GLOSSARY

adjoin: When the opening verses -- the tetrons -- are also taken into account. Hence, all the base verses are incremented by one (adjoin base verses) except for chps 1 and 9. In general, an adjoin base verse may not be a base verse itself.
adjoin isotupe: An isotupe corresponding to an adjoin base verse.
adjoin norm: When the norms of the tetrons are also included.
adjoin versor: Versor corresponding to adjoin base verse.
alternating EP: Those verses with the same parity of their chps: the ENVs of the ECs and the ONVs of the OCs.
alternating OP: Those verses with the opposite parity of their chps: the ENVs of the OCs and the ONVs of the ECs.
antion: A set formed from the combination of EPN and OPK.
ascension: The ordinal position of a chp based on its base verse relative to the set of all base verses in ascending order. In the case of repetition the position is determined by the corresponding chp.
AV: Adjoin Verse, also denoted by W.
bar: The ordinal position of a chp within the disjoint sets of basals or imbasals. Similar to ord, a chp can identify with only one unique bar, but, two chps, one from each set may share the same bar.
B-chain: A sequence of chps, where any two adjacent ones form a B-link.
B-link: A pair of chps, where, one is the bar of the other one.
basal: Chp number is also a base verse.
base cept: The number of cepts of some versor.
base verse: The verse-count of some chp.
bijection: A 1-1 and onto map between two sets.
bisect: Dividing the chps into two sets with the same cards, where the chps in one set and the verses in another set have equal sum.
brace: A number is braced if it can be partitioned into smaller components, where any component is linked to some other one.
BV: Base Verse.
BW: Adjoin Base Verse, also denoted by BW.
Card: Cardinality.
Cardinality: The number of elements in a set.
C-chain: A sequence of versors, where any two adjacent ones form a C-link.
cept: See versor.
ceptal: Versor number is also a base cept.
CGV: Chp number is Greater than its Verses.
chain: A sequence of chps or versors, where any two adjacent ones are mutually connected via a link of some type, e.g., O-link, or V-link, etc. If all the links are of the same type, the chain is homogeneous, otherwise, it's heterogeneous. In the latter case, the type of each link is identified separately, for instance, an OSV-chain, consists of three links of types O, S, and V in that order.; A sequence of BVs from various chps connected via repeated applications of given maps bounded at the begining with a head tetron. The elements of the chains are nodes.
chp: Chapter.
C-link: A pair of versors, where, one is the cept of the other one.
CLV: Chp number is Less than its Verses.
C:m-n: The set of all chps with base verses between m and n inclusively, for 3 ≤ m < n ≤ 286. In other words, it is the union of isotupes C:i, for m ≤ i ≤ n. The BV's are subject to restriction and may not be contiguous over the range from m to n.
cobase: Two base verses whose difference is also a base verse.
cochain: Conjugate of a chain.
cochp: Conjugate of a chp, where every verse is replaced with its conjugate.
complement: The set of all elements that are not in a specified subset.
conjugate: Symmetric counterpart of a node from the corresponding mirror chain of opposite handedness. Conjugate of a conjugate is the identity.
conn: The ordinal position of a chp within the disjoint sets of antion or diop. A chp can identify with only a unique conn, but, two chps, one from each set may share the same conn.
contrariety: The property of a chp as to whether it belongs to antion or diop.
C:V: Verse V of chp C, where 1 ≤ C ≤ 114 and 1 ≤ V ≤ 286. The value of V cannot exceed the base verse corresponding to chp C.
cycle: A homogeneous loop. All the nodes are of the same type and obtained by the repeated application of a particular operation, e.g., cept, or ascension. Any element in a cycle can serve as the starting point to generate the remaining nodes by keep applying the same operation. By convention, a cycle is labeled by its smallest element.
declaration: The first verse in an init-chp where the init-set is introduced. It is always in verse one, with the exception of chp 42, where the second verse is also a declaration. The declaration itself may be an entire verse or only part of the beginning of the verse.
diop: A set formed from the combination of EPK and OPN.
disjoint: Having no elements in common.
dot product: The sum of the products of the corresponding elements of two vectors, also known as the scalar product. The two vectors must have the same number of elements.
EC: Even numbered Chp.
EC^*: Even numbered Cept.
EE: Even numbered chp with Even number of verses.
EE^*: Even numbered versor with Even number of cepts.
E-link: A pair of nodes, where, one is the vex of the other one.
ENC: Even Numbered Cept.
ENV: Even Numbered Verse.
ENW: ENVs, plus the tetrons.
EO: Even numbered chp with Odd number of verses.
EO^*: Even numbered versor with Odd number of cepts.
EP: The chp number and its verses are of Equal/Even Parity.
EP^*: The versor number and its cepts are of Equal/Even Parity.
EPK: The overlap between the EP and the keon.
EPN: The overlap between the EP and the napen.
EV: Even Versed chp.
EV^*: Even numbered Versor.
EW: Even Versed chp, when the tetrons are also included in the count.
FC: Free Chp.
FC^*: Free Cept.
