Provide a full mechanism, using the reagents/reaction conditions in the picture. Use curly arrow notation as appropriate.

HO Me Me NaCIO, 78% 11 PMBO 1. Ph3P+CHBr NaHMDS, 78% OTBDPS HO 2. TBSOTf 2,6-lutidine, 96% PMBO 3. TBAF, ACOH, 77% 1. (COCI)2, DMSO, Et3N 2. HSCHCHCHSH BF3*OEt 85% (2 steps) Me Me 13 OTBS Me Me S OTBDPS Sml2, PhCHO quant., d.r. >20:1 Me Me 16 9 OH 1. SO3 py, Et3N DMSO 2. NACIO OTBDPS PMBO PGO OH OPMB 88% (2 steps) PMBO 10 Me Me DIBALH, 95% OTBS tBuLi, HMPA, THF -78 to -50 C Me Me 76%, 88% based on recovered 9 OTBDPS 14: PG = Bz 8: PG = H COH 6 PMBO HG-II, CSA crotonaldehyde 77%, d.r. >20:1 HO PMBO S. Me Me OH MesN Cl... CI Ru Pr 12 Me Me HG-II CHO NMes OTBDPS OTBDPS 15 Scheme 2. Synthesis of carboxylic acid 6. CSA=10-camphorsulfonic acid, d.r.= diastereomer ratio, HMDS=hexamethyldisilazide, HMPA = hex- amethylphosphoramide, Mes=mesityl, py=pyridine, TBAF = tetra-n-butylammonium fluoride, Tf=trifluoromethanesulfonyl.