Revelation’s 82 Positions: Part 4 Reference Appendix

Revelation word counts · Part 4 reference appendix

This appendix keeps the numerical framework visible: every band in the original master grids, the calendar operations, the seal ladder, the full-sequence mirrors, and the chronological branches behind the main discussion. It distinguishes the source’s fixed data from alternative constructions and corrects explanatory arithmetic without changing the established word counts.

Part 4 · Main discussion

In this appendix

A. Definitions and calculation rules

The word token identifies an occurrence in the selected Greek word groups. Position identifies its place in the arranged model, including conceptual bookends. Band is the interval assigned to a position. The same occurrence can receive a weekly calendar label, a symbolic month label, and a scaled year band; those are separate assignments.

Term	Meaning in this study
MT / LXX / SP	Masoretic Text / Septuagint / Samaritan Pentateuch. Each chronological comparison requires its stated textual configuration.
W-grid	Seven-year bands beginning at spring 6 BC.
M-grid	Thirty-year bands beginning at spring 6 BC.
Weekly calendar	Seven-day bands placed in a 364-day, 30–30–31 quarterly arrangement.
Month label	The sequence Nisan through Adar, repeated every 12 M-grid positions. It does not supply a historical month for an AD event.
Quarter day	The fourth day beyond 360 within a completed 364-day year, counted as one after each three symbolic months.
Included / withheld	Whether the 10 thunder occurrences receive duration. The occurrences themselves remain counted in the inventory.
Anchored expansion	A converted number laid out as a new comparison span from a stated fixed anchor. It generates a model coordinate.
SKL	Sumerian King List, used here through an explicitly comparative chronology.

A1. Boundaries and inclusive labels

Use astronomical year coordinates only as a calculation device: an AD year A has coordinate A; a BC year B has coordinate 1 − B. Thus 6 BC has coordinate −5. This mathematical zero is the civil year 1 BC; it does not insert a civil “year zero.” With start coordinate s = −5 and band width u, position i begins at s + ui and ends at s + u(i + 1).

Start(i, u) = −5 + ui; End(i, u) = −5 + u(i + 1).

For chronology tables, “AD 25–55” means a 30-year interval between like-season boundaries. Adjacent bands share a boundary; they do not both contain a whole extra boundary year. A convenient interval notation is [25, 55), meaning “from 25 up to 55.” By contrast, the weekly date label Nisan 1–7 names seven consecutive days inclusively, from the start of day 1 to the start of day 8.

The earlier 81-band arrangement covers #0–80. Its M-grid midpoint is AD 1210, inside #40, and its end is AD 2425. Adding #81 gives 82 bands, with midpoint at the #40/#41 boundary, AD 1225, and end AD 2455. The corresponding W-grid midpoint of the full 82-band construction is AD 282. The index midpoint, a band’s center, and a shared band boundary cannot be exchanged merely because each can be called “the middle.”

For the compressed reading, retain the original lexical labels but use a second, compressed index. Positions #0–42 keep index i. Original #43–52 are withheld. Original #53–81 receive index i − 10. For example, original #53 becomes compressed index 43, and original #81 becomes compressed index 71. A 72-position mirror pairs compressed index k with 71 − k; it does not invariably pair original label i with 81 − i.

A2. Complete seven-year table

All 82 original bands are preserved. The 13 rows arrange positions by their place within a 91-unit block; they are not 13 separate seven-position groups. Reading each column downward gives the successive positions. The final column is necessarily incomplete.

Heptad Group	Cycle 1	Cycle 2	Cycle 3	Cycle 4	Cycle 5	Cycle 6	Cycle 7
Heptad 1	#0 (6 BC–AD 2)	#13 (AD 86–93)	#26 (AD 177–184)	#39 (AD 268–275)	#52 (AD 359–366)	#65 (AD 450–457)	#78 (AD 541–548)
Heptad 2	#1 (AD 2–9)	#14 (AD 93–100)	#27 (AD 184–191)	#40 (AD 275–282)	#53 (AD 366–373)	#66 (AD 457–464)	#79 (AD 548–555)
Heptad 3	#2 (AD 9–16)	#15 (AD 100–107)	#28 (AD 191–198)	#41 (AD 282–289)	#54 (AD 373–380)	#67 (AD 464–471)	#80 (AD 555–562)
Heptad 4	#3 (AD 16–23)	#16 (AD 107–114)	#29 (AD 198–205)	#42 (AD 289–296)	#55 (AD 380–387)	#68 (AD 471–478)	#81 (AD 562–569)
Heptad 5	#4 (AD 23–30)	#17 (AD 114–121)	#30 (AD 205–212)	#43 (AD 296–303)	#56 (AD 387–394)	#69 (AD 478–485)
Heptad 6	#5 (AD 30–37)	#18 (AD 121–128)	#31 (AD 212–219)	#44 (AD 303–310)	#57 (AD 394–401)	#70 (AD 485–492)
Heptad 7	#6 (AD 37–44)	#19 (AD 128–135)	#32 (AD 219–226)	#45 (AD 310–317)	#58 (AD 401–408)	#71 (AD 492–499)
Heptad 8	#7 (AD 44–51)	#20 (AD 135–142)	#33 (AD 226–233)	#46 (AD 317–324)	#59 (AD 408–415)	#72 (AD 499–506)
Heptad 9	#8 (AD 51–58)	#21 (AD 142–149)	#34 (AD 233–240)	#47 (AD 324–331)	#60 (AD 415–422)	#73 (AD 506–513)
Heptad 10	#9 (AD 58–65)	#22 (AD 149–156)	#35 (AD 240–247)	#48 (AD 331–338)	#61 (AD 422–429)	#74 (AD 513–520)
Heptad 11	#10 (AD 65–72)	#23 (AD 156–163)	#36 (AD 247–254)	#49 (AD 338–345)	#62 (AD 429–436)	#75 (AD 520–527)
Heptad 12	#11 (AD 72–79)	#24 (AD 163–170)	#37 (AD 254–261)	#50 (AD 345–352)	#63 (AD 436–443)	#76 (AD 527–534)
Heptad 13	#12 (AD 79–86)	#25 (AD 170–177)	#38 (AD 261–268)	#51 (AD 352–359)	#64 (AD 443–450)	#77 (AD 534–541)

A3. Complete thirty-year table

The seven columns arrange successive cycles of 12 symbolic months. Their headings describe model cycles, not additional literal years superimposed on the AD spans. An asterisk marks a quarter-ending month; it records where a quarter day is counted separately. The displayed bands themselves remain 30 years wide and are not silently enlarged to 31.

