File_52b: Technical Tables for Inverse-Number Architecture

https://490d.com/file_52a-inverse-number-architecture-of-the-rounded-chronology/

This file is the technical supplement to File_52a. File_52a states the architecture. File_52b supplies the dense tables, constrained chains, and secondary corroborations. The two files are meant to be read together.

1. Operational rules

Base-10 reversal rule. The difference between a number and its digit-reversal is divisible by 9.
Rounded inverse axiom. When a rounded span is inverted and the result falls off the mod-5 lattice, normalize it to the nearest multiple of 5 before reapplying it chronologically.
Placeholder rule. Leading-zero reversals retain decimal placeholder force. Thus 30 → 30, 60 → 60, 100 → 100, 500 → 500, 130 → 310, 240 → 420, 230 → 320.
Anchor rule. The regular inverse chains are reckoned from 1406 BC or 1446 BC as specified. The cumulative inverse lifespan chain is reckoned from 1406 BC.

2. Macro event tables

2.1 Regular trunk and primary inverse

Node	Date	Forward span	Inverse span	Rebuilt inverse node
Creation	4106 BC	1650	5610	12026 BC
Flood	2456 BC	1050	5010	6416 BC
Conquest	1406 BC	—	—	1406 BC

Rebuilt inverse line:

12026 BC → 6416 BC → 1406 BC

2.2 Regular corroborating backbone

Segment	Forward	Inverse
Creation → Noah birth	1050	5010
Noah birth → Flood	600	600
Flood → Conquest	1050	5010
Total	2700	10620

1406 + 10620 = 12026 BC

2.3 Regular main branch: Creation / Jared / Flood / Abraham / Conquest

Node	Date	Forward span	Inverse span	Rebuilt inverse node
Creation	4106 BC	460	640	12746 BC
Jared	3646 BC	1190	9110	12106 BC
Flood	2456 BC	290	920	2996 BC
Abraham	2166 BC	760	670	2076 BC
Conquest	1406 BC	—	—	1406 BC

Rebuilt inverse line:

12746 BC → 12106 BC → 2996 BC → 2076 BC → 1406 BC

2.4 Secondary Entry branch from the Exodus anchor

Node	Date	Forward span	Inverse span	Rebuilt inverse node
Creation	4106 BC	460	640	13376 BC
Jared	3646 BC	1190	9110	12736 BC
Flood	2456 BC	290	920	3626 BC
Abraham	2166 BC	290	920	2706 BC
Entry	1876 BC	430	340	1786 BC
Exodus	1446 BC	—	—	1446 BC

Rebuilt inverse line:

13376 BC → 12736 BC → 3626 BC → 2706 BC → 1786 BC → 1446 BC

2.5 Cumulative trunk and primary inverse

Node	Date	Forward span	Inverse span	Rebuilt inverse node
Creation	14006 BC	9170	7190	12026 BC
Flood	4836 BC	3430	3430	4836 BC
Conquest	1406 BC	—	—	1406 BC

Rebuilt inverse line:

12026 BC → 4836 BC → 1406 BC

2.6 Secondary cumulative inverse: emergence of 13016 BC

Shem-centered decomposition

Segment	Forward	Inverse
Creation → Shem	8570	7580
Shem → Flood	600	600
Flood → Conquest	3430	3430
Total rebuilt	—	11610

1406 + 11610 = 13016 BC

Noah-centered decomposition

Segment	Forward	Inverse
Creation → Noah	7620	2670
Noah → Flood	1550	5510
Flood → Conquest	3430	3430
Total rebuilt	—	11610

1406 + 11610 = 13016 BC

2.7 Cumulative main branch: Creation / Jared / Flood / Abraham / Conquest

Forward cumulative rounded sequence:

Creation 14006 BC
Jared 9456 BC
Flood 4836 BC
Abraham 2431 BC
Conquest 1406 BC

Forward spans:

Segment	Forward span
Creation → Jared	4550
Jared → Flood	4620
Flood → Abraham	2405
Abraham → Conquest	1025

Raw inversion:

Forward	Raw inverse	Mod-5 inverse used
4550	5540	5540
4620	2640	2640
2405	5042	5040
1025	5201	5200

Rebuilt cumulative branched inverse line:

Inverse node	Date
Inverse Creation	19826 BC
Inverse Jared	14286 BC
Inverse Flood	11646 BC
Inverse Abraham	6606 BC
Conquest anchor	1406 BC

3. Rounded begetting-age inverse table (regular fine print)

This table uses only the rounded begetting ages from Adam through Isaac, with Jacob retained as the terminal son-date at 2006 BC. Joseph’s 91→90 is noted but is not part of the Adam-to-Moses begetting-father chain.

Patriarch	Beg. (rounded)	Inverse used
Adam	130	310
Seth	105	500
Enosh	90	90
Kenan	70	70
Mahalalel	65	55
Jared	160	610
Enoch	65	55
Methuselah	185	580
Lamech	180	810
Noah	500	500
Shem	100	100
Arphaxad	35	55
Shelah	30	30
Eber	35	55
Peleg	30	30
Reu	30	30
Serug	30	30
Nahor	30	30
Terah	70	70
Abraham	100	100
Isaac	60	60
Jacob (terminal son-date)	—	—
Joseph*	90	90

4. Full regular inverse begetting chronology

Jacob remains 2006 BC, since Jacob is 600 years before 1406 BC and is the final specified son-date in the Adam-to-Moses begetting chain.

Order	Node	Beg. (rounded)	Inverse used	Inverse date (BC)
0	Jacob	—	—	2006
1	Isaac	60	60	2066
2	Abraham	100	100	2166
3	Terah	70	70	2236
4	Nahor	30	30	2266
5	Serug	30	30	2296
6	Reu	30	30	2326
7	Peleg	30	30	2356
8	Eber	35	55	2411
9	Shelah	30	30	2441
10	Arphaxad / Flood	35	55	2496
11	Shem	100	100	2596
12	Noah	500	500	3096
13	Lamech	180	810	3906
14	Methuselah	185	580	4486
15	Enoch	65	55	4541
16	Jared	160	610	5151
17	Mahalalel	65	55	5206
18	Kenan	70	70	5276
19	Enosh	90	90	5366
20	Seth	105	500	5866
21	Adam	130	310	6176
22	Adam apparent age	30	30	6206

5. Key spans from the regular inverse begetting line

Relation	Span	Reading
6176 → 2496	3680	25/23 → 4000
2496 → 2066	430	Flood to Isaac
2596 → 2166	430	Shem to Abraham
6176 → 1876	4300	430×10
1876 → 1446	430	historical 430
6176 → 1446	4730	430×11
3096 → 1446	1650	old Creation→Flood trunk relocated
2496 → 1446	1050	old Creation→Noah trunk relocated
2496 → 2006	490	Jacob / 7 / 70 grammar
2496 → 536	1960	40×49 = 4×490
4541 → 2091	2450	5×490
4541 → 1991	2550	1260 + 1290
6206 → 1406	4800	120×40
5866 → 966	4900	10×490
6176 → 4106	2070	23×90
2070×70/69	2100	exact
6206 → 4136	2070	Adam apparent age carried over
4106 → 2496	1610	23×70

6. Regular inverse branch audit values

6.1 Primary inverse Creation 12026 BC

Relation	Span	Reading
12026 → 1446	10580	23×460
10580×25/23	11500	exact
12026 → 1526	10500	exact
12026 → 1406	10620	29.5×360
12026 → 4106	7920	22×360
14006 → 12026	1980	5.5×360
1980 + 7920	9900	exact
6416 → 2456	3960	11×360
3960 : 7920	1:2	Flood bridge : Creation bridge

6.2 Branched inverse Creation 12746 BC

Relation	Span	Reading
12746 → 12026	720	exact
12746 → 6	12740	35×364 = 26×490
12746 → 14006	1260	exact
12746 → 4106	8640	24×360
12746 → 2456	10290	343×30
12746 → 1406	11340	1260×9
12746 → 1476	11270	23×490
15446 → 1446	14000	7000 + 7000
15446 → 1406	14040	39×360

