SMT FAQ posted:

To get the Hangon-shinshu, take the southeast elevator on 431F up to 444F. Walk
across the disappearing path, and turn north into the little cubbyhole at the
side of the room. There's a pit there, and it'll drop you back down to 431F.
Head south down the corridor you're dropped into until you see a big door. Go
through it and you'll be outside the tower. (and get a view of how ludicrously
high up you are) Clime along the path/stairs along the wall, and when you turn
the corner, ride the elevator block to the north back up to 444F. From there,
head up the stairs and go through the side door. You'll be in a room with three
doors. Take the south one and you'll find a Manekata who will ask if you know
about the treasure, and, if you say no, tell you that you must "fall, then walk
a painful path" to get it. On the north side of the chamber is a Sub-Terminal.
The west door will take you further into the puzzle. You'll be in a chamber with
a large pit, and phantom paths to the north and south. Take the north path to a
small ledge against the north wall. From there, take the east phantom path from
the ledge to the center platform floating in the middle of the pit. From there,
take the west phantom path to the southern ledge with the Dominion on it. The
Dominion will tell you that Chiaki is waiting for you to the south. But you
don't want to bother with her just yet, so for the time being ignore the south
elevator. There are two protrusions facing north on this ledge--take the phantom
path on the western one, and it will lead you to the western door. It'll lead to
a room full of damage floors--run through them and into the center of the room,
where you'll be dropped down a pit back to 431F.

Now, this is the tough part. This room is just riddled with pit traps, so you
need to be careful. However, there are no pit traps on the damage floors--so you
need to walk from damage floor to damage floor to keep from falling. To start,
run to the damage floor a bit north of you. Follow the damage "path" and sprint
to the second damage floor to the north of you. On this floor, turn to the east
and run down the short corridor, turning south at the corner. Once you get back
into the main room, DON'T immediately run for the damage floor because there's a
pit right in front of you to the south. Instead, hug the east wall to get onto
the damage floor. Follow the floor to the south, and you'll see about a two-
"block" gap between the north damage area and the south damage area. Go ahead
and run across this gap to the south damage area, because it's safe. On this
damage area, stand in the "corner" of the "L" and face west. Run three "blocks"
to the west, then turn south and step onto the damage area. Walk through the
damage area and there should be a passage off to your east. Walk down it, and
you'll be dropped down a pit to 418F. Walk down the short hallway and you'll be
teleported to another room on 418F...where you'll find the Hangonshinshu in a
chest surrounded by damage floor! After you get it, you're just a teleport and a
couple of elevator-blocks away from the Sub-Terminal on 444F again.

Side note here: If you super-impose your map levels between 418F and 431F,
you'll note the south edge of the riddled-with-pits room on 431F is actually not
above the damage-floor-all-over-the-place room in 418F toward the south edge of
the room. There's actually a pit trap in this area along the west wall that will
drop you into a little corridor that'll teleport you into a room where you can
find a Ikutama--a nice little treasure. You'll have to fight Shadows and Mots
to get it though.