Symbolic Month	Yr 1	Yr 2	Yr 3	Yr 4	Yr 5	Yr 6	Yr 7
Nisan (1)	#0 (6 BC–AD 25)	#12 (AD 355–385)	#24 (AD 715–745)	#36 (AD 1075–1105)	#48 (AD 1435–1465)	#60 (AD 1795–1825)	#72 (AD 2155–2185)
Iyar (2)	#1 (AD 25–55)	#13 (AD 385–415)	#25 (AD 745–775)	#37 (AD 1105–1135)	#49 (AD 1465–1495)	#61 (AD 1825–1855)	#73 (AD 2185–2215)
Sivan (3)*	#2 (AD 55–85)	#14 (AD 415–445)	#26 (AD 775–805)	#38 (AD 1135–1165)	#50 (AD 1495–1525)	#62 (AD 1855–1885)	#74 (AD 2215–2245)
Tammuz (4)	#3 (AD 85–115)	#15 (AD 445–475)	#27 (AD 805–835)	#39 (AD 1165–1195)	#51 (AD 1525–1555)	#63 (AD 1885–1915)	#75 (AD 2245–2275)
Av (5)	#4 (AD 115–145)	#16 (AD 475–505)	#28 (AD 835–865)	#40 (AD 1195–1225)	#52 (AD 1555–1585)	#64 (AD 1915–1945)	#76 (AD 2275–2305)
Elul (6)*	#5 (AD 145–175)	#17 (AD 505–535)	#29 (AD 865–895)	#41 (AD 1225–1255)	#53 (AD 1585–1615)	#65 (AD 1945–1975)	#77 (AD 2305–2335)
Tishrei (7)	#6 (AD 175–205)	#18 (AD 535–565)	#30 (AD 895–925)	#42 (AD 1255–1285)	#54 (AD 1615–1645)	#66 (AD 1975–2005)	#78 (AD 2335–2365)
Cheshvan (8)	#7 (AD 205–235)	#19 (AD 565–595)	#31 (AD 925–955)	#43 (AD 1285–1315)	#55 (AD 1645–1675)	#67 (AD 2005–2035)	#79 (AD 2365–2395)
Kislev (9)*	#8 (AD 235–265)	#20 (AD 595–625)	#32 (AD 955–985)	#44 (AD 1315–1345)	#56 (AD 1675–1705)	#68 (AD 2035–2065)	#80 (AD 2395–2425)
Tevet (10)	#9 (AD 265–295)	#21 (AD 625–655)	#33 (AD 985–1015)	#45 (AD 1345–1375)	#57 (AD 1705–1735)	#69 (AD 2065–2095)	#81 (AD 2425–2455)
Shevat (11)	#10 (AD 295–325)	#22 (AD 655–685)	#34 (AD 1015–1045)	#46 (AD 1375–1405)	#58 (AD 1735–1765)	#70 (AD 2095–2125)
Adar (12)*	#11 (AD 325–355)	#23 (AD 685–715)	#35 (AD 1045–1075)	#47 (AD 1405–1435)	#59 (AD 1765–1795)	#71 (AD 2125–2155)

A4. Complete 364-day weekly calendar

This is the original 30–30–31 weekly assignment, with the 82 bands running for 574 days: one complete 364-day year plus 210 days. The calendar begins with #0 at Nisan 1–7; #52 begins the second year. The month and day labels are part of the symbolic model. They do not assign historical dates to Revelation’s composition or visions.

Symbolic Week	Q1 (Nisan-Sivan)	Q2 (Tammuz-Elul)	Q3 (Tishrei-Kislev)	Q4 (Tevet-Adar)	Q5 (Y2 Nisan-Sivan)	Q6 (Y2 Tammuz-Elul)	Q7 (Y2 Tishrei-Kis.)
Week 1	#0 (Nisan 1-7)	#13 (Tammuz 1-7)	#26 (Tishrei 1-7)	#39 (Tevet 1-7)	#52 (Nisan 1-7)	#65 (Tammuz 1-7)	#78 (Tishrei 1-7)
Week 2	#1 (Nisan 8-14)	#14 (Tammuz 8-14)	#27 (Tishrei 8-14)	#40 (Tevet 8-14)	#53 (Nisan 8-14)	#66 (Tammuz 8-14)	#79 (Tishrei 8-14)
Week 3	#2 (Nisan 15-21)	#15 (Tammuz 15-21)	#28 (Tishrei 15-21)	#41 (Tevet 15-21)	#54 (Nisan 15-21)	#67 (Tammuz 15-21)	#80 (Tishrei 15-21)
Week 4	#3 (Nisan 22-28)	#16 (Tammuz 22-28)	#29 (Tishrei 22-28)	#42 (Tevet 22-28)	#55 (Nisan 22-28)	#68 (Tammuz 22-28)	#81 (Tishrei 22-28)
Week 5	#4 (Nisan 29-Iyar 5)	#17 (Tammuz 29-Av 5)	#30 (Tishrei 29-Hesh. 5)	#43 (Tevet 29-Shev. 5)	#56 (Nisan 29-Iyar 5)	#69 (Tammuz 29-Av 5)
Week 6	#5 (Iyar 6-12)	#18 (Av 6-12)	#31 (Heshvan 6-12)	#44 (Shevat 6-12)	#57 (Iyar 6-12)	#70 (Av 6-12)
Week 7	#6 (Iyar 13-19)	#19 (Av 13-19)	#32 (Heshvan 13-19)	#45 (Shevat 13-19)	#58 (Iyar 13-19)	#71 (Av 13-19)
Week 8	#7 (Iyar 20-26)	#20 (Av 20-26)	#33 (Heshvan 20-26)	#46 (Shevat 20-26)	#59 (Iyar 20-26)	#72 (Av 20-26)
Week 9	#8 (Iyar 27-Sivan 3)	#21 (Av 27-Elul 3)	#34 (Heshvan 27-Kislev 3)	#47 (Shevat 27-Adar 3)	#60 (Iyar 27-Sivan 3)	#73 (Av 27-Elul 3)
Week 10	#9 (Sivan 4-10)	#22 (Elul 4-10)	#35 (Kislev 4-10)	#48 (Adar 4-10)	#61 (Sivan 4-10)	#74 (Elul 4-10)
Week 11	#10 (Sivan 11-17)	#23 (Elul 11-17)	#36 (Kislev 11-17)	#49 (Adar 11-17)	#62 (Sivan 11-17)	#75 (Elul 11-17)
Week 12	#11 (Sivan 18-24)	#24 (Elul 18-24)	#37 (Kislev 18-24)	#50 (Adar 18-24)	#63 (Sivan 18-24)	#76 (Elul 18-24)
Week 13	#12 (Sivan 25-31)	#25 (Elul 25-31)	#38 (Kislev 25-31)	#51 (Adar 25-31)	#64 (Sivan 25-31)	#77 (Elul 25-31)

The fixed weekday overlay employed in Part 2 puts Nisan 1 on Wednesday. The separate Sunday/Wednesday/Friday creation-day overlays discussed below are alternative points of reference, not three simultaneous weekday names for this table’s Nisan 1.

