rigoros
strict
Very strict, uncompromising, and harsh in enforcing rules, measures, or principles.
Die Polizei kündigte an, rigoros gegen Falschparker vorzugehen.
The police announced that they would take strict action against illegal parkers.

rigorous
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strict
Very strict, uncompromising, and harsh in enforcing rules, measures, or principles.
Die Polizei kündigte an, rigoros gegen Falschparker vorzugehen.
The police announced that they would take strict action against illegal parkers.

The word 'rigoros' (rigorous/strict) can stand not only as an adjective before a noun, but also as an adverb describing a verb. In this case, it is not declined and describes the manner of an action.
Die neue Regelung wird rigoros umgesetzt.
The new regulation is being implemented strictly.
'rigoros' (rigorous/strict) is not a word for everyday usage, but belongs to a more formal or educated style. You often find it in newspaper articles, scientific texts, or official communications.
Die Regierung kündigte rigorose Sparmaßnahmen an.
The government announced rigorous austerity measures.
The context makes the meaning clear. If it is about rules, laws, or taking action against people, 'rigoros' usually means 'strict'. If it is about science, methods, or testing, it means 'thorough' or 'exact'.
Die Einhaltung der Sicherheitsvorschriften wird rigoros kontrolliert.
Compliance with the safety regulations is strictly monitored.
In the meaning of 'strict', 'rigoros' is often connected with verbs and nouns related to acting and controlling. Typical phrases are 'rigoros vorgehen' (to take strict action), 'rigoros durchgreifen' (to crack down hard), 'rigorose Maßnahmen' (strict measures), or 'rigorose Kontrollen' (strict controls).
Die Firma geht rigoros gegen jede Form von Diskriminierung vor.
The company takes strict action against every form of discrimination.
hard
'hart' and 'rigoros' can both describe someone as strict and uncompromising. 'hart' is more general and can refer to behavior, decisions, or judgments. 'rigoros' is stronger and usually means that rules, measures, or principles are enforced without exception. It often sounds somewhat more formal than 'hart'. If someone reacts strictly or harshly, 'hart' fits; if someone acts very consistently and without compromise, 'rigoros' is more precise.

Die Firma kontrolliert die Sicherheitsregeln rigoros, damit keine Unfälle passieren.
The company rigorously checks the safety rules so that no accidents happen.
Die Lehrerin war hart, aber sie erklärte der Klasse den Grund für ihre Entscheidung.
The teacher was strict, but she explained the reason for her decision to the class.