# C11 — Conquest and the 1058 correspondences fit the existing coordinate chart

21 September 2026 · Bounded continuation of C03 and C09–C10.

**No fourth numerical coordinate is needed for the sourced Conquest and 1058 extensions.** On the retained L=598 layer, the added positions are determined by the existing t coordinate. The complete C03 attachment still has four chart placements representing two Creation witnesses. C10's companion cases supply two additional **Creation→Conquest→MT Flood-close** paths, but they do not complete the original three-stage Creation expansion chain.

The proposed full-week **300→299** compression likewise introduces no free continuous parameter once that rule is declared. Its seven interior endpoint pairs coincide with existing native pairs after a one-member reindexing. The additional closing **4413n BC** boundary remains a derived comparison boundary outside the native SP Creation week. The compression's source interpretation therefore remains conditional.

**The source-stage coordinate attachment.** The recovered chart uses signed paired centers

\[
q=(t-L,\ t,\ t+8395,\ t+M,\ t+M-L)
\]

at u=23, with

\[
t=j-5290,\qquad L=600+2d,\qquad M=23w.
\]

Here M is the selected **Shem Mirror width**, not an MT Creation coordinate. A BC coordinate C has signed center −C and display (C+1)t/Cn BC; a reflected regular coordinate R has center +R and display AD Rt/(R+1)n. The paired Mirror axis remains January AD1, with no civil year zero.

C03 already attaches ordinary SP Creation at **b=t+868**, ordinary reflected MT Flood at **F=t+7745**, and reflected SP primary Noah at **N=t+8395+L**. The constants retain their source meanings: 7745=8395−650, and the 868 is the measured cumulative-to-Creation attachment. Creation stays Normal/G2.

Set

\[
E=L+460,\qquad U=t-E.
\]

U is the signed cumulative **LXX ON earlier** member paired with the cumulative **OFF later** member t. The interval [U,t] has length E. At L=598, E=1058, and the new Conquest point is

\[
\boxed{Q=U+7745=t+6687.}
\]

Consequently,

\[
\boxed{Q-b=5819,\qquad F-Q=1058,\qquad F-b=6877.}
\]

The Conquest coordinate is checked against the held reflected field **1399 through 1406**; it is not admitted merely because these differences work.

**All new positions are explicit functions of the old chart.** The following table is restricted to the qualified L=598 source layer.

| Added position | Signed coordinate | Endpoint role |
|---|---|---|
| U | t−1058 | Cumulative LXX ON earlier member |
| Q | t+6687 | Reflected Conquest member |
| B | t+7935 | Reflected MT Flood, retained 430/ON/+60 frame |
| A | −t−10580 | C10 cumulative MT ON Flood member, BC |
| Nᵦ | −t−8993 | C10 regular SP Noah birth, BC |
| Bᵦ | −t−7935 | C10 regular MT ON/+60 Flood midpoint, BC |
| Z | −t−5290 | C10 Christ-period landing, BC |

The constants are inherited rather than fitted: **7935=7745+190=8993−1058**, **10580=8993+1587**, and **5290=8993−3703**. Thus the C10 signed BC sequence satisfies

\[
A\xrightarrow{1587}N_b\xrightarrow{1058}B_b\xrightarrow{2645}Z.
\]

The retained MT midpoint comparison adds **190=130+60** to the ordinary MT Flood coordinate. It does not replace the ordinary full-430/Terah-0/MT-SP-Cainan-OFF profile of the Creation chain. LXX native ON and derived OFF remain distinguished. Regular Gears remain confined to Noah/Shem/Flood; SP companions remain confined to Noah/Shem. A Flood close retains its independent event-year origin.

**One interval has two translated images.** This is the compact relation joining C09 and C10:

\[
I=[U,t],\qquad I+7745=[Q,F],\qquad I+8993=[B,N].
\]

The first image is **reflected Conquest→ordinary MT Flood**. The second is **reflected alternate-frame MT Flood→SP Noah**. Reflecting the second paired interval reverses its endpoint order and gives C10's actual BC comparison **SP Noah→alternate MT Flood**.

Both images have length 1058, and

\[
\boxed{[B,N]=[Q,F]+1248,\qquad1248=8993-7745=650+598.}
\]

This identifies the previously retained 1248 flank as the displacement between these two interval images. The older relation **8993−6877=868+1248=2×1058** is unchanged: its actual outer flanks remain 868 and 1248. They are not relabeled as two consecutive 1058 segments.