A5. Compressed boundaries and the two bookends

Original label	Compressed index	W-grid, included	W-grid, withheld	M-grid, included	M-grid, withheld
#0	0	6 BC–AD 2	6 BC–AD 2	6 BC–AD 25	6 BC–AD 25
#20	20	AD 135–AD 142	AD 135–AD 142	AD 595–AD 625	AD 595–AD 625
#21	21	AD 142–AD 149	AD 142–AD 149	AD 625–AD 655	AD 625–AD 655
#42	42	AD 289–AD 296	AD 289–AD 296	AD 1255–AD 1285	AD 1255–AD 1285
#53	43	AD 366–AD 373	AD 296–AD 303	AD 1585–AD 1615	AD 1285–AD 1315
#68	58	AD 471–AD 478	AD 401–AD 408	AD 2035–AD 2065	AD 1735–AD 1765
#69	59	AD 478–AD 485	AD 408–AD 415	AD 2065–AD 2095	AD 1765–AD 1795
#80	70	AD 555–AD 562	AD 485–AD 492	AD 2395–AD 2425	AD 2095–AD 2125
#81	71	AD 562–AD 569	AD 492–AD 499	AD 2425–AD 2455	AD 2125–AD 2155

At the seven-year scale, omitting 10 bands subtracts 70 years; at the 30-year scale, it subtracts 300. The band widths and the 6 BC anchor remain fixed. The same operation can be applied at other scales, but a festival alignment must then be recalculated rather than carried over automatically.

B. Calendar ratios and quarter-day accounting

B1. The three related ratios

Schematic measure	Day length	Ratio	Basic count relation	Calibrated day value
Priestly service model	336	25/23	23 → 25	336 × 25/23 = 8400/23
Prophetic measure	360	70/69	69 → 70	360 × 70/69 = 8400/23
Enochian measure	364	300/299	299 → 300	364 × 300/299 = 8400/23

The expressions in the final column are exactly equal. The factors 70/69, 25/23, and 300/299 are different operations on different input units, but their calibrated day value belongs to one rational family. With a comparison year of 365.2423 days, the shared value is about 0.0249087 day, or 35.87 minutes, shorter per year. This is an approximation to a tropical year; it cannot be described as perfect astronomical synchronization across unlimited time.

At the shared rational calibration, 69 reference years equal 70 schematic 360-day years; 23 reference years equal 25 schematic 336-day years; and 299 reference years equal 300 schematic 364-day years. The direction matters. Multiplying a day length by its ratio gives the comparison day length. Multiplying a count of reference years by the same ratio gives a larger count of shorter schematic years. Extending that new count from an anchor is a further modeling operation.

For example, the converted counts from 1656 are 1680 prophetic years and 1800 priestly years. Their common schematic duration is 1680 × 360 = 1800 × 336 = 604,800 days. The separate numerical identities 1680 = 5 × 336 and 1800 = 5 × 360 are also true, but they must not determine the calendar-unit labels of the converted counts. Key of 23, conversion table and unit explanation.

B2. The 299- and 293-year comparisons

The source’s 299-year comparison is retained as 299 → 300 on the 364-day scheme. It is not a further refinement beyond the shared rational value, since 364 × 300/299 = 8400/23 exactly. It also cannot be substituted into the 360-day year: 299 solar years do not approximately equal 300 years of 360 days.

The distinct calibration is 364 × 294/293 = 365.242320819… days. At the source’s comparison value of 365.2423 days, 294 × 364 = 107,016 days, while 293 × 365.2423 = 107,015.9939 days, a difference of 0.0061 day, or about 8.8 minutes, across the complete cycle. This displays the source’s numerical closeness without calling a rounded decimal an exact identity. The site’s File 53, §14A treats this as a calibration display within its Enoch accounting; it does not open an additional unrestricted chronological conversion operator.

The claim that 293 solar years nearly equal 294 336-day priestly years is not retained: those units do not agree. The 294/293 display concerns 364-day years. Nor does its close numerical fit show that a specific ancient community implemented a 293-year intercalation rule.

B3. Historical and symbolic calendar claims

The priestly number 24 is grounded in the course list of 1 Chronicles 24. Twice traversing 24 weekly courses yields 48 weeks, or 336 days. The Qumran texts incorporate priestly service cycles in a 364-day year, according to Jonathan Ben-Dov’s research account. This supports comparison between priestly rotation and annual calendar; it does not establish the entire two-rotation block as an independently attested civil year. Ben-Dov, 2015.

First Enoch 82:4–7, 11–20 describes 364 days, four additional days, and leaders assigned to the heavenly order. The names of the four seasonal leaders in the Charles translation are Mîlkî’êl, Hel’emmêlêk, Mêl’êjal, and Nârêl. Uriel is the revealer of the system. Equating the fourth church marker with Uriel is the study’s typological choice, not a name supplied by Revelation. The four days complete the schematic quarters; they do not by themselves correct the difference between 364 and a tropical year. 1 Enoch, primary text.

The reference to a 28-day lunar period in 1 Enoch 78:9 remains relevant as evidence that 28 occurs in the text’s lunar discussion. It does not establish 12 uniform 28-day months. The same chapter discusses differing lunar months. The equation 12 × 28 = 336 is therefore identified here as the numerical construction used in the study.

B4. Complete quarter-day counter

After n completed positions, the accumulated count is floor(n/3). The first additional day follows #2, the second follows #5, and so on. “After #11” and “before #12” refer to the same boundary. The table includes every completed group through #80; there is no 28th complete group within 82 positions.

Boundary	Group	Accumulated quarter days	Completed positions	Interpretive location
After #2	Church	1	3	First marker: after #2
After #5	Church	2	6
After #8	Church	3	9
After #11	Church	4	12	Fourth marker: after #11, before #12
After #14	Church	5	15
After #17	Church	6	18
After #20	Church	7	21	Church–seal boundary
After #23	Seal	8	24
After #26	Seal	9	27
After #29	Seal	10	30
After #32	Seal	11	33
After #35	Seal	12	36
After #38	Seal	13	39
After #41	Seal	14	42	Accumulated count within the seal group
After #44	Thunder	15	45
After #47	Thunder	16	48
After #50	Thunder	17	51
After #53	Trumpet	18	54
After #56	Trumpet	19	57
After #59	Trumpet	20	60
After #62	Trumpet	21	63
After #65	Trumpet	22	66
After #68	Trumpet	23	69	Trumpet–bowl boundary
After #71	Bowl	24	72
After #74	Bowl	25	75
After #77	Bowl	26	78
After #80	Bowl	27	81	Final complete group of three

There are seven quarter-day boundaries during the 22-position seal group: after #23, #26, #29, #32, #35, #38, and #41. The total from #0 is 14 at the end of #42. Thus 660 + 7 = 667 describes the seal group alone, whereas AD 1285 + 14 = AD 1299 describes a cumulative endpoint adjustment. They cannot be substituted for one another.

The general difference between M and W at the same boundary is 23n. Its 70/69 expansion adds n/3. When n is not divisible by three, that increase is fractional, while the count of completed quarter days remains an integer. The statement that the two counts agree exactly therefore applies at completed three-position boundaries, including n = 3, 21, and 69.

B5. Key-of-23 reference ladder

Factorization	Value	Use in the argument
23 × 1	23	Per-position M–W difference; also the increase at the 69-position boundary.
23 × 7	161	The square root in 25,921 = 161².
23 × 29	667	Seal-group duration 660 plus seven local quarter-day equivalents.
23 × 30	690	Exodus-related 30-unit steps.
23 × 40	920	Ascending route of the first seal-ladder row in E1.
23 × 60	1380	Selected MT/LXX chronological difference; also a seal-ladder value.
23 × 62	1426	Descending route of the first seal-ladder row.
23 × 69	1587	Difference between W and M after 69 positions.
23 × 72	1656	Difference between the ends of the compressed W and M grids.
23 × 90	2070	1929 BC → AD 142; or 1446 BC → AD 625. Also 69 × 30.
23 × 111	2553	1929 BC → AD 625.
23 × 120	2760	1446 BC → AD 1315.
23 × 140	3220	1922 BC → AD 1299.
(23 × 7)²	25921	25,920 + 1 = 49 × 23².

