You guys might want to read the sources I post rather than go off half-cocked.
Yes, the cotton fibers are woven into the shroud, at least that is what my source states.

Sigh. No it doesn't. Do you actually bother to read the material you seagull post here? Or just link to whatever crap a google search suggests might support your opinions? You don't even bother to quote sections of the "paper" you link to, just hope desperately that others will accept it.
Your first lie: Hall didn't state that the cotton fibres were woven into the cloth. This appears to be deliberate misrepresentation on your part. He states that a small number of cotton threads were found.
It was Gilbert Raes who claimed that the cotton fibres were "inside the threads" of the linen. Note that even he, a shroudie, doesn't claim that the cotton was woven into the cloth. Further he was referring to an examation performed in 1975, some fifteen years before the sampling for radiocarbon dating, on a different sample....
Finally, there's actually no evidence that the threads were, in fact, cotton as no proper analysis of teh threads was carried out. Doug Farr, who used MassSpec on the fibres extracted from the Raes sample stated:
Both positive and negative SIMS spectra show simple, low mass species expected for cellulose and other organic fibres like cotton. Impurities detected were Na, F and Cl. No consistent significant differences were observed in the surface chemistry between the thin and fuzzy ends of the fibre.
So, no evidence either way. Of course Bob Villarreal deliberately misrepresented Farr's results.
Now, later a better test regime was carried out. (How many here remember doing FTIR analyses?)
This
would show differences between cotton and lined (due to the differences in C=O and C-O double and single bonds. Kevin Hubbard carried out such analyses (and they were presented at a shroudie conference more than a decade ago, curiously
@bobdroege7 seems to have missed this data in his googleings.....

).
And the result: the threads could not be distinguished as either cotton or linen.
So, the executive summary:
1. there is actually no evidence of cotton threads being present.
2. If they were present, which could happen, no-one has seen them woven into the cloth.
3. And if they were there and dates from (say) 1300 they would need to make up the entire sample in order to given the radiocarbon date obtained, and yet the examination of the sample showed it to be linen, possibly with a few stray cotton threads (≪1%) and insufficient to alter the dating.
The 'C level' summary:
@bobdroege7 is wrong again. The overwhelming evidence supports the shroud being created around 1300CE.