For Part 1, File_00 to File_30 of Repository, see https://490d.com/the-490d-unified-chronology-knowledge-graph-repository/
RESTART CAPSULE — 490d Unified Chronology (v10.1, ZERO-HISTORY / MACHINE-OPTIMIZED)
STITCHED EDITION: v6.6 + Pressure-Test Clarification Splices (no deletions of fundamental tables/locks)
Purpose: Single self-contained context window for a fresh chat restart (no dependence on prior messages).
Scope: Regular (MT/SP/LXX), Cumulative (MT/SP/LXX), SKL/Berossus lattice, Prime-Lattice integration (A007530), and the operators/constants required to compute/validate the inlined locks; any non-inlined prime operators/rows are explicitly tagged as ‘DEFINED IN PRIME FILES 29–41’ and therefore non-executable in a zero-history restart.
Logic Engine: §1–§6 (operators, baselines, cumulative, SKL/Berossus, verification, query recipe)
Prime System: §1.18 (interface/constraints) + §7 (axioms/architecture) + Appendix A (Master Prime Table + validation)
Counting convention: Civil BC/AD with no year 0, unless explicitly stated otherwise.
Civil-span identity (no year 0):
[
\text{BC}+\text{AD}-1=\text{Total}.
]
0) NON-NEGOTIABLE OPERATING RULES (repository rules)
If a computation requires an operator/row tagged ‘DEFINED IN PRIME FILES 29–41’, stop and report ‘dependency not present in restart capsule’ (do not infer).
No invention / no guessing. Use only operators/constants defined herein. If something is not defined here, mark it “defined in prerequisite file” and do not infer.
Deterministic math. Dates are integers or x.5 decimals. No rounding unless explicitly stated.
Dual-state preservation. If a node has multiple valid modal states, preserve and compute all states.
No blanks / no placeholders. Replace all placeholders with explicit definitions or explicit dependency notes.
Audit-first. If two values conflict, do not choose—classify as modal states (Base vs Envelope / Normal vs Harmonic) per the rules below.
0.1 PRESSURE-TEST SPLICE: ALLOWED NUMBER TYPES (hard rule; additive)
All internal calculations use exact rationals and exact halves only:
Integers: (k)
Halves: (k+\tfrac12) (may be printed as “.5” only)
Exact rationals (e.g., (25/23,\ 70/69,\ 300/299,\ 23/40))
No decimal floats are permitted other than the literal print form “.5”.
0.2 PRESSURE-TEST SPLICE: DISPLAY-ONLY INTEGERIZATION (no computational rounding)
Define a single display operator:
[
\mathrm{DispInt}(x):=\lfloor x\rfloor.
]
Rules:
DispInt is permitted only for printing tables.
No rounding is allowed in computation.
If an envelope yields a half, preserve it internally; apply DispInt only at final display.
1) LOGIC ENGINE (OPERATORS, CONSTANTS, LOCKS)
1.1 FIXED EPOCH (anchors; matrix variants disabled after this boundary)
| Event | Date (BC) | Notes |
|---|---|---|
| Exodus (Primary) | 1446 | fixed anchor |
| Exodus (Subordinate Lens) | 1231 | Ramesside/Late-Date lens (non-replacement; §1.15) |
| Tabernacle | 1445 | — |
| Aaron birth | 1529 | optional (+0.5) Tishri shift formalized by (L) (§1.10) |
| Moses birth | 1526 | Nisan/Spring trunk anchor |
| Aaron death | 1407 | summer |
| Moses death / Conquest begins | 1406 | winter / start |
| Six years’ war | 1406–1400 | 6 years |
| First Sabbath year (land rests) | 1399 | — |
| Joshua death | 1366 | age 110 |
1.2 UNIVERSAL FOUR-POSITION MATRIX (Adam → Terah epoch)
Baseline = MT Minimum. Derive positions:
| Position label | Variants applied | Net add | Example (MT Creation endpoint 3899 BC) |
|---|---|---|---|
| Minimum | none | 0 | 3899 |
| Terah (+60) | +60 only | +60 | 3959 |
| Sojourn (+215) | +215 only | +215 | 4114 |
| Maximum | (+60) and (+215) | +275 | 4174 |
Sequential gap note:
[
215-60=155.
]
Epoch scope (where variants apply):
| Epoch | Range | Active variants |
|---|---|---|
| Adam → Terah’s death | Creation → (~)1816 BC (MT/LXX) or 1876 BC (SP) | full matrix (+0,+60,+215,+275) |
| Abraham → Levi’s death | 1951–1567 BC (minimum) | (±215) only |
| Aaron birth onward | 1529 BC → | fixed |
1.3 CREATION DATES BY TRADITION (Regular / Minimum Baselines)
Definition (scope): The values below are the Minimum Creation Endpoints (end of Creation week) for each tradition. The Universal Four-Position Matrix (§1.2: +0, +60, +215, +275) applies to each baseline individually (i.e., each tradition has its own Minimum / +60 / +215 / Maximum positions derived from its own baseline).
Tradition
Creation endpoint (end of Creation week)
Relationship
MT
3899 BC
baseline
SP (Normal / Toggle ON)
4199 BC
MT (+300)
LXX
5279 BC
MT (+1380)*
Gap architecture (locked checks):
[
4199-3899=300,\quad 5279-4199=1080,\quad 5279-3899=1380=300+1080.
]
- Scope Rule (CRITICAL): “MT (+1380)” is an endpoint gap only (Creation-endpoint alignment). It must not be used as a blanket transform for Flood or post-Flood nodes; those must be computed from the internal LXX tables (§2.3).
1.3a CREATION WEEK WRAPPER, YEAR-6 ANCHORS, AND OPERATIONAL DEFAULTS
(A) Creation Week wrapper (table convention; day–year extension)
For any tradition/baseline with Creation endpoint (CE) (the year label at the end of the Creation week), define the Creation Week wrapper as a 7-year block:
Interval semantics (hard): CW(CE) denotes the half-open span [CE, CE+7) in year-units; the printed ‘Birth=CE+7, Death=CE’ are boundary labels, not inclusive endpoints.
[
\mathrm{CW}(CE) := [,CE+7 ;\rightarrow; CE,],
]
printed in tables as:
Creation Week “Birth” = (CE+7)
Creation Week “Death” = (CE)
Length = 7
(This matches the existing rows: MT 3906→3899, SP 4206→4199, LXX 5286→5279.)
Literal-days placement : The literal 7-day creation week is placed inside the endpoint year label (CE) for civil-year tables; the six prior “days” are represented schematically as the six preceding years.
(A2) Creation-Week Day-6 year label (distinct from prime-domain Year-6 anchors)
Define the Creation-Week Day-6 year label for any Creation endpoint (CE) as:
[
\mathrm{CW6}(CE):=CE+2.
]
Thus:
[
\mathrm{CW6}(\text{MT})=3901,\quad
\mathrm{CW6}(\text{SP})=4201,\quad
\mathrm{CW6}(\text{LXX})=5281\ \text{BC}.
]
Disambiguation rule : (\mathrm{CW6}(CE)) is the Creation-Week Day-6 label inside the schematic wrapper, and must not be conflated with the prime/chronology Year-6 anchor (Y6_{\text{start}}(CE)=CE+217) (which yields 4116/4416/5496 BC).
(B) Prime/chronology Year-6 anchor (critical; high-frequency node)
Define the prime/chronology Year-6 anchor for any (CE) as:
[
Y6_{\text{start}}(CE) := CE + 217.
]
Thus the deterministic Year-6 anchors for the three traditions are:
[
Y6_{\text{start}}(\text{MT})=4116,\quad
Y6_{\text{start}}(\text{SP})=4416,\quad
Y6_{\text{start}}(\text{LXX})=5496\ \text{BC}.
]
Interpretation : (Y6_{\text{start}}) is the year in which animals and Adam are created (Day-6) and it lasts a full year in the schematic sense. This node is treated as a canonical Creation-phase anchor in harmonic targeting (especially prime vectors).
Apparent-age marker (display-only node): For the prime/chronology Year-6 anchor (Y6_{\text{start}}), define Adam’s “apparent age 30” window as:
[
\mathrm{AdamApp30}(T):=[,Y6_{\text{start}}(T)+30\ \rightarrow\ Y6_{\text{start}}(T),],
]
e.g., MT: ([,4146\ \rightarrow\ 4116,]\ \text{BC}).
Rule: this is a Creation-phase annotation (identity tag) used for interpretation and targeting; it does not alter any patriarchal lifespans or post-Creation chronology.
(C) Operational default vs baseline (prevents AI confusion)
Baseline endpoints (CE): The tables list the Minimum Creation endpoints (CE\in{3899,4199,5279}) because they are the base states required to generate the full Four-Position Matrix (§1.2) deterministically.
Operational-default Creation anchors (high-use): Unless explicitly stated otherwise, Creation-phase harmonic targeting (especially prime vectors) defaults to the prime/chronology Year-6 anchors:
[
{4116,4416,5496}\ \text{BC},
]
which correspond to the standard operating assumption: 430 years in Egypt, no Terah +60 (i.e., the +215 lens applied to the minimum baseline, then Gear-2 +2).
Matrix generation reminder: From each baseline (CE), the four matrix endpoints are produced by the fixed add-sequence:
[
(0);+;60;+;155;+;60,
]
yielding ({CE,\ CE+60,\ CE+215,\ CE+275}) for each tradition.
Scope: This subsection defines only Creation-phase wrappers and anchors; it does not alter patriarchal lifespans or post-Creation chronology.
1.4 ENTRY DUALITY (baseline vs functional super-anchor; explicit rule)
Two states must be preserved:
Baseline Entry (Minimum): ((E_{\min}=1661\ \text{BC})) (215-year Egypt span)
Functional Super-Anchor (Entry +215 lens):
[
E_{\max}=E_{\min}+215=1876\ \text{BC}.
]
Rule: never substitute (1876) for baseline (1661); use (1876) as convergence/super-anchor while retaining (1661) as minimum calculation state.
1.4a: ABRAHAM CALL (+215 LENS) NODE (additive)
Derived node (sealed; lens identity): define the Abraham-call node in the +215 lens:
[
A_{\text{Call},+215} := 2091\ \text{BC} = 1876 + 215.
]
Scope: this identity is a lens-state node (Sojourn +215 applied within the Abraham epoch) and does not overwrite the MT minimum call-year node (1876 BC).
Optional identity note (preserved as modal meaning, not forced derivation): in the Terah +60 state, (2091) is also read as Terah’s death (Acts 7 alignment).
DISAMBIGUATION (HARD):
The civil label “1876 BC” is used for multiple tagged nodes in different epochs. Treat them as distinct identifiers even if the year label coincides:
E_max = 1876 BC (Entry super-anchor; Jacob-entry lens)
A_Call_min = 1876 BC (MT minimum Abraham-call)
Rule: never unify nodes by year label alone; unify only by (tag + epoch + mode).
1.5 SHEM (±2) ANOMALY (localized vs propagating)
Regular chronology (localized): anomaly affects Noah and Shem only. - MT/LXX (exclusive norm): Noah side (−2) vs Shem side (+2) ⇒ opposite-direction, see §2.4.
- SP Toggle-ON (inclusive boundary): “SP Toggle-ON is an inclusive boundary read that preserves Shem’s +2 while compressing Noah’s −2 to a +1 label shift.” (see §1.7a, §2.4).
Cumulative chronology (propagating): (±2) propagates through the chain and contributes to the envelope defined in §1.11.
1.6 2ND CAINAN SWITCH (Luke 3:36 / LXX Gen 11)
When restoring Cainan to MT/SP:
Mode
Add value
Meaning
Regular
(+130)
begetting-age insertion
Cumulative
(+460)
lifespan insertion
LXX already includes 2nd Cainan in baseline (no adjustment).
1.7 SP TOGGLE LOGIC (“inclusive reckoning”; (-1) year through the Flood)
SP Ideal: 4200 BC.
SP Normal (Toggle ON): 4199 BC (= 4200 − 1), standard for FILE_18.
Toggle ON “(-1) year” effect applies through the Flood; post-Flood resumes standard intervals.
Shem pivot / superposition: Shem legitimately appears as 2990/2991 BC and 2390/2391 BC (dual layer: Noah-bound vs Arphaxad-bound).
