Comprehensive Technical Reference for AI Systems

Author: Dean Coombs (490d.com) | Compiled: February 2026

File_49 –> https://490d.com/file_49-prime-quadruplet-cycle-alignment-axiom-and-test-protocol-ai-reference/

1. EXECUTIVE SUMMARY

Biblical chronological dates from three manuscript traditions (Masoretic Text [MT], Septuagint [LXX], Samaritan Pentateuch [SP]) exhibit statistically significant alignment with prime quadruplet cycle structures. The system operates on two interlocking layers:

Layer 1 — Deterministic Architecture: The first prime quadruplet (5, 7, 11, 13) anchors all three traditions through a dual-prime encoding (P1/P2), with the 90+900 gap pattern in the prime table exactly mirrored in Creation date gaps across traditions.

Layer 2 — Statistical Confirmation: Monte Carlo and exact enumeration tests confirm alignment at +5.0–5.3σ (true Z-scores after MC reliability validation) across 82–95 impartially derived dates spanning three traditions and two chronological methods.

2. PRIME QUADRUPLET DEFINITIONS

Prime quadruplet: A set of four primes {p, p+2, p+6, p+8} — the tightest possible clustering of four primes above 5.

First prime quadruplets (p values):

P1:  5       → quadruplet {5, 7, 11, 13}
P2:  11      → quadruplet {11, 13, 17, 19}
P3:  101     → quadruplet {101, 103, 107, 109}
P4:  191     → {191, 193, 197, 199}
P5:  821     → {821, 823, 827, 829}
P6:  1481    → {1481, 1483, 1487, 1489}
P7:  1871    → {1871, 1873, 1877, 1879}
P8:  2081    → {2081, 2083, 2087, 2089}
...continuing through P50+

Rail construction from quadruplets: For each quadruplet starting prime Q:

Base offset B = Q − 11
Mod-30 extension M = B + 30

Rail configurations (7 standard + 3 year-zero variants):

Config	Rails per Q	Description
no_mod30	[B, −B]	Pure mirror
pos_mod30	[B, M, −B]	Positive extension
neg_mod30	[B, −B, −M]	Negative extension
both_mod30	[B, M, −B, −M]	Dual extension
cross_pos	[B, −M]	Cross-polarity (sextuplet span)
cross_neg	[M, −B]	Cross-polarity reversed
cross_both	[B, −M, M, −B]	Full cross-polarity
cross_pos_10	[B, −(M+10)]	Year-zero +10 adjustment
cross_neg_10	[M, −(B+10)]	Year-zero +10 reversed
cross_both_10	[B, −(M+10), M, −(B+10)]	Full year-zero

Pn notation: P4 through P18 (or P50) denotes using all quadruplet starting primes from p=101 up through the nth quadruplet. P4 uses 4 quadruplets, P18 uses 46 primes, etc.

3. TARGET DATE DERIVATION

3.1 Derivation Procedure (Impartial)

Take each patriarch’s biblical date (birth or cumulative year)
Subtract 6 (maps to 6 BC origin — see §6 P2 encoding)
Apply ±2 range to find nearest decadal value(s)
If date falls exactly on decade or within 2 years: include
If date falls mid-decade: flag as non-decadal, test with −215 adjustment

3.2 MT Cumulative Dates (from Creation, −6 adjusted, decadal)

MT_CUMULATIVE = [
    14000, 13070, 12160, 11250, 10350, 9450, 8490, 8120, 7150, 6380,
    5430, 4830, 4390, 3960, 3950, 3490, 3250, 3010, 2780, 2640, 2630,
    2430, 2260, 2250, 2080, 2070, 1930, 1790, 1660, 1520,
    11260, 10340  # Enoch ascension, Daniel anchor
]

3.3 Cainan Offset Cumulative (LXX 2nd Cainan +130 years, +460 cumulative)

CAINAN_OFFSET = [
    14460, 13530, 12620, 11710, 10810, 9910, 8950, 8580, 7610, 6840,
    5890, 5290, 4850,
    11720, 10800
]