The 1380 comparison belongs to selected MT/LXX chronological configurations. It is not a claim that every LXX manuscript has the same Creation-to-Flood difference from MT. The 2553-year line measures Jacob’s 1929 BC departure coordinate to AD 625; the separate Danielic arch begins at 1926 BC and has length 2550. Both survive with their distinct anchors.

C. Chronological source tables and their qualifications

The following two tables preserve the date fields of the original Part 4 as a reference snapshot. They make its calculations reproducible; they are not a replacement for the current canonical chronology tables. In particular, cumulative lifespans, normal begetting chronology, rounded coordinates, and optional calendar overlays remain different families.

The main discussion follows the site’s normal MT settings: Creation endpoint 4114 BC, Flood 2458 BC, Abraham 2166 BC, 430 years in Egypt, and the 6 BC New Testament anchor. The +60 Terah option is not required to produce Abraham’s 2166 BC birth in that frame. The original regular table itself gives Terah 2236 BC and Abraham 2166 BC, a difference of 70. Its prose statement that a +60 addition establishes the same baseline was therefore inconsistent. Current chronological setting.

C1. Original cumulative chronology snapshot

The starred column records the original narrow cumulative range; the next column gives its broader seven-year window. The widths are model conventions involving the Aaron/Moses endpoints and Noah/Shem choices. Exodus 7:7 gives rounded ages of 83 and 80, but does not establish a precise 3.5-year birth interval. The 123.5 entry below belongs to the source’s seasonal construction; Aaron’s stated lifespan is 123 years.

Patriarch	3-yr gap of Aaron/Moses (BC)	7-yr Span forwarded	Lifespan (years)
Adam	*14009 – 14006	14011 – 14004	930
Seth	*13079 – 13076	13081 – 13074	912
Enos	*12167 – 12164	12169 – 12162	905
Kenan	*11262 – 11259	11264 – 11257	910
Mahalaleel	*10352 – 10349	10354 – 10347	895
Jared	*9457 – 9454	9459 – 9452	962
Enoch	*8495 – 8492	8497 – 8490	365
Methuselah	*8130 – 8127	8132 – 8125	969
(Flood) Lamech	*7161 – 7158	7163 – 7156	777
Noah	*6384 – 6381	6386 – 6379	950
Shem	*5434 – 5431	5436 – 5429	600
Flood to Arphaxad: “Shem, Ham & Japheth” allow ±2	*4834 – 4831	4836 – 4829	±2
Arphaxad	*4834-4831	4836-4829	438
Shelah	*4396 – 4393	4398 – 4391	433
Eber	*3963 – 3960	3965 – 3958	464
Peleg	*3499 – 3496	3501 – 3494	239
Reu	*3260 – 3257	3262 – 3255	239
Serug	*3021 – 3018	3023 – 3016	230
Nahor	*2791 – 2788	2793 – 2786	148
Terah	*2643 – 2640	2645 – 2638	***205
Abraham	*2438 – 2435	2440 – 2433	175
Isaac	*2263 – 2260	2265 – 2258	180
Jacob	*2083 – 2080	2085 – 2078	147
Levi	*1936 – 1933	1938 – 1931	137
Kohath	*1799 – 1796	1801 – 1794	133
Amram	*1666 – 1663	1668 – 1661	137
Aaron/Moses	*1530/1526	1531/1524	123.5/120
Death: Aaron/Moses	*1407/1406	NA	(Exodus *1446)
Joshua begins a new line	1296	NA	110

The “(Flood) Lamech” wording is an inherited source label and must not be mistaken for the Flood coordinate used in this article. The calculations use 4836 BC, the leading boundary of the displayed 4836–4829 Flood/Arphaxad window. The source’s narrow and broad Creation ranges are likewise distinct from the rounded 14006 BC reference used in its larger comparisons. Joshua’s final row begins a new construction, as the source says, rather than continuing the same patriarchal sum.

The original notes also discuss a 460-year addition for the LXX second Cainan, a 120-year MT/SP cumulative difference, and Terah’s 205/145-year alternatives. These are retained as variant operations requiring their own source configuration. Substituting 145 for 205 changes an otherwise fixed sum by 60 years; that substitution alone cannot remove a 120-year difference. A claim to complete reconciliation would need a second specified adjustment.

The proposed 120-year connection with Genesis 6:3 and the jubilee factor 3430 = 70 × 49 remain comparative observations. The snapshot does not supply enough paired endpoint detail to turn every statement in the old note into an independently specified calculation. The current cumulative appendix is the controlling reference for the broader method.

C2. Original regular chronology snapshot

The original dates and event notes are retained below. Dates marked “implicit,” or described as traditional or likely, remain interpretations within that source. They are not newly established biblical dates. The table’s Noah/Shem and Aaron rows also retain their original variant and seasonal labels; current normal settings should be consulted before combining them with another article’s dates.

(MT) Creation to the Flood
Patriarch/Event	Lifespan (BC)	Years Lived	Key Events
Creation	4121 – 4114	7	Seven days of Creation as years
Adam	4114 – 3184	930
Seth	3984 – 3072	912	*Cain’s birth (4115, 4113; mid. 4114); Abel’s birth (4046, 4044; mid. 4045) implicit. Inverse pattern of Terah’s age at Abram’s birth.
Enosh	3879 – 2974	905
Kenan	3789 – 2879	910
Mahalalel	3719 – 2824	895
Jared	3654 – 2692	962
Enoch	3492 – 3127	365
Methuselah	3427 – 2458	969
Lamech	3240 – 2463	777
Noah	3058 – 2108	950	See below note
“120 yrs to Flood”(2578-2458) FLOOD (2458 – 2457) Post-Flood to Abraham
Shem	2556 – 1956	600	See notes for Noah & Shem in LXX table concerning “2-yrs”
Arphaxad	2456 – 2018	438
Salah	2421 – 1988	433
Eber	2391 – 1927	464
Peleg	2357 – 2118	239	Tower of Babel (2357 with ±1 implied)
Reu	2327 – 2088	239
Serug	2295 – 2065	230
Nahor	2265 – 2117	148
Terah	2236 – 2031	205
Patriarchal Period
Abraham	2166 – 1991	175	Call of Abram (2091 BC), Covenant of Pieces (2081 BC), Covenant of Circumcision & Destruction of Sodom (2067 BC)
Sarah	2156 – 2029	127
Ishmael	2080 – 1943	137
Isaac	2066 – 1886	180	Wedding of Isaac (2026) *Sacrifice of Isaac within 7yr period (2051, 2049, 2046, 2044) implicit.
Jacob	2006 – 1859	147	Jacob flees Esau (1929 BC) Jacob works for wives (1929-1922-1915 BC) Jacob returns to Canaan (1909 BC) Gen. 48:1 implies 147th yr = 3 jub.; hence, 147th is fig. “Year of Jub” (1860-1859 BC)
Esau	2006 – ?	–	Esau marries (1966 BC)
Levi	1919 – 1782	137
Judah	1918 – 1789	129	Death year per tradition
Joseph	1915 – 1805	110	Joseph sold as slave (1898 BC) 7 years plenty (1885-1878 BC) 7 years famine (1878-1871 BC)
Benjamin	1906 – ?	–	Birth of Benjamin (likely 1906 BC)
Egypt to Exodus
Israelites in Egypt	1876 – 1446	430
Kohath	–	133
Amram	–	137
Aaron	1529 – 1406	123	Birth (summer of 1530 exact) Death (summer of 1407)
Moses	1526 – 1406	120	Birth (winter of 1526 exact) Flees to Midian (1486 BC) Exodus (1446 BC) Tabernacle (1445 BC) Death (winter of 1406)
Conquest (1406-1400 BC) First Sabbath year of rest (1399 BC) Conquest and Judges
Joshua, “And also וְגַם all that GENERATION died” (Judges 2:9-10)	1476 – 1366	110	“Generation” of 40-yrs implied (1406-1366)