1.7a PRESSURE-TEST SPLICE: SP ANOMALY PROTOCOL (sealed; additive clarification)
In SP Toggle-ON (antediluvian domain only):
(\mathrm{Anom}{SP}(\text{Noah}) := +1) (\mathrm{Anom}{SP}(\text{Shem}) := +2)
Post-Flood (Toggle OFF): revert to the standard ((\pm 2)) Shem anomaly rule as defined in this capsule (see §2.4).
1.8 KINGS OF JUDAH DUAL-LEDGER +50 (Jubilee Expansion)
Historical anchor:
[
1446-480=966\ \text{BC}.
]
Schematic harmonic:
[
1446-430=1016\ \text{BC}.
]
Offset operator:
[
J_{50}:=1016-966=50.
]
Dual-Ledger Rule :
Actual (Historical): sums reigns with co-regencies to match secular history (931 BC division / 586 BC fall).
Verbatim (Schematic): sums reigns without co-regency deduction.
Interpretation: the 50-year difference is an intentional Jubilee expansion harmonizing the 430-year Ezekiel cycle with the 480-year 1 Kings 6:1 cycle.
1.9 ARK WARNING NODE
Node definition: the 120-year warning (Gen 6:3).
Placement:
[
\text{ArkWarning}=\text{Flood}+120.
]
Function: creates a (480+120) harmonic structure (mirroring the Temple 480) within the antediluvian timeline.
1.9a PRESSURE-TEST SPLICE: ARK WARNING DOMAIN (sealed; explicit inclusion/exclusion)
Define ArkWarning per enabled tradition/mode:
For each enabled Flood anchor (\mathrm{Flood}T): [ \mathrm{ArkWarning}_T := \mathrm{Flood}_T + 120. ] Enabled domains (explicit): MT Regular Flood SP Regular Flood LXX Regular Flood Flood_GearRail anchors (2456/2458/2460) are excluded unless ArkWarning is explicitly invoked in GearRail ontology (not default). MT Cumulative Mode A Flood ((\mathrm{CumFlood}_A)) MT Cumulative Mode B anchor ((\mathrm{CumFlood}{B,\ anchor}))
Excluded domains (explicit):
SKL tiers
Berossus tiers
Babel/Kish objects
(Those cosmological tiers are a different ontology and do not receive Gen 6:3 warning nodes.)
1.10 OPERATOR (L) (Luminary Protocol; Aaron vs Moses)
[
L:=3+\tfrac12=3.5\ \text{years}.
]
Integer gap: 1529→1526 = 3 years (historical); phase gap: L=3.5 years (Tishri↔Nisan harmonic). These are distinct representations.
Mechanism :
Aaron anchored to Tishri/Fall contributes (+0.5).
Integer historical birth gap is 3 years (structurally partitioned).
Moses anchored to Nisan/Spring.
1.11 “7-YEAR ENVELOPE” (normalized idiom vs spread)
Define two representations of the same timing phenomenon:
(A) Normalized biblical idiom (Nisan→Nisan):
Many biblical spans are stated as whole-year counts under a Nisan-to-Nisan normalization. For the present envelope, the normalized idiom is:
EnvNorm = 7 years (normalization label; Nisan→Nisan idiom).
(B) Physical/spread envelope (Tishri→Nisan allowance):
Because the system permits a Tishri↔Nisan phase offset (cf. Luminary Protocol L = 3.5 in §1.10), the same “7-year” idiom admits a full spread of an added half-year:
EnvSpread = 7.5 years (computational width; allows Tishri↔Nisan phase offset).
(C) Computation rule (hard):
All arithmetic uses EnvSpread = 7.5 when envelope width is required. EnvNorm = 7 is a label and must not be produced by rounding/flooring.
(D) Table rule (hard):
Tables may print either EnvNorm or EnvSpread, but must label which representation is printed (Normalized vs Spread). No computational rounding is permitted.
If a display column must integerize, use DispInt (§0.2) explicitly (display-only).
1.11a HINGE LOCK + DUAL-ANCHOR GROOVE (repository fulcrum; additive)
Hinge Lock :
Pivot datum: Dec. 31, 1 BC → Jan. 1, AD 1 (Western civil hinge), tradition-tagged as Christ’s Day-8 circumcision. This pivot is the mid-bridge in both the mod-30 quad mirror and mod-210 sextuplet traverse: 90 + 30 + 90 = 210, with the central 30 straddling the BC/AD hinge. Schematic rendering: Tishri → Nisan = 7×30 = 210 days (360-day mapping).
Second-Adam Dual-Anchor (sealed; non-contradictory):
7-year block start: Nisan 6 BC → Nisan AD 2 (7y). Year-6 phase: Nisan 1 BC → Nisan AD 1 (Year-6 is a full Nisan-to-Nisan phase, not a single day). Traditional placement inside Year-6: conception at spring/Nisan 1 BC, birth at Dec. 25, 1 BC, leaving ~3 months in Year-6 until Nisan AD 1; the Pivot datum occurs at Day-8 circumcision (Dec. 31, 1 BC → Jan. 1, AD 1). Thus 6 BC = block-start framing (pre-incarnate lens) and 1 BC/AD 1 = Year-6/pivot framing (Second-Adam lens).
John Offset Groove (sealed; day-level alignment):
John is the +6-month counter-phase: Tishri 7 BC → Tishri AD 1 (7y), locking to Christ’s Nisan block as a Nisan/Tishri double-groove. Creation analogue: 3906 Nisan→3899 Nisan BC paired with 3907 Tishri→3900 Tishri BC. Function: enables day-precise alignment (half-year shifts) without breaking the 7-year normalization of §1.11.
1.12 SP SPECIAL LOCKS
1.12.1 SP Noah begetting “502(())” and month-boundary rule (501 vs 502) SP Flood: 2892 BC. Text constraint: “Shem was 100 years old two years after the flood” (\Rightarrow) 2891 BC ((\rightarrow)) Shem born 2991 BC. Inclusive Reckoning Note: In SP Toggle-ON mode, the phrase “two years after the flood” counts the Flood year as Year 1. Thus 2892 (Year 1) → 2891 (Year 2). Arphaxad is placed at 2891 BC in this mode. Noah birth: [ 2892+600=3492\ \text{BC}. ] Integer gap: [ 3492-2991=501. ] Month-boundary toggle: if Shem is born late in the year relative to Noah’s birth month, ordinal counting enters the 502nd year, yielding 502 as a textual/state age. Preservation rule: retain both valid states: 501 = integer gap state 502 = ordinal/textual age state Function of (((*))): flags a harmonic adjustment preserving the “100-year Shem–Arphaxad” constraint within SP compression.
1.12.2 SP Terah “145 (205 ideal)” — Terah Dual-Lock
Normal (145): literal SP text (Gen 11:32) anchoring Terah’s death to Abraham’s Call (1876 BC).
Ideal (205): architectural shadow lifespan (matching MT) required for the 1000-year harmonic ((H_{1000})) (§1.12.3).
Rule: simultaneous states, not competing variants.
1.12.3 Operator (H_{1000}) (1000-Year Harmonic; Shem–Abraham chiasm)
[
H_{1000}:=1000\ \text{years}.
]
Logic frame:
100: Shem’s age at Arphaxad’s birth
1000: millennial bridge between Shem and Abraham in SP Ideal (Terah viewed architecturally)
100: Abraham’s age at Isaac’s birth
Function: frames post-Flood era with an “Abrahamic Century” concept and a millennial bridge in SP Ideal chronology.
1.13 HEZEKIAH PROTOCOL (Units-as-Time axiom; precedent)
Rule: numeric units can function as temporal scalars in defined contexts.
Precedent claims:
(185,000) slain soldiers (\Rightarrow) 185,000 prophetic years.
Dial of Ahaz: 10 degrees (\Rightarrow) 720 years (precession-linked).
This axiom is cited as precedent supporting macro-scaling (e.g., (3.5) days (\times 360=1260) years).
1.14 KEY OF 23 RATIOS (numeric definitions sealed)
Priestly / Ring:
[
K_{23}^{(336)}:=\frac{25}{23}.
]
Prophetic / Pinion:
[
K_{23}^{(360)}:=\frac{70}{69}.
]
Enochian / Spider:
[
K_{23}^{(364)}:=\frac{300}{299}.
]
1.14a PRESSURE-TEST SPLICE: A-SPACE + CIVIL TRANSFORMS + SCALING (sealed; additive)
A-space definition (astronomical year numbering with year 0):
(A=1) corresponds to AD 1
(A=0) corresponds to 1 BC
(A=-1) corresponds to 2 BC, etc.
Civil → A (civil has no year 0):
If civil is AD (y): (A=y)
If civil is BC (y): (A=1-y)
A → civil (inverse; deterministic; preserves halves):
If (A\ge 1): output AD (A)
If (A\le 0): output BC ((1-A))
Mirror identity (no year 0) in A-space form:
Given a locked span (S) (integer), the civil identity is (BC+AD-1=S).
In A-space, if (A_{BC}=1-BC), then the matching AD year is:
[
A_{AD}=S + A_{BC}.
]
(So the mirror pairing is a translation by (S) in A-space.)
Scaling scope rule (CRITICAL; resolves no-year-0 distortion):
There are two distinct kinds of scaling, and they must not be conflated:
Coordinate scaling (absolute year labels; BC/AD/A-space coordinates).
Any scaling applied to an absolute year (e.g., multiplying/dividing a labeled year, or applying a rational operator that produces another labeled year) MUST occur in A-space only:
Convert civil label → A-space
Perform all coordinate scaling in A-space (exact rationals / halves only)
Convert back A-space → civil label
Span scaling (durations / differences / totals).
Scaling applied to a span (e.g., (1656), (21160), (2730), (12600), etc.) is pure integer/rational arithmetic and is permitted directly (no A-space transform required), because spans do not cross the civil “no year 0” boundary.
Boundary rule (deterministic): If an expression contains both absolute labels and spans, first compute the span from the labels (in the civil system or via A-space as appropriate), then apply any ratio scaling to the resulting span.
1.14b PRESSURE-TEST SPLICE: SOTHIC DRIFT FACTOR (exact rational; additive)
Define:
[
K_{\text{Sothic}}:=\frac{23}{40}
\quad\Rightarrow\quad
400\times\left(\frac{23}{40}\right)=230.
]
(Use (23/40) in place of any orphan decimal such as “0.575” in verification lines.)
1.15 SUBORDINATE EXODUS ANCHOR (lens operator; non-replacement)
Baseline:
[
E_{\text{primary}}=1446\ \text{BC}.
]
Lens:
[
E_{\text{sub}}=1231\ \text{BC}.
]
Rule: use 1231 BC only when calculating the specified prophetic mirror track (repository lens), and never as a substitute for 1446 BC.
1.16 FILE_11 — THREE-GEAR PROTOCOL & HARMONIC ENGINE (fully inlined)
1.16.1 Sliding Gear Axiom
Definition: the “Creation Anchor” in Regular Chronology is a dynamic variable determined by the “Son of Noah” selected as the chronological bearer. Genesis 11:10 creates a 3-state gate.
Gear Definitions (FILE_11)
Define total gear shifts (from Gear 1 baseline):
[
G_1=0,\quad G_2=+2,\quad G_3=+4.
]
Incremental extension from Gear 2 to Gear 3:
[
\Delta G_{3|2}=G_3-G_2=+2.
]
Interpretive tags (preserved):
Gear 1 (Japheth): Base / Minimum Baseline / “Left Turn.”
Gear 2 (Shem): Covenant / Covering alignment / “Straight Path.”
Gear 3 (Ham): Extension / Maximum tension / “Right Turn.” Required for MT harmonic verification.
1.16.2 Directional Protocols (FILE_11)
Theorem 2.1 — Left Turn (Gear 1 / Japheth)
Anchor:
[
A_{\text{Left}}=2456\ \text{BC}\quad\text{(Flood/Arphaxad convergence; defined in FILE_11)}.
]
Paths:
Path A (Priestly/Ring):
[
1656\times\left(\frac{25}{23}\right)=1800,\quad
2456+1800=4256\ \text{BC}.
]
Path B (Prophetic/Pinion):
[
1656\times\left(\frac{70}{69}\right)=1680,\quad
2456+1680=4136\ \text{BC}.
