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U.S. Patent Application No. 64/136,443 – USPTO
K.O.R.J.
C.O.D.E
1
C.O.D.E
METHOD
LIBERATION THROUGH THE MINUS
The second action in letter counting · five (5) points
Steven Korj · 2026
Here is one arithmetical action, the numbers it gives, three (3) limits it does not cross, and the program by which all of this was counted. Points one (1), two (2) and four (4) are open to a check right here in the text, except for one line, where it is stated how many word forms stand at one sum. Point three (3) is checked by a run of the program from point five (5): the count there goes over one billion six hundred eighty-two million six hundred sixty-seven thousand sixty-six (1,682,667,066) pairs, and nobody counts that many on paper.
1 · THE ACTION
Letter numbers were added up for more than a thousand (1000) years. Take the same word and the same table of values, but instead of addition do this.
Write out the numerical values of the letters of the word. Keep each distinct value once (1). Arrange them in descending order. Subtract the neighbours from top to bottom.
The first difference obtained is called the SUPPORT. The number of differences obtained is called the DEPTH. Nothing else has changed: not the table, not the values, not the order of the letters — only the last action.
If all the letters of a word carry one and the same value, it has one (1) distinct value, and there is nothing to subtract from: there is no support, the depth equals zero (0). Such words are not thrown out of the count, and two (2) words without a support are counted as matching by support. There are twenty-one (21) such words in the list, and two hundred ten (210) pairs among them — twelve millionths (0.000012) of a percent of all the pairs of the list. If that same rule is changed and two (2) "no support" are not counted as a match, the background of the support on the same list stays the same to the third (3) decimal place: four and eight hundred sixty-one thousandths (4.861) percent.
2 · THE VALUES OF THE LETTERS
alef 1 · bet 2 · gimel 3 · dalet 4 · he 5 · vav 6 · zayin 7 · chet 8 · tet 9 · yod 10 · kaf 20 · lamed 30 · mem 40 · nun 50 · samekh 60 · ayin 70 · pe 80 · tsadi 90 · qof 100 · resh 200 · shin 300 · tav 400.
The final forms ך ם ן ף ץ count as the ordinary letters: twenty (20), forty (40), fifty (50), eighty (80), ninety (90).
An example, to check. נחש, serpent: fifty (50), eight (8), three hundred (300). In descending order: 300, 50, 8. The support is two hundred fifty (250), the depth is two (2). משיח, the anointed one: forty (40), three hundred (300), ten (10), eight (8). In descending order: 300, 40, 10, 8. The support is two hundred sixty (260), the depth is three (3). The sums of both are three hundred fifty-eight (358).
3 · THE NUMBERS ON A LIST OF WORDS
Fifty-eight thousand twelve (58,012) of the most frequent Hebrew word forms are taken. The list comes with the publicly available library wordfreq, version 3.1.1: language he, function top_n_list, the top sixty thousand (60,000) entries, only those made of the signs of the basic row, with a length from two (2) up, were selected, repeats removed. This list is publicly available and current as of today, I did not compile it: it comes with the library as it is.
Between these word forms there are one billion six hundred eighty-two million six hundred sixty-seven thousand sixty-six (1,682,667,066) pairs. The pairs whose sums are equal are two million two hundred thirty-one thousand three hundred seventy-two (2,231,372).
Three (3) numbers for each gauge. SEPARATED — the share of the pairs of equal sum in which the value came out different. BACKGROUND — the share of matches among all the pairs of the list taken whole, without any selection by sum. LIFT — the share of matches at equal sums, divided by the background; in other words, how many times the equality of the sums raises the match.
gauge separated background lift
support 82.2 % 4.861 % 3.7
depth 70.2 % 25.125 % 1.2
both together 93.1 % 1.328 % 5.2
A check with the length of the word fixed. The pairs in which both the sum and the length are equal are five hundred fifty-nine thousand three hundred sixty (559,360). The support separates seventy-four and eight tenths (74.8) percent of them, and the background here is taken not as the general one but among the pairs of equal length, and equals five and one hundred fifty thousandths (5.150) percent. The lift comes out as four and nine tenths (4.9) — higher than three and seven tenths (3.7) without the length fixed.
The words "among all the pairs of the list taken whole" in the definition of the background are taken exactly. If the background is counted only over the pairs with different sums, it comes out otherwise. Both readings, at one and the same precision of three (3) decimal places, stand side by side.
background all pairs different sums difference
support 4.861 % 4.844 % 0.017
depth 25.125 % 25.119 % 0.006
both together 1.328 % 1.320 % 0.008
The difference in all three (3) is less than two (2) hundredths. The program prints both columns and the difference between them.
4 · THREE (3) LIMITS
The first (1). The support does not always separate widely. אחד, one, and אהבה, love: the sums are thirteen (13) each, the supports are four (4) and three (3) — a difference of one (1). The depth of both is two (2) and does not separate them at all.
The second (2). Several words can stand at one sum, and the support will not separate them all. At the sum three hundred ninety-five (395) there are eighty-two (82) word forms in the list. Let us take three (3) of them: שופט, judge, support two hundred twenty (220); שלטון, power, support two hundred fifty (250); נשמה, soul, support two hundred fifty (250). The judge is set apart by the support, but the power and the soul it does not separate: they have one support for the two (2) of them. They are separated by the depth, four (4) and three (3).