F:n: All n-numbered FV's, 1 ≤ n ≤ 286.
free: Free norm; norm = 0.
frev: The number of free verses.
FV: Free Verse.
GC: A normal Chp; norm ≥ 1.
G-chain: A sequence of chps, where any two adjacent ones form a G-link.
G-link: A pair of chps, where, one is the grin of the other one.
Gn: Of norm n, 1 ≤ n ≤ 7.
GH: Gn, for norm n > 1 - Higher normed.
Gm:n: All n-numbered Gm's, for 1 ≤ m ≤ 7 and 1 ≤ n ≤ 286. Some restrictions may apply, since, in general, an m-normed verse n may not exist for a given n.
G:n: All chps with n-numbered GV's, 1 ≤ n ≤ 286.
grin: The ordinal position of a chp within the sets keon or napen. Two chps, one from each set, may have an identical grin, but, it is unique within each set.
grinian: A bijection between keon and napen, where the elements between them are mapped in such a way that the total separation between their corresponding weights (such as base verses) is an extremum - usually a minimum.
grinity: The property of a chp as to whether it belongs to keons or napens.
grob: norm
group: A non-empty set G and a binary operation called multiplication, which is closed and associative: For a, b ∈ G, ab ∈ G, and (ab)c = a(bc). There is a unique identity element e, which commutes with and leaves all elements intact: ae = ea = a. Each element a in the set has a unique inverse a^-1, which it commutes with and their product is the identity: aa^-1 = a^-1a = e. If, additionally, the elements also commute under the multiplication; ab = ba, for all a,b ∈ G, the group is called abelian, otherwise, it's non abelian.
GV: A normal Verse; norm ≥ 1.
Gvec: A Vector of GV's.
GW: Adjoin normal Verse; when the tetrons are also included.
ilon: A verse of an init-chp that contains only one of the letters from the declaration.
IC: Init Chp.
imax: A verse of an init-chp that contains all the letters from the declaration.
imbasal: Chp number is not a base verse.
incept: Versor number is not a base cept.
index: The ordinal position of a number within the sets of primes or composites. A pair of prime and composite numbers may have the same index, however, it is unique within each set. Since, one is neither a prime nor a composite, it forms a singleton, therefore, acquiring an index of one.
init-chp: Initialed Chp.
init-count: The count of the init-letters in an init-chp.
init-letter: One of the 14 letters (half the alphabet) initializing a set of 29 chps.
init-set: A subset of the init-letters consisting of one to five letters, first appearing in the declaration and consequently throughout the init-chp. There are 14 such sets with various combinations of the 14 init-letters.
init-verse: A verse of an init-chp.
inot: A verse of an init-chp that contains no letter from the declaration.
ipor: A verse of an init-chp that contains only some but not all of the letters from the declaration.
isec: A verse of an init-chp that contains at least one letter from the declaration.
isocom: isocover − set.
isocover: The smallest set of isotupes containing the set.
isopan: The number of isotupes in isocover.
isotupe: A base verse and all the chps it laces with V-links. There are as many isotupes as there are distinct base verses.
KC: Keon Chp.
keon: The set of chps formed by the combination of the normal and the un-init chps. It has 57 elements and it's the complement of the napen.
kernel: The subset of those elements that are mapped to the empty set.
KV: The verses of a KC.
KW: The adjoin verses of a KC.
lace: A generalization of the link. Two numbers are laced when one or both can be partitioned into smaller components, where, a component from the first is linked with one from the second. In the special case where, the numbers themselves are the sole components and may not be further broken up into smaller components, it reduces to the familiar link.
lactorize: The factorization of a number into several components whose concatenation laces with the number itself.
loop: A closed link or chain, where the end node links back to the beginning node. For instance, 36 and 83 form a loop since, each one is the verse-count of the other one. Another example is a chain of 22, 49, and 78 forming an OOV-loop.
monotupe: An isotupe with an O2O mapping; a single chp is associated with only one base verse.
M2O: A Many-To-One mapping or relationship between two sets, where many elements from the first set are mapped to only one element from the second set. An example of this type of mapping is when several chps have the same number of verses.
:n: All n-numbered verses, 0 ≤ n ≤ 286.
napen: The set of chps formed by the combination of the init and the free chps. It has 57 elements and it's the complement of the keon.
natural order: The base verses are arranged in ascending order.
NC: Napen Chp.
node: An element in a sequence that functions as a chp or versor that links to an adjacent entry.
norm: The number of occurrences of the key word GOD. It is always ≤ 7.
normal: Of norm ≥ 1.
nove: The number of normal verses.
NV: The verses of an NC.
NW: The adjoin verses of an NC.
Nvec: A vector of norms of the corresponding elements of Gvec.
OC: Odd numbered Chp.
OC^*: Odd Cept versor.
O-chain: A sequence of chps, where any two adjacent ones form an O-link.
OE: Odd numbered chp with Even number of verses.
OE^*: Odd numbered versor with Even number of cepts.
O-link: A pair of chps, where, one is the ord of the other one.