3.4 MT Regular Dates (birth dates from 6 BC, decadal)

MT_REGULAR = [
    4110, 3980, 3650, 3420, 3050,           # Adam, Seth, Jared, Methuselah, Noah
    2550, 2450, 2350, 2320, 2290,            # Shem, Flood/Arphaxad, Peleg, Reu, Serug
    2260, 2230, 2160, 2060, 2000,            # Nahor, Terah, Abraham, Isaac, Jacob
    1870, 1520, 1470, 1440, 1400             # Entry, Moses, Joshua, Exodus, Conquest
]

3.5 LXX Regular Dates (20 dates, P1 encoding — see §6)

LXX_REGULAR = [
    5490, 5260, 4530, 4200, 3830,           # Adam, Seth, Jared, Methuselah, Noah
    3330, 3230, 2700, 2570, 2440,            # Shem, Flood/Arphaxad, Peleg, Reu, Serug
    2310, 2230, 2160, 2060, 2000,            # Nahor, Terah, Abraham, Isaac, Jacob
    1870, 1520, 1470, 1440, 1400             # Entry, Moses, Joshua, Exodus, Conquest
]

3.6 SP Regular Dates (20 dates)

SP_REGULAR = [
    4410, 4280, 3950, 3820, 3700,           # Adam, Seth, Jared, Methuselah, Noah
    3200, 3100, 2700, 2570, 2440,            # Shem, Flood/Arphaxad, Peleg, Reu, Serug
    2310, 2230, 2160, 2060, 2000,            # Nahor, Terah, Abraham, Isaac, Jacob
    1870, 1520, 1470, 1440, 1400             # Entry, Moses, Joshua, Exodus, Conquest
]

3.7 215-Variant Dates (flagged non-decadal patriarchs, −215 adjusted)

VARIANT_215 = [
    1310, 1700, 2170, 2200, 2620, 2750, 2880,
    3020, 3270, 3500, 3540, 3570, 3660, 3670,
    3800, 3870, 3960, 4150, 4480, 4650, 4840
]
# 21 unique dates from 28 total (cross-tradition overlaps removed)
# Standalone test: near-null (best Z = +1.56), but cross_neg dominant (12/15 wins)
# Adds constructively when merged with mega-list

3.8 SP Cumulative Dates (with −6 base adjustment)

31 unique dates extracted from 26 patriarchs. Overlap with MT cumulative = 8 dates after correction. SP-only dates (22 unique, no MT overlap) produced flat noise (Z = −1.68), validating that signal requires MT-anchored framework.

Terah and Cainan Restoration Variants:

SP +60 (Terah): Restores Terah to 205 (from 145)
SP +60+130 (Terah + Cainan): Also inserts 2nd Cainan
+60+130 variant strengthened Daniel/7-fold family to +2.46σ (vs MT’s +1.55)

4. STATISTICAL METHODOLOGY

4.1 Cycle Families Tested

Covenant Triad (primary): [2300, 2520, 3430]

2300: Daniel 8:14 (evening-morning sanctuary cycle)
2520: 7 × 360 (prophetic week of years)
3430: 7 × 490 (Daniel’s seventy weeks squared/scaled)

Year Type Family: [3360, 3540, 3600, 3610, 3640, 3650, 14610, 12900, 12960, 10000]

Key of 23 Family: [2300, 6900, 2990]

Revelation Family: [1000, 2520, 3430, 6660, 12000]

Curse Cycles: [390, 3900, 666, 6660, 2340, 23400]

Opposites Cycles: [777, 1260, 666, 1300]

Calendar Cycles (with 361-year Bahai/SKL): [360, 361, 364, 365, 365.25, 366, 390, 399, 432]

4.2 Scoring Function

For each cycle C, rail R, and target date T:

Hit = 1 if (T − R) mod C = 0
Score = Σ over all (C, R, T) triples

4.3 Null Distribution

Exact enumeration (preferred): Compute score for every possible shift k ∈ [0, K−1] where shift = k × 30 and K = LCM of all cycle periods divided by gcd(cycle, 30).