The Shem entry 2556–1956 BC is the source’s displayed alternative; the site’s normal Gear-2 birth is 2558 BC, with Arphaxad fixed at 2456 BC. The Aaron row mixes civil-year and seasonal labels: the main article uses the normal 1530 BC birth and the biblical lifespan 123. No displayed range is used to revise the established lexical count.

The conjectural Cain and Abel dates, the Isaac-sacrifice window 2051–2044 BC with internal points 2049 and 2046, the Judah lifespan tradition, and the Benjamin date remain source proposals. The source links the sacrifice window with a 23 × 520 = 11,960-year comparison to cumulative Creation; a particular match requires the chosen endpoint in each window. These proposals are not necessary for the Part 4 token formulas.

C3. Additional anchors and creation-day overlays

Anchor or alternative	Value retained	Status
Restoration frame	538–536 BC	Series framework; Ezra 3 and Daniel 10 supply the related month references, not every BC assignment.
Backward grand-jubilee comparison	1028 BC → 538 BC = 490	A generated comparison; not the date of Solomon’s Temple.
Normal Temple reference	966 BC	Kept distinct from the 1028 BC comparison.
Jacob’s first labor term	1929–1922 BC	Source chronology; seven elapsed years.
Jacob-pivot	1926 BC	Integer comparison coordinate within that term; exact temporal midpoint is 1925.5 BC.
Danielic intermediate coordinate	666 BC	1926 − 666 =1260; 666 +625 −1=1290.
Alternate Creation comparison	3966 BC	3966 +355 −1=4320. Source’s asserted LXX attribution lacks a specified variant recipe here.
Figurative Abraham comparison	2136 BC	A deliberate 30-year shift from 2166; not Abraham’s normal birth date.
Creation overlay day 1	6 BC	Beginning of the modeled annual creation week.
Creation overlay day 4	3 BC	Fourth annual position of that overlay.
Creation overlay day 6	1 BC → AD 1	Sixth annual position; distinct from a historical date established by the token count.

The original three creation-day starting points are preserved as an overlay: day 1/Sunday at 6 BC, day 4/Wednesday at 3 BC, and day 6/Friday at 1 BC. Day 6’s annual band runs from spring 1 BC to spring AD 1. These positions arise by mapping a creation week onto seven years. Describing them as “priestly,” “Enochian,” and “Talmudic” does not, without separate evidence, establish that those ancient communities all used these exact Nisan or incarnation dates. The fixed Wednesday weekly grid in A4 remains a distinct arrangement.

The comparative 1656 pattern is strongest here in its explicit MT derivation. The original also assigns 1656 to Creation-to-Noah’s-birth in its selected LXX arrangement and Creation-to-Noah’s-death in SP/Jubilees comparisons. These are configuration-dependent claims. File 53’s SP discussion explicitly uses a one-year compression or an inclusive “600th-year” route; that qualification matters when presenting the number as shared across traditions. File 53, §14A.

D. Detailed token and macro-scale calculations

D1. Chronological branches at the seals and first trumpet

Comparison	Arithmetic	Result	Interpretation / branch
First seal: W–M boundary	625 −142	483 =69 ×7	×70/69 gives 490, increasing by 7.
Jacob departure to W seal boundary	1929 +142 −1	2070 =23 ×90	Distinct from the 1926 BC divided-week comparison.
Jacob departure to M seal boundary	1929 +625 −1	2553 =23 ×111	Unexpanded source span.
Jacob-pivot to intermediate point	1926 −666	1260	First Danielic arch.
Intermediate point to first seal	666 +625 −1	1290	Second Danielic arch.
Exodus to first seal	1446 +625 −1	2070	×70/69=2100; adds 30.
Alpha end to final seal end	1285 −25	1260	Unexpanded boundary.
Alpha end to expanded final seal	1315 −25	1290	Optional 30-year extension.
Seal-group duration	22 ×30	660	22 lexical seal tokens remain fixed.
Seal group with local quarter days	660 +7	667 =23 ×29	Separate adjustment branch.
Cumulative quarter-day endpoint	1285 +14	AD 1299	14 from the beginning of #0.
Jacob wedding to adjusted end	1922 +1299 −1	3220 =23 ×140	×25/23=3500.
Exodus to AD 1315	1446 +1315 −1	2760 =23 ×120 =69 ×40	×70/69=2800.
Seal beginning to AD 1315	1315 −625	690 =23 ×30	One more 30-year band beyond the 660-year group.
Exodus to AD 1285	1446 +1285 −1	2730 =7.5 ×364	First trumpet beginning when thunders withheld.
Jared to AD 1315	3654 +1315 −1	4968 =23 ×216	216=6 ×6 ×6.
Cumulative Creation endpoint to AD 1315	14004 +1315 −1	15,318 =23 ×666	Corrects the source’s displayed 15,320 arithmetic typo.
Conquest to first trumpet W beginning	1406 +366 −1	1771 =23 ×77	Full model.
Conquest to first trumpet M beginning	1406 +1585 −1	2990 =10 ×299	×300/299=3000, giving AD 1595.
Alpha anchor to adjusted trumpet boundary	1595 +6 −1	1600 =40 ×40 =4 ×400	Anchored expansion, not an altered observed event.

The original D1 heading called AD 1285–1315 the “first thunder” in the withheld scenario. That interval is #43 on the full M-grid and becomes original #53’s interval when thunders are withheld. In the compressed sequence it belongs to the first trumpet; an omitted thunder is not simultaneously a retained band.

The original Creation row printed a calculation ending “15,320” beside the value 15,318. The correct arithmetic is 14004 + 1315 − 1 = 15,318 = 23 × 666. The row’s endpoints and its intended factorization are preserved. Its Exodus row also confused the beginning and end of the AD 1285–1315 band: 2730 reaches AD 1285, while 2760 reaches AD 1315.