]
Theorem 2.2 — Right Turn (Gear 3 / Ham)
Anchor (FILE_11):
[
A_{\text{Right}}=4176\ \text{BC}.
]
Target:
[
1446\ \text{BC}.
]
Span:
[
4176-1446=2730\ \text{years}=7.5\times 364=7\times 390.
]
1.16.2a PRESSURE-TEST SPLICE: FLOOD DISAMBIGUATION & RAILS (sealed)
Disambiguation Rule (HARD): “Flood” is not a single node. Preserve these distinct identifiers:
Flood_Regular(T): the historical baseline Flood per tradition (MT 2243; SP 2892; LXX 3023).
Flood_GearRail: FILE_11 harmonic rail anchors (2456/2458/2460) used in prime/gear theorems.
CumFlood_A: cumulative trunk Flood (4831 BC; §3.1).
CumFlood_B_anchor / CumFlood_B_epoch: Mode-B cumulative anchor and its 7-year epoch (5291; 5296–5289; §3.1a).
Machine Guard: never unify nodes by the label “Flood” alone; unify only by (tag + mode + ontology).
Gear Rail Anchors (Flood_GearRail):
A_Left := 2456 BC (Gear 1 / Japheth / Prime P10).
A_Straight := 2458 BC = 2456 + 2 (Gear 2 / Shem).
A_RightRail := 2460 BC = 2456 + 4 (Gear 3 / Ham), if referenced.
1.16.3 Theorem of the Gap (301 / 299 / 300)
Defined gaps (FILE_11):
Structural Gap: 301 years (SP Gear 2 (\leftrightarrow) MT Gear 2).
Harmonic Gap: 299 years (SP Gear 2 (\leftrightarrow) MT Gear 3).
Virtual Gap: 300 years (interpreted as “299 Solar (\rightarrow) 300 Enochian” for the Spider gear).
1.16.4 MT Harmonic Verification — Kenan Sector (FILE_11)
Theorem 4.1 — The Kenan Lock (1830 harmonic) [ESTABLISHED]
Start from MT Kenan minimum (=3574 BC). Apply Sojourn lens first:
[
3574+215=3789.
]
Then:
[
3789+130+2=3921.
]
Then remove Sojourn lens (as defined in FILE_11 step chain):
[
3921-215=3706.
]
Target super-anchor:
[
1876.
]
Result:
[
3706-1876=1830.
]
Checksums (FILE_11):
[
910+460+460=1830,\qquad 5\times 360+30=1830.
]
Theorem 4.2 — Double Cainan Bridge (7800 / 2300) [ESTABLISHED]
[
11721-3921=7800=60\times 130,
]
[
4391-2091=2300=5\times 460.
]
1.16.5 Watcher Harmonics (FILE_11)
[
9459-4859=4600=10\times 460,
]
[
4600+2300=6900=15\times 460.
]
1.16.6 Filling Protocol (Creation Mapping) (FILE_11)
Cumulative Year
Template Day
Theme
Active Gear
11721 BC
Day 4
Filling (Lights)
Gear 3
11719 BC
Day 6
Filling (Man)
Gear 2
11717 BC
Day 7
Rest (Sabbath)
Gear 1
1.16.7 Kenan Death Mirror (Temple–Sanctuary Fractal) (FILE_11)
Mirror:
[
10814+10347-1=21160.
]
Conversion:
[
21160\times\left(\frac{25}{23}\right)=23000=10\times 2300.
]
1.16.7a PRESSURE-TEST SPLICE: DERIVED COMPONENTS FOR THE 21160 MIRROR (sealed; minimal provenance)
Define the two addends used in the FILE_11 mirror identity (§1.16.7) as locked constants sourced from the MT Cumulative forwarded-window rails:
[
K_A := 10814,\qquad K_B := 10347.
]
Source class : (K_A) and (K_B) are Forwarded 7-year-span endpoints from the MT Cumulative (“Long”) chronology tables (including the +2nd-Cainan enabled rail where applicable).
(Example anchor: (10814) appears as the upper endpoint of the forwarded 7-year window in the +2nd Cainan cumulative rail.)
Locked identity (as used):
[
K_A + K_B – 1 = 21160.
]
Rule: (K_A) and (K_B) are treated as locked constants for the mirror conversion step:
[
21160 \times \left(\frac{25}{23}\right) = 23000.
]
1.16.8 SP locks (FILE_11)
1656 rest lock:
[
4414-2758=1656.
]
SP bridge:
[
13398-4198=9200,\quad
9200\times\left(\frac{25}{23}\right)=10000,\quad
400\times\left(\frac{23}{40}\right)=230\ \text{days}.
]
(Last term is the exact rational form of the legacy decimal statement.)
1.16.8a PRESSURE-TEST SPLICE: SP REST-LOCK CONSTANTS + NOAH EDGE NOTE (sealed; additive)
SP rest-lock constants (sealed; FILE_11):
[
\mathrm{SP_Cre}_{+215} := 4414\ \text{BC} = 4199 + 215.
]
[
\mathrm{SP_RestLockNode} := 2758\ \text{BC}.
]
Locked relation (as used in FILE_11):
[
4414 – 2758 = 1656.
]
Edge-rule note (SP Noah inclusive reckoning): The SP Toggle-ON domain includes a legitimate inclusive/exclusive boundary effect in Noah’s terminal-year phrasing (“in the 601st year…”), so the (2758) node may carry a narrowly localized boundary-state interpretation; preserve such boundary-state notes as modal if invoked, but do not propagate them globally unless explicitly specified.
1.17 RESOLUTION PATCH (modal-state rules; deterministic closure)
1.17.1 MT Cumulative Jared (9454 vs 9459) — Base year vs Forwarded-span upper rail (no rounding)
Trunk Table (FILE_18 / Moses line, Nisan): Jared = 9454 BC (base anchor year).
Forwarded 7-year span protocol (Aaron/Moses envelope rail): Jared is also carried as the forwarded span 9459→9452 BC, where 9459 is the upper endpoint of the forwarded 7-year window (not rounding).
Rule: preserve both representations explicitly (no rounding):
J_base = 9454 BC (base anchor year).
J_span = [9459 → 9452] BC (forwarded 7-year window).
J_upper = 9459 BC (upper endpoint of the forwarded window).
(If any half-year appears in other envelope contexts, preserve it internally; DispInt is display-only (§0.2).)
1.17.2 Cumulative 2nd Cainan nodes (4853 / 4859 / 4393 / 4391)
Definitions:
4853 BC: Moses-line (base) birth node of 2nd Cainan (FILE_18 insertion point).
4859 BC: Upper harmonic bound of that same birth node (envelope upper), used by FILE_11 to lock the 4600 loop.
4393 BC: Base death node from Moses-line birth minus lifespan 460:
[
4853-460=4393.
]
4391 BC: Lower harmonic bound of that death node (envelope lower), per envelope drift logic used in FILE_11.
Rule: Preserve both modal rails:
[
C2_{\text{birth}}={4853\ (\text{base}),\ 4859\ (\text{upper})},
\quad
C2_{\text{death}}={4393\ (\text{base}),\ 4391\ (\text{lower})}.
]
1.17.3 SP Creation anchors (4199 vs 4198) — Primary vs Special Harmonic
SP Ideal: 4200 BC.
SP Normal (Toggle ON; primary): 4199 BC (standard in FILE_18).
SP Gear 1 (special harmonic anchor): 4198 BC.
Meaning: SP Gear 1 is the pure integer floor prior to full engagement of the (+1) inclusive toggle used for Flood counting; used specifically for the 9200-year deep-time bridge.
Rule: treat:
[
\text{SP primary} = 4199,\quad \text{SP harmonic} = 4198.
]
1.18 PRIME LATTICE INTERFACE (A007530) (spliced; no external lookup required)
1.18.1 Definitions
Let (P_n) denote the ordinal index (n) of the prime-quadruplet-start sequence (A007530).
Let (Q_n) denote the quadruplet start value at ordinal (n).
Prime-lattice power is carried by ordinal index (n); (Q_n) is the associated value.
1.18.2 Modulo-30 Law
Exceptional start: (Q_1=5).
For all (n>1): the start value satisfies
[
Q_n\equiv 11\pmod{30}.
]
1.18.3 Physical/Apparent rail generation
Define prime rails (difference exactly 30):
Prime Base / Physical rail:
[
B_n := Q_n-5.
]
Prime Mirror / Apparent rail:
[
M_n := Q_n+25.
]
Rail separation:
[
M_n-B_n=30.
]
Pressure-test splice insert (tie-line): Prime rails are the in-capsule realization of the Mod-30 mirror separation (30) in civil BC coordinates via ((M_n-B_n=30)), while Prime Mod-30 Mirror is the sign-axis pairing executed in A-space.
1.18.4 Canonical anchor whitelist for PRIME VECTORS (vector policy; does not constrain Appendix A targets)
This capsule distinguishes two separate concepts:
(A) Prime-table targets (Appendix A ontology):
Appendix A may list many civil Targets (including deep-time or auxiliary targets). The existence of a Target in Appendix A does not automatically authorize its use as an anchor in prime-vector targeting operations.
(B) Prime-vector anchor whitelist (this policy):
When performing prime-vector targeting/validation operations (i.e., selecting civil anchors as endpoints for locked-span checks), the permitted anchor set is restricted to the following whitelist unless a later section explicitly expands it:
Prime Creation anchors (C6–G2 harmonic anchors; do not replace §1.3): MT 4116 BC; SP 4416 BC; LXX 5496 BC.
Epochal anchors: 2456 BC (Flood_GearRail / Gear 1); 1876 BC (Entry super-anchor); 1446 BC (Exodus); 1406 BC (Conquest).
Messianic anchors: 6 BC (Incarnation block-start / Nativity-window start); 1 BC (Birth focal point within Year-6 / hinge framing of §1.11); AD 25 (Ministry); AD 33 (Death).
Restoration anchors: 536 BC (historical); 486 BC (cosmic / Berossus anchor).
Guard (hard): A value may be a valid Appendix A Target yet remain non-whitelisted for prime-vector anchoring. Do not “promote” a Target into the whitelist unless an explicit section-level authorization states so.
1.18.5 Span policy
Prime spans (S) are treated as locked constants in this capsule.
Validation is permitted using the Civil-span identity (no year 0) and canonical anchor differences, but failures must be preserved (modal/out-of-band) rather than “corrected.”
2) REGULAR (HISTORICAL) CHRONOLOGIES — BASELINE TABLES (fully inlined)
2.1 MT REGULAR BASELINE (Minimum)
Anchors: Exodus 1446 BC; Entry 1661 BC (baseline)
2.1.1 Creation → Flood (MT Minimum)
Patriarch/Event
Birth (BC)
Death (BC)
Lifespan
Begetting
Creation Week
3906
3899
7
—
Adam
3899
2969
930
130
Seth
3769
2857
912
105
Enosh
3664
2759
905
90
Kenan
3574
2664
910
70
Mahalalel
3504
2609
895
65
Jared
3439
2477
962
162
Enoch
3277
2912
365
65
Methuselah
3212
2243
969
187
Lamech
3025
2248
777
182
Noah
2843
1893
950
500
FLOOD
2243
2242
1
—
2.1.2 Post-Flood → Terah (MT Minimum)
Patriarch/Event
Birth (BC)
Death (BC)
Lifespan
Begetting
Shem
2341
1741
600
100
Arphaxad
2241
1803
438
35
Shelah
2206
1773
433
30
Eber
2176
1712
464
34
Peleg
2142
1903
239
30
Reu
2112
1873
239
32
Serug
2080
1850
230
30
Nahor
2050
1902
148
29
Terah
2021
1816
205
70/130
Abraham
1951
1776
175
—
Isaac
1851
1671
180
60
Jacob
1791
1644
147
90/130
Levi
1704
1567
137
—
2.2 SP REGULAR BASELINE (Minimum)
Anchor: Exodus 1446 BC. SP Normal = 4199 BC (Toggle ON) through Flood.