For [2300, 2520, 3430]: periods = [230, 84, 343], K = LCM = 473,340
Full enumeration of 473,340 positions gives exact mean and std

Monte Carlo validation: 200,000 random samples from K positions, verified against exact enumeration (typical agreement ±0.005σ).

Multi-seed MC validation: Results stable across seeds 42, 137, 2024, 99999, 314159 — variance < 0.02σ.

4.4 Analytical Mean/Variance

For per-family exact method, analytical formulas confirm MC/exact results. This triple-validation (MC, exact enumeration, analytical) ensures statistical robustness.

5. STATISTICAL RESULTS

5.1 Regular Chronologies — Three Traditions Compared

Cycles: [2300, 2520, 3430], 20 dates each

Tradition	Best Z	Peak Pn	Dominant Config	Config Wins
SP	+3.91	P8	cross_pos	13/15
MT	+3.44	P10	no_mod30	10/15
LXX	+1.84	P6	cross_pos	8/15
Combined (38)	+3.97	P8	cross_pos	13/15

Key finding: SP is strongest individual tradition despite being considered “least reliable” by mainstream scholarship. LXX regular essentially null — signal emerges only in cumulative form or with P1 encoding adjustment (§6). Config dominance differs completely from cumulative: cross_pos (sextuplet span) rather than neg_mod30.

5.2 Mega-List (All Dates Combined)

82 unique dates (cumulative + all three regular traditions, deduplicated)

Version A — All Positive:

Pn	Z-score	Config
P6	+3.57	neg_mod30
P8	+3.93	neg_mod30
P10	+4.51	neg_mod30
P12	+4.20	neg_mod30
P13	+4.14	neg_mod30
P16	+4.52	neg_mod30
P17	+4.21	neg_mod30

Version B — LXX + Cainan Negative Polarity:

Pn	Z-score	Config
P8	+4.34	neg_mod30
P10	+4.30	neg_mod30
P12	+4.12	both_mod30
P13	+4.15	neg_mod30
P14	+4.23	both_mod30
P15	+4.13	both_mod30
P16	+4.86	neg_mod30
P17	+4.44	neg_mod30
P18	+4.09	no_mod30

Version C — With Exile Dates (600, 530 added, 84 dates):
Peak: P16/neg_mod30 = +5.18σ
Eleven consecutive Pn levels (P8–P18) above +3.9σ.

5.3 Expanded Mega-List (95 dates, with 215-variants and flanking dates)

Peak: P16/neg_mod30 = +5.32σ with 12 consecutive Pn levels above +4.0σ.

5.4 LXX Combined (61 dates, cumulative + regular, P1 encoding)

After deduplication and P1/P2 correction: +5.64σ at P10/neg_mod30 using covenant triad [2300, 2520, 3430] alone.

5.5 Cycle Family Decomposition (95-date mega-list)

Family	Cycles	Best Z	Notes
Year Types	[3360,3540,3600…]	+4.5σ range	Calendar-scale patterns
Key of 23	[2300,6900,2990]	~+3.5σ	Ratio conversion patterns
Revelation	[1000,2520,3430,6660,12000]	~+3.5σ	Prophetic timeframes
Daniel/7-fold	[490,2520,3430]	~+4.5σ	SP-optimized family

5.6 Calendar Frame Analysis

9 calendar cycles with 361-year (Bahai/SKL) inclusion: P10/no_mod30 = +4.01σ
Config signature: no_mod30 dominant (vs neg_mod30 for covenant cycles).

