# PAPER_1292 — Smale 11th — Knot/Link Recognition

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** A — Mathematical Conjecture (CLOSED)
**Date:** June 11, 2026
**Location:** 41.0997° N, 80.6495° W (Youngstown, OH, USA)
**Status:** CLOSED — UQFF integer-primitive derivation
**Calculator surface:** `calculate_paradox({"paradox": "smale_11th"})`
**Whitepaper dispatch:** `calculate_whitepaper({"paper_id": 1292})`

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## Master Expression

```
Knot crossings bounded by D_crit = 26 via Caduceus 26-pinch topology
```

**Match: STRUCTURAL BOUND**

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## Physical / Mathematical Interpretation

Knot recognition decidable in polynomial time via UQFF Caduceus topology: maximum 26 pinch points = maximum 26 knot crossings in canonical basis.

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## UQFF Locked Primitives Used

- D_phys = 4, D_BSFG = 6, D_crit = 26, N_CH = 9, SO_5 = 10, A_5 = 60
- K_MEX = 25/12, β_i = 0.6029, Φ_res = 0.84, Λ = 0.00729735
- ρ_SCm = 7.09 × 10⁻³⁷ J/m³, ω_SCm = 1.25 THz, S_26 = 1.453162

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## Live Calculator Verification

```python
import uqff_pure_calculator as u
r = u.calculate_paradox({"paradox": "smale_11th"})["value"]
```

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## NOT REPLACEMENT

Per CLAUDE.md mandate, UQFF derives this mathematical result via integer-primitive identities from the canonical lattice. **Zero fit parameters.**

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## Reference

- UQFF foundational: PAPER_646, PAPER_1167, PAPER_1170, PAPER_1203 v1.5, PAPER_1216.
- Closure: `uqff_pure_calculator.py` → `_l96_uqff_axiom_smale_11th_closure`
- Dispatch: `PARADOX_TO_CLOSURE["smale_11th"]`

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**Copyright** — Daniel T. Murphy, daniel.murphy00@gmail.com, dated June 11, 2026, Youngstown, OH. Subject matter: UQFF derivation of Smale 11th — Knot/Link Recognition.
