coxeter groups). The 2D-RT-face-in-6D tangent-bundle decomposition $6+6+6 = 18$ is a 6D-ambient consistency cross-check (Anchor B), not a second independent icosahedral anchor (every 6D-ambient theory with this triple-decomposition yields 18 regardless of icosahedral structure; see App H O.26). $N = 5$ from RT pentagonal vertex enumeration. Combination rule $c = -D/N$ pairing the integers as a ratio is Tier 3 pending O.26b	Non-perturbative Hessian evaluation deferred
Muon Second-Order Correction ( $+\phi^8\alpha^2$ )	Exponent arithmetic Tier 2; absolute 21 ppm Tier 3 conditional	The exponent identity $11-3=8$ fixes the displayed $\phi^8\alpha^2$ arithmetic; pole-mass precision assumes SM-equivalent radiative-discipline ansatz	Absolute 21 ppm residual is conditional on unmodeled GCT higher loops matching the SM-equivalent higher-loop contribution at the scored pole-mass precision
Proton Holonomy Correction ( $+\phi^{-1}$ )	Tier 2 mechanism + Tier 3 sheet/exponent handle	Berry phase $\pi$ limit on the SU(2) weak holonomy; coherent two-sheet contribution pending AKN-action derivation	O.5 / AKN-action closure
Proton Mass Exponent ( $15+\phi^{-1}$ )	Tier 2 mechanism + Tier 3 sheet/exponent handle	Baryonic-triad closure $3 \times 5 = 15$ plus weak-holonomy correction; current ~0.015% tree-level residual is not full hadron-sector closure from the current postulate set, and ppm display is suppressed for this offset-fitted handle	O.5 / AKN-action closure
Bottom-Quark Coefficient ( $5/4$ )	Tier 2	$A_5$ representation-dimension ratio $\dim(5E)/\dim(4D)$	—
Light-Quark Masses (rational-exponent: $m_u, m_s, m_t$ )	Tier 2	Mixed-Harmonic Area Law ( $\phi^2$ ); integer or $\mathbb{Z}[\phi]$ -integer exponents	—
Light-Quark Masses (FK-determinant: $m_d, m_c$ ; CKM $s_{23}, s_{13}$ )	Tier 3	Fuglede–Kadison determinant on the finite cage; continuum limit deferred	5–20% discretization residuals disclosed; see Open Problem O.5 (Ch10)
Fine-Structure Constant ( $\alpha^{-1}_{bare} = 360\phi^{-2}$ )	Tier 2 mechanism + Tier 3 specific multiplier	600-cell gauge edge-count mechanism; selection of the 360 multiplier and anti-screening magnitude remain O.19/O.5 closure targets	3442 ppm bare residual; phason anti-screening pathway deferred (App Z §Z.5–§Z.6)
Higgs VEV ( $v \approx 246$ GeV)	Tier 2 mechanism + Tier 3 calibrated integer factor + Tier 3 numerical residual	Absolute Pipeline $v = m_\mu \times 1440 \times \phi$ , with $1440 = N_{\rm cage} \times N_{C_3} = 144 \times 10$ the canonical muon-defect-saturation pathway (V3 Ch05 §5.2.1); App H O.20 supplies enumeration-level closure, records that 1440 is non-unique in factorisation, and treats the three independent icosahedral cross-check factorisations $(120 \times 12)$ , $(24 \times 60)$ , $(15 \times 96)$ as dimensional cross-checks	The structural derivation is geometric; quantitative agreement with the experimental value is reported in App R
Weinberg Angle (bare) ( $\sin^2\theta_W = \phi^{-3}$ )	Tier 1 algebraic value + Tier 2 physical identification	Volume ratio $V_\perp / V_\parallel = \phi^{-3}$ (Ch04 §4.3.1); uniqueness of $\phi^{-3}$ among rational $\phi^n$ powers given the substrate-invariant inputs T1.a–T1.c is proved in App U §U.9 Theorem U.9; coupling-to-volume identification ( $SU(2)_L \propto V_\parallel$ , $U(1)_Y \propto V_\perp$ ) is the Tier 2 framework postulate	—
