How many signatures are required to start the formal decision making stage of a direct democracy mechanism?

Constitution of the Republic of Palau (1979) http://www.palauembassy.com/Documents/ConstitutionE.pdf

Article XIII

GENERALPROVISIONS

Section 3.Citizens may enact or repeal national laws, except appropriations, byinitiative. An initiative petition shall contain the text of the proposed lawor of the law sought to be repealed and be signed by not less than ten percent(10%) of the registered voters. An

initiativepetition shall take effect if approved at the next general election by amajority of the persons voting on the initiative. A law enacted by initiativeor a repeal of a law by initiative may not be vetoed by the President. A lawenacted or repealed by initiative may be subsequently amended, repealed orreenacted only by another initiative pursuant to the provisions of thissection.

Article XIV

AMENDMENTS

Section 1.

An amendment tothis Constitution may be proposed by a Constitutional Convention, popularinitiative, or by the Olbiil Era Kelulau, as provided herein:

(a) at leastonce every fifteen (15) years, the Olbiil Era Kelulau may submit to the votersthe question: “Shall there be a Convention to revise or amend theConstitution?”. If a majority of the votescast upon the question is in the affirmative, a Constitution Convention shallbe convened within six (6) months thereafter, in a manner prescribed by law; 
(b) by petition signed by not less than twenty-five percent (25%) of

the registeredvoters; or

(c) byresolution adopted by not less than three-fourths (3/4) of the

members of eachHouse of the Olbiil Era Kelulau.

Article IX

Section 17. Thepeople may recall a member of the Olbiil Era Kelulau from office. A recall isinitiated by a petition which shall name the member sought to be recalled,state the grounds for recall, and be signed by not less than twenty-fivepercent (25%) of the number of persons who voted in the most recent electionfor that member of the Olbiil Era Kelulau. A special recall election shall beheld not later than sixty (60) calendar days after the filing of the recallpetition. A member of the Olbiil Era Kelulau shall be removed from office onlywith the approval of a majority of the persons voting in the election, and suchvacancy shall be filled by a special election to be held in accordance withlaw. A recall may be sought against an individual member of the Olbiil EraKelulau no more than once per term. No recall shall be permitted against amember who is serving the first year of his first term in the Olbiil EraKelulau.

Article VIII

EXECUTIVE

Section 10. ThePresident or Vice President may be removed from office by a recall. A recall isinitiated by a resolution adopted by not less than two-thirds (2/3) of themembers of the state legislatures in not less than three-fourths (3/4) of thestates. Upon receipt by the

presidingofficers of the Olbiil Era Kelulau of the required number of certifiedresolutions, the Olbiil Era Kelulau shall establish a special election board tosupervise a nationwide recall referendum to be held not less than thirty (30)days nor more than sixty (60) days, after

receipt of therequired number of certified resolutions.

Citizen's initiative - 10% of the registered voters; Recall of a member ofOlbiil Era Kelulau (Parliament) - 25% of the number of persons who voted in themost recent election for that member.