6.3 Branched inverse Jared 12106 BC

Relation	Span	Reading
3646 → 6	3640	10×364
12746 → 3646	9100	25×364
12106 → 1526	10580	23×460
12106 → 4106	8000	exact
12106 → 2106	10000	exact

6.4 Secondary Entry branch values

Relation	Span	Reading
2706 → 1446	1260	exact
2706 → 6	2700	exact
13376 → 1876	11500	exact
2996 → 6	2990	23×130
2076 → 6	2070	230×9

7. 2nd Cainan overlay on the regular inverse begetting line

If 2nd Cainan is reinserted into the MT line with begetting age 130, then 130 → 310 on the inverse rail. The effect is to add +310 to the inverse dates prior to Arphaxad. The resulting overlay is unexpectedly robust.

7.1 Key overlay nodes

Node	Base inverse date	+310 overlay	Key returns
Flood	2496	2806	1400 to 1406; 2800 to 6
Noah	3096	3406	2000 to 1406; 1960 = 4×490 to 1446
Seth	5866	6176	4300 to 1876
Adam	6176	6486	6480 = 18×360 to 6; 5040 = 2520+2520 to 1446; 4320 to 2166
Adam apparent age	6206	6516	extension of the same rail

7.2 Shem-death and 350 note

A related adaptive value is 350:

40 + 310 = 350
1050 = 3×350
2356 → 2006 = 350
2106 + 350 = 2456
Shem death 1956 + 40 + 310 = 2306

Key returns from 2306 BC:

Relation	Span	Reading
2306 → 6	2300	exact
2306 → 1406	900	exact
2306 → 1876	430	exact

Thus 350 appears to be an intrinsic fitting-number, not merely a byproduct of the Cainan displacement.

8. Full cumulative inverse lifespan chronology

The same inverse rules are now applied to the rounded lifespans of the 26 patriarchs, reckoned from the 1406 BC anchor.

#	Patriarch	Rnd. Life	Raw inverse	Inverse used	Inverse date (BC)
—	Moses (death) anchor	—	—	—	1406
26	Moses	120	021	210	1616
25	Amram	135	531	530	2146
24	Kohath	135	531	530	2676
23	Levi	135	531	530	3206
22	Jacob	145	541	540	3746
21	Isaac	180	081	810	4556
20	Abraham	175	571	570	5126
19	Terah	205	502	500	5626
18	Nahor	150	051	510	6136
17	Serug	230	032	320	6456
16	Reu	240	042	420	6876
15	Peleg	240	042	420	7296
14	Eber	465	564	565	7861
13	Shelah	435	534	535	8396
12	Arphaxad	440	044	440	8836
—	Flood	—	—	—	8836
11	Shem	600	006	600	9436
10	Noah	950	059	590	10026
9	Lamech	775	577	575	10601
8	Methuselah	970	079	790	11391
7	Enoch	365	563	565	11956
6	Jared	960	069	690	12646
5	Mahalalel	895	598	600	13246
4	Kenan	910	019	190	13436
3	Enosh	905	509	510	13946
2	Seth	910	019	190	14136
1	Adam	930	039	390	14526
—	Adam apparent age	30	03	30	14556

Totals:

Span	Total
Adam inverse → Moses death	13120
Adam apparent-age inverse → Moses death	13150

9. Key spans from the cumulative inverse lifespan line

9.1 Flood and Shem rail

Relation	Span	Reading
8836 → 4836	4000	inverse cum Flood to original cum Flood
9436 → 4836	4600	inverse Shem to original cum Flood
9436 → 6	9430	23×410
8836 → 6	8830	exact

9.2 Jacob / Levi / Abraham rail

Relation	Span	Reading
3746 → 1446	2300	exact
3746 → 1406	2340	6.5×360
3206 → 1406	1800	exact
5126 → 1526	3600	exact
5126 → 1446	3680	25/23 → 4000
5126 → 3746	1380	60×23

9.3 Creation-side notes

Relation	Span	Reading
14526 → 14006	520	13×40
14526 → 1526	13000	exact
14556 → 1446	13110	23×570
14526 → 1296	13230	270×49
14556 → 1406	13150	exact

