The Rules Differences page has been updated, as Spirit Monsters were discovered to have a functional errata / ruling related to their mandatory End Phase Trigger Effects. Apply the following ruling for Spirit Monsters, Lightsworns, and any mandatory Trigger Effect that activates in a certain Phase:
This effect keeps activating (if its activation is negated) until it finally resolves (even if it resolves negated) [REF].
Also, the Functional Errata page has been updated to include "Mark of the Rose", as it has recently been pointed out to have 2 Trigger-like Effects up until its erratum in Fusion Enforcers [REF]. The individual card rulings have also been updated.
These Trigger Effects won't activate while the effect of "Cold Wave" lingers.
How does this Rule Update affect YOU?
If "Light and Darkness Dragon" negates the activation of "Judgment Dragon's" mandatory Trigger Effect, that effect activates again.
If on your turn, your Spirit Monster's effects are negated by your opponent's "Forbidden Chalice", in the End Phase the Spirit Monster's Trigger Effect activates & resolves negated and will not activate again.
This is because normal rules of priority apply, andthe turn player must resolve effects first [REF].
If your "Forbidden Chalice" targets your Spirit Monster on your turn, in the End Phase:
you can activate & resolve your Spirit Monster's Trigger Effect negated (it stays on the field) [REF].
you can have "Forbidden Chalice's" effect wear off, then have your Spirit Monster's Trigger Effect activate & resolve successfully (returning it to your hand).
If "Skill Drain" negates "Judgment Dragon's" mandatory Trigger Effect, that effect won't activate again.
After many months of investigation we've reached a roadblock... there's no evidence that Konami's rulings change  regarding "Rivalry of Warlords" and "Gozen Match" took effect at or before SJC Edison. Thus the responsible and prudent course of action is to apply the Upper Deck Entertainment rulings  to the cards. This change only affects the ability to Tribute Summon (not Special Summon).
Moving forward, apply these UDE rulings to Rivalry and Gozen:
If you have only 1 monster on the field face-up, you may Tribute it for a monster that is a different Type/Attribute.
If you have 2 monsters on the field face-up of the same Type/Attribute, you cannot Tribute 1 of them for another monster that is a different Type/Attribute (even "Jinzo") as you would then have 2 different Types/Attributes.