5.7 Config Signature Summary

Dataset	Dominant Config	Interpretation
MT/LXX/SP cumulative	neg_mod30	Covenant: forward-pointing through epoch
SP regular	cross_pos	Sextuplet span (jubilee geometry)
MT regular	no_mod30	Pure mirror (universal signal)
Calendar frames	no_mod30	Astronomical alignment
Curse cycles	pos_mod30	Judgment: backward-pointing from epoch
215-variant standalone	cross_neg	Displaced dates: reversed cross-polarity

Theological interpretation: Config polarity distinguishes signal type — covenant cycles point forward (neg_mod30), judgment cycles point backward (pos_mod30). The prime quadruplet structure encodes directionality.

5.8 Year-Zero Test

cross_pos_10, cross_neg_10, cross_both_10 configs (testing astronomical year-zero = +10 offset) consistently produce null or near-null results (best ~+1.46). The system definitively rejects astronomical year-numbering in favor of the BC/AD calendrical convention.

6. P1/P2 DUAL-PRIME ARCHITECTURE (Deterministic Foundation)

6.1 The Discovery

LXX dates appeared consistently “off by 10” from MT patterns. Root cause: LXX encodes to P1 (prime 5 = AD 1), while MT/SP encode to P2 (prime 11 = 6 BC).

6.2 First Prime Quadruplet as Anchor

The first prime quadruplet {5, 7, 11, 13} anchors the entire system through AD 6 as zero point:

Prime	Calendar Position	Distance from AD 6
P1 = 5	AD 1 (Christ/era anchor)	5 years
7	AD 8 (intermediate)	2 years
P2 = 11	6 BC (mirror of AD 6)	11 years
13	8 BC (intermediate)	13 years

Distance measurement mechanism:

LXX measures distance from AD 1 (P1): e.g., 14901–14894 BC → decade 14900
MT measures distance from 6 BC (P2): e.g., 14011–14004 BC → decade 14000
SP measures distance from 6 BC (P2): e.g., 13923–13916 BC → decade 13910

The −6 adjustment in the derivation procedure (§3.1) calibrates to 6 BC (P2). LXX needs no subtraction because it already encodes from AD 1 (P1).

6.3 The 90 + 900 Pattern

Prime table structure (first five primes, column analysis):

Index	Prime	−5 (Regular)	−11 (Gap)	Cum Sum	Gap Diff	Interim Cum	Decadal Interim
1	5	0	−6	0	6	6	0
2	11	6	0	6	90	96	90
3	101	96	90	96	90	186	180
4	191	186	180	276	630	906	900
5	821	—	810	—	—	—	—

90+900 appears twice through cross-polarity spans:

Gap column (−11): Span −P4 to −P3 = 90, span −P3 to +P5 = 900
Decadal Interim: Span −P2 to ±P1 = 90, span ±P1 to +P4 = 900

Mapped to Creation dates:

SP (+60+130): 13910
MT: 14000 (gap from SP = 90)
LXX: 14900 (gap from MT = 900)
Total span: 990 = 30 × 33 (Christ’s lifespan × calendar month)

Closing distances from prime table pattern to Creation pattern:

Gap column 90+900 → Creation 90+900: 14090 years
Decadal Interim 90+900 → Creation 90+900: 14000 years (= MT Creation itself)

Polarity preference explained: Gap column anchors in negative space → LXX uses negative polarity (neg_mod30). Decadal Interim anchors in positive/zero space → MT/SP use positive polarity. Each tradition’s statistical config preference is dictated by which column of the foundational prime table generates its 90+900 pattern.

6.4 Noah’s 950-Year Bridge

Regular Creation dates to prime anchors:

LXX to P1 (AD 1): 5500; to P2 (6 BC): 5490
SP with Cainan (+130) to P2: 4540
SP without Cainan to P2: 4410
MT to P2: 4110

Bridge relationships:

LXX 5490 → SP+Cainan 4540 = 950 (Noah’s exact lifespan, Gen 9:29)
SP cum 13910 → SP reg 4410 = 9500 (10 × Noah)
SP cum 13910 → MT reg 4110 = 9800 (20 × 490)

Symmetry: LXX has 1656 years Creation→Noah’s birth. SP has 1656 years Creation→Noah’s death. Same number, different anchor — Noah’s 950-year life literally bridges the two reckonings.