2.2.1 Creation → Flood (SP Normal / Toggle ON)
Patriarch/Event
Birth (BC)
Death (BC)
Lifespan
Begetting
Creation Week
4206
4199
7
—
Adam
4199
3269
930
130
Seth
4069
3157
912
105
Enosh
3964
3059
905
90
Kenan
3874
2964
910
70
Mahalalel
3804
2909
895
65
Jared
3739
2892
847
62
Enoch
3677
3312
365
65
Methuselah
3612
2892
720
67
Lamech
3545
2892
653
53
Noah
3492
2542
950
502((*))
FLOOD
2892
2891
1
—
2.2.2 Post-Flood / Shem-Line → Abraham (SP; Shem superposition + Terah dual-lock)
(Note: Shem is born pre-Flood but spans the boundary; listed here for continuity.)
Shem states: 2990/2390 (Noah-bound) and 2991/2391 (Arphaxad-bound).
Patriarch/Event
Birth (BC)
Death (BC)
Lifespan
Begetting
Shem
2991/2990
2391/2390
600
100
Arphaxad
2891
2453
438
135
Shelah
2756
2323
433
130
Eber
2626
2222
404
134
Peleg
2492
2253
239
130
Reu
2362
2123
239
132
Serug
2230
2000
230
130
Nahor
2100
1952
148
79
Terah
2021
1876
145 (205 ideal)
70
Abraham
1951
1776
175
—
2.3 LXX REGULAR BASELINE (FULL DATA; MINIMUM RUNNABLE) (stitched replacement of v6.6 §2.3 placeholder; no table deletions elsewhere)
Scope Rule (CRITICAL): Creation endpoint offset only:
[
5279 = 3899 + 1380.
]
Do not apply +1380 to Flood or post-Flood nodes. Compute Flood and patriarchal nodes from the internal LXX table values below (LXX diverges internally via its begetting-age structure and the inclusion of 2nd Cainan).
Base: Creation endpoint = 5279 BC. Flood = 3023 BC.
Patriarch/Event
Birth (BC)
Death (BC)
Notes
Creation Week
5286
5279
7 years
Adam
5279
4349
930
Seth
5049
4137
912
Enosh
4844
3939
905
Kenan
4654
3744
910
Mahalalel
4484
3589
895
Jared
4319
3357
962
Enoch
4157
3792
365
Methuselah
3992
3023
969
Lamech
3805
3028
777
Noah
3623
2673
950
FLOOD
3023
3022
1
Shem
3121
2521
600
Arphaxad
3021
2556
465
2nd Cainan
2886
2426
460
Shelah
2756
2296
460
Eber
2626
2122
504
Peleg
2492
2253
239
Reu
2362
2123
239
Serug
2230
2000
230
Nahor
2100
1921
179
Terah
2021
1816
205
Abraham
1951
1776
converges with MT minimum
(If begetting ages are required, add them as a separate explicit table; this table closes the “assumed present” breach.)
2.4 REGULAR (\pm 2) (Shem anomaly) mapping
Tradition
Noah (Literal → Ideal)
Shem (Literal → Ideal)
MT
2843–1893 → 2841–1891
2341–1741 → 2343–1743
SP
3492–2542 → 3493–2543
2991–2391 → 2993–2393
LXX
3623–2673 → 3621–2671
3121–2521 → 3123–2523
2.5 BOOK OF JUBILEES (JUB) — HOLOGRAPHIC LENS (DERIVATIVE MODE; MINIMAL)
Role rule (hard): JUB is a derivative “side-road” projection. It must not overwrite MT/LXX/SP baselines in §§2.1–2.4.
2.5.1 Locked anchors (civil BC)
JUB Creation = 3856 BC
JUB Flood = 2549 BC
2.5.2 SP→JUB offset (343/344 hinge; sealed)
SP Normal is Toggle ON (inclusive labeling) at Creation endpoint 4199 BC.
SP Exclusive label (projection reference) is 4200 BC.
Define both offsets (both valid; choose by SP state used):
ΔJ_theol (Toggle ON / inclusive SP labels): 4199 − 3856 = 343 = 7 × 49
ΔJ_math (Exclusive SP labels): 4200 − 3856 = 344
Selection rule (machine guard):
If the SP date comes from §2.2.1 (Toggle ON table; Creation endpoint 4199), use ΔJ_theol = 343.
If an SP date is explicitly in the exclusive label system (Creation endpoint 4200), use ΔJ_math = 344.
343 vs 344 is not a contradiction; it is the inclusive/exclusive hinge.
2.5.3 Antediluvian transfer operator (sealed; scoped)
For antediluvian nodes only:
From SP Toggle ON tables: JUB_date = SP_date − 343
From SP Exclusive labels: JUB_date = SP_date − 344
(Example checks: SP Creation 4199 → 3856; SP Flood 2892 → 2549.)
2.5.4 Verification locks (hard; must pass)
(1) Creation→Flood span: 3856 − 2549 = 1307
(2) Creation→Conquest (50 jubilees): 3856 − 1406 = 2450 = 50 × 49
(3) Flood-to-Christ signature (Enoch×Jubilee):
2548 = 7×364 (=52×49).
Since JUB Flood is 2549 BC, the elapsed BC-only span to 1 BC is 2548 years (2549−1); do not introduce year 0.
2.5.5 Post-Flood usage rule (minimal, non-overwrite)
JUB post-Flood is hybrid by design: SP antediluvian backbone + MT patriarchal framework (100+60+130).
Repository rule when invoking JUB post-Flood: prefer JUB stated patriarchal ages (which match MT) over contradictory jubilee/week-derived placements after Abraham (FILE_20 §7A2).
2.6 PRIME–CIVIL INTERFACE + NT GENEALOGY BRIDGE + SCALING LAWS
Incarnation / Genealogy Origin Label (P1 vs P2; sealed; invariance enforced)
The civil-year system (BC/AD; no year 0) is a coordinate label used to express fixed historical dates (e.g., 1446 BC Exodus; 966 BC Temple; 586 BC fall). These dates are not “chosen” from P1 or P2; they are historically anchored and invariant.
Prime-lattice invariance (hard): All prime-node civil coordinates are rigid because the lattice is rigid. In particular, P2→P1 is fixed by the prime-start gap 11 − 5 = 6, and all other prime placements propagate by fixed deltas (e.g., P3 has ΔQ=90 from P2 and therefore remains the same civil coordinate regardless of whether one references P2 or P1 as an explanatory hinge).
Allowed (genealogy-only): OriginLabel may be P2-light (6 BC) or P1-hinge (AD 1 / 1 BC) for constructing 70-year projection brackets.
Invariant (hard): Historical anchors and prime-node civil coordinates never change under OriginLabel selection.
P1-hinge origin label: AD 1 / 1 BC hinge (P1 singularity; “end-of-six / hinge” framing).
This origin-label selection affects only derived schematic bracket endpoints (e.g., “Shadow Creation” style projections) and must never modify any historically anchored year or any prime-node civil coordinate.
Axis mechanics (A-space / Z-space; deterministic; genealogy-only)
Use A-space (§1.14a / FILE_42): A=0 ↔ 1 BC; A=+1 ↔ AD 1.
Define an optional hinge-centered coordinate for genealogy work only: Z := A − 1.
Then P1 is the natural zero-axis: Z(P1)=0.
Direction of propagation is selected by Gospel orientation (Luke backward; Matthew forward); step-size remains 70 years per generation.
Micro-table (optional but recommended):
Civil | A-space | Z-space (A−1)
1 BC | 0 | −1
AD 1 (P1) | 1 | 0
Guard (hard; insert once before the first 70-year multiplication in §2.6):
OriginLabel(P1) vs OriginLabel(P2) is permitted only for schematic genealogical brackets; any attempt to shift historical anchors or prime-node civil placements under this rule is invalid.
Classification guard (optional one-liner; use once where 5250/2800/8050/8750 first appear):
If a result differs by an integer multiple of 70 solely because P1-origin vs P2-origin was selected, classify it as AxisState(P1) vs AxisState(P2) (genealogy-only) and do not propagate it into non-genealogical prime targets.
Source compression: FILE_42 (Prime–Civil interface), FILE_43 (Matthew/Luke bridge), FILE_44 (macro scaling).
Status: DEFINED (additive; no baseline overrides).
Hard rule: This module introduces a second mapping layer (“Prime–Civil Cluster Mapping”) that must not be conflated with Appendix A TargetRules.
2.6.1 DISAMBIGUATION GUARDS (mandatory)
Two distinct mapping layers must be preserved:
Prime-Table Mapping (Appendix A): uses stored spans S and TargetRules (§7.0.4).
Prime–Civil Cluster Mapping (this module): uses A-space continuity and an early-cluster embedding rule.
Do not reconcile by force. If a P# appears to “target” different civil dates across these two layers, treat them as distinct tagged nodes:
P#_PrimeTable (Appendix A ontology; uses S + TargetRule or lookup/exception).
P#_Cluster (this ontology; uses A-space embedding and mod-30 continuity).
2.6.2 PRIME–CIVIL CLUSTER MAPPING (P1–P3) (FILE_42 core; CLUSTER ONTOLOGY ONLY)
Mandatory notation (hard): In this subsection, every prime symbol MUST carry the Cluster suffix. Do not write bare “P1/P2/P3” here. If Appendix A is referenced, use _PrimeTable explicitly (e.g., P2_PrimeTable) and do not reconcile the two ontologies. Locked notation (prime-quad start sequence A007530): Quad start: (Q) Quad: ({Q,\ Q+2,\ Q+6,\ Q+8}) Rails: (B:=Q-5,\ M:=Q+25), so (M-B=30) A-space civil rendering (align with §1.14a): If (A\ge 1\Rightarrow) AD (A) If (A\le 0\Rightarrow) BC ((1-A)) Early BC-cluster embedding rule (cluster layer only): [ A := 1 – B. ] Guard (hard): This embedding rule is NOT a §7.0.4 TargetRule. It is a separate Prime–Civil Cluster Mapping interface rule and must not be used to compute Appendix A Targets. (A) (P2{\text{Cluster}}) as the first sextuplet-embedded quad seed
First sextuplet is ({7,11,13,17,19,23}); embedded quad begins at (Q=11\Rightarrow P2_{\text{Cluster}}).
(P2_{\text{Cluster}}:\ Q=11\Rightarrow B=6\Rightarrow A=1-6=-5\Rightarrow 6\ \text{BC}.)
LOCK:
(P2_{\text{Cluster}}(\text{base}) = 6\ \text{BC}.)
Mirror continuity (mod-30 carried into A-space):
[
A(P2_{\text{Cluster}}(\text{mirror})) = A(P2_{\text{Cluster}}(\text{base})) + 30 = -5 + 30 = 25 \Rightarrow \text{AD }25.
]
LOCK:
(P2_{\text{Cluster}}(\text{mirror}) = \text{AD }25.)
(B) (P3_{\text{Cluster}}) propagation by (\Delta=90) in A-space (cluster layer only)
(P3_{\text{Cluster}}:\ Q=101\Rightarrow B=96.)
The base-rail jump from (P2_{\text{Cluster}}) to (P3_{\text{Cluster}}) is:
[
\Delta B = 96-6=90.
]
Thus, by A-space propagation:
[
A(P3_{\text{Cluster}}(\text{base})) = A(P2_{\text{Cluster}}(\text{base})) – 90 = -5 – 90 = -95 \Rightarrow 96\ \text{BC}.
]
LOCK:
(P3_{\text{Cluster}}(\text{base}) = 96\ \text{BC}.)
Mirror propagation:
[
A(P3_{\text{Cluster}}(\text{mirror})) = A(P2_{\text{Cluster}}(\text{mirror})) + 90 = 25 + 90 = 115 \Rightarrow \text{AD }115.
]
LOCK:
(P3_{\text{Cluster}}(\text{mirror}) = \text{AD }115.)
(C) (P1_{\text{Cluster}}) singularity + restored geometry at the pivot
(P1_{\text{Cluster}}:\ Q=5) lies before the first sextuplet; it is treated as a singular pivot and is not required to obey the same embedding/propagation conditions as (P2_{\text{Cluster}}) and (P3_{\text{Cluster}}).
Pivot placement rule (cluster layer only): the (P2_{\text{Cluster}}) base gap is (B=6), which is carried across the civil hinge to set the pivot year:
LOCK:
(P1_{\text{Cluster}}(\text{pivot}) = \text{AD }1.)
Restored geometry (23→25) to preserve mod-30 at the singularity:
The natural prime mirror candidate (-23) would yield a 28-step separation from (+5). The restored geometry uses (-25) so that the framing separation is 30.
