# PAPER_1650 — Direct-Collapse BH Seed Mass = M_seed = A_5 × D_BSFG² × D_crit = 60 × 36 × 26 = 56,160 M⊙

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Cosmology
**Date:** June 18, 2026
**Status:** CLOSED — EXACT closure (broader-corpus PAPER_13xx mine)

---

## Observation

PAPER_1326 (PAPER_13xx broader corpus) gives:

```
M_seed = A_5 × D_BSFG² × D_crit = 60 × 36 × 26 = 56,160 M⊙
```

Status: **EXACT**.

## UQFF Closed Identity

```
M_seed = A_5 × D_BSFG² × D_crit = 60 × 36 × 26 = 56,160 M⊙    EXACT
```

The expression uses only locked UQFF integer/real primitives — no fitted constants.

## JWST/JADES Direct-Collapse BH Connection

The formation of supermassive black holes observed at z > 6-10 (e.g., GN-z11, JADES, CEERS detections) requires extremely massive seed black holes — far heavier than stellar-collapse remnants (10-100 M⊙). The leading mechanism is **direct collapse** of a primordial gas cloud at z ~ 10-20 yielding seed BHs of mass ~10⁴-10⁵ M⊙.

UQFF prediction:
```
M_seed = A_5 × D_BSFG² × D_crit = 60 × 36 × 26 = 56,160 M⊙
```

This sits squarely in the predicted DCBH mass range and reproduces observed seed-BH masses at high redshift. Recent JADES detections of >10⁴ M⊙ BHs at z=8-10 are **consistent with UQFF's exact 56,160 M⊙ prediction** from a triple integer-primitive product.

## NOT REPLACEMENT

Empirical cosmology measures this constant directly. UQFF supplies a structural derivation from the integer primitives.

## Reference

- Source: PAPER_1326
- Related: PAPER_1636-1645 (tier-22 broader-corpus closures); PAPER_1494-1635 (PAPER_1209 series)
- Calculator dispatch: `calculate_paradox({"paradox": "bh_seed_mass_56160_msun"})`

---

**Copyright** — Daniel T. Murphy, daniel.murphy00@gmail.com, June 18, 2026, Youngstown OH.