ONC: Odd Numbered Cept.
1-1: A map where distinct elements from one set are mapped to distinct elements in another.
onto: A map from A to B, where, every element in B is connected to an element from A.
ONV: Odd Numbered Verse.
OO: Odd numbered chp with Odd number of verses.
OO^*: Odd numbered versor with Odd number of cepts.
OP: The chp number and its verses are of Opposite/Odd Parity.
OP^*: The versor number and its cepts are of Opposite/Odd Parity.
OPK: The overlap between the OP and the keon.
OPN: The overlap between the OP and the napen.
ord: The ordinal position of a chp within the sets of initialed or un-initialed chps. Since, a chp is either initialed or un-initialed, it can only have one unique ord. On the other hand, two chps, one from each set, may have identical ords.
order: The order of a group is the number of the elements in the group. The order of an element a in the group, is the smallest positive integer n > 0, such that aⁿ = e, the identity element.
O2M: In One-To-Many mapping between two sets, an element from the first set is mapped to multiple elements in the second set. An example of this type of mapping is an O2M declaration, where a single declaration appears in several init-chps.
O2O: A One-To-One mapping. It signifies the pair-wise correspondence between elements of two sets. An element of one set is associated or mapped to a unique element in the other set. For instance, an O2O declaration appears in only one init-chp.
OV: Odd Versed chp.
OV^*: Odd versor.
OW: Odd Versed chp, when the tetrons are also counted.
par: The ordinal position of a chp within the sets EP or OP. It's unique for a given element, but may be identical for two chps.
parian: A 1-1 map between EP and OP, where the elements between them are mapped in such a way that the total separation between their corresponding weights (such as base verses) is an extremum - usually a minimum.
P-link: A pair of nodes, where, one is the par of the other one.
polytupe: An isotupe with an M2O mapping; several chps are associated with only one base verse.
pron: The symmetric correspondence between pairs (EE, OE) and (EO, OO), where the high and low ordinal positions are cross mapped.
QCD: Que Continuum and Discontinuum.
quartet: The grinity+parity tetric sets EPK, OPK, EPN, OPN.
S-chain: A sequence of chps, where any two adjacent ones form an S-link.
self-adjoin: An adjoin base verse that is also a base verse.
singleton: A set consisting of only one element.
singular: Alias for G1; norm = 1. Also, a map is singular, when its kernel is non empty.
S-link: A pair of chps, where, one is the ascension of the other one.
sox: The ordinal positions of isotupes according to their base verses arranged in standard order. All chps within a given isotupe are labeled with the same sox which is unique for each isotupe.
standard order: The order in which the base verses appear when their corresponding chps are arranged in ascending order.
stripe: A set of contiguous verses of the same type; either normal or free. In chps with both type of verses, the normal and the free stripes alternate. On the other hand, a free chp forms a single stripe.
surpular: Alias for GH; norm > 1.
T-chain: A sequence of chps, where any two adjacent ones form a T-link.
tecot: The union of cochains -a pair of mirror symmetric chains of opposite handedness- where the nodes mesh together alternatively and symmetrically. The two head tetrons form the boundaries encompassing the internal BVs.
tetric: A division into four sets with two pairs of cards, 27 and 30.
tetron: The distinguished phrase which serves as the opening verse in all chps except for 1 and 9. In chp 1, it is verse one, and in chp 9 it is absent, where, it is compensated in chp 27, in which it appears both as the opening verse, and additionally, as the last part of verse 30. As an opening verse it is always unnumbered.
T-link: A pair of chps, where, one is the tux of the other one.
T:n: An isotupe with base verse n, for 3 ≤ n ≤ 286. In particular, n cannot take on arbitrary values. Only a subset of valid values within the specified range is allowed.
tron: The symmetric correspondence between pairs (EPK, OPN) and (EPN, OPK), where the high and low ordinal positions are cross mapped.
tupe: The number of chps in an isotupe. All monotupes are of tupe 1 and polytupes are of higher tupes.
tux: The ordinal positions of isotupes according to their base verses arranged in ascending order. All chps within a given isotupe are labeled with the same tux which is unique for each isotupe.
UC: Un-init Chp.
un-init: Un-initialed.
V-chain: A sequence of chps, where any two adjacent ones form a V-link.
vector: An ordered set or array of numbers.
veriant: An adjoin base verse that is not a base verse.
versor: The versor and cept are the symmetric counterpart of chp-verse pair, where the roles are reversed. A versor n consists of cepts, which themselves are C:n's; for those chps that contain verse n. Versor n can be thought of :n, where individual verses are tagged with their corresponding chps they belong to. The cepts within a versor may not in general be contiguous, since, not all chps contain a particular verse n. This in turn implies that the ordinal position of a cept C:n within a versor in general may be different from C.
vesp: The number of verses.
V-link: A pair of chps, where, one is the BV of the other one.
W-link: A pair of chps, where, one is the BW of the other one.
WS: Weighted Sum - the dot product of Gvec and Nvec.
X-link: A pair of numbers, where, one is the index of the other one.