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ACROSS

 1  Highest-ranking mountain? That’s a laugh! (5)

 4 A university kicks final examinations? (9)

 9 Start work with a joke, no? (5,2)

10 Old town is opposed to major Republican funder dropping $1,000 (7)

11 Recordings of our cousins running around, stripped nude (10)

12 978-0991245260 for Kosman and Picciotto’s latest recycling bins (4)

13 Hearing to bring an action against this woman’s bar offering (5)

15 Leaked: Democrat torn (7)

18 Stein, Ben: mostly a piece of work (4,3)

19 Proztific Hungarian composer (5)

21 Like part of a Cartesian plane (4)

22 One place to put options when dealing with “noble savage” (2,3,5)

26 Train worker managed outside mail in error (7)

27 Get cozy with laid-back breakfast choice containing a piece of lox (7)

28 Sense stew cooking with honey (9)

29 Zero to a million and 10 items suggested in 1A and here can be found in
the diagram. They are ignored in the wordplay. The End. (5)

DOWN

 1 Praise software overseeing big-city utility (8)

 2 Had longings where iniquity is rising (5)

 3 Deity’s dopier hat falling apart (9)

 4 What could make you lose sleep: organizations devoted to journalism
and cultural funding (5)

 5 Incomplete hint involves composer on tour (9)

 6 Way to caress Henri’s head (4)

 7 Strong men, before the middle of the month, put right? No sir! (9)

 8 Tin cross is a mysterious figure (6)

14 Support vehicle overturned on scale, concealing identity (9)

15 Rhythmic physical display, holding round mass in upper hand (9)

16 Communist leadership built poor convertible (9)

17 Nearly engrave a word commonly encountered in Le Monde, Time,
and so forth (2,6)

20 Sign of corrosion, for the most part (6)

23 Brazen woman doesn’t finish eating kosher shells (5)

24 Instrument’s mixture of blue and green (5)

25 Leave out something said repeatedly by techies (4)

SOLUTION TO PUZZLE NO. 3471

ACROSS 1 2 defs. 5 CHIS + EL 10 anag.
11 BULL(ET)S 12 DE(AT HAND)T + AXES
(Ted rev.) 14 TO + PB + A + NANA
16 CON + GA 17 F(UM)ED
19 “prying fan” 21 FOR TUNE, HUNTER
25 C(RIMS)ON 26 anag. 27 REG(G)AE
(rev.) 28 WE(ARIES)T

DOWN 1 “board’s tiff” 2 GA(SLAM)P 3 OVERHEA(R)D 4 GO TIN
6 HE(LI)X 7 STET + SON 8 LOS + T 9 anag. 13 anag.
15 A + F + FLU + [g]ENT 16 COND(UCT)OR (cut anag.) 18 MUFFIN + G
20 P(ETNA + M)E 22 R AS TA 23 ERAS + E 24 [o]SCAR