Weinberg Gram Boundary Scalar (GUT) ( $\rho_G = \phi^{-2}$ ; normalized Cartan share $=0.276393$ )	Tier 1	Gram projection theorem on $SU(2) \leftrightarrow E_\parallel$ , $U(1) \leftrightarrow E_\perp$ (Ch04 §4.3.2)	Physical Weinberg-angle input remains the separate volume-coupling value $\sin^2\theta_W^{\rm bare}=\phi^{-3}$
Weinberg Angle ( $M_Z$ ) ( $\sin^2\theta_W(M_Z) = 0.23122$ )	Tier 3 (Observational)	Z-pole measurement; used as the RGE endpoint	Not a prediction — the running matches observation by construction
Right-Handed Hypercharges ( $Y_R = 2Q$ )	Tier 2	Topological proof on the internal phase space	—
CP Violation ( $\delta_{CP} = 360°\phi^{-1}$ )	Tier 3	PMNS-sector phase ansatz; $222.49^\circ$ sits above the current normal-ordering global-fit central region; Jarlskog geometry remains O.7	O.7
Cabibbo Angle	Tier 2 bare + Tier 3 transfer	Bare $\phi^{-3}$ face-tunneling is Tier 2; $(1-5\alpha)$ lepton-to-hadron transfer pending O.5	—
PMNS Mixing Angles ( $\theta_{23}$ and remaining)	Tier 3	Icosahedral 3-fold symmetry; structural ansatz pending FK closure	$4.09\sigma$ tension on $\theta_{23}$ documented; Ch09 §9.4.2
Phason Anti-Screening	Tier 2	6D lattice action at one loop	Sign requirement (+); magnitude approximately 0.34%; QLQCD-1L evaluation deferred (App M §M.7; App Z §Z.6)
Polaron Unity Proposition	Tier 3 conditional for trefoil case and general-prime extension	Trefoil-case Polaron Unity is Tier 3 conditional pending O.18 fixed-slice reduction + finite-quotient meridian trace + represented-progroup direct-product/operator-factor closure; the general-prime extension adds O.18 Anderson-Putnam-to-knot-complement extension + canonicity of K -> A_K + finite-quotient meridian trace construction, plus O.35 trivial-amenable-radical, O.36 primary representation, and O.32 KO-dimension sign verification.	O.18 + O.35 + O.36 + O.32
Neutrino Mass Scale ( $m_e\,\phi^{-36}$ )	Tier 2	Second-order phason coupling limit	—
3.55 keV Line	Tier 2	$m_e/144$ identity audit on the vacuum binding energy	—
PTA Anisotropy ( $\ell=6$ )	Tier 2 harmonic-form mechanism + Tier 3 specific amplitude pending O.15(b)	Icosahedral spherical harmonics; topological-glass mode structure	Specific $\phi^{-18}$ amplitude inherits the O.15(b) RG-map closure target
PTA $\Delta\Gamma_{max}$ Amplitude ( $\approx 1.73 \times 10^{-4} = \phi^{-18}$ )	Tier 2 mechanism + Tier 3 amplitude pending O.15(b)	Phason–graviton linear perturbation formula	Integer $D=18$ is a core integer postulate; $K_\perp/K_\parallel=\phi^{-D}$ RG-running awaits O.15(b)
Phason Vacuum Cosmology ( $w=-1$ )	Tier 2	Frozen phason strain; baseline equation of state	—
Muon $g-2$ HVP arbitration channel ( $\Delta a_\mu \approx 250.65 \times 10^{-11}$ )	Tier 3 fitted/equal-weight $1/5$ coefficient + A3; tension under WP2025	WP2025 leaves a $\sim0.6\sigma$ SM-experiment gap; the GCT correction overshoots the residual by $3.34\sigma$	Not load-bearing empirical support under the current baseline; decisive status requires a future independently reopened R-ratio / lattice-HVP gap
Biogenic Dark Energy — Lagrangian Structure ( $\mathcal{L}_{DE} \propto \dot{\mathcal{I}}$ )	Tier 2	Phason vacuum action at the macroscopic scale (V2 Ch14 §14B.1)	—
Biogenic Dark Energy — Susceptibility ( $\chi \approx 10^{121}$ )	Tier 3	Imported holographic ratio; equals $A_H/(4\ell_P^2)$	—