A-space continuity from (A=1):
[
A(P1_{\text{Cluster}}(\text{extension})) = 1 + 30 = 31 \Rightarrow \text{AD }31.
]
LOCK:
(P1_{\text{Cluster}}(\text{extension}) = \text{AD }31) (geometry node; not asserted as “the” crucifixion year).
Disambiguation reminder (mandatory; restates §2.6.1 locally):
P#_Cluster results in this subsection are Prime–Civil Cluster Mapping outputs.
P#_PrimeTable results are Appendix A outputs computed only by stored (S) + TargetRule (§7.0.4), lookup, or explicit exception tags.
Do not reconcile P#_Cluster with P#_PrimeTable unless an explicit bridge operator is defined in-capsule.
2.6.3 JOHANNINE TEMPLE LOCKS (FILE_42 §3)
Schematic anchor: Herod Temple foundation = 20 BC.
Civil hinge arithmetic (no year 0):
John 2:20 (“46 years”):
[
20\text{ BC} + 46 = \text{AD }27.
]
LOCK: Temple46 = AD 27.
John 8:57 (“not yet 50”), via priestly operator:
[
46\times\left(\frac{25}{23}\right)=50,\quad 20\text{ BC}+50=\text{AD }31.
]
LOCK: Temple50 = AD 31 (aligns with P1_Cluster(extension)).
Terah mirror source for +60 (macro mirror claim):
30 BC ↔ AD 31 spans 60 (no year 0):
[
30\text{ BC}\rightarrow 1\text{ BC}=29,\quad 1\text{ BC}\rightarrow \text{AD }31=31,\quad 29+31=60.
]
LOCK: (+60) ↔ (30 BC / AD 31 mirror) (interpretive mapping).
2.7 NT GENEALOGY BRIDGE (MATTHEW/LUKE) (FILE_43 core)
Locked carrier unit:
$$G := 70\ \text{years per generation}.$$
2.7.1 Luke lattice (universal line)
Names: 76 ⇒ span:
$$76\times 70 = 5320.$$
LOCK: LukeSpan = 5320.
Intervals: 75 ⇒
$$75\times 70 = 5250.$$
LOCK: LukeIntervals = 5250.
Brackets from the birth anchor (6 BC):
Full span bracket:
$$6\text{ BC} + 5320 = 5326\text{ BC}.$$
LOCK: LukeHead = 5326 BC.
Shadow Creation via the 30-rail companion (36 BC) using 75 intervals:
$$36\text{ BC} + 5250 = 5286\text{ BC}.$$
LOCK: CreationDay1 = 5286 BC (identified as LXX Creation-Week Day-1 wrapper start in this module).
Shadow Creation paired from 6 BC using 75 intervals:
$$6\text{ BC} + 5250 = 5256\text{ BC}.$$
LOCK: ShadowCreationDay1 = 5256 BC.
Rail separation preserved:
$$5286-5256=30\quad\text{mirrors}\quad 36\text{ BC}-6\text{ BC}=30.$$
2.7.2 Matthew lattice (covenant line) — corrected (41-name list; overlap-count = 42; dual bracket)
Textual counting guard (Matthew 1): Matthew’s “14+14+14” framing employs intentional overlap at a partition node (David and/or Jeconiah counted in overlapping partitions), so the unique named list = 41, while the literary total = 42 is obtained by overlap-counting. This is Matthew-internal theological compression and is treated here as schematic law (not a defect).
Carrier unit (inherits §2.7 lock):
$$G:=70.$$
(A) Name-list bracket to the birth hinge (span = 2800 = 40×70)
This bracket is the Abraham→(Christ birth hinge at 6 BC) span used by the Key-of-23 expansion logic in §2.8, i.e., the name-list bracket (41 unique names presented, but the span is measured to the birth hinge).
Schematic slots to the birth hinge: (40 \Rightarrow)
$$40\times 70 = 2800.$$
LOCK: MattSpan_BirthHinge = 2800.
From birth anchor (6 BC) back to Abraham’s carrier start:
$$6\text{ BC} + 2800 = 2806\text{ BC}.$$
LOCK: MattAbrahamAnchor = 2806 BC.
Guard (hard): MattSpan_BirthHinge (2800) is the birth-hinge bracket used by §2.8 (MirrorVolume 8050 = 5250 + 2800). It MUST NOT be replaced by MattSpan_Carrier (2870) in any §2.8 computation.
(B) Carrier bracket including the Christ generation end (span = 2870 = 41×70)
In the corrected Matthew lattice, Jesus occupies the terminal carrier, and the terminal carrier is explicitly cross-era:
Terminal carrier (no year 0):
$$6\text{ BC}\rightarrow \text{AD }65 = 70.$$
Thus the Matthew carrier chain contains 41 carriers from Abraham’s carrier start (2806 BC) to the Christ-generation end marker (AD 65):
$$41\times 70=2870.$$
LOCK: MattSpan_Carrier = 2870.
Cross-era verification (no year 0):
$$2806\text{ BC}\rightarrow \text{AD }65:\quad 2806+65-1=2870.$$
LOCK: MattCarrierEnd = AD 65.
(C) Double-knot allowance at both ends (overlap-closure protocol; non-arithmetic)
Because Matthew’s literary 42 is achieved by overlap-counting, the lattice permits a “double-knot” closure at either end without changing the locked spans:
- Head-side knot: the pre-Abraham carrier (MattHead) may be read as Terah’s rung and/or as the overlap-carrier that permits Abraham to be counted in the overlap total.
- Christ-side knot: the Christ carrier may be read as a doubled terminal (6 BC → AD 65 → AD 135) as a compositional closure, analogous to Luke’s “God/Adam” head-knot (5326–5256–5186 BC).
Guard (hard): This double-knot is a compositional/structural reading used to explain Matthew’s overlap-counting behavior; it is NOT a new arithmetic operator and does not alter MattSpan_BirthHinge, MattSpan_Carrier, MattAbrahamAnchor, or MattCarrierEnd.
(D) Head bracket (pre-Abraham carrier; lattice alignment node)
The head bracket is retained as the single pre-Abraham carrier immediately above Abraham’s carrier start:
$$2806+70=2876\text{ BC}.$$
LOCK: MattHead = 2876 BC.
Guard (mandatory): “MattHead” is a lattice framing node (the carrier immediately prior to Abraham in the 70-grid). It is not a claim about Genesis chronology; it is used to form the Jubilee bridge in §2.7.3.
2.7.3 Jubilee bridge (Luke ↔ Matthew)
$$5326 – 2876 = 2450 = 50\times 49 = 5\times 490.$$
LOCK: LukeHead − MattHead = 2450 (50 Jubilees).
Here ‘MattHead’ is the pre-Abraham lattice framing node from §2.7.2(C), not a Matthew name-count claim.
2.8 KEY-OF-23 GENEALOGICAL EXPANSION + 700-YEAR SEAL (FILE_42 §6–7; FILE_43 §6)
Mirror-sum volume (historical; uses MattSpan_BirthHinge = 2800, not MattSpan_Carrier = 2870):
$$8050 = 5250 + 2800 = 115\times 70.$$
LOCK: MirrorVolume = 8050.
Guard (hard; span provenance): MirrorVolume uses LukeIntervals = 5250 and MattSpan_BirthHinge = 2800 only:
$$8050 := 5250 + 2800.$$
Prohibition (hard): MattSpan_Carrier = 2870 MUST NOT be substituted into 8050, 8750, or Seal700.
Priestly expansion:
$$8050\times\left(\frac{25}{23}\right)=8750,\quad \text{since } \frac{8050}{23}=350,\ 350\times 25=8750.$$
LOCK: 8050 → 8750 via 25/23.
Cubic target:
$$\frac{8750}{70}=125=5^3.$$
LOCK: 8750 = (5^3)\times 70.
700-year coefficient (“breath”):
$$8750-8050=700=10\times 70.$$
LOCK: Seal700 = 700.
Applications (sealed in this module):
Matthean extension:
$$2800+700=3500,\quad 3500+3500=7000.$$
LOCK: 2800 → 3500 → 7000.
Cumulative breathing toggle (uses MT cumulative Adam anchor 14006 BC from §3.1):
$$14006-5256=8750,\quad 14006-(5256+700)=8050.$$
LOCK: 14006 ↔ (5256 / 5956) toggles 8750 ↔ 8050.
2.9 SCALING LAWS (10× / 100× / HEPTADIC RESOLUTION) (FILE_44 core)
2.9.1 10× triad at the Creation head (400/700/1000)
Anchor set used by the file (module-local):
5556 BC (LXX “Adam cluster” anchor in FILE_44)
5256 BC (ShadowCreationDay1)
5956 BC (ShadowCreationDay1 + 700)
4556 BC (Noah-node: 5256 − 700)
Locked spans:
[
5556-4556=1000,\quad 5256-4556=700,\quad 5956-5556=400.
]
LOCK: 10× macro-triad = (400/700/1000).
5556 BC is an Appendix-A prime-table Target used here as a module-local scaling anchor; it is not added to the prime-vector anchor whitelist of §1.18.4 unless explicitly invoked as a vector endpoint in a prime-vector operation.
2.9.2 Heptadic Seal from Cumulative Harmonic Anchor (12558)
Inputs (CumAdam_H from §3.1b):
14004 − 1446 = 12558.
Resolution operators:
12558 × (300/299) = 12600.
12558 × (70/69) = 12740.
Generation-resolution output (system definition: 26 generations Adam→Moses):
12740 ÷ 26 = 490 = 7 × 70.
Guard: these are span-resolutions; no A-space coordinate scaling is invoked.
2.9.3 Flood Gear ladder (1050) (ties Luke/Matt rails to MT Flood rail)
Schematic Noah nodes (module-local):
[
5256-700=4556,\quad 2806+700=3506.
]
Ladder:
[
4556\rightarrow 3506\rightarrow 2456\rightarrow 1406,\quad \text{each step }1050.
]
LOCK: FloodGear1050 ladder.
Sub-gear notes retained (non-collapsing):
[
2456-2106=350,\quad 3506-2106=1400=2\times 700.
]
Deep-time resonance:
[
14006-3506=10500=10\times 1050.
]
LOCK: 1050 resonates as 10× in deep time.
2.9.4 Matthean Expansion & Enochian Mirror (P2-Referenced; exact spans)
Matthean expansion (using the 700-year seal):
4200 + 700 = 4900 = 10 × 490.
Exact bisection (cumulative anchor to 4206):
14006 − 4206 = 9800 = 2 × 4900.
Enochian mirror (span-sum under P2 reference; no rounding):
Using spans defined in §3.1b:
14000 + 4200 = 18200 = 50 × 364.
Guard: this is a span identity; it must not be reinterpreted as coordinate mirroring unless §1.14a A-space rules are explicitly invoked.
2.10 SUMMARY TABLE (core machine locks from FILE_42–44)
Class
Lock
Identity
Prime–Civil Cluster
P2 base
6 BC
Prime–Civil Cluster
P2 mirror
AD 25
Prime–Civil Cluster
P1 pivot / extension
AD 1 / AD 31
John Temple
20 BC + 46 / +50
AD 27 / AD 31
Luke
76×70 / 75×70
5320 / 5250
Luke heads
6 BC + 5320 / 36 BC + 5250
5326 BC / 5286 BC
Shadow Creation
6 BC + 5250
5256 BC
Matthew (birth-hinge bracket; used by §2.8)
40×70; 6 BC + 2800; +70 head
2800; 2806 BC; 2876 BC
Matthew (carrier bracket)
41×70; 2806 BC → AD 65 (no year 0)
2870; AD 65
Jubilee Bridge
5326 − 2876
2450 = 50×49 = 5×490
Mirror Volume
5250 + 2800
8050 = 115×70
Key-of-23 Expansion
8050×(25/23)
8750 = 125×70 = 5³×70
700 Seal
8750 − 8050
700 = 10×70
Flood Gear
4556→3506→2456→1406
1050 + 1050 + 1050
Heptadic Seal
14004−1446
12558; ×(300/299)=12600; ×(70/69)=12740; 12740/26=490
3) CUMULATIVE (ACCUMULATIVE / LONG) MATRIX (minimum essentials; fully inlined)
3.1 MT CUMULATIVE TRUNK (Anchor: Conquest = 1406 BC; Moses line, Nisan)
Key scalar:
[14006-1406=12600=10\times 1260.]
