Beating The Painted Sky seems to remove this encounter (for the day, I would imagine), even when you get no special reward.
My first time offering something to the painting, I went with flower+peat, and it gave a painted star.
Hat: guard helm
Weapon: painted parasol
Offhand: Coin of the Seasons
Shirt: coat of defensive circuitry
Pants: scrubs bottoms
Gadget: blazing PDA
Ocean Sight (9)
Dripping with Gore (166)
Leaping Dodge 3
Evil Eye 5
Steam of Needles 5
Awaken Students 1
Starry Gaze 2
More data regarding stars:
My adventures in the museum today:
- Tried to bind it (non-combat choice) - 3 XP Will
- Offered it a star - 10 XP Perc/Ref
- Offer it Flower+Lace - combat with the sky, lost
- Offer it Feather+Lace - gain painted star
When I got the star, I had the following (when I got the combat, I had more or less the same, but without half those buffs):
Hat: frigid scarf
Weapon: quivering needler
Offhand: tome of binding
Shirt: holocaust coat
Pants: heavy containment pants
Gadget: dragon twin statuette
Rose Balm (6)
Pep in your Step (10)
Industrial Mohawk (10)
Fearsome Visage (10)
Fires of Inspiration (19)
Ocean Sight (20)
Fungal Resilience (20)
No Pain (20)
Drunken Marksman (20)
Tooth Dream (20)
Guiding Wind (20)
Dripping with Gore (28)
Gummy Pumpkin (30)
Second Hand Gift (50)
Shotgun Blast (4)
Explosive Shot (4)
Stream of Needles (5)
Starry Gaze (2)
The starry thing continues to show up after you have the Whispers skill. No change in text for study it or bind it that I could see. (Also no change for burning vision.)
Nothing for trying to bind it with Evil Eye and at least 1 of every hall of paintings-derived tech we know of (skeletal mount, starry gaze, call the firebird and open parasol) in my deck.
Writing for the long-neglected GOC Casefiles canon.
So, up until now I've gotten combats every single time. Today I did the last two offerings I hadn't done before, Feather+Flower and Feather+Lace, both of which resulted in fights. I then tried studying it, to see if anything happened there after doing all options, but there was no change. I then decided to try fighting it. Went back, offered Flower+Peat, and got a painted star.
Same deck, outfit and effects that have resulted in getting fights every time beforehand.
It can still rummage through my mind ("without resistance" when I don't know enough Evil Eye) if I try to stare it down when I have 37 Etheric Defense.
EDIT: And I just got a painted star, by offering a flower + peat. In addition to studying the sky and staring it down today (which I had done before), I fought the Phoenix for the first time this run. I lost, but maybe that's enough?
EDIT 2: Fighting the Phoenix alone doesn't do it. Today I fought it and then offered a lace in peat and got a fight. Then I offered a flower and lace and got a star.
EDIT 3: No go with lace in peat or flower in peat. Got a star with flower + feather. I'll try and see if I can get a flower from each of the 6 different offering options and then maybe offer a star.
EDIT 4: It still doesn't like lace + peat or flower + peat today. No go with feather + lace or feather + peat. Flower + feather worked. So much for the no repeats theory.