The third (3). The order of the letters and the repeats this action does not read. משה and השם — one and the same three (3) values: three hundred (300), forty (40), five (5). The support of both is two hundred sixty (260), the depth of both is two (2). Neither addition nor subtraction separates them. A repeated letter it does not read either: ים, sea, and מים, water, — the set of values of both is one and the same, forty (40) and ten (10), the support of both is thirty (30), the depth of both is one (1). They are separated only by the sum, fifty (50) and ninety (90).
5 · THE CODE
Below is the whole program by which everything above was counted. Install the library, save the lines into a file, run it. It prints the same numbers that stand above, and nothing beyond them.
# -*- coding: utf-8 -*-
# MINUS · the whole count of the short article
# pip install wordfreq==3.1.1
from wordfreq import top_n_list
from collections import Counter
# AZ runs in Unicode order: א ב ג ד ה ו ז ח ט י ך כ ל ם מ ן נ ס ע ף פ ץ צ ק ר ש ת
# In Unicode the FINAL form stands BEFORE the ordinary one: ך before כ, ם before מ,
# ן before נ, ף before פ, ץ before צ. That is why five values in ZN go in pairs:
# 20 20 · 40 40 · 50 50 · 80 80 · 90 90 — the final and the ordinary, one and the same.
AZ = [chr(c) for c in range(0x05D0, 0x05EB)] # 27 signs of the row
ZN = [1,2,3,4,5,6,7,8,9,10,20,20,30,40,40,50,50,
60,70,80,80,90,90,100,200,300,400] # the finals equal the ordinary ones
VAL = dict(zip(AZ, ZN))
def mery(w):
z = [VAL[c] for c in w]
u = sorted(set(z), reverse=True)
return (sum(z), # sum
u[0] - u[1] if len(u) > 1 else None, # support
len(u) - 1, # depth
len(w)) # length
seen, W = set(), []
for w in top_n_list('he', 60000):
if len(w) >= 2 and all(c in VAL for c in w) and w not in seen:
seen.add(w); W.append(w)
M = [mery(w) for w in W]
par = lambda n: n * (n - 1) // 2
vse = par(len(W))
slito = lambda kk: sum(par(v) for v in
Counter(tuple(m[k] for k in kk) for m in M).values())
print('word forms', len(W), '· all pairs', vse)
ravn = slito([0]); print('pairs of equal sum', ravn)
print(' gauge separated background lift')
for kk, imya in [([0,1],'support'), ([0,2],'depth'), ([0,1,2],'both together')]:
razvela = 100 * (1 - slito(kk) / ravn) # share of the separated pairs
fon = 100 * slito(kk[1:]) / vse # share of the matches among ALL pairs
print(' %-13s %5.1f %% %6.3f %% %.1f'
% (imya, razvela, fon, (100 - razvela) / fon))
# the same with the length fixed: pairs and background only among equal-length words
dl = slito([0,3])
razvela = 100 * (1 - slito([0,1,3]) / dl)
fon = 100 * slito([1,3]) / slito([3])
print('pairs of equal sum and equal length', dl)
print(' %-13s %5.1f %% %6.3f %% %.1f'
% ('support', razvela, fon, (100 - razvela) / fon))
# the second reading of the word "background": only the pairs with DIFFERENT sums
print('background under two readings, all numbers to three decimal places:')
print(' gauge all pairs different sums difference')
for kk, imya in [([1],'support'), ([2],'depth'), ([1,2],'both together')]:
# the columns are rounded to three places, and the difference is taken between them,
# so that every number of the table follows from its two neighbours
a = round(100 * slito(kk) / vse, 3)
b = round(100 * (slito(kk) - slito([0]+kk)) / (vse - ravn), 3)
print(' %-13s %8.3f %% %11.3f %% %9.3f' % (imya, a, b, round(a - b, 3)))
bez = [m for m in M if m[1] is None]
print('words with no support', len(bez), '· pairs among them', par(len(bez)),
'· share %.6f %%' % (100 * par(len(bez)) / vse))
c1 = Counter(m[1] for m in M)
print('background of the support if "no support" is not counted as a match: %.3f %%'
% (100 * sum(par(v) for k, v in c1.items() if k is not None) / vse))
print('word forms at the sum 395', sum(1 for m in M if m[0] == 395))
WHAT IS NOT SAID HERE
What these differences mean. Why the support of some words coincides and of others does not. Where one more action came from and who counted with it before. Whether it catches kinship where kinship is there — and by what experiment that is measured.
The answers are gathered in the mini-book "LIBERATION THROUGH THE MINUS".
THE INVITATION
The numbers are open, all of them to the last. The program is printed in full. The table of values lies in any reference book.
Count. Set your own checks. The three (3) places where the action separates weakly or does not separate at all stand in point four (4) — start from there.
The mini-book also holds the most detailed criticism of this work that has been written, and the answer to it.
Dear readers, this article is published in its original language on Zenodo.
Link: K.O.R.J. C.O.D.E 1 C.O.D.E: Высвобождение Минусом | Zenodo
U.S. Patent Application No. 64/136,443 – USPTO
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Steven Korj
Slava MCC
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