Selected trunk nodes (chronological; earliest → latest):
Node Date (BC)
Adam 14006
Kenan 11259
Jared (base) 9454
2nd Cainan birth (base insertion) 4853
Flood 4831
2nd Cainan death (base) 4393
Shelah 4393
Abraham_Cum_trunk = 2435 BC (MT cumulative trunk table state)
Abraham_Cum_prime = 2436 BC (prime-table mapped state; Appendix A P45-A)
Rule: preserve both. Do not reconcile unless a prerequisite file defines the bridge operator.
Moses 1526
Conquest 1406
Envelope modal nodes (per §1.17):
Jared upper: 9459
2nd Cainan birth upper: 4859
2nd Cainan death lower: 4391
3.1a: CUMULATIVE FLOOD MODE-B ANCHOR vs 7-YEAR EPOCH WINDOW (additive; preserves §3.1)
Preserve two cumulative modes:
Mode A (Standard Trunk): CumFlood_A := 4831 BC (as in §3.1)
Mode B (Expanded “+460” rail; 2nd Cainan enabled): define the Mode-B functional anchor as:
CumFlood_B_anchor := CumFlood_A + 460 = 5291 BC.
Define the Mode-B 7-year epoch span explicitly:
CumFlood_B_epoch := 5296–5289 BC (7-year span; endpoint difference = 7; wrapper-style).
CumFlood_B_anchor = 5291 BC is Year 6 inside that wrapper-style span.
Clarifier : This is analogous to CW(CE): birth = CE+7, death = CE (see §1.3a).
Ordering statement (deterministic):
Mode-B comparisons use CumFlood_B_anchor when an anchor year is required for arithmetic checks and prime vectors.
Use CumFlood_B_epoch only when the 7-year schema itself is being referenced.
CUMULATIVE FLOOD MODAL NOTE (do not unify):
CumFlood_A = 4831 BC (trunk cumulative Flood; 3.1)
CumFlood_H = 4836 BC (prime-harmonic flood-target used in prime architecture statements; do not treat as trunk unless a bridge operator is explicitly defined)
Bridge operator between 4831 and 4836 is DEFINED IN PRIME FILES 29–41 (do not infer).
3.1b Cumulative Harmonic Modalities + P2-Referenced Spans (sealed; no rounding)
Purpose: Expose the two P2-referenced spans used in the NT-genealogy/scaling module (§2.9) and define the CumAdam harmonic state used in the Heptadic Seal, without rounding and without inventing new civil anchors.
(1) CumAdam_H (Heptadic): 14004 BC
Provenance: within the cumulative Adam anomaly window (14006–14004) already permitted by repository practice.
Scope: used only as the input to the Heptadic Seal computation in §2.9.2 (spans to Exodus).
(2) Span_Adam→P2Base (exact span; not a date): 14000 years
Definition: exact BC-only span from CumAdam (14006 BC) to the P2 Base anchor (6 BC).
Calculation: 14006 − 6 = 14000.
Scope: used only where §2.9 invokes the “P2-referenced span” convention (BC-only span; no civil hinge required).
(3) Span_4206→P2Base (exact span; not a date): 4200 years
Definition: exact BC-only span from 4206 BC to the P2 Base anchor (6 BC).
Calculation: 4206 − 6 = 4200.
Scope: used only for the Matthean-bisection statements in §2.9.4 and related scaling lines.
Guard (hard): “14000” and “4200” in this subsection are spans, not civil-year nodes. They must not be inserted into date tables as new anchor years.
3.2 MT CUMULATIVE + 2ND CAINAN (convergence rule)
Adam:
[ 14006\rightarrow 14466\quad(+460). ]
Convergence: the 460-year bulge is consumed when 2nd Cainan’s lifespan (460) is subtracted; snaps back at Shelah (4393 BC).
3.3 SP CUMULATIVE (Anchor: Joshua death = 1296 BC)
Node
Date (BC)
Adam
13398
Flood
4711
Terah
2580
Joshua death
1296
3.4 LXX CUMULATIVE + Jubilees Creation Lock
Node
Date (BC)
Adam
14896
Flood
5745
Peleg
3856
Conquest
1406
Jubilees Creation Lock:
[
\text{LXX Cumulative Peleg}=3856\ \text{BC}=\text{Jubilees Creation }3856\ \text{BC}.
]
4) SKL & BEROSSUS INTEGRATION (fully inlined)
4.1 Constants (locked)
[
72,\quad 6480=90\times 72,\quad 12960=180\times 72,\quad 25920=360\times 72,\quad 720=2\times 360.
]
[
3.5\ \text{days}\times 360=1260\ \text{years}.
]
Scale:
[
360\ \text{Sumerian years}=1\ \text{Biblical year}.
]
4.2 50-year Idealistic Shift (locked node restriction)
[
486\ \text{BC}=536+50.
]
486 BC is computational anchor for Berossus projections; 536 BC remains historical anchor.
4.3 Berossus Flood derivation (locked)
[
486\ \text{BC}+34{,}080=34{,}566\ \text{BC}.
]
4.4 Three-tier Flood matrix (locked; 4-date sets per tier)
Tier 3 (SKL Lower): 20,886 / 20,916 / 21,606 / 21,636 BC
Tier 2 (SKL Upper): 27,366 / 27,396 / 28,086 / 28,116 BC
Tier 1 (Berossus): 33,846 / 33,876 / 34,566 / 34,596 BC
Tier gaps:
[
34{,}566-28{,}086=6480,\quad 28{,}086-21{,}606=6480,\quad 34{,}566-21{,}606=12960.
]
Metonic pathway:
[
34{,}566-20{,}886=13{,}680=12{,}960+720.
]
4.5 Exodus lock (locked)
[
27{,}366-25{,}920=1{,}446\ \text{BC}.
]
4.6 Sanctuary Fractal + Key of 23 (locked)
[
28{,}086-486=27{,}600=12\times 2{,}300,\quad
27{,}600\times\left(\frac{25}{23}\right)=30{,}000,\quad
30{,}000-27{,}600=2{,}400=2{,}886-486.
]
[
486\ \text{BC}+30{,}000=\text{AD }29{,}515,\quad
486\ \text{BC}-30{,}000=30{,}486\ \text{BC}.
]
4.7 Babel/Kish rigid 4-point object + 50-year separation (locked)
Short: 2906, 2936, 3626, 3656 BC
Long: 2856, 2886, 3576, 3606 BC
Equalities:
[
2906=2856+50,\quad 2936=2886+50,\quad 3626=3576+50,\quad 3656=3606+50.
]
Breakpoint rule: 50-year offset exists at Babel/Kish and Restoration pairing only.
4.8 “23-Kings totals” mapping (locked)
[
24{,}510-17{,}980=6{,}530=6{,}480+50.
]
Mapping: Short ({2936/2906}(\rightarrow)) Tier 3 Flood; Long ({2886/2856}(\rightarrow)) Tier 2 Flood.
4.9 Pathway rule (locked)
Ideal ⇒ Upper Pixel; Metonic ⇒ Lower Pixel. (+30 is a global mode rail.)
4.10 Berossus mirror check (locked)
[
33{,}846\ \text{BC}+235\ \text{AD}-1=34{,}080,\quad
33{,}876\ \text{BC}+205\ \text{AD}-1=34{,}080.
]
Primary axis: 34,566 BC ↔ 486 BC. Secondary axis: 33,846 BC ↔ AD 235.
Verification:
[
34{,}566-33{,}846=720.
]
4.11 Apparent Mode (+30) as global system state (locked)
Physical: (2906 ↔ 536), (2856 ↔ 486).
Apparent: (2936 ↔ 566), (2886 ↔ 516).
4.12 Generation protocol (locked)
Choose Tradition (Short/Long), Pathway (Ideal/Metonic), Mode (Physical/Apparent).
Build: Lower Base → +720 Upper Base → +30 rail; tier moves by (\pm 6480).
5) ARITHMETIC VERIFICATION (core checks; fully inlined)
From
To
Span
Check
MT min Creation
SP min Creation
300
(4199-3899=300)
MT min Creation
LXX min Creation
1380
(5279-3899=1380)
Entry baseline
Entry super-anchor
215
(1876-1661=215)
Entry super-anchor
Exodus
430
(1876-1446=430)
Entry baseline
Exodus
215
(1661-1446=215)
Entry super-anchor
Exile
1290
(1876-586=1290)
Cum. Adam
Conquest
12600
(14006-1406=12600)
FILE_11 Right-Turn
Exodus
2730
(4176-1446=2730=7.5×364=7×390)
FILE_11 Kenan lock
Super-anchor
1830
(3706-1876=1830)
FILE_11 Mirror
Total
21160
(10814+10347-1=21160)
FILE_11 Sanctuary conversion
Total
23000
(21160×25/23=23000)
FILE_11 SP rest lock
Span
1656
(4414-2758=1656)
FILE_11 SP bridge
Span
9200
(13398-4198=9200; 9200×25/23=10000)
(Pressure-test splice: coordinate scaling uses A-space only per §1.14a; span scaling is permitted directly; Sothic drift uses (23/40) per §1.14b.)
6) QUERY RECIPE (deterministic machine steps)
Identify mode: Regular / Cumulative / Cosmic / Prime / Jubilees (derivative).
Identify tradition: MT / SP / LXX (and SP state: primary 4199 vs harmonic 4198 where specified; and SP label system: Toggle ON vs Exclusive only when explicitly invoked).
Identify epoch: Adam→Terah / Abraham→Levi / fixed.
Apply allowed operators: matrix (+60,+215,+275); Shem (± 2) (localized vs propagating); 2nd Cainan (+130/+460); luminary (L=3.5); jubilee (J_{50}=50); Key-of-23 ratios; gear gates (G_1,G_2,G_3) and ((ΔG_{3|2})); lattice tier/pixel/pathway/mode; subordinate Exodus lens 1231 only when invoked; prime-lattice rails and locked spans per §1.18 and §7.
Jubilees projection branch (mode = Jubilees; sealed minimal per §2.5):
Use JUB anchors: Creation 3856 BC; Flood 2549 BC.
Antediluvian conversion from SP:
- If SP dates are taken from §2.2.1 (Toggle ON; Creation endpoint 4199): subtract 343 (ΔJ_theol).
- If SP dates are explicitly in SP Exclusive labels (Creation endpoint 4200): subtract 344 (ΔJ_math).
Mandatory verification:
- 3856 − 2549 = 1307
- 3856 − 1406 = 2450 (=50×49)
- 2548 = 7×364 (=52×49) and 2548 BC → 1 BC = 2548 years (BC-only subtraction).
Do not overwrite MT/LXX/SP highway baselines; label all results as JUB-mode.
Validate using §5, lattice locks (§4), and prime locks (Appendix A; see §7.0–§7.7).
Preserve modal states explicitly:
Jared cumulative: 9454 (base) / 9459 (upper)
2nd Cainan cumulative: birth 4853 (base) / 4859 (upper); death 4393 (base) / 4391 (lower)
Cumulative Abraham: 2435 (trunk; 3.1) / 2436 (prime-mapped; Appendix A P45-A)
SP creation: 4199 (primary) / 4198 (special harmonic)
SP label hinge (when explicitly invoked): 4199 (Toggle ON / inclusive) vs 4200 (Exclusive label)
SP Shem: 2990/2991 and 2390/2391
SP Noah: 501/502
SP Terah: 145/205
Entry: 1661 baseline vs 1876 super-anchor
JUB anchors (locked): Creation 3856; Flood 2549; SP→JUB offsets: 343 (Toggle ON) / 344 (Exclusive)
Abraham call (+215 lens): 2091
Prime rails: (B_n=Q_n−5), (M_n=Q_n+25) (difference 30)
Prime Creation anchors (prime/chronology Year-6 anchors): MT 4116; SP 4416; LXX 5496 (do not replace §1.3 baselines)
7) PRIME HARMONIC ARCHITECTURE (LATTICE & ORDINALS)
P# identity convention (A007530 / prime-quadruples)
Definition. A prime-quadruple is {k, k+2, k+6, k+8} with all four primes.
OEIS canonical term. In this capsule, the canonical value attached to P# is k(P#), the OEIS A007530 term (the start of the quadruple).
Derived terminal. Define t(P#) := k(P#) + 8. The terminal t is used only when explicitly named.