These are finite correspondences between checked endpoints. Their affine formulas do not establish a translation action on every chronology or a second Mirror axis.

**The complete C03 attachment keeps its original domain.**

| Join | Shared Noah arc | (t,L,M) | Attached Shem comparison | Reflected Conquest |
|---|---|---|---|---|
| J02 | N02 | (−5287,598,7843) | MT OFF/430, G1 birth→G2 death | AD1400t/1401n |
| J03 | N02 | (−5287,598,8280) | SP primary OFF/**215**, G2→G3 | AD1400t/1401n |
| J04 | N02 | (−5287,598,8625) | LXX **native ON**/430, G2→G3 | AD1400t/1401n |
| J05 | N04 | (−5285,598,7843) | MT OFF/430, G2→G3 | AD1402t/1403n |

The Shem settings stay attached to their own comparison records. In particular, J03's SP Shem is native-215 while its shared Noah/Flood chain is full-430. The three N02 placements remain one Creation witness with different Shem comparisons.

The original positions recover t, L and M by

\[
t=q_1,\qquad L=q_1-q_0,\qquad M=q_3-q_1.
\]

Appending the new affine functions cannot add a free parameter. The full symbolic coefficient rank remains **3**. On the four admitted placements the finite affine rank remains **2**, because L is fixed; the new positions alone have rank **1**, varying only with t. This distinction preserves the original chart's three-coordinate result without claiming source support outside the finite attachment.

**The old links retain a precise phase behavior.**

| Retained link | Chart change | Effect on C11's added positions |
|---|---|---|
| E002, J02→J05 | Δt=+2, L and M held | U, Q and B increase by 2; the four C10 BC signed positions decrease by 2 |
| E048, J02→J03 | ΔM=437 | All C11 positions held |
| E063, J03→J04 | ΔM=345 | All C11 positions held |

The sign difference follows from paired reflection: if R(x)=−x and Tδ(x)=x+δ, then **R∘Tδ=T−δ∘R**. It is therefore expected that the reflected Conquest/Flood side moves in the opposite signed direction to C10's BC chain. On Creation and Conquest, the correspondence selects members of fixed weeks; it supplies no Gear transport for either week.

**The companion cases support a larger partial domain.** Independently checking all eight native SP Creation origins gives exactly four complete **11+2=13** paths when MT Flood starts and closes are both allowed:

| Arc | t | SP Creation, Nisan BC | Reflected Conquest | Reflected ordinary MT Flood | C10 BC Noah→MT ON/+60 Flood | Full C03 expansion chain? |
|---|---:|---:|---|---|---|---|
| N01 | −5288 | 4420 | AD1399t/1400n | AD2457t/2458n, G2 close | 3705→2647 | No |
| N02 | −5287 | 4419 | AD1400t/1401n | AD2458t/2459n, G2 start | 3706→2648 | Yes |
| N03 | −5286 | 4418 | AD1401t/1402n | AD2459t/2460n, G3 close | 3707→2649 | No |
| N04 | −5285 | 4417 | AD1402t/1403n | AD2460t/2461n, G3 start | 3708→2650 | Yes |

Every Creation→Conquest leg is 5819; every Conquest→Flood leg is 1058. These close cases were outside C09's expressly Flood-start comparison. Their inclusion here adds two qualified **prefix paths**, not two complete new 6877→7475→8125 chains.

For N01 and N03 the full C03 formula would demand MT Noah births at **3055** and **3057**, neither admitted in the held three-Gear MT field. Its designated SP companion-death midpoint would be **2756** or **2758**, which are also outside the SP companion-death field. Other numerical coincidences do not repair those role mismatches.

The historical join qualification is also different. **N01 has the retained J01**, with SP native-215 companion Shem **2992→2394**. **N03 has a retained Noah/Flood arc but no complete retained Shem join.** Transporting J01's Shem pair by +2 would require **2994→2396**: the birth is admitted, but the companion death is not. The old A09 chart records contain no L=598 row. C11 therefore records N03's partial (t,L) attachment without inventing an M placement or a completed historical join.

The principal C10 chain **5296n→3709n→6n BC** remains valid as 3+7. Its stronger extension would have t=−5284, midpoint 2651n, cumulative ON member 6342, and ordinary MT Flood candidate **2461**. The required Flood and cumulative ON endpoints are outside their held fields. C10's separately supported Tishri reading is retained; phase is not changed to fill the Nisan gap.