D2. Alpha, bowls, Omega, and covenant spans

From	To	Elapsed span	Role
2166 BC	6 BC	2160 =6 ×360	Abraham to the model anchor.
6 BC	AD 2155	2160 =72 ×30	Compressed M-grid through Omega.
2166 BC	AD 355	2520 =7 ×360	Through the beginning of #12; six units plus one.
3966 BC	AD 355	4320 =12 ×360	Alternative Creation comparison.
2166 BC	AD 715	2880	Beginning of #24; additional 100-fold magnification gives 288,000.
2136 BC	AD 745	2880	Figurative shifted anchor to #24’s end.
536 BC	AD 715 /AD 745	1250 /1280	The unchanged #24 boundaries do not produce 1290.
6 BC	AD 478 /AD 485	483 /490	Beginning and end of #69 on W.
1876 BC	AD 2425	4300 =10 ×430	Omega beginning, thunders included.
1876 BC	AD 2455	4330	Omega end, thunders included.
1876 BC	AD 2125	4000 =10 ×400	Omega beginning, thunders withheld.
1876 BC	AD 2155	4030	Omega end, thunders withheld.
AD 499	AD 2155	1656 =23 ×72	Compressed W–M endpoint difference.

The 4300/4000 pair is measured to Omega’s beginning. The 4330/4030 pair includes its whole 30-year band. The difference between scenarios is 300 years in either case. The 400 and 430 of Genesis 15 and Exodus 12 need not designate identical starting events; their 30-year numerical difference supplies the comparison without rewriting the MT’s 430-year Egyptian sojourn.

D3. Cumulative, generation, and pillar comparisons

From / operation	To / result	Span or equality	Qualification
4836 BC	6 BC	4830 ×70/69=4900	Cumulative Flood/Arphaxad leading coordinate.
4836 BC	AD 2065	6900 ×70/69=7000	First bowl M-grid beginning; expanded comparison.
4836 BC	AD 2095	6930 ×70/69=7030 +10/23	First bowl M-grid end; not 7000.
4830 +2160	6990	10 short of 7000	Unexpanded cumulative-to-compressed-end total.
1399 BC	AD 562	1960 =40 ×49	End#80 /start#81, full W-grid.
1399 BC	AD 492	1890 =1960 −70	Same boundary with thunders withheld.
1406 BC	AD 5595	7000	70-year scale, #80 beginning.
2456 BC comparison branch	AD 5595	8050 =7 ×1150	Endpoint recovery from original outline; branch family not inferred from date alone.
2106 BC comparison branch	AD 5735	7840 =16 ×490	70-year scale, #81 ending; same qualification.
6 BC	AD 29,515	29,520 =82 ×360	Full 360-year-per-position scale.
AD 715	AD 29,515	28,800 =400 ×72	M-grid#24 beginning to pillar.
1446 BC	AD 29,515	30,960 =430 ×72	Exodus to pillar.
AD 2425	AD 29,515	27,090 =21 ×1290 =63 ×430	Omega M-grid beginning to pillar.
262,086 BC	6 BC	262,080 =360 ×728 =360 ×(2 ×364)	Adam/Alulim comparative coordinate.

The 70-year scale’s three large comparisons require more precision than the original outline provided. Its 7000-year Conquest relation reaches #80’s beginning, AD 5595, not #81’s beginning at AD 5665. The 8050 and 7840 identities are recoverable using the comparison coordinates 2456 BC and 2106 BC; the table identifies them as that branch. With the normal 2458 and 2108 BC coordinates, those spans are 8052 and 7842. The shared labels 2456 and 2106 alone do not establish whether a particular source calculation came from a regular Gear-1 or rounded chronology. No family is silently substituted.

The source’s proposed pillar links with 1290 remain available at exact M-grid boundaries: AD 29,515 − AD 2395 = 27,120, which is not a multiple of 1290, while AD 29,515 − AD 2425 = 27,090 = 21 × 1290 = 63 × 430. The last equality reaches Omega’s beginning. Using AD 2455 gives 27,060, so the endpoint cannot be shifted casually.

The outline also proposed a 30,000-year comparison to a mirrored 605 coordinate. The original diagram supplies a leading pillar boundary, AD 29,395, in addition to AD 29,515. Using the signed coordinate −605 gives 29,395 − (−605) = 30,000. The later boundary instead gives 29,515 − (−605) = 30,120. Under A1’s astronomical notation, coordinate −605 means 606 BC; it should not be written as a negative BC year. Thus the 30,000-year branch uses the figure’s earlier pillar boundary and its explicitly stated reflection.

The 262,086 BC Adam/Alulim coordinate is a comparative construction. The primary King List names Alulim and gives a reign of 28,800 years, but does not give the BC coordinate or identify him with Adam. The model’s calculation to 6 BC is exact given its chosen anchor; the historical identification is a separate interpretation. Oxford Electronic Text Corpus of Sumerian Literature, King List.

D4. Precessional and further scale totals

Unit per position	82-position total	72-position total	Related observation
1 hour	82 hours	72 hours	The earlier 81+3-hour branch is separately described in F3.
1 day	82 days	72 days	Ordinal #80 is the 81st position when #0 is first.
7 units	574	504	504=7 ×72.
30 units	2460	2160	2160=30 ×72=(7+23) ×72.
70 years	5740 years	5040 years	Full Omega AD 5665–5735.
84 units per modeled priestly quarter	6888	6048	84=3 ×28; distinguish 91-day Enochian quarters.
360 years	29,520 years	25,920 years	72 ×360 is the schematic precessional circle.
1000 years	82,000 years	72,000 years	Further magnification;30 units would equal 30,000 years.
Cosmic circle plus one	25,921	161² =49 ×23²	Explicit symbolic addition to 25,920, not an astronomical measurement.

“Great month,” “great week,” and “star day” name the study’s analogy using 72 years per degree. Their totals are exact in that scheme. They are not precision measurements of an invariant celestial cycle. The 84-unit seasonal option follows the 336-day, four-quarter model; a season in the 364-day arrangement has 91 days. These two seasonal widths should not share an unqualified label.

At 1000 years per unit, a 30-unit symbolic month totals 30,000 years. The original outline names this further scale without completing every proposed comparison. It is preserved as an available scale, not a requirement that every other calendar operation produce the same result under every magnification.

E. Two explicit mirror constructions

“Atbash” refers by analogy to reversing an ordered series, as Hebrew Atbash pairs the first letter with the last. It is not a claim that these date equations are a literal cipher written in Revelation. The original Part 4 used two different reflections. Retaining its numerical results requires stating the axis of each rather than calling both simply “the BC/AD mirror.”

Construction	Coordinate reflection	Axis	Example
Local seal ladder	R(x) = 1 − x	x = 0.5	AD 142 becomes coordinate −141, the civil label 142 BC.
Whole-sequence mirror	R(x) = −x	x = 0	AD 25 becomes coordinate −25, the civil label 26 BC; 6 BC, coordinate −5, becomes +5.

A reflection around an independently specified date must use that date’s coordinate. For an axis a, the formula is R(x) = 2a − x. Choosing a different axis changes the resulting spans by twice the axis shift. In particular, reflection around the 6 BC model anchor, a = −5, produces the full band totals; it does not produce the constants in E3 below. These distinctions also separate symbolic reflections from actual years elapsed between historical events.

