Two unclued lights are terms for the same style. One, consisting of two words, forms a cryptic indication of each of two unclued lights. The other is a word that can be divided into three words; each of these defines each of two of the other unclued lights.
Across
1 Part of thesis systematically weak (5)
6 Leading note on cubist works (8)
13 Turning cold during brilliant spectacle (9)
15 Fish indeed covered with fungus (8, two words)
16 Doorkeepers having no time for steady gazers (6)
17 Commander with note for trumpeter (5)
26 Undermine plodding student (3)
28 Device operating switch very quietly in test (7)
29 Bird of prey in glade, one leg injured (11, two words)
33 Government clears networks (5)
34 Apocryphal book succeeded? Very much (6, two words)
35 Ascetic, when beset by any sin, tormented (8)
37 Honour to hold old instrument (4)
38 Phosphate quickly coating one unfinished article of food (9)
39 Outline of plan for stirring up sects (10)
40 Attacker backing remarks about odd parts of theory (8, hyphened)
Down
1 Old country with endless anxiety for apes (8)
2 Noticing, so nervously, people concealing identities (10)
3 Split, not against prophet (4)
5 Parts of crustaceans flourishing on good shores (11, two words)
7 Relative annual return not obvious (7)
8 Expression of impatience with gold coach (5)
9 Omit too much on runner with power (8)
10 Not so full of regret, weak leader of empire upset group of countries (9, two words)
11 Evil way without love (5)
16 Slowly, in enclosure, one with hesitation identifying flower (11)
18 Force in cryptic hint (3)
20 Not a bloke to go wild for...
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