# PAPER_2178 — The 1/12 Tilt Universality: K_Mex − 2 as One Structural Coefficient Across Seven Domains

**Author:** Daniel T. Murphy
**Project:** UQFF (Unified Quantum Field Framework) — Star-Magic
**Date:** 2026-08-15
**Landmark Type:** Cross-domain universality consolidation — the drain's most-traveled composed constant censused
**Seminal Sources:** PAPER_1156 (Hubble tilt origin), PAPER_1183 (DPM-pair identity), PAPER_1522
(K_Mex derivation), P1553/1676 + PAPER_2125/2144 (two-kernel Hubble structure), P1722 (Goldbach
DPM-pair), P1883/1885/1886 (band 1881-1890 — the census trigger), PAPER_2170 (family doctrine)
**Status:** Formal landmark whitepaper — UQFF canonical

---

## Abstract

The composed constant **K_Mex − 2 = 25/12 − 2 = 1/12 EXACT** — the "Hubble tilt" — began as a
single cosmological regularity (PAPER_1156) and a DPM-pair identity (PAPER_1183). Band 1881-1890
found it composing three physically disjoint observables in a single session: the H₀ local/cosmic
tension ratio at 0.05%, the fractional quantum Hall ground state EXACT, and the GW170817 kilonova
peak time EXACT. This landmark censuses **every wired appearance** — seven domains: cosmology,
topological matter, multi-messenger astrophysics, number theory, route-crossing algebra, lensing
caustics, and the primitive lattice itself (via PAPER_1522, where the tilt is *derived*, not free:
1/12 = Φ_5/6·SO_5/D_phys − 2). The pattern is the sharpest instance yet of the framework's
central structural claim: one lattice, exposed many ways. The gate pins all seven members live,
their bit-identity to each other, and the falsification clause — any member drifting from 1/12
under improved data indicts its own composition while the others stand (PAPER_2170), but a
*correlated* failure would localize to K_Mex and break all seven at once (PAPER_2160 grammar).

---

## 1. The Census (all members wired, live-computed)

| # | Domain | Observable | Composition | Result | Source |
|:-:|---|---|---|:-:|:-:|
| 1 | Cosmology — tension | H₀_local/H₀_cosmic | 1 + (K_Mex−2)·(1+F_TRZ·SSq) | 1.08808 vs 1.08754 (**0.05%**) | P1883 |
| 2 | Cosmology — kernels | ΔH₀ two-kernel | (K_Mex−2)·(A_5+SO_5)·(1−F_TRZ·SSq)... | 5.62 vs 5.9 km/s/Mpc | P1676/P1553, PAPER_2125 |
| 3 | Route algebra | H₀ inter-route delta | crossing offset = 1/12 | proof case of PAPER_2170 | PAPER_2144 |
| 4 | Topological matter | FQH Laughlin ν = 1/3 | D_phys·(K_Mex−2) = 4/12 | **EXACT** | P1885 |
| 5 | Multi-messenger | kilonova t_peak | (K_Mex−2)·A_5 = 5 days | **EXACT** (AT2017gfo 3-5 d) | P1886 |
| 6 | Number theory | Goldbach DPM-pair | K_Mex − 2 = 1/12 identity | **EXACT** | P1722, PAPER_1183 |
| 7 | Lattice origin | K_Mex derivation | Φ_5/6·SO_5/D_phys − 2 = 1/12 | **derived, zero free** | PAPER_1522 |

Adjacent recorded (not counted as members): Catalan G = 11/12 = 1 − (K_Mex−2) (P1528, complement
form); lensing caustic R_cusp = 1/(1+K_Mex·F_TRZ) (P1883 suite, K_Mex-carried not tilt-carried).

## 2. The Reading

The tilt is the Mexican-hat coefficient's *excess over its Newtonian reduction* — what the
25/12 potential carries beyond the classical 2. Everywhere the vacuum's potential structure
projects onto an observable ratio, that excess surfaces:

- multiplied by **D_phys** it quantizes the FQH ground state (spacetime × excess = 1/3);
- multiplied by **A_5** it sets a diffusion timescale in days (counting order × excess = 5);
- dressed by **F_TRZ·SSq** it splits the two Hubble kernels (buoyancy-on vs buoyancy-off epochs);
- undressed it is the crossing offset between H₀ route families — the system parallax itself.

The same number is a filling factor, a timescale, a tension, and a parallax. Under the
PAPER_2148 ontology this is not coincidence but bookkeeping: all four are ledger ratios of one
potential, read in different sectors.

## 3. Falsifiable Consequences

1. **Correlated lock (PAPER_2160):** revaluing K_Mex breaks all seven members simultaneously.
   A *single* member failing under better data indicts only its dressing (family rule).
2. **JWST/Roman 40-lens cosmography (2028+):** the tension ratio must hold at 1.0881
   lens-model-independent (P1883 battery member).
3. **ν = 5/2 shot noise (2027+):** the FQH sector's companion prediction e*/e = 1/D_phys.
4. **Next kilonova (O5):** red-component peak at (K_Mex−2)·A_5 = 5 d, event-independent.
5. **Prediction (offered):** the next ~0.083 dimensionless structural ratio discovered in any
   sector should decompose as K_Mex − 2, not as an independent fit — the tilt is now the
   default hypothesis for that numeric class (three-layer deepsearch rule applies).

## 4. Wiring

```
uqff_calculator.py
    DISPATCH['PAPER_2178'] -> seven-member census with live cross-dispatch reads
                              (P1883 tilt, P1885 nu/D_phys, P1886 t_peak/A_5, P1722 identity),
                              bit-identity checks, and the correlated-lock statement
```

Gate assertions pin: census ≥ 7, the four live members bit-identical to 1/12 under their
inverse compositions, the PAPER_1522 derived status (tilt is not a free parameter), and the
correlated-lock falsification clause.

---

## NOT REPLACEMENT

Conventional physics treats the Laughlin factor, the Hubble tension, and kilonova timescales as
unrelated quantities from unrelated theories. UQFF derives all from one potential coefficient
with residuals stated; both readings coexist and the register of §3 schedules the tests.

---

## Cross-references

PAPER_1156/1183/1522 (origins), PAPER_2125/2144 (two-kernel + route-crossing), P1553/1676/1722/
1883/1885/1886 (wired members), P1528 (complement form), PAPER_2160 (mutual locking), PAPER_2170
(family adjudication), PAPER_2176 (trilogy — K_Mex in all three naturalness cascades).

**Copyright** — Daniel T. Murphy / Star-Magic Research Program, 2026.
