Prefix used before a number to mean 'exactly that number' or 'precisely'. Common in formal or written contexts.
Noon is exactly twelve o'clock.
The gate closes at noon.
I want to hear an honest answer.
In the ritsuryō system, Senior Third Rank was higher than Junior Third Rank.
The 正 was the highest of the four administrative positions in the ritsuryō system.
true identity; true form; true colors · consciousness; one's senses
front; facade; main entrance
New Year; New Year's (esp. first three days) · first month of the year; January
sanity; sound mind; consciousness; soberness
noon; midday
New Year (esp. first three days) · first month of the year; January
correct doctrine; orthodox sect
net; actual; full · net weight · net price; cost price · actual content; substantive part; useful part
revealing the truth; demonstrating the truth
midnight
correct practices; right conduct
center of a Noh stage · Shōchū era (1324.12.9-1326.4.26)
authentic text; original document
true dharma; true teachings of Buddha · age of the true law
judge of the Imperial Prosecuting and Investigating Office; judicial officer; minister of justice · Imperial Prosecuting and Investigating Office
official register; authenticated copy; play script
pure silk
high Buddhist priest; bishop (Buddhist)
right mindfulness · true faith (in rebirth in the Pure Land)
public storehouse for tax grain and valuables (ritsuryō system)
downstage center
right livelihood
direct retribution; body and mind resulting from karma
right concentration
guest of honor · main guest at a tea ceremony
seat of honor
correct meaning; original meaning · true heart; sincere intention
on the hour; exactly at the hour
price tag; price label
The kanji 正 carries the core meaning of 'correct' or 'proper'. The prefix use for 'exactly' before numbers is a natural extension. The archaic court rank and administrative uses are historical and not productive in modern Japanese.