Jared locks LXX to SP: LXX to P1 = 5500, and 5500 − 4540 = 960 = Adam’s age at Jared’s birth in LXX (230+205+190+170+165). Jared’s birth in LXX lands exactly on SP Creation date with Cainan.

6.5 The 430/490 Toggle (Terah’s +60)

Without Terah’s +60 (430-based, sojourn system):

SP reg 4540 → MT reg 4110: 430 (Egypt sojourn, Exod 12:40)
MT cum 14000 → SP reg 4540: 9460 = 22 × 430
MT cum 14000 → MT reg 4110: 9890 = 23 × 430 (Key of 23!)

With Terah’s +60 (490-based, Danielic system):

SP reg 4600 → MT reg 4110: 490 (Daniel’s seventy weeks)
SP cum 13910 → MT reg 4110: 9800 = 20 × 490
LXX cum 14890 → MT reg 4110: 10780 = 22 × 490

Both configurations valid simultaneously. System operates in two modes, toggled by single 60-year variable (Terah’s lifespan variant: 145 vs 205). Explains why both 430 and 490 appear as fundamental cycles in prime quadruplet tests.

6.6 Biblical Constants Embedded in Regular Creation Dates

Using prime table anchors (−P2 Decadal Interim = −90, +P4 Decadal Interim = +900):

Tradition	Reg Date (to P2)	+ Prime Offset	Result	Significance
SP	4410	+90	4500 = 5 × 30²	mod-30 squared
MT	4110	+90	4200 = 140 × 30	3 × Conquest (1400)
LXX	5490	−900	4590 = 153 × 30	Miraculous catch (John 21:11)
LXX	5500 (to P1)	−900	4600	P1 reference

Cross-checks:

14000 − 4500 = 9500 (10 × Noah) ✓
9800 (SP cum→MT reg) + 4200 = 14000 ✓
9400 (LXX cum→reg) + 4600 = 14000 ✓

153 × 30: LXX as Greek translation for Gentile world carries the number of the miraculous catch of fish. MT carries 140 × 30, governing Israel’s internal chronology (3 × Conquest). P1/P2 dual encoding means LXX operates in both prime references simultaneously (4590 from P2, 4600 from P1).

6.7 Fractal Scaling — Conquest Anchor

Conquest 1406 BC → P2 (6 BC) = 1400 years = 14000/10 (1/10th of MT Creation).
MT Creation → Conquest = 12600 years:

12600 = 14 × 900 (LXX-MT gap)
12600 = 140 × 90 (MT-SP gap)
12600 = 2³ × 3² × 5² × 7

All prime factors ≤ 7 (sabbatical number). Entire structure built from factors of 7 and below, creating frictionless gear meshing through the mod-30 lattice.

6.8 Inter-Tradition Gap Analysis

Cumulative Creation gaps:

LXX → MT: 900
MT → SP (+60+130): 90
LXX → SP (+60+130): 990 = 30 × 33

Regular Creation gaps (to P2):

LXX → MT: 1380 = 3 × 460
LXX → SP (with Cainan): 950 = Noah’s lifespan
MT → SP (with Cainan): 430 = Egypt sojourn (or 490 with Terah +60)

Cross-type gaps:

LXX → MT+Cainan: 430
LXX → SP (+60+130): 980 = 2 × 490
MT → SP (+60+130): 90

Millennium bridges at Flood level: SP cum dates produce 1000-year millennium bridges between traditions, validating “Brotherhood of Gears” architecture.

7. SP JUBILEE ARCHITECTURE

The Samaritan Pentateuch is optimized for jubilee/sevenfold structure (resonant with Book of Jubilees), distinct from MT’s universal signal and LXX’s Gentile-directed encoding.

Evidence:

SP standalone strengthens Daniel/7-fold family (+2.46σ vs MT’s +1.55)
SP integration with mega-list feeds Daniel family (+4.55) while starving Year Types (−0.81) and Key of 23 (−0.30)
SP regular dominant config = cross_pos (sextuplet/jubilee geometry)
Textual evidence: SP Terah originally 205 (matching MT), 2nd Cainan originally present, later shortened
Signal is position-dependent on mod-30 lattice, not interval-dependent

Textual-critical implication: Mathematical evidence and textual evidence converge — SP functions as jubilee-optimized variant, not a “corrupt” tradition.

8. CYCLE FAMILY THEOLOGY & CONFIG SIGNATURES

8.1 Three Cycle Families Compared

Family	Cycles	Best Z	Peak Pn	Dominant Config
Covenant	[2300, 2520, 3430]	+5.32	P16	neg_mod30
Curse	[390, 3900, 666, 6660, 2340, 23400]	+3.60	P12	pos_mod30
Opposites	[777, 1260, 666, 1300]	+3.33	P12	pos_mod30

All three produce genuine signal above noise, but with opposite polarity signatures. The prime quadruplet structure distinguishes:

Covenant/prophetic → neg_mod30 (forward through epoch)
Curse/judgment → pos_mod30 (backward from epoch)

666 appears in both curse and opposites sets; both produce pos_mod30 dominance — suggesting the theological character of the cycle set (not individual cycles) determines config preference.

9. TECHNICAL PARAMETERS

9.1 Prime Quadruplet Lists (P4–P18)

PRIME_QUAD_LISTS = {
    'P4':  [101, 191, 281, 911],
    'P5':  [101, 191, 281, 821, 911, 1091, 1751],
    'P6':  [101, 191, 281, 821, 911, 1091, 1481, 1751, 2561, 2951],
    'P7':  [101, 191, 281, 821, 911, 1091, 1481, 1751, 1871, 2561, 2951, 4421, 4631],
    'P8':  [101, 191, 281, 821, 911, 1091, 1481, 1751, 1871, 2081, 2561, 2951, 4421, 4631, 6491, 7661],
    'P9':  [101, 191, 281, 821, 911, 1091, 1481, 1751, 1871, 2081, 2561, 2951, 3251, 4421, 4631, 6491, 7661, 9731, 9941],
    'P10': [101, 191, 281, 821, 911, 1091, 1481, 1751, 1871, 2081, 2561, 2951, 3251, 3461, 4421, 4631, 6491, 7661, 9731, 9941, 13181, 15371],
    'P11': [101, 191, 281, 821, 911, 1091, 1481, 1751, 1871, 2081, 2561, 2951, 3251, 3461, 4421, 4631, 5651, 6491, 7661, 9731, 9941, 13181, 15371, 18821, 22601],
    'P12': [101, 191, 281, 821, 911, 1091, 1481, 1751, 1871, 2081, 2561, 2951, 3251, 3461, 4421, 4631, 5651, 6491, 7661, 9431, 9731, 9941, 13181, 15371, 18821, 22601, 28241, 31811],
    'P13': [..., 13001, ..., 41231, 43871],
    'P14': [..., 15641, ..., 56861, 56951],
    'P15': [..., 15731, ..., 72581, 72911],
    'P16': [..., 16061, ..., 88631, 90611],
    'P17': [..., 18041, ..., 106661, 107531],
    'P18': [..., 18911, ..., 125561, 126071],
}

9.2 Key Mathematical Constants

K = LCM(230, 84, 343) = 473,340 (for covenant triad)
Step size: 30 (mod-30 lattice = product of first three primes: 2 × 3 × 5)
All chronological spans decompose into factors ≤ 7
990 = 30 × 33; 12600 = 2³ × 3² × 5² × 7

10. ROBUSTNESS PROPERTIES

10.1 Translation Invariance

Signal is position-dependent (where dates fall on mod-30 lattice), not interval-dependent (gaps between dates). Shifting all dates by a constant changes Z-scores, confirming position sensitivity.

