What turned up when the cartridge was taken apart, with the evidence next to it. What is not settled is in Open questions.
There is no fall damage and no minimum height anywhere. What there is, is one byte: 0xE13A, written at the moment you press the button (0x6DAA).
Normally it is the Y you jumped from plus sixteen —sixteen points lower on the screen, which from the ground is just the ground—. But if you jump while standing on one of the two middle water-jet planks, with X between 0x48 and 0x9F, it is that plank's height, with nothing added.
From then on, two checks compare against it. Walking, 0x6960 kills you if your Y minus 0x11 has reached it; landing on a plank, 0x656C does the same with 0x10. So the very same landing is harmless or fatal depending on where the jump started, and jumping off a high plank means the ground itself is a fatal distance away.
Many of the house's cartridges hide their catalogue number and the title in katakana at the end of the ROM; Manuel Pazos (@ManuelPazosMSX) found it. This one does not: the last byte with any content is at 0x7C3C, and behind it there are only 963 bytes of 0xFF padding. Nor is it somewhere else: all 16,384 positions were swept with a search that does find it in the cartridges of the series that carry it.
Not a map, not a generator: two tables of thirty-two bytes, at 0x5C32 and 0x5C52, indexed by SCENE modulo 32. One says which fixed obstacles the screen is built with and the other which things move in it.
5C32 03 82 20 04 88 00 01 20 41 10 C0 00 88 40 88 20
01 04 50 80 50 40 10 20 10 82 00 05 41 88 01 50
5C52 80 A0 08 08 08 0C 80 0C 10 08 60 08 00 80 18 02
10 08 48 A0 40 C0 08 09 08 00 01 10 58 10 18 40
SCENE itself, at 0xE054, is a plain counter that goes up or down by one and, on passing 255, drops back to 56 (0x43F2) —not to 0, and not to 1—. Going the other way it sticks at 1 and turns you round. Beyond thirty-two screens the park repeats; what does not repeat is the stage number, which edits the pair before it is used.
There is no interpolation, no pendulum and no trigonometry. 0x555B is a table of nine pointers, and each one is a small drawing: tile, tile, then 0xFE, 0xFD or 0xFC to drop a row —one column left, the same, or one right— and 0xFF to finish. That is the whole swing.

The phase counter runs 0 to 15, and from 9 upwards it is negated and read backwards (0x60D9), so nine drawings make a full swing out and back. Two vines are drawn per screen, twelve columns apart, on two counters that tick at different rates —every 8 and every 10 frames—, which is why they are never in step.
And behind each drawing's 0xFF come three more bytes: the Y and the two X of the tip. That is the only place the game knows where the rope ends, and it is what your hands are checked against (0x6C3C).
In graphics mode 2 the screen is three thirds and each one has its own patterns. The vine hangs from row 6 and reaches row 12, so it straddles the seam between the first third and the middle one — and the cartridge loads its tiles accordingly: the top of a vine is tiles 0xB0-0xB6, copied into the first third (0x594C), and everything from row 8 down is tiles 0x60-0x9B, copied into the middle one (0x5940). Neither set exists in the other bank.
That is not something playing shows you; it falls out of putting the loader's addresses next to the drawings' tile numbers.
At 0x447E, in plain sight, the tile codes being the ASCII of the letters:
ALL STAGE CLEAR
PROGRAM A.H Y.I
SOUND Y.O
CG R.S C.K
They are painted in one place only: 0x445B, when the stage counter wraps from 99 back to 00. The layout list in front of them (0x4468) is six entries long —a rule of 18 tiles on row 5, the ALL STAGE CLEAR on row 6, another rule on row 7, and the three credit lines on rows 16, 17 and 18—.
No full names: initials only, and nothing else in the cartridge is signed except the KONAMI 1984 on the title screen and at the foot of the scoreboard.
The sound player has a table of note periods at 0x7960 —ten bytes— and, right after it, a table of 34 track pointers at 0x796A. The two overlap by design: the eleventh and twelfth notes, periods 60 and 56, are the bytes 3C 38, and those same two bytes are entry 0 of the pointer table, reading as the address 0x383C.
Entry 0 is never asked for —sound numbers start at 1— so nothing is broken by it. It saves two bytes.
Sound 6 is asked for every time the bee leaves the screen and every time you leave a screen, and all it does is shut the effects channel up: it is the only way to stop the bee's buzz, which loops on a 0xFE.
Its track is the single byte 0xFF at 0x79DB — which is not a track at all: it is the 0xFF that ends the fanfare's channel A. Nine of the 34 entries in the table point at that one byte: sound 6, and the unused channels of every three-channel sound.
The eighteen blocks of the water jet (0x5701) are nineteen bytes each: 6×3 tiles of drawing, and then one byte that is not drawn at all — the height at which the plank ends up, from 0x52 at the bottom to 0x32 at the top, two at a time.
0x60B7 draws the block and returns that byte, and 0x604B stores the four of them in 0xE148-0xE14B. When the player lands, 0x650E compares his Y against those four numbers. The picture and the physics come out of the same nineteen bytes, so they cannot drift apart.
The ATHLETIC LAND logo is not a picture that gets uploaded. It is 34 tiles, 0x40 to 0x61, unpacked once by the run-length decompressor, and then 0x47CB is called once per frame and each call places one column: two tiles, on rows 5 and 6, at column 8 plus however many columns have already gone in.

Seventeen calls draw the logo, and the counter keeps going to 52: the calls after the seventeenth paint the KONAMI 1984 underneath and then say there is nothing left.
Things that are there and go unused. None is a guess; each was looked for.
0000, and jumping there would restart the machine. No instruction writes a 9 to 14 into 0xE138.