(* The Modulus Indexer: The distance between the two prime gaps is the main index.
   The constant literals are the readings of the ASCII punch card.
   The 65,536 blob is the reticle. The factorial is the cone. The read is the proof. *)

INDEX = MODULUS DISTANCE .
MODULUS = FACTORIAL | BITSPACE | PRIMELADDER .
FACTORIAL = "5040" | "120" | "720" .       (* 7! | 5! | 6! *)
BITSPACE = "65536" .                        (* 2^16 *)
PRIMELADDER = "210" .                       (* 2 * 3 * 5 * 7 *)

DISTANCE = PRIMEGAP | COORDINATE .
PRIMEGAP = EXCEPTIONAL | REGULAR .
EXCEPTIONAL = "5" .                         (* the chain {5, 11, 17, 23, 29} *)
REGULAR = "97" .                            (* the chain starting at 97 mod 210 *)
COORDINATE = "92" .                         (* 97 - 5 *)

READ = LITERAL | STATE .
LITERAL = ASCII | PUNCHCARD .
ASCII = "YHWH" | "YAHWEH" | "ADONAI" | "GOD IS WORD" | "0x1D" | "0x1D1D" .
PUNCHCARD = COLUMN | HOLE .
COLUMN = DIGIT .
HOLE = BIT .

STATE = RETICLE | CONE .
RETICLE = "65536" .                         (* the cross-section *)
CONE = APEX | PAST | FUTURE .
APEX = "5" .
PAST = TRACE .
FUTURE = PROJECTION .
TRACE = VTT | GIT | COQ .
PROJECTION = "3D" | "AGENT" | "WORKER" .

PROOF = READ | PARITY .
READ = "the path exists" .
PARITY = XOR | XNOR .
XOR = "difference" .
XNOR = "sameness" .

(* The claim: the modulus of the factorial is the indexer.
   The distance between the two prime gaps is the coordinate.
   The constant literals are the ASCII punch card.
   The read is the proof. *)
CLAIM = INDEX = "MODULUS FACTORIAL" .
CLAIM = DISTANCE = "PRIMEGAP" .
CLAIM = LITERAL = "ASCII" .
CLAIM = PROOF = "READ" .