Ordinal meaning. P# is the ordinal index within A007530 (e.g., P23 is the 23rd quadruple). The ordinal is itself meaningful in the system (e.g., 23, 46, 69, 92 as multiples of 23).
Signed-mirror coordinate layer (pure integer layer)
We allow signed integers as mirror coordinates (…−k, …, −11, −5, +5, +11, …). This is a coordinate device (not a claim about “negative primes” in standard number theory).
All signed-mirror spans are computed by plain integer subtraction in ℤ.
Critical distinction (do not conflate):
Prime-space mirror labels (e.g., −19, −109) are lattice mirror markers in the signed-mirror integer layer.
Calendar years (BC/AD) are rendered from integer coordinates only by the rendering map below, or by §1.14a where authoritative.
Calendar rendering layer (BC/AD)
Calendar labels are a derived rendering of an integer year y:
If y ≤ 0: BC = 1 − y (so 0 → 1 BC, −5 → 6 BC)
If y ≥ 1: AD = y
Guard: For coordinate transforms and scaling, §1.14a is authoritative; this section 7 rendering map is explanatory only and must not override §1.14a.
Axis-crossing identity (calendar only)
When converting a BC/AD span across the BC/AD divide (no year 0), use:
BC + AD − 1 = total_span.
(Do not force “−1” into the signed-mirror integer layer; it belongs to calendar rendering only.)
Two-track operator (the +30 track)
Many prime nodes have a second render on the +30 track. Define:
render_track(base) = base
render_track_plus30(base) = base + 30
(Do not assume every node must be printed with both tracks; use it only where the file already invokes it or where an anchor explicitly requires it.)
Mirror pairing that preserves mod-30
Example (canonical illustration):
{11, 13, 17, 19} ↔ {−19, −17, −13, −11} (reversed order)
so that the mod-30 bridge pairs:
11 ↔ −19
13 ↔ −17
17 ↔ −13
19 ↔ −11
Invariant gap note (why reversal does not change the lattice)
For successive quadruples {k,…} and {k′,…}, the corresponding positions differ by the same constant gap (e.g., 17→107 = 90 and 19→109 = 90). Therefore reversing order on the negative side preserves all interval geometry; it only reverses orientation.
Why sextuplets inherit the quad mirror logic (90+30+90 = 210)
Initial-Conditions Statement (restated: same logic, unforced)
Quadruples establish the governing rule.
After the boundary case P1 = 5, every A007530 quadruple start k lies on the same mod-30 residue rail (k ≡ 11 (mod 30)). This automatically yields a mirror-consistent mod-30 pairing structure.
The mirror rule is purely geometric, not interpretive.
Using the canonical seed example, the quadruple {11, 13, 17, 19} pairs to {−19, −17, −13, −11} in reversed order, but the pairings preserve the same constant separation:
11 with −19, 13 with −17, 17 with −13, 19 with −11.
Each pair differs by 30. Reversal changes direction only; it does not change spacing.
Sextuplets do not introduce a new rule; they must preserve the same continuity condition at their natural modulus.
Prime sextuplets occupy admissible positions on the mod-210 grid. If the quad lattice is required to remain mirror-consistent under its natural modulus (30), then the sextuplet lattice must remain mirror-consistent under its natural modulus (210). This is the same constraint applied at the next structural scale.
The seed sextuplet forces no “extra choice”; it is the minimal bridge that already contains the quad core.
The first sextuplet {7, 11, 13, 17, 19, 23} contains the quad core (11, 13, 17, 19). Therefore, passing through this seed sextuplet is not an added assumption; it is the smallest configuration where sextuplet structure and quad structure coexist.
The 210 separation is the smallest mirror-preserving traverse generated by that shared logic.
Using sextuplet centers as the invariant markers: the seed center is 15 and the next sextuplet center is 105, so the outer step is 105 − 15 = 90. The seed sextuplet also supplies the same internal mirror bridge of 30. Therefore the smallest mirror-consistent traverse is:
90 + 30 + 90 = 210.
Conclusion.
The mod-210 span is not imposed as a separate rule. It is the emergent continuation of the quad mirror rule (mod 30) when the same continuity requirement is applied to the sextuplet lattice’s native modulus (210).
Do not mix lattices inside the A007530 quad table. The quad table reports only the mod-30 quad renderings (e.g., 96/126 rails for Q=101). Any mod-210 sextuplet renderings must be handled in the sextuplet modules (FILE_38–41 logic), as a separate mapping layer.
7.0 PRIME LATTICE AXIOMS (executable; stitched clarification)
Prime-table computation uses §7.0.4 TargetRules; civil span identity across BC/AD uses §0.
7.0.1 Definitions
((P_n)) = ordinal (row index)
((Q_n)) = prime quadruplet start value
Rails:
[
B_n := Q_n – 5 \quad (\text{Base / Physical rail})
]
[
M_n := Q_n + 25 \quad (\text{Mirror / Apparent rail})
]
[
M_n – B_n = 30.
]
Rail-use note (critical): Some locked targets (notably P92 → Creation anchors) are computed on the M-rail using ((T_{BC}=M-S)), not on the B-rail.
7.0.1.a RAIL GEOMETRY (VISUAL GUARD; NON-AUTHORITATIVE)
Rails are raw integers: (B=Q-5), (M=Q+25), so (M-B=30) (geometry only).
Civil dates are NOT read from (B/M). Civil targets are produced only by locked (S) + TargetRule (or lookup/exception).
Example: P3-A uses (T_{BC}=B-S): (96-90 = 6\ \text{BC}) (matches Appendix A).
7.0.1.b P2 DUAL-OPERATOR PROTOCOL (mandatory guard)
Two distinct 30-year operators exist at P2_Cluster and must not be conflated:
Quad-window operator (local rails; within one quad)
Rails: (B := Q – 5), (M := Q + 25), hence (M – B = 30).
For P2_Cluster (Q = 11): (B = 6), (M = 36).
This yields the local 30-year rail window: 36 BC ↔ 6 BC (a rail consequence).
Mod-30 bridge operator (cross-era; A-space continuity)
From the locked A-space anchor P2_Cluster(base) = 6 BC (A = −5), continuity gives:
A(mirror) = A(base) + 30 = −5 + 30 = 25 ⇒ AD 25
This yields the cross-era 30 bridge: 6 BC ↔ AD 25 (civil hinge; no year 0).
Guard (hard): “36 BC ↔ 6 BC” is a rail/quad-window artifact; “6 BC ↔ AD 25” is an A-space continuity artifact. Treat them as separate operators even though both realize a 30-span.
7.0.2 Mod-30 Law + boundary note (interpretive-structural; non-numeric)
For ((n>1)): ((Q_n \equiv 11 \ (\mathrm{mod}\ 30))).
Exceptional start: ((Q_1=5)).
Boundary note (geometry-first, no “forced override”):
P1 is the singular pivot preceding the first sextuplet-embedded quad seed. Its “natural” mirror candidate in prime-space is −23 (prime), but (5 – (-23) = 28), which does not preserve the lattice’s mod-30 continuity framing at the pivot. The system therefore carries a restored geometry node at −25 so that (5 – (-25) = 30) remains invariant as a framing statement. (This does not alter the numeric rail definitions above; it distinguishes a geometry node from a prime node at the singular pivot.)
7.0.3 Prime-table sealing policy (critical)
Span ((S)) is a stored locked constant, not derived from ((B)) and ((M)). “Formula” cells are non-authoritative annotations.
Authority order:
[
Q, B, M, S, Target, TargetRule \text{ are authoritative.}
]
“Formula/Theme” text is descriptive only.
7.0.4 Deterministic TargetRule (sealed; scoped)
Each prime row MUST specify exactly one TargetRule chosen from this set:
(T_{BC} = B – S)
(T_{BC} = M – S)
(T_{AD} = (S – B) + 1)
(T_{AD} = (S – M) + 1)
Exceptions:
Rows explicitly tagged EXCEPTION (see §7.1.1) may use their stated exception rule.
Rows sealed as lookup (see §7.1.2) have Target fixed and do not require a TargetRule from the set.
Guard: Any row not tagged EXCEPTION or lookup MUST use exactly one rule from the set above.
7.0.5 Duplicate ordinals (mandatory disambiguation)
Duplicate ordinals must be labeled with suffix rails, e.g.:
P23-A, P23-B
P26-A, P26-B
P46-A, P46-B
P92-A, P92-B, P92-C
7.1 PRIME CREATION ANCHORS (C6–G2 harmonic anchors; sealed)
Derived harmonic targets for Prime vectors. Do not replace §1.3 baselines.
Define the prime-domain Creation anchors by:
[
C6\text{–}G2(\text{Tradition}) = CreationEndpoint^*(\text{Tradition}) + 215 + G_2,\quad
G_2 = +2.
]
MT Harmonic: ((3899+215+2=4116\ \text{BC})).
SP Harmonic: ((4199+215+2=4416\ \text{BC})).
LXX Harmonic: ((5279+215+2=5496\ \text{BC})).
Dual-tag identity rule: 4116 BC is preserved as a node carrying simultaneous identities (gear-state identity and Creation-Day/Year framework identity) while functioning as the MT prime-domain Creation anchor.
APPENDIX A (Prime Module): Selected Locked Rows (subset shown) + Verification Locks
APPENDIX A SCOPE NOTE (hard)
This appendix lists only the rows explicitly invoked by the locks in 7.2–7.7 and/or otherwise required for this capsule’s runnable checks. Prime rows not shown here are DEFINED IN PRIME FILES 29–41 and are not to be inferred.
Appendix A validation rule (hard): computation vs rendering
Compute the candidate civil date by applying the row’s TargetRule (integer arithmetic), then compare it to the printed Target.
TargetRule type classification (hard):
“BC rule” = ((T_{BC}=B-S)) or ((T_{BC}=M-S)).
“AD rule” = ((T_{AD}=(S-B)+1)) or ((T_{AD}=(S-M)+1)).
Output-type lock:
BC rules output a BC label by definition (do not reinterpret as signed).
AD rules output an AD label by definition.
Compare only like-with-like:
compare computed civil label (BC/AD) to the printed Target label (BC/AD).
do not compare “signed year y” directly to a civil Target label.
Rendering-map prohibition (critical):
Do not apply the signed rendering map to Appendix A Targets; Targets are already-rendered civil dates.
The signed rendering map ((y \le 0 \Rightarrow BC = 1-y;\ y \ge 1 \Rightarrow AD = y)) is used only when an intermediate result is explicitly stored as a signed integer (y) (e.g., lattice/mirror coordinate work), not for Appendix A Targets.
Normalization helpers (only if needed):
signed(AD n) = n
signed(n BC) = 1 − n
if y ≥ 1 → AD y
if y ≤ 0 → (1 − y) BC
Column definitions
Ordinal (P_n) = row index (n)
Value (Q_n) = quadruplet start value
Base (B_n) = Q_n − 5
Mirror (M_n) = Q_n + 25
Span (S) = locked constant
TargetRule = one of §7.0.4, except where explicitly tagged (see §7.1.1) or sealed as (lookup) (see §7.1.2).
Theme = descriptive tag
Guard (hard): Where Appendix A references “Matthew span,” it must be tagged explicitly as MattSpan_BirthHinge (2800) or MattSpan_Carrier (2870). Bare “Matthew span” is disallowed.
Selected Locked Rows
Prime
Q
B=Q−5
M=Q+25
S (locked)
Target
TargetRule
Theme
P1-A
5
0
30
S_P1 (defined in prime files 29–41)
AD 1
(lookup)
Singularity / Naming pivot
P2-A
11
6
36
3600
3606 BC
EXCEPTION TAG: P2A_COSMIC_SQUARE_DEEP_TIME
Cosmic Square. Note: For Christ Hinge operators (36 BC / 6 BC / AD 25), see §7.0.1b.