E1. The 22-position seal ladder

Let i run from 21 to 42, and pair it with j = 63 − i. For the descending path, reflect the W-grid start of i by 1 − x and measure to the M-grid end of j. The first row is AD 1285 − (−141) = 1426 = 62 × 23. The reflected value −141 is a coordinate, not a civil date written “−141 BC.”

The original ascending factor column uses a complementary endpoint choice. It is recovered by reflecting the W-grid end of j and measuring to the M-grid start of i. This gives the ascending factor 40 on the first row. The two routes are:

Descending D(i) = M-end(j) − [1 − W-start(i)] = 23(83 − i).
Ascending A(i) = M-start(i) − [1 − W-end(j)] = 23(i + 19).

Seal ordinals	Global labels	Reflected W start coordinate	Paired M end	Descending path	Ascending path
1 → 22	#21 → #42	-141	AD 1285	1426 = 62 ×23	920 = 40 ×23
2 → 21	#22 → #41	-148	AD 1255	1403 = 61 ×23	943 = 41 ×23
3 → 20	#23 → #40	-155	AD 1225	1380 = 60 ×23	966 = 42 ×23
4 → 19	#24 → #39	-162	AD 1195	1357 = 59 ×23	989 = 43 ×23
5 → 18	#25 → #38	-169	AD 1165	1334 = 58 ×23	1012 = 44 ×23
6 → 17	#26 → #37	-176	AD 1135	1311 = 57 ×23	1035 = 45 ×23
7 → 16	#27 → #36	-183	AD 1105	1288 = 56 ×23	1058 = 46 ×23
8 → 15	#28 → #35	-190	AD 1075	1265 = 55 ×23	1081 = 47 ×23
9 → 14	#29 → #34	-197	AD 1045	1242 = 54 ×23	1104 = 48 ×23
10 → 13	#30 → #33	-204	AD 1015	1219 = 53 ×23	1127 = 49 ×23
11 → 12	#31 → #32	-211	AD 985	1196 = 52 ×23	1150 = 50 ×23
12 → 11	#32 → #31	-218	AD 955	1173 = 51 ×23	1173 = 51 ×23
13 → 10	#33 → #30	-225	AD 925	1150 = 50 ×23	1196 = 52 ×23
14 → 9	#34 → #29	-232	AD 895	1127 = 49 ×23	1219 = 53 ×23
15 → 8	#35 → #28	-239	AD 865	1104 = 48 ×23	1242 = 54 ×23
16 → 7	#36 → #27	-246	AD 835	1081 = 47 ×23	1265 = 55 ×23
17 → 6	#37 → #26	-253	AD 805	1058 = 46 ×23	1288 = 56 ×23
18 → 5	#38 → #25	-260	AD 775	1035 = 45 ×23	1311 = 57 ×23
19 → 4	#39 → #24	-267	AD 745	1012 = 44 ×23	1334 = 58 ×23
20 → 3	#40 → #23	-274	AD 715	989 = 43 ×23	1357 = 59 ×23
21 → 2	#41 → #22	-281	AD 685	966 = 42 ×23	1380 = 60 ×23
22 → 1	#42 → #21	-288	AD 655	943 = 41 ×23	1403 = 61 ×23

The pair factors sum to 102 in each row; the path spans sum to 2346 = 102 × 23. At i = 32, the two directed routes both give 1173 = 51 × 23. This is the arithmetic equality highlighted by the source. It occurs in the directed #32 → #31 row.

The ordered center of 22 seal tokens is the boundary between #31 and #32, the 11th and 12th seal occurrences. The source sometimes called it #32/#33 and associated that boundary with the pause before the seventh seal. That was a different boundary. The token list locates #31 at Revelation 6:12, #32 at Revelation 7:2, and #33–37 at Revelation 7:3–8; #38 is the opening of the seventh seal in Revelation 8:1. The protected references allow a broad sixth-to-seventh-seal association, but not the statement that all these boundaries are identical.

The source table displayed 11 forward pairs and then the reverse #32/#31 row, which it called the “central pivot.” The complete directed table above preserves its values and exposes the endpoint convention that generates the 51 × 23 equality. The narrative comparison with ascending and descending angels remains a typological interpretation of this ladder.

E2. The whole-sequence mirror

For N bands of width u, pair index i with N − 1 − i. Reflect the first band’s start by R(x) = −x, then measure to the paired band’s end. The result is independent of i:

[−5 + u(N − i)] − [5 − ui] = Nu − 10.

This proves the constant within the chosen construction. The minus 10 comes from the doubled −5 anchor coordinate. It is not 10 missing years of elapsed history. For the 82-position model, the reversed index center is the #40/#41 boundary. For the 72-position model, it is compressed #35/#36; the original labels there are also #35/#36 because the withheld thunders occur later.

First label	Reflected M start coordinate	Partner,82 positions	M end,82	Path span	Partner,72 positions	M end,72	Path span
#0	5	#81	AD 2455	2450	#81	AD 2155	2150
#1	-25	#80	AD 2425	2450	#80	AD 2125	2150
#2	-55	#79	AD 2395	2450	#79	AD 2095	2150
#35	-1045	#46	AD 1405	2450	#36	AD 1105	2150
#40	-1195	#41	AD 1255	2450	#31	AD 955	2150

The source’s full-model row #40 ↔ #41 correctly uses AD 1255 as the paired M-grid end. Its withheld counterpart AD 955 is also retained, but belongs to original #31, the correct reversed partner of #40 after compression. Relabeling original #41 as AD 955 would change an unchanged pre-thunder band. The table therefore gives each scenario’s actual partner.

E3. Paired paths and mixed-scenario means

Scale / scenario	One path	Two equal paths	Mixed-scenario sum / mean
M:82 positions	82 ×30 −10=2450	4900	2450+2150=4600; mean 2300
M:72 positions	72 ×30 −10=2150	4300	4600 ×25/23=5000
W:82 positions	82 ×7 −10=564	1128	564+494=1058; mean 529=23²
W:72 positions	72 ×7 −10=494	988	Same mixed mean 529

For the M-grid, the two identical full-model paths sum to 4900; the withheld-model paths sum to 4300. These are sums of two constructed path lengths, not a claim that one ordinary historical interval from Alpha to Omega contains that many years. The author’s terms “half” and “full circuit” refer to this two-path display.

The mixed-scenario M-grid sum is 2450 + 2150 = 4600; its mean is 2300, recalling Daniel 8:14. Applying 25/23 to 4600 gives 5000, which can be expressed as 100 units of 50. This last use of 50 is distinct from the 49-year jubilee-cycle convention used in the 2450 = 50 × 49 display.

The mixed W-grid sum is 564 + 494 = 1058; its mean is 529 = 23². For #1, the original illustration is reproduced by AD 562 − (−2) = 564 in the full model and AD 492 − (−2) = 494 in the compressed model. At each scale, the mean follows from the same fixed formula with N = 82 and 72. It is therefore a compact invariant of the construction rather than a separately discovered fact in every row.

