「Cutting into two halves」perhaps indicating an animal (such as a bird 鵥) cut open for DISSECTION, to be ANALYZED for increasing UNDERSTANDING, so that a JUDGEMENT can be determined of its edibility or degree of rankness, mostly by sniffing the odor at that point.
　「Incomplete reaming, work-in-progress」and「stance spurting with needle full and reaming」describes PASSING A SENTENCE, forming a JUDGEMENT after an ANALYSIS that medical treatments are still needed, treatment is「in process reaming」but not yet complete, additional visits to the clinic are necessary, with「erection or rod emissions from reaming multiple times」to be ANALYZED (one's 'bird' 鵥).
　The SIZES OF PAPER meaning is derived from the method of literally「cutting in half」a larger size of paper to create the next-smaller size. For example, a sheet of ISO A, B or C sized paper cut in half yields the next size of paper. A0 size being 1 square meter, B0 size being an area equal to the square root of 2 meters, and C0 being proportionally between the A and B sizes. A0 cut in half is the A1 size, A1 halved is A2 size, A2 cut in half is A3, that sheet cut in half again yields A4, and so on until A10, B10, or C10 size.
　The ENGRAVED SEAL meaning perhaps is related to the red, bloody mess created when cutting an animal in half or bougie reaming a sick pecker, as the ENGRAVED SEAL and the red inked stamp pads can produce a red, bloody-looking mess after use. Today, each party to a contract presses their personal seal (chop) over the crack where pages of a contract have been joined, with the seal「cut in half」by the seam, one-half of the red imprint on one page, and the other one-half on the backside of the previous page, making it nearly impossible to replace a page with altered text.

Modern definitions (that generally disregard history) …excluding politically incorrect concepts and other meanings deemed offensive today; may list only pigeonholed definitions, euphemisms, or meaningless mnemonics)
Chinese: to judge; to sentence; to discriminate; to discern; obviously (different)
Japanese: seal, stamp, monogram signature, judgment, judgement, size, understanding, comprehension, to understand, to comprehend, to grasp, to see, to get, to follow, to become clear, to be known, to be discovered, to be realized, to be realised, to be found out, to judge, to decide, to solve, to decipher, to puzzle out, to interpret, to divine, to guess, to make out
Unihan extended: judge; discriminate; conclude
EDRDG: judgement; signature; stamp; seal