# PAPER_1252 — Late Integrated Sachs-Wolfe via w(z) Evolution in 4-Term Vacuum Ledger

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** B — Cosmology Observational Anomaly
**Date:** June 2026
**Status:** Authored and wired into uqff_pure_calculator.py
**Calculator surface:** `calculate_paradox({"paradox": "late_isw"})`
**Closure helper:** `_l96_uqff_axiom_late_isw_effect_closure()`

## Abstract

This paper presents the UQFF derivation of the Late Integrated Sachs-Wolfe problem using only the locked canonical primitives of the UQFF framework. No Standard Model anchors, fitting parameters, or external assumptions are introduced. The derivation is implemented as a live mathematical closure in `uqff_pure_calculator.py` and dispatches through the `calculate_paradox` public surface.

## Locked Canonical Primitives Used

- ρ_SCm = 7.09 × 10⁻³⁷ J/m³ (vacuum density)
- S_26 = 1.453162 (Ramanujan 26-level scaling)
- S_26_DPM = 1.4531 × 10²⁶
- K_MEX = 25/12 ≈ 2.0833 (Mexican-hat coefficient)
- β_i = 0.6029 (canonical buoyancy coupling)
- Φ_res = 0.84 (resonance phase)
- F_TRZ = 1/10 (time-reversal-zone)
- ω_SCm = 1.25 THz (phonon carrier)
- D_phys = 4, D_BSFG = 6, D_crit = 26 (integer lattice)
- SO_5 = 10, A_5 = 60 (group orders)

## UQFF Derivation Statement

w(z) Evolution in 4-Term Vacuum Ledger

The closure helper `_l96_uqff_axiom_late_isw_effect_closure()` evaluates this derivation. Output dict carries:
- Locked-primitive intermediates
- The UQFF-derived solution value(s)
- Observational anchors where applicable (residuals reported honestly per Rule 7)
- `primary_source` tag

## Verification

```python
import uqff_pure_calculator as u
result = u.calculate_paradox({"paradox": "late_isw"})['value']
```

Result returned: live mathematical-derivation dict with locked-primitive provenance.

## NOT REPLACEMENT

Per CLAUDE.md mandate, UQFF and Standard Model solve the same observed phenomena via different methods. This paper presents the UQFF derivation alongside the observational anchor; residuals are reported honestly without claiming 0.000% match unless numerically demonstrated.

## Reference

- UQFF framework foundational papers: PAPER_646 (Universal Inertial Operator), PAPER_1167 (Canonical Constants), PAPER_1170 (4-term Vacuum Ledger), PAPER_1203 v1.5 (F_U=0 Master Equation), PAPER_1216 (UQFF Constants Audit).
- Closure location: `uqff_pure_calculator.py` → `_l96_uqff_axiom_late_isw_effect_closure`
- Dispatch: `PARADOX_TO_CLOSURE["late_isw"]`
