C133 — Five direct 13K edges, with a correction to their boundary alignment

22 September 2026 · One bounded source-graph classification after C132. K = 529. The attached File_18 and File_09 are accessible and byte-identical to the controlling copies used through C132.

Finding. The direct 4421 BC → reflected AD 2456 comparison was already recorded in C05 and remains the frozen C127 graph edge opening_13. Its two typed source nodes are opening_Creation and opening_MT_Flood. It is an existing source-qualified 13K interval, not a newly discovered fifth witness.

Correction to C131/C132: this opening 13K comparison and the fifth C10/C12 Noah row P6 lie at opposite ends of the common four-row pattern. Their shared designation as a “fifth” row did not establish a common source binding. C131/C132 associated P6 with the opening's unavailable Conquest AD 1398. Preserving the existing source-profile links instead aligns P6 to Creation 4416 → Conquest AD 1403 → proposed Flood AD 2461. Creation and Conquest are admitted there; the proposed Flood is outside the held ordinary MT field.

Existing graph evidence

The five directed source edges are opening_13, N01_13, N02_13, N03_13, and N04_13. Each goes from fixed native SP Creation to reflected ordinary MT Flood, with full-430, Terah-zero and Cainan-OFF profiles. The first is G1 Flood start; the other four are G2 close/start and G3 close/start. The SP Creation members are selected within the fixed Normal/G2 field; no Gear is transported to Creation.

For the opening edge the complete paired interval is

C05's I_6877 supplies exactly those endpoints. C127 retains them as sourced nodes with the same profile, event and phase tags. The opening edge's proposed 11K waypoint is AD 1398, absent from the retained Conquest field, as C122 already records. Its direct 13K status therefore survives while its Conquest-mediated status fails.

For N01–N04, the existing graph has both source-qualified 11K+2K paths and their 3K+8K+2K refinements. Their edge sums reproduce the direct 13K edges exactly. The inserted 8K preimages remain generated boundaries. The five direct comparisons are not five independent numerical constraints.

The two five-member registers are offset by one row

Let d index native Creation member selection from the opening. On the direct 13K family,

The proposed Conquest waypoint is $q=f-1058=1398+d$. This is a finite description of the retained members, not a new chronology operator or a Creation Gear.

The four shared rows preserve the graph's 868 cumulative-OFF-to-native-Creation link and 190 alternate-to-ordinary MT Flood profile link. With D the cumulative LXX OFF BC base, X the SP Noah BC base and M the alternate MT Flood base, the alignment is

Thus the C10/C12 Noah rