For Part 2: Files_31-46 about Pi, Primes and Berossus +50 are found in a separate document due to length constraints.)
Part-3-Files_47-forward_machine-reference-document-for-490d-unified-chronology-repository/
https://490d.com/file_49-prime-quadruplet-cycle-alignment-axiom-and-test-protocol-ai-reference/
https://490d.com/file_50a-prime-quadruplet-naturalized-master-table-indices-1-100/
https://490d.com/file_50b-the-prime-quadruplet-chronology-unified-harmonic-system-v2-1/
https://490d.com/file_50c-christ-birth-grid-as-the-clutch-foundation-for-skl-berossus-p1-p13/
Repository: 490d Unified Chronology Knowledge Graph
Status: Verified and Locked (Zero-History / Machine-Optimized)
Companion File: File_50c (Bipartite Grid Landing and SKL/Berossus Naturalization)
0) Scope and operator semantics
This file extends File_50c by showing that start/end landings are only half the structure. The second half is integration as a unit, where paired prime nodes constrain both (i) local anchor landings (mod720 on the 360-grid) and (ii) large-span envelopes (notably the Key-of-23 70/69 expansion) to yield coherent macro-block identities (e.g., 1200×336, 1400×336).
Operator layers (explicitly allowed):
- 360-grid layer: Candidate landings are generated strictly by the Bipartite Grid Landing operator defined in File_50c, which mechanically yields exact 720-year boundary brackets (or Tri-Node 0-strikes) with zero intermediate drift.
- mod30 prime-node layer: Prime-node values may appear in decadal/mod30 space with the File_50c admission gate.
- Mixed-mode invariants: Equalities are admissible when each side is a permitted expression under (1)–(2), and when any expansions are explicitly stated as operators (e.g., ×70/69).
Scope limitation: The boundary-pairing analysis in this section examines only the primes that land on epoch start/end points across the four king lists. This does not imply that the remaining primes between P1 and P100 lack chronological significance. Many carry independent alignments to biblical anchors documented elsewhere in the repository (e.g., File_50b, Capsule Appendix A). The boundary analysis isolates one layer of the system’s structure; it is not exhaustive of the primes’ chronological content.
1) The SKL ↔ Berossus bridge invariant (P63/P64 ↔ P98/P99)
Under the strict Bipartite Grid Landing rules (File_50c), the primes generate definitive dual-bracket or tri-node outputs on the 360-grid (before the +6 civil clutch):
- L(P63) = {266,400; 267,120}
- L(P64) = {268,560; 269,280}
- L(P98) = {464,400; 465,120; 465,840} (Exact Tri-Node 0-Strike)
- L(P99) = {467,280; 468,000}
The SKL ↔ Berossus bridge utilizes the strict bracket outputs to form the invariant difference:
ΔB = 198,720 (Derived mechanically: 467,280 − 268,560 = 198,720).
Key-of-23 step:
198,720 / 69 = 2,880
2,880 × 70 = 201,600
So: ΔB × (70/69) = 201,600.
This yields the expanded envelope identity:
201,600 = (468,000 − 266,400) = 600 × 336.
2) The “double-201,600” integration (two occurrences, run together)
There are two distinct 201,600 blocks that “run together” in the integrated structure:
- Block A (direct): P29 → P64 = 201,600 (stated as an observed system identity; operator-consistent).
- Block B (expanded): P64 (mod720 anchor) → P99 (mod720 anchor) = 198,720 × (70/69) = 201,600.
This documents two 201,600 spans with different provenance: one direct, one expanded.
3) The 336-lattice interpretation and the 6/7 creation motif
Define the 336-lattice unit:
201,600 = 600 × 336.
Then the paired 201,600 blocks yield:
(201,600 + 201,600) = 403,200 = 1200 × 336.
This is structurally coherent with the repository’s creation typology: 600 + 600 corresponds to a doubled 600-block (in 336-units), and later 700 + 700 (below) mirrors “six + seventh” framing (creation/rest).
4) P29 normalization and 200 × 336
P29 prime-node is treated as: 67,200 naturalized to 67,230 (mod30 admission).
The clean 336-lattice identity:
67,200 = 33,600 + 33,600 = 200 × 336.
Within the File_50c semantics, the system allows the mod30 naturalization (67,200 → 67,230) while retaining compatible mod720 behavior at the anchor level (i.e., “within the skin” of the SKL margin). This permits 336-lattice coherence without violating the 30-difference constraint governing the prime-node layer.
5) Integrated macro-span: 800 × 336 and 1400 × 336 (with Key-of-23)
Using the 336-lattice blocks:
From the P29-scale base: 67,200 (= 200 × 336) and its paired structure yields a coherent “built-up” block at 800 × 336 when combined with the relevant 201,600 span(s).
Adding the further 201,600 reach to the P98/P99 end yields:
800 × 336 + 600 × 336 = 1400 × 336.
Thus the integrated unit can be expressed schematically as:
- 1200 × 336 (double-201,600) forming the interior reinforcement.
- 1400 × 336 (700 + 700 in 336-units) forming the completed envelope symmetry.
6) Anchor methodology transferred to the “other end”: SKL start anchoring
The SKL/Berossus anchor complex (End of the 23 Kings) is generated not by loose mod720 parameters, but by an unbroken, deterministic cluster of prime nodes that perfectly blanket the epoch.
6.1) P9 / P10: The Epoch Core
- P9 ($V_{90}$ = 3240) lands in the First Half of the grid, mechanically generating the strict bracket: 2886 BC / 3606 BC.
- P10 ($V_{90}$ = 3420) lands in the Second Half of the grid, mechanically generating the mirror bracket: 2886 BC / 3606 BC.
- Result: A Double Dual Hit mathematically locking the Babel/Kish Long anchor without requiring human intervention.
6.2) P6 / P7 / P8: The Abrahamic Extension
The remaining extension of this anchor boundary—2166 BC—is captured by the contiguous triplet of P6, P7, and P8. (P6 operates as an Exact Tri-Node Strike targeting 1446 BC and 2166 BC simultaneously, while P7 and P8 act as Single Hits clamping the 2166 BC boundary).
This proves that the full ±(2×360) = ±720 structure applies consistently at both ends (SKL and Berossus).
7) Epoch-boundary prime pairing across all four lists (The Sparsity Proof)
7.0 Scope & The Mathematical Verdict
This section documents that every epoch boundary in the SKL/Berossus system is identified by at least one prime landing—and in almost all cases, by a dedicated cluster.
When all 100 primes are filtered through the strict Bipartite Grid Landing operator (File_50c):
- 73 primes yield absolute silence (zero hits).
- The 27 active primes collapse into just 16 distinct structural targets.
- 21 of those primes act exclusively to bolt down the epochal boundaries and list starts/ends.
7.1 Flood-side pairing (P19, P20, P21 Cluster Clamp)
Rather than isolated hits, the prime lattice uses contiguous ordinal indices to heavily fortify systemic resets:
- P19 (Single Hit) locks the extreme lower −720 edge (20,166 BC).
- P20 (Dual Hit) mechanically generates the exact core anchors (20,886 BC / 21,606 BC).
- P21 (Single Hit) securely clamps the +720 upper edge (21,606 BC).
7.2 Intermediate king landings & Sparsity
Out of the ~25–30 intermediate king positions across all four lists, almost none receive a prime landing. The mod720 funnel is too narrow to randomly populate the timeline. The only exceptions are highly significant theological or transitional figures: Seth (P57), Jared (P36), Enoch (P29), and Alalgar (P59/P60).
(Note: P29 specifically hits Enoch at exactly 201,600 years from Adam/Alulim [P64] on the literal prime values prior to any chronological processing: 268,811 − 67,211 = 201,600. This is a property of the primes, not an artifact of landing rules).
7.4 Textual-critical note: Amelon and the P91 Exact Strike
The earliest SKL prism lists 8 kings before the Flood. Berossus lists 10. The 2+8 division occurs at the same named figure in both traditions: Enosh / Amelon (3rd from Adam).
Under the rigorous Bipartite Grid Landing, P91 ($V_{90}$ = 419,040) is an Exact Tri-Node Strike. It lands flawlessly on 419,046 BC and 419,766 BC.
This definitively reclassifies Amelon: he is not an intermediate king. He is the foundational boundary of the original 8-king epoch, and the prime lattice clamps him with maximum structural authority.
7.6 Index-layer observations (Purified under Bipartite Grid Rules)
Explicit Disclaimer: The index-level regularities documented below are strictly declared observations, not claims of demonstrated design. Index numbers are ordinal positions within the A007530 sequence, not intrinsic mathematical properties of the primes themselves. These regularities are recorded because they remain mathematically present and internally consistent even after all “partial hits” have been eradicated by the strict Mod720 rules, but they await formal null-model testing before any significance claims are asserted.
Table 7.6A — The 10 / 10² Structural Scaling
Because the new mechanical rules formally designate P8/P9 and P98/P99 as unbreakable contiguous clusters, the decimal scaling between them is mathematically airtight:
| From | To | Index Sum | Structure | Architectural Function |
| −P2 | P8 | 10 | Seed | Math Zero $\rightarrow$ Babel Epoch (Lower Clamp) |
| −P1 | P9 | 10 | Seed | Civil Zero $\rightarrow$ Babel Epoch (Core Dual Hit) |
| −P2 | P98 | 100 = 10² | Square | Math Zero $\rightarrow$ Berossus Adam (Lower Clamp) |
| −P1 | P99 | 100 = 10² | Square | Civil Zero $\rightarrow$ Berossus Adam (Upper Clamp) |
Observation: The index perfectly scales the distance from Ground Zero (the Seed) to the two most foundational starts of civilization—the post-Flood anchor and the ultimate pre-Flood outermost boundary (the Square). P8/P9 and P98/P99 are the only contiguous boundary pairs in the system where both primes generate exact anchor strikes, and they sit exactly at this $10 \rightarrow 10^2$ scaling.
Table 7.6B — Cross-polarity centesimal mirror (Index sums = 100)
When loose “partial hits” are strictly excluded from the dataset, the centesimal mirror purifies, reflecting only the most rigid boundaries across the index-50 midpoint:
| Negative Polarity | Positive Polarity | Index Sum | Boundary Reflection |
| −P1 (Civil Zero) | +P99 (Berossus Adam Upper Clamp) | 1 + 99 = 100 | Outermost Bounds |
| −P2 (Math Zero) | +P98 (Berossus Adam Lower Clamp) | 2 + 98 = 100 | Outermost Bounds |
| −P36 (Jared/Watchers Core) | +P64 (SKL Adam Core) | 36 + 64 = 100 | Pre-Flood Core |
Observation: The outermost clamps of the system (P98/P99) reflect perfectly against the Ground Zero anchors (P1/P2). Internally, the exact dual hit for the SKL Start (P64) reflects perfectly to match the exact dual hit for the Jared/Watchers transition (P36)—the mathematical start of the king list reflecting against its greatest theological fracture point.
Table 7.6C — The 6² / 5² / 6² Architectural Palindrome
Under strict rules, P63 does not score a bracketed hit on a king (that is strictly P64’s role for SKL Adam). Instead, P63 generates the 360-grid coordinate 266,400—the exact mathematical floor of the 201,600 Macro-Block bridge.
| Span | Index Gap | Structure | Measurement |
| P2 $\rightarrow$ P38 | 36 | 6² | Ground Zero $\rightarrow$ Final Pre-Flood King |
| P38 $\rightarrow$ P63 | 25 | 5² | Final Pre-Flood King $\rightarrow$ Macro-Block Bridge Floor |
| P63 $\rightarrow$ P99 | 36 | 6² | Macro-Block Bridge Floor $\rightarrow$ Outermost Boundary Clamp |
Observation: The palindrome ($6^2, 5^2, 6^2$) measures the deep-time geometric architecture of the lattice, stepping systematically from the origin, to the Flood boundary, to the floor of the integration bridge, to the outermost clamp.
7.7 Status caveat
As stated in §7.6, whether these index-layer patterns are a consequence of a shared decimal/heptadic architecture native to the source traditions, or an independent arithmetic coincidence of the prime enumeration, remains an open question. They are preserved here strictly for data completeness.
Appendix A — Conditional P23 expansion toward Berossus Flood proxy
This P23 note is conditional, reliant upon the Key-of-23 operator.
Arithmetic chain:
23 × 23 × 60 = 31,740.
Apply the Key-of-23 style rescaling: 31,740 × (25/23) = 34,500.
Interpretation: 34,500 is treated as a proxy magnitude that approaches the Berossus Flood region (~34,566 BC).
Structural note:
34,500 → −34,500 spans 69,000, and 69,000 × (70/69) = 70,000 (Key-of-23 expansion). This “corner expansion” (69k→70k) is part of the broader behavior where the Key-of-23 operator induces systematic envelope expansions at major boundaries.
End of File_50d (v3.0)