P3-A
101
96
126
90
6 BC
(T_{BC}=B−S)
Prophetic Season (Δ=90 bridge to 6 BC)
P4-A
191
186
216
1440
1446 BC
(lookup)
Exodus
P5-A
821
816
846
1250
2066 BC
EXCEPTION TAG: (T_{BC}=B+S)
Isaac
P6-A
1481
1476
1506
14610
1446 BC
(lookup)
Exodus (Wilderness)
P7-A
1871
1866
1896
490
1406 BC
(T_{BC}=M−S)
Conquest
P8-A
2081
2076
2106
2100
6 BC
(T_{BC}=M−S)
Tri-Seal
P9-A
3251
3246
3276
2300
946 BC
(T_{BC}=B−S)
Solomon (Temple)
P10-A
3461
3456
3486
1000
2456 BC
(T_{BC}=B−S)
Flood (Gear 1)
P11-A
5651
5646
5676
4200
1446 BC
(T_{BC}=B−S)
Exodus (Joseph)
P12-A
9431
9426
9456
7000
2456 BC
(T_{BC}=M−S)
7 Millennia
P13-A
13001
12996
13026
10140
2856 BC
(T_{BC}=B−S)
Babel
P14-A
15641
15636
15666
11760
3906 BC
(T_{BC}=M−S)
Creation Week
P15-A
15731
15726
15756
15750
6 BC
(T_{BC}=M−S)
Incarnation block-start (Nativity-window start)
P16-A
16061
16056
16086
14610
1446 BC
(T_{BC}=B−S)
Sothic Exodus
P17-A
18041
18036
18066
18060
6 BC
(T_{BC}=M−S)
430 × 42 Stations of Sojourn
P18-A
18911
18906
18936
19440
AD 535
(T_{AD}=(S−B)+1)
Restoration Mirror
P19-A
19421
19416
19446
18050
1366 BC
(T_{BC}=B−S)
Joshua Death
P20-A
21011
21006
21036
19600
1406 BC
(T_{BC}=B−S)
Conquest (Jubilee Sq)
P21-A
22271
22266
22296
22050
216 BC
(T_{BC}=B−S)
Cube of Man
P22-A
25301
25296
25326
25300
26 BC
(T_{BC}=M−S)
Sanctuary Twin
P23-A
31721
31716
31746
31740
AD 25
(T_{AD}=(S−B)+1)
Messiah Prime
P23-B
31721
31716
31746
27600
4116 BC
(T_{BC}=B−S)
MT Creation Lock (C6–G2)
P24-A
34841
34836
34866
34300
536 BC
(T_{BC}=B−S)
Sabbath Law
P25-A
43781
43776
43806
43830
AD 25
(T_{AD}=(S−M)+1)
Mosaic-Christ
P26-A
51341
51336
51366
50700
666 BC
(T_{BC}=M−S)
Beast Lock (BC)
P26-B
51341
51336
51366
52000
AD 666
(lookup)
Beast Lock (AD)
P27-A
55331
55326
55356
50000
5326 BC
(T_{BC}=B−S)
Luke Head Lock
P28-A
62981
62976
63006
64400
AD 1406
(lookup)
Tabernacle (Mirror)
P29-A
67211
67206
67236
66700
536 BC
(T_{BC}=M−S)
Cyrus Decree
P30-A
69491
69486
69516
69000
516 BC
(T_{BC}=M−S)
Temple Complete
P31-A
72221
72216
72246
71300
946 BC
(T_{BC}=M−S)
Solomon
P32-A
77261
77256
77286
73600
3656 BC
(T_{BC}=B−S)
MT Watchers (Jared)
P33-A
79691
79686
79716
75900
3786 BC
(T_{BC}=B−S)
Gear 3 Watchers
P34-A
81041
81036
81066
78200
2836 BC
(T_{BC}=B−S)
Babel
P35-A
82721
82716
82746
80500
2216 BC
(T_{BC}=B−S)
Abrahamic Pivot
P36-A
88811
88806
88836
82800
6006 BC
(T_{BC}=B−S)
Creation Capstone
P37-A
97841
97836
97866
95830
2006 BC
(T_{BC}=B−S)
Jacob (Israel)
P38-A
99131
99126
99156
101080
AD 1948
(lookup)
Modern Israel
P39-A
101111
101106
101136
100100
1006 BC
(T_{BC}=B−S)
David
P40-A
109841
109836
109866
112000
AD 2165
(T_{AD}=(S−B)+1)
Abraham Mirror. Uses MattSpan_BirthHinge = 2800 (Abraham → 6 BC); not MattSpan_Carrier = 2870.
P41-A
116531
116526
116556
115989
537 BC
(T_{BC}=B−S)
Exile Terminus
P42-A
119291
119286
119316
123480
AD 4195
(T_{AD}=(S−B)+1)
42nd Generation
P43-A
122201
122196
122226
129430
AD 7205
(T_{AD}=(S−M)+1)
Daniel 12 Extension
P44-A
135461
135456
135486
135520
AD 33
(lookup)
Christ’s Death
P45-A
144161
144156
144186
141750
2436 BC
(T_{BC}=M−S)
Cumulative Abraham
P46-A
157271
157266
157296
158700
AD 1406
(lookup)
LXX Master
P46-B
157271
157266
157296
153180
4116 BC
(T_{BC}=M−S)
MT Creation Lock
P47-A
165701
165696
165726
165600
96 BC
(T_{BC}=B−S)
P3 (Sextuplet 210-Anchor; 100×1656)
P48-A
166841
166836
166866
161280
5556 BC
(T_{BC}=B−S)
LXX Adam
P49-A
171161
171156
171186
168070
3116 BC
(T_{BC}=M−S)
Noah (Rest Lock)
P50-A
187631
187626
187656
187656
1876 BC
(lookup)
Jubilee Capstone
P69-A
295871
295866
295896
292560
3336 BC
(T_{BC}=M−S)
Shem Birth (LXX)
P92-A
420851
420846
420876
416760
4116 BC
(T_{BC}=M−S)
MT Creation (C6–G2)
P92-B
420851
420846
420876
415380
5496 BC
(T_{BC}=M−S)
LXX Creation (C6–G2)
P92-C
420851
420846
420876
418140
2736 BC
(T_{BC}=M−S)
Shem Death (LXX)
Companion render note (non-authoritative; do not treat as TargetRule computation):
For P23, (M-S = 31746 – 31740 = 6) (rail integer). When rendered through the early-cluster A-space embedding used in §2.6.2, this corresponds to the 6 BC birth anchor. Guard: this is a companion render note, not an Appendix A TargetRule computation.
7.1.1 Explicit exception notes (P2, P5)
P5 uses ((T_{BC}=B+S)) (exception tag).
Row P2 does not match ((B-S)). To preserve the established “Cosmic Square” lock without forcing correction, the capsule seals one explicit exception:
P2 uses ((T_{BC}=B+S)) (exception tag).
(Any attempt to eliminate exceptions would require altering the established target, which is prohibited under the “no invention / no forced correction” rule.)
7.1.2 Lookup rows (sealed harmonic locks)
P4, P6, P26-B, P28-A, P38-A, P44-A, P46-A, and P50-A are sealed harmonic locks with Target fixed. TargetRule is intentionally “lookup.”
7.2 THE KEY OF 23 TETRAD (P23–P92) (sealed with explicit dependency notes)
Master Architecture of Variance (V).
Operator V: DEFINED IN PRIME FILES 29–41 (not re-derived in capsule; treated as a locked rule-set).
P23 (Messiah): targets all Creation anchors via harmonic expansion (locked mapping).
MT (4116). SP (4416). LXX (5496).
P46 (Double Witness): targets Creation via operator V (DEFINED IN PRIME FILES 29–41).
MT (Beast Lock): LOCKED VECTOR (see Appendix A, P26 and operator V in §7.2).
LXX: LOCKED VECTOR (DEFINED IN PRIME FILES 29–41).
Master: LOCKED VECTOR targets AD 1406 (Mirror Conquest).
P69 (Triple Witness): targets Shem Birth (locked mapping).
Formula: DEFINED IN PRIME FILES 29–41.
Gap (P46 → P69): DEFINED IN PRIME FILES 29–41; encodes Shem’s 600-year lifespan (harmonic + L).
P92 (Quadruple Witness): targets Shem Death and Creation gaps via 1380 steps (locked mappings).
For P92, use (M = Q+25 = 420{,}876).
MT: (420{,}876 – 416{,}760 = 4{,}116\ \text{BC}).
LXX: (420{,}876 – 415{,}380 = 5{,}496\ \text{BC}).
Shem death: (420{,}876 – 418{,}140 = 2{,}736\ \text{BC}).
Formula (LXX): DEFINED IN PRIME FILES 29–41.
Formula (MT): DEFINED IN PRIME FILES 29–41.
Gap: 60 years (Terah Variant) (interpreted; numerical operator for this gap is DEFINED IN PRIME FILES 29–41).
7.3 THE SANCTUARY ENNEAD (P28–P36) (sealed with explicit dependency notes)
Theme: Temple Ladder.
Law: DEFINED IN PRIME FILES 29–41.
Constraint: symmetric 1080 ladder (Modulo 69 expansion) DEFINED IN PRIME FILES 29–41.
1080 Ladder (Adjustments to Mod 69): DEFINED IN PRIME FILES 29–41.
P28: LOCKED VECTOR (Tabernacle).
P30: LOCKED VECTOR (Temple Complete).
P33: LOCKED VECTOR (Watchers).
P36: LOCKED VECTOR (Creation Capstone).
Clarifier: this 4,836 BC result is a derived ratio sub-lock (CumFlood_H) and is not the Appendix A Target for P36-A (which is 6006 BC).
P36 Span 82,800 / 69 = 1,200 implies Target 4,836 BC (CumFlood_H: prime-harmonic flood-target; not the trunk cumulative Flood CumFlood_A = 4,831 BC).
Bridge operator between 4,831 and 4,836 is DEFINED IN PRIME FILES 29–41 (do not infer).
4,836 BC → 6 BC = 4,830 = 69 × 70.
The capstone generates the expansion ratio (DEFINED IN PRIME FILES 29–41) governing the system.
7.4 THE RARE CLUSTER LATTICE (Quintuplets & Sextuplets) (sealed with explicit dependency notes)
Governed by the Priestly Master Constant (DEFINED IN PRIME FILES 29–41).
Inner Pillars (Quint P6 ↔ P7): Mirror Sum = 3360 (Exodus ↔ Abraham).
Outer Pillars (Quint Q2 ↔ Q4): Linear Gap = 3360.
Sextuplet Lattice (Sext P16 ↔ P19): Linear Gap = 3360 (Wilderness ↔ Kingdom).
Grand Unification (Q2 ↔ P25): Gap = 43,680 (DEFINED IN PRIME FILES 29–41) (Curse × Priestly).
Danielic Mirror (P19 ↔ P25): Sum = 63,210 (DEFINED IN PRIME FILES 29–41).
7.5 THE CREATION CORE (S-PRIMES & ZIPPER) (explicit dependency notes)
Source: FILE_39 (primes are locked constants; derivations not required in capsule).
Day 1: S97 (Width).
Day 2: P19 (Height/Firmament).
Day 3: P25 (Depth/Square).
Day 6: S11,664,547 (Man).
Day 7: S82,984,537 (Sabbath Seal).
Zipper Constant (Z): DEFINED IN PRIME FILES 29–41 (locks Manuscript Divergence).
7.6 VARIANT GENERATION (Sextuplet Moduli) (sealed with explicit dependency notes)
Source: FILE_38.
Modulus 210 (Sextuplet Width): generates the Seder Olam (+210) and Sojourn (+215) variants (routing axiom; explicit equations DEFINED IN PRIME FILES 29–41).
Modulus 30 (Quadruplet Width): generates the Kings (+50) and Terah (+60) variants via center-shifts (routing axiom; explicit equations DEFINED IN PRIME FILES 29–41).
Zero-Center Shift: DEFINED IN PRIME FILES 29–41 (Terah gap operator).
7.7 JACHIN MIRROR & RESTORATION (FILE_41)
Pillar Jachin: AD 29,515.
Mirror Anchor: AD 535 (Restoration).
Span:
[
29{,}515 – 535 = 28{,}980 = 23 \times 1{,}260.
]
Theological Lock: distance from Restoration to Eternity is exactly 23 cycles of the Tribulation (1260-year cycles).
END OF CAPSULE (v10.1, STITCHED EDITION).
Self-contained: unresolved symbols are explicitly marked as DEFINED IN PRIME FILES 29–41 (per Rule 1 & Rule 4), and all other values are deterministic.
For Part 1, File_00 to File_30, see https://490d.com/the-490d-unified-chronology-knowledge-graph-repository/