**Full-week compression is a boundary rule with an exact interior reindexing.** To avoid confusion with the chart variable M, denote the MT Creation week by H:

\[
H_i=4121-i,\quad C_i=4421-i,\quad Q_j=1399+j,
\qquad0\le i,j\le7.
\]

The complete 8×8 endpoint comparison gives

\[
C_i+Q_j=5820+j-i.
\]

Therefore native 5819 comparisons satisfy **j=i−1**, with i=1,…,7. Dean's proposed compression instead sets

\[
C_i^*=H_i+299=C_i-1,
\]

so that

\[
C_i^*+Q_j=5819+j-i.
\]

Its full-week match satisfies **j=i**, with i=0,…,7. But

\[
\boxed{C_i^*=C_{i+1}\quad\text{for }i=0,\ldots,6.}
\]

Thus seven compressed endpoint pairs **(Cᵢ*,Qᵢ)** are exactly the native interior pairs **(Cᵢ₊₁,Qᵢ)**. Their two descriptions retain different provenance: the compressed account uses the preceding MT Creation member as its held 299-year anchor. Coordinate coincidence does not establish that compression as the source-generating rule.

| Range | Geometric relationship | Source status |
|---|---|---|
| Compressed offsets 0–6 | Same seven endpoint pairs as native offsets 1–7 | Native endpoints already available; compression provenance remains conditional |
| Compressed offset 7 | 4413n BC → AD1406t/1407n | Additional derived Creation boundary, outside native SP 4421–4414 |

This resolves the parameter question. The fixed rule **300→299** does not require an additional continuously varying chart coordinate. It does require a label identifying the **derived boundary rule and its preimage**, and the full-week statement requires the conditional 4413 endpoint. Those source assumptions do not follow from an affine-rank calculation.

**Compression must be applied at the declared member.** Applying it to C01's existing origins while holding their ordinary MT Flood targets illustrates the distinction:

| Original native chain | Same-index compressed Creation and matched Conquest | Held ordinary MT Flood | New consecutive widths |
|---|---|---:|---|
| 4419 BC → Conquest 1400 → Flood 2458 | 4418 BC → Conquest 1401 | 2458 | 5819 + **1057** = **6876** |
| 4417 BC → Conquest 1402 → Flood 2460 | 4416 BC → Conquest 1403 | 2460 | 5819 + **1057** = **6876** |

AD numerals in this table are paired centers. Shifting the Flood by another +1 would change the first target to G3 close 2459 and leave the second target 2461 unsupported; it would also require unsupported MT Noah births 3057/3059 to preserve the full expansion chain.

The original sourced pairs are recovered by compressing the **preceding** SP member: **4420→4419** with Conquest 1400, or **4418→4417** with Conquest 1402. These recover the existing native witnesses; they do not add independent witnesses or move Creation by a Gear.

**The L=598 restriction remains necessary.** The adjacent formal control t=−5287, L=600 makes the Conquest candidate 1398, the Creation→Conquest width 5817, and the following interval 1060. The C10-style refinement becomes **1587+1060+2643**, with unequal midpoint halves **2647 and 2643**. This numerical control does not activate another source attachment. It shows why a formula available in the three-coordinate space still needs the selected layer and endpoint checks.

**Evidence and recoverable checkpoint.** `evidence/check_c11.py` passes **138 exact checks**. The packet freezes ten inputs: controlling File_18/File_09, the original chart and selection certificate, and the relevant C03/C09/C10 reports and results. The checks reconstruct native endpoints from File_18, validate the four complete C03 placements and three internal links, test the four partial/full interval attachments, check all 64 Creation–Conquest member pairs, and retain the companion, compression and adjacent-layer exclusions.

`C11_COORDINATE_REGISTER.json` records every affine row and its domain. `C11_RESULTS.json` records placements, interval maps, boundary comparisons and controls. Both result files have a byte-identical isolated replay; the packet includes input, replay and artifact SHA256 manifests. The original 66-record chart is unchanged. No canonical source was edited, no historical campaign was rerun, and no later expansion stage was claimed as sourced.

The completed checkpoint is **C01–C11**, alongside the recovered original Reports **01–10**. Interrupted Reports **11–25** remain unestablished as completed; C11 is a new continuation supplement, not a recovery claim for original Report 11. The 5292 typo confirmation and intended seasonal envelope remain unresolved as recorded in C10.

**Best next bounded step:** extend C06's minimal endpoint relations to include Conquest and the 3+2+5 partition, then determine which added relations are independent and which follow from the retained 598/460/650 structure. Keep the full-week compression as a separately typed conditional rule. **High is sufficient.**