A Demonstrably Valid Cipher:

Hypnerotomachia Poliphili, 1499

P
O
L
I
A
M
F
R

A
T
E
R
F
R
A
N

C
I
S
C
V
S
C
O

L
U
M
N
A
P
E
R

A
M
A
V
I
T

POLIAMFRATERFRANCISCVSCOLVMNAPERAMAVIT

POLIAM FRATER FRANCISCVS COLVMNA PERAMAVIT

Brother Francisco Colonna madly loved Polia.

Demonstration of Validity, after the Friedmans' methods

the plain-text solution must make sense, in whatever language it is supposed to have been written
- it must be grammatical ('Hearts green slow mud' would not do) and
- it must mean something ('Pain is a brown Sunday' would not do either).
- It does not matter whether what the solution says is true or not; it may be a pack of lies, but that is not the cryptologist's business.
the cipher system and the specific key also have to obey certain rules. The specific keys may be few or many, simple or complicated, but
- they must be unambiguous
- once the rules are known, it must be possible to apply them precisely and inflexibly

General rule: the cipher is an acrostic
Specific key: take the display capital letters of each chapter in order.

What are the odds against this solution's being an accident?

Use the Vulgate Bible as a representative sample text

Of the 648,974 words in the Vulgate, 37,664 (or about 8.2%) begin with the letter "P." Assuming that the Vulgate is a reasonable sample, we could say there is about a 1 in 17 chance that the first display capital would be a "P."
There is about a 1 in 41 chance that the second letter would be an "O";
1 in 60 chance that the third letter would be an "L";
1 in 10 chance that the fourth letter would be an "I";
1 in 12 chance that the fifth letter would be an "A"; and
1 in 19 chance that the sixth letter would be an "M."

There is then about 1 chance in (17*41*60*10*10*12*19) or 1 in 100,422,924 that the first 6 display letters would be "POLIAM."

If we go through the entire set of display capitals at the beginnings of the chapters, we find that there is about 1 chance in 10,100,128,459,604,200,000,000,000,000,000,000,000,000,000,000,000 that the display capitals would be in this order: "POLIAMFRATERFRANCISCVSCOLVMNAPERAMAVIT."

1 in 10,100,128,459,604,200,000,000,000,000,000,000,000,000,000,000,000