The source describes the seal mirror as Alpha-to-Tav and the complete mirror as Alpha-to-Omega. Both express reversal, but they employ different reflections and, in the local ladder, different grid widths and endpoint choices. Their theological kinship should not obscure their mathematical differences.

F. Festival positions and hour-scale continuation

F1. Fixed positions retained from the tables

Position	Weekly table	M-grid month label	Interpretive association
#2	Nisan 15–21	Sivan	Passover/Unleavened Bread week on the weekly scale.
#12	Sivan 25–31	Nisan	Church-address center; proposed Paschal center on the month scale.
#24	Elul 18–24	Nisan	Elder’s announcement; a different scale supplies each label.
#26	Tishri 1–7	Sivan	First seal opened at the model’s autumn festival beginning.
#27	Tishri 8–14	Tammuz	Week containing Tishri 10/Atonement.
#28	Tishri 15–21	Av	Tabernacles week.
#29	Tishri 22–28	Elul	Week beginning with the eighth-day assembly.
#42	Tevet 22–28	Tishri	Final seal occurrence; Tabernacles association belongs to month scale.
#62	Sivan 11–17,year 2	Sivan	Third trumpet,Rev 8:10; week contains the model’s Sivan 15.
#68	Tammuz 22–28,year 2	Kislev	Seventh trumpet,Rev 11:15; not Pentecost week in this table.
#80	Tishri 15–21,year 2	Kislev	Final bowl occurrence,Rev 21:9; Tabernacles/New Jerusalem association.
#81	Tishri 22–28,year 2	Tevet	Added Omega; begins with Tishri 22 on weekly scale.

The table deliberately retains #62 and #68 in their established places. It does not repair the source’s Pentecost claim by moving the seventh trumpet. Sivan 15 is the model’s fixed festival label; the historical and inclusive-count conventions behind it are explained in Part 2. With Wednesday Nisan 1 and two initial 30-day months, counting 50 days inclusively from Nisan 26 reaches Sivan 15. Counting instead from the Sunday Nisan 19 during Unleavened Bread reaches Sivan 8. These starting conventions cannot be combined.

The midmonth description of #12 and #24 is also a matter of convention. The start of ordinal day 15 occurs after 14 completed days; the midpoint boundary of an exactly 30-day interval occurs after 15. The phrase “Passover axis” names the proposed festival focus in the middle of the band, not an assertion that all time-of-day endpoints coincide.

The original outline suggested further Hanukkah connections at #80/#81 on the M-grid, using 1150/2300 spans to #42’s Tishri month and #4’s Av month. The month assignments survive: #80 is Kislev, #81 Tevet, #42 Tishri, and #4 Av. The proposed day labels require an additional rule. The M-grid starts of #4 and #42 are 1140 years apart; shifting an endpoint by 10 yields 1150, and doubling yields 2300. A particular Av 10, Tabernacles, or Hanukkah comparison must specify whether day labels are counted inclusively or as elapsed offsets. The source did not provide a complete endpoint derivation here, so the connection remains a proposed branch rather than a completed exact alignment.

F2. The 1335, Pentecost, and Sinai extension

Daniel 12:12 supplies 1335; the comparison with 1260 yields 75. With Nisan and Iyar each 30 days, Sivan 15 is day 75 by ordinal count. An extension of 75 elapsed days from a year’s beginning finishes at the end of that day; 74 elapsed days reach its beginning. No festival coordinate follows from 1260 + 75 unless the ending of 1260 and the day-boundary convention have been established.

The related Sinai model treats days 75–81 as seven days inclusively and identifies #80, the 81st position when #0 counts as the first day, with the seventh day of waiting. This is a symbolic placement of Exodus 24:16, which records the six days and the call on the seventh. The passage does not provide the Nisan-based day number used in the construction. The connection with the two witnesses likewise combines the text’s resurrection imagery with a festival reading, not an explicit Pentecost date in Revelation 11.

F3. The earlier 81 + 3 hour proposal

The original Appendix F was subsequently developed into Part 5. Its compact arithmetic remains part of the source history: the 81 bands #0–80, read as hours, plus three hours of darkness give 84 hours, or 3.5 days. The three hours refer to the sixth-to-ninth-hour darkness in Matthew 27:45. Revelation 11:9–11 supplies a separate 3.5-day period for the two witnesses.

Component	Duration	Qualification
#0–80 read as hour bands	81 hours	The earlier construction omits the additional Omega band #81.
Darkness comparison	3 hours	An additional symbolic component; not an unnoticed gap in the token inventory.
Combined symbolic total	84 hours = 3.5 days	81 + 3 = 84 exactly.
Two witnesses	3.5 days	The period stated in Revelation 11; compared typologically with the cross.

This does not establish an 84-hour elapsed burial interval for Jesus. Nor can the three hours be added to an 82-band arrangement while retaining the same total. Part 5 distinguishes centered hour bands, mirrored positions, and the historical Passion narrative before extending the comparison. The original statement that all scales “must” yield the same harmonies has therefore been replaced with the more limited claim that each scale can be examined under its own explicit rules.

F4. Structural proportions

Relationship	Result	Proposed comparison
Seals + trumpets + bowls	22 + 16 + 12 = 50	Jubilee/Pentecost number
Full framework minus seals	82 − 22 = 60	Sexagesimal unit; the source invokes the Babylonian sos
Compressed framework minus seals	72 − 22 = 50	Another expression of the 50 comparison
Alpha + thunders + Omega	1 + 10 + 1 = 12	12 × 30 = 360 units

The equations describe group proportions. Their association with release, festival counting, or sexagesimal timekeeping is the interpretive step. The 50th-year language of Leviticus 25 and the 50-day count of Leviticus 23 remain distinct from an elapsed 49-year jubilee interval; the source uses both numbers in different comparisons.

G. Sources and scope

The controlling local source is the original Part 4, read with Parts 1–3 and 5. The full originals accompany the editorial package so that every substantive branch can be traced. The source’s repeated outline, drafting instructions, duplicate conclusions, unfinished figure instructions, and statements of mathematical inevitability as proof of divine authorship have been consolidated into an explicit argument and reproducible reference tables.

Primary biblical checks use the public-domain World English Bible, especially Daniel 8–12; Ezra 3; Revelation 1, 5–12, 21–22; Genesis 15, 28–29; Leviticus 23 and 25; and Exodus 24. Calendar qualifications refer to 1 Enoch 78 and 82 and Jonathan Ben-Dov, “Astronomy and Calendars at Qumran” (2015). Astronomical and comparative qualifications use NASA’s account of precession and Oxford’s Sumerian King List translation.

For the site’s current chronological conventions, consult The Key of 23 appendix, the cumulative chronology appendix, and the Unified Chronology source index. The Revelation study remains an exploratory numerical and theological reading. Its alternatives and expanded coordinates do not silently revise those controlling chronology files.

Part 4 · Main discussion

Reference appendix prepared with the complete Part 4 replacement. Established lexical counts, occurrence labels, and the three master grids are preserved. Explicit changes concern definitions, arithmetic, endpoint labels, historical qualifications, and the presentation of speculative interpretations.