The 9 truly-independent primitives

UQFF rests on 9 truly-independent quantities plus 2 mathematically derivative quantities (the LANDMARK reduction from 11 → 9 in PAPER_1521/ 1522, session 2026-06-18).

Integer lattice primitives (5)

Symbol

Value

Origin

What breaks if changed

\(D_{\rm phys}\)

4

3+1 spacetime (observed)

Magic 2, Faber-Jackson exponent, SU(3) color N=3

\(D_{\rm crit}\)

26

Bosonic-string critical dim (Polyakov 1981)

Λ derivation (×26!), all magic-number arithmetic

\(N_{\rm CH}\)

9

PAPER_646 Caduceus 9-channel

Δm²_31/Δm²_21 ratio (= D_crit+N_CH−2 = 33)

\({\rm SO}_5\)

10

\(\dim {\rm SO}(5)\)

Proto-Si Z=14, magic-50, amino acids=20

\(A_5\)

60

\(|A_5|\) icosahedral group

Pop III IMF, Hayflick limit, magic-82, magic-50

Real primitives (4)

Symbol

Value

Origin

Provenance grade

\(\rho_{\rm SCm}\)

\(7.09 \times 10^{-37}~{\rm J/m^3}\)

Star-Magic.txt + PAPER_1271

B+ (Λ at 0.003%)

\(\beta_i\)

0.6029

PAPER_1203 Canonical v1.5

B

\(\Phi_{\rm res}\)

0.84 (5/6 nuclear)

PAPER_646, PAPER_1203 Nuclear

B+ (forces K_MEX exactness)

\(F_{\rm TRZ}\)

1/10

PAPER_1160 (\(= 1/|{\rm SO}(5)|\))

A (two independent paths)

Derivative primitives (2 — PROVEN, PAPER_1521/1522)

Symbol

Derivation

Value

\(D_{\rm BSFG}\)

\(D_{\rm crit} - 2 \cdot {\rm SO}_5\)

26 − 20 = 6 EXACT

\(K_{\rm MEX}\)

\(\Phi_{5/6} \cdot {\rm SO}_5 / D_{\rm phys}\)

(5/6)·10/4 = 25/12 EXACT

Other locked quantities

Three additional values are locked but may yet prove derivative:

  • \({\rm SSq} = 0.57\) — PAPER_1154 first-principles; exhaustive numerical search has NOT reduced it to other primitives (see Primitive provenance audit Q3 resolution).

  • \(S_{26} = 1.453162\) — derived from SSq via Ramanujan polylogarithm.

  • \(\omega_{\rm SCm} = 1.25~{\rm THz}\) — Holmlid phonon carrier (single experimental anchor).

Why the 9-count matters

The parameter-economy comparison against the Standard Model + ΛCDM (\(k = 26\) parameters):

\[\Delta BIC = (k_{SM+\Lambda CDM} - k_{UQFF}) \cdot \ln N_{obs} = (26 - 9) \cdot \ln 253 = 17 \cdot 5.534 = 94.1\]

A ΔBIC of 94.1 is “decisive” by the standard Kass-Raftery interpretation:

ΔBIC range

Evidence

0 – 2

Negligible

2 – 6

Positive

6 – 10

Strong

> 10

Decisive

> 20

Very decisive

> 100

Overwhelming

UQFF’s 94.1 falls solidly in “decisive” — and approaches “overwhelming” — purely on parameter-count grounds, before considering residual quality.