Biogenic Dark Energy — Magnitude	Tier 4	First-principles magnitude overshoots observation by $10^{220}$	Explicitly quarantined (V2 Ch14 §14B.0)
Biogenic Equation of State ( $w(z) < -1$ )	Tier 3	Phason negative inertia; phantom-phase hypothesis	DESI DR2 sign-opposite tension; sign labelled Tier 3
$\lambda_{bio}$ (Coupling)	Tier 3	Calibrated fit	—
$\chi$ (Holographic Ratio)	Tier 2	Holographic identity $\chi = A_H / (4\ell_P^2)$	—
Phason Mass Gap ( $m_{\rm phason}^{\rm operative}$ )	Tier 3	Operative biogenic-DE quartic mass scale $1.7\times10^{-5}$ eV; not the $M_P\phi^{-147}$ Weinberg-candidate ansatz and not $\hbar H_0$	O.1 / O.37
Biological Phason Freezing ( $E_{bio}$ )	Tier 3	Polaron topological state; self-consistency bound	—
Selection Semantics	Tier 3	Bayesian update via Consistent Histories	Philosophical framework

T.2 Notes on the Audit

Every entry whose tier depends on a deferred computation (the $N=144$ Hessian, the App C APS boundary integral, the QLQCD-1L closure, or the Fuglede–Kadison determinant) carries the explicit dependency in the Notes column. The tier listed is the present standing; any future elevation requires the dependency to close.
The Polaron Unity Proposition is classified Tier 3 conditional for the canonical trefoil-knot Identity Polaron case and for the general prime-knot extension under the modular reduction of Appendix Y. The finite-level ambient space is $M_n \cong S^1 \times \mathbb{R}^3$ , so the classical 3-manifold Wirtinger/product argument requires a fixed-slice reduction $H_{Y.1}$ not yet proved by the Ch11 ansatz. Downstream uses inherit this conditional disposition; closure requires O.18 fixed-slice reduction + finite-quotient meridian trace + Anderson-Putnam-to-knot-complement extension, O.35 trivial-amenable-radical, O.36 primary representation, and O.32 KO-dimension sign verification before promotion from Proposition to Theorem.
Theorem T-McKay (App U §U.7) is classified Tier 1/2 under a modular reduction parallel to App Y's treatment of Polaron Unity. Four of the five forcing lemmata are closed at Tier 1 in the published literature (T-McK.1a Schur cover; T-McK.2 McKay correspondence; T-McK.3 Elser–Sloane projection; T-McK.4 $\phi$ from the $H_4$ Cartan/root metric), with explicit bibliographic anchors to McKay 1980, Elser & Sloane 1987, Moody & Patera 1993, and Humphreys' Reflection Groups and Coxeter Groups §3.7. The single remaining open step (Lemma T-McK.1b, App U §U.7.6.3) is the APS spectral-flow computation of the icosahedral $\eta$ -invariant on the boundary $\partial \mathcal{M}_{RT}$ of the rhombic-triacontahedron acceptance window; the reduction to a finite operator-algebra computation follows from Atiyah–Patodi–Singer 1975 + Connes 1994 + Connes–Moscovici 1995. Both the 6D Parent Lattice and Spin-Statistics rows inherit this disposition; closure of U.7.6.3 elevates the entire chain to Tier 1.
The Higgs VEV entry distinguishes the structural derivation (Tier 2) from the comparison with the experimental value (reported in App R). The Tier 2 status refers to the geometric pipeline; experimental agreement is a separate empirical question.
Where a result is reported in two locations of the manuscript with different precision figures (e.g., the tau lepton precision), the canonical figure lives in App R (Precision Scorecard), and every front-matter and chapter abstract cites App R rather than restating the figure.