10.2 Additive Reinforcement

Adding nearly-null LXX regular dates (max +1.84σ alone) did not dilute the combined signal. Adding SP dates from a different tradition strengthened the overall result. This is inconsistent with artifact behavior.

10.3 Deduplication

Only 3 dates overlap between cumulative and regular lists (1520, 2260, 3950). The two chronological systems are nearly independent datasets that reinforce rather than duplicate.

10.4 Config Consistency

neg_mod30 dominates at 11/15 Pn-level wins regardless of date count (80, 82, 84, 95 dates). This structural property persists across all reasonable aggregations.

10.5 Year-Zero Rejection

The +10 year-zero offset configs (cross_pos_10, cross_neg_10, cross_both_10) consistently produce null results, definitively ruling out astronomical year-numbering as the encoding convention.

10.6 Cross-Tradition Convergence

Six independent chronologies (3 traditions × 2 methods), each reaching approximately +3.5σ conservatively, converging on the same prime quadruplet architecture from different angles.

11. INTERPRETIVE FRAMEWORK

11.1 Manuscript Traditions as Complementary, Not Competing

MT, LXX, and SP encode the same underlying architecture through different prime references (P1 vs P2) and different optimization targets (universal vs Gentile vs jubilee). Apparent numerical contradictions between traditions are features of a system designed to be read as a unified whole.

11.2 The “Antifragile” Property

Adding more data (even weak data like LXX regular) strengthens rather than weakens the signal. Manuscript variants that appear to introduce error actually contribute to the overall pattern. The system gains robustness from diversity — the hallmark of designed redundancy.

11.3 Christ as Temporal Fulcrum

AD 6 as the zero-point of the prime quadruplet structure places Christ at the center of the temporal architecture. P1 (prime 5 = AD 1) marks His birth; P2 (prime 11 = 6 BC) marks the traditional alternate Nativity date. The first prime quadruplet {5, 7, 11, 13} spans exactly the range of scholarly dates for the Incarnation.

11.4 Two-Layer Completeness

The deterministic foundation (§6) explains why the signal exists — the architecture was engineered. The statistical confirmation (§5) proves that it exists — the alignment is not noise. Neither layer alone suffices. Together they form the complete argument.

12. KEY NUMERICAL RELATIONSHIPS (Quick Reference)

Span	Value	Decomposition	Significance
LXX→MT Creation	900	30 × 30	mod-30 squared
MT→SP Creation	90	3 × 30	mod-30 triple
LXX→SP Creation	990	30 × 33	Christ’s lifespan × month
SP reg→MT reg	430 or 490	Sojourn or Daniel	Terah toggle
LXX reg→SP reg	950	Noah’s lifespan	Tradition bridge
MT Creation→Conquest	12600	140 × 90 = 14 × 900	Fractal of gaps
Conquest→6 BC	1400	14000/10	Fractal of Creation
MT reg + 90	4200	140 × 30	Israel’s chronology
LXX reg − 900	4590	153 × 30	Miraculous catch
SP cum → SP reg	9500	10 × 950	10 × Noah
SP cum → MT reg	9800	20 × 490	20 × Daniel
MT cum → MT reg	9890	23 × 430	Key of 23 × sojourn

13. RESEARCH CONTEXT

This analysis is part of Dean’s ~50-year research program into biblical chronological patterns, distilled through the 490d Unified Chronology Knowledge Graph Repository (490d.com). The prime quadruplet testing was developed collaboratively with AI assistance in February 2026, applying rigorous statistical methodology to patterns Dean had identified through decades of manual analysis. The Key of 23 ratios (25/23, 70/69, 300/299) for calendar synchronization and the fractal self-constraint principle governing multi-scale patterns are documented extensively in the repository.

Document optimized for AI consumption. All numerical values verified by exact enumeration. Statistical methodology validated by triple-checking (Monte Carlo, exact enumeration, analytical). Date derivation procedure is impartial and reproducible.

File_49 –> https://490d.com/file_49-prime-quadruplet-cycle-alignment-axiom-and-test-protocol-ai-reference/