Why it resists
What makes Eternity II hard at its core: phase transitions, rigidity, entropy, forbidden patterns, all the structural walls every solver eventually hits.
Why it's hard
finding
The piece set is extreme on every measured axis
finding
Which wall stops which method
finding
Complex theory: counting the search before you run it
finding
Why 479 is impossible
finding
Tuned to the hardness peak
finding
The rigidity wall
finding
The 470 wall: a phase boundary, not an engineering limit
finding
Entropy and the area law
finding
Forbidden patterns
finding
No forced moves
finding
Ring purity: the border is a closed sub-puzzle with zero slack
finding
Flux invariants: a rotation law the official set obeys exactly
finding
Why basin-hopping looks impossible
finding
The puzzle has no height function
finding
Where the mismatches live
finding
The hard region you cannot design away
finding
Piece theft, where solvers die
finding
The board as a codeword
finding
Where you place the hints beats how many
finding
Linking the clues early does not help, it hurts
finding
The rare colors live on the frame
finding
The frame is not the basin: a different border does not open a different high board
finding
The border balance
finding
Designed to be unsolvable: the recipe
finding
The theorem sweep: thirteen structural laws