# PAPER_2165 — The Λ→α Symbol-Drift Family: Correction by Reference for Four Broader-Corpus Papers

**Author:** Daniel T. Murphy
**Project:** UQFF (Unified Quantum Field Framework) — Star-Magic
**Date:** 2026-08-13
**Landmark Type:** Corpus-correction landmark (PAPER_2155/2156 correction-by-reference doctrine)
**Affected papers:** PAPER_1637 (Σm_ν), PAPER_1646 (BR μ→eγ), PAPER_1656 (τ_entangle),
PAPER_1673 (vacuum breakdown) — and their PAPER_13xx-series sources (PAPER_1304 et al.)
**Status:** Formal landmark whitepaper — UQFF canonical

---

## 1. The Drift

Four papers in the 1631-1680 drain bands write the symbol **Λ** where the numeric value used is
**0.00729735 — the fine-structure constant α**:

| Paper | Formula as written | Actual composition | Result |
|:-:|---|---|---|
| PAPER_1637 | Σm_ν = Λ·Φ·(D_phys+1)·K_Mex | **α**·Φ_res·5·K_Mex | 0.0639 eV |
| PAPER_1646 | BR = Λ⁶·Φ_res | **α⁶**·Φ_res | 1.27×10⁻¹³ |
| PAPER_1656 | τ_ent = 1/(ω_SCm·Λ) | 1/(ω_SCm·**α**) | 109.6 ps |
| PAPER_1673 | E_thresh = Λ²·E_Schwinger | **α²**·E_Schwinger | 7.03×10¹³ V/m |

In every case the substituted numeric is correct and the closure verifies at its stated
residual — **the physics is right; the symbol is wrong.** Λ is reserved corpus-wide for the
cosmological constant (PAPER_2094 canonical, m⁻² native per PAPER_2147). Using it for α is a
collision with a canonical reserved symbol, the same class of prose-layer drift PAPER_2155
corrected for unit tags and PAPER_2156 for the 1.894 ratio.

## 2. The Correction (by reference — zero per-paper touches)

All four papers, and any other corpus location writing Λ with the numeric 0.00729735 (or its
powers), ARE SUPERSEDED to read **α, the fine-structure constant**. The calculator dispatches
already carry the corrected reading with in-formula disclosures; this landmark supplies the
corpus-level supersession so the whitepaper prose need not be individually edited.

Likely injection vector: the PAPER_13xx broader-corpus series was drafted in a session where α
was locally denoted Λ (possibly from "λ (lambda) coupling" shorthand); the drift then propagated
by template into the four wired papers. Consistent with one-session template injection
(PAPER_2155 pattern); forensic confirmation optional and low-priority.

## 3. Standing Rules (extending PAPER_2155/2156)

1. **Reserved-symbol collision check:** before wiring any formula, symbols carrying canonical
   corpus meanings (Λ, α, β_i, Φ, SSq, F_TRZ, K_Mex) must be verified against the *numeric*
   actually used. Numeric identity outranks the written symbol (sibling of "executable outranks
   prose").
2. α's appearances in UQFF closures are legitimate observed-anchor usage (PAPER_2149
   hybrid-form doctrine); α itself has a UQFF projection-sector derivation (PAPER_591 family,
   0.138%) and an integer-primitive mantissa route (P1549, lead A_5·K_Mex = 125). The drift
   correction changes no value anywhere.
3. Any future drift family of ≥3 instances gets a correction-by-reference landmark at
   discovery, not at arc-end — this family was disclosed in-formula at wire time but its
   corpus paper lagged three bands; the lag is the process lesson.

## 4. Wiring

```
uqff_calculator.py
    DISPATCH['PAPER_2165'] -> the four-member drift registry with corrected symbol,
                              numeric-identity checks against alpha and its powers
```

Gate assertions pin: four members, each member's numeric = α^k for its stated k, the corrected
symbol present in all four source formulas ("SYMBOL DRIFT" disclosures), and Λ-reservation
integrity (no drift member touches the PAPER_2094 cosmological value).

---

## NOT REPLACEMENT

This is corpus hygiene, not physics: no value, residual, or prediction changes. The correction
protects the framework's reserved-symbol discipline so that Λ means one thing everywhere.

## Cross-references

PAPER_2155/2156 (correction-by-reference precedents), PAPER_2147 (presentation-layer Rule 4),
PAPER_2094 (Λ canonical reservation), PAPER_591/1549 (α's own UQFF routes), PAPER_1637/1646/
1656/1673 (affected, superseded on the symbol only), PAPER_2149 (hybrid-form doctrine).

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

---

## REVISION 2026-08-13 (PAPER_2169) — Drift verdict lifted; dual-name canonized

Daniel-directed deep search of the Star-Magic legacy layer recovered the derivation this paper's
"drift" verdict assumed absent: the predecessor executable defines
`Λ_ledger = 1/(8π·β_i·UA·(D_crit/D_bsfg)²) = 1/137.030` — **α at 0.0043%, derived.** The
recurring Λ is the vacuum ledger's saturation constant, a UQFF-native named quantity; the
whitepaper layer inherited its name and numeric but lost its derivation in crossover.

- The seven members (now including P1726/P1735/P1736) re-read as Λ_ledger — legitimate physics,
  not error. The DRIFT classification is LIFTED.
- The symbol-hygiene rule STANDS in sharpened form: **Λ_ledger with subscript, never bare Λ**
  (bare Λ stays reserved for the PAPER_2094 cosmological constant).
- The gate's numeric-identity checks remain valid — they now verify the derivation.
- Full disposition: PAPER_2169 (authoritative).
