This refers to the base of the weapon to which padding is affixed. For melee weapon cores the best things to use are carbon/graphite rods (such as from non-metallic golf clubs), kite spar, bamboo, PVC tubing or fiberglass. Other materials will be checked for safety on a case-by-case basis.
Metal and wooden cores are not legal, although metal may be used to counter-weight weapons provided it is permanently attached, and not in a place that may inadvertently strike an opponent.
The ends of all weapon cores must be blunted by capping them with a layer of foam and tape at a minimum.
For throwing weapons acceptable options are denim, loose rubberbands, sweatshirt material, or similar.