10. Cumulative branch audit values

10.1 13016 BC rail

Relation	Span	Reading
14006 → 13016	990	exact
13016 → 12026	990	exact
12026 → 4106	7920	8×990
13016 → 1406	11610	1290×9 = 430×27

Thus:

14006 / 13016 / 12026 / 4106
990 + 990 + 7920 = 9900

10.2 Branched cumulative inverse nodes

Node	Date	Key spans
Inverse Creation	19826 BC	19826 → 12026 = 7800 = 3900 + 3900
Inverse Jared	14286 BC	12880 = 28×460 = 23×560 to 1406; 4830 to 9456; 4830×70/69 = 4900
Inverse Flood	11646 BC	10120 = 23×440 to 1526; 10240 = 40×2^8 to 1406
Inverse Abraham	6606 BC	5160 = 430×12 to 1446; 4730 = 430×11 to 1876; 5200 = 13×400 to 1406

11. 2nd Cainan overlay on the cumulative inverse lifespan line

If 2nd Cainan is reinserted into the cumulative inverse lifespan line, his lifespan 460 inverts to 640. Since Shelah’s inverse date is 8396 BC, Cainan is placed 640 years earlier.

Node	Base inverse date	Cainan increment	Overlay date
Shelah	8396	—	8396
Cainan	—	640	9036

Key returns:

Relation	Span	Reading
9036 → 3746	5290	23×230
3746 → 1446	2300	exact
9036 → 1446	7590	23×330 = 69×110

This placement is especially apt because Cainan’s own structure is 130 + 330 = 460.

Creation-side Cainan extension. The cumulative inverse Adam node 14526 BC, when expanded by Cainan’s inverted lifespan 460 → 640, yields 15166 BC. This extension appears to fit the inverse architecture unusually well. From 15166 BC to the Exodus 1446 BC are 13720 years = 343×40 = 7×7×7×40 = 28×490, so the span is governed both by the cube of seven and by the 490-family. The remaining 40 years to the Conquest preserve the Exodus–Conquest relation already central to the system. From 15166 BC to the Conquest 1406 BC are 13760 years = 430×32. Moreover, if actual cumulative Creation is likewise expanded by Cainan’s literal 460 years, then 14006 + 460 = 14466 BC, and 15166 BC → 14466 BC = 700 exactly. Thus the Cainan extension does not merely lengthen the inverse cumulative Creation rail; it relocates it onto the heptadic, 490, and 430 families in a way that appears more integrated than the unextended 14526 BC node.

12. Mirror compatibility notes

One example suffices to show that the inverse rails also pass the mirror test.

12.1 Inverse Flood mirror

Relation	Span	Reading
6176 → 2496	3680	25/23 → 4000
2496 BC + 4000	AD 1405	mirror of 1406 BC
3096 BC → AD 1405	4600	inverse Noah to mirror of Conquest

Thus the inverse line remains interoperable with the bidirectional mirror system.

13. Methodological conclusion

The significance of the inverse system does not rest on a few selected macro-nodes such as Creation, Flood, Abraham, Entry, Conquest, and Christ. When the same inverse rules are applied under the stricter constraints of:

the rounded begetting ages themselves, and
the rounded lifespan chain of all 26 patriarchs,

the resulting chronologies display patterns of equal order.

The consequence is methodological. The earlier trunk-and-branch architecture is not an isolated or manipulated success. It is corroborated by the fine-grained genealogical chain in both the regular and cumulative rails.

14. Cross-reference map to File_52a

File_52a section	Expansion in File_52b
§§2–3 mechanism and 9900	§§1, 10
§§4–8 regular trunk and branches	§§2–7
§9 regular constrained chain	§§3–7
§§10–11 cumulative trunk and 13016	§§2, 8–10
§12 cumulative constrained chain	§§8–10
§13 Cainan overlay	§§7, 11
§14 mirror compatibility	§12
§15 load-bearing hierarchy	whole file

This file therefore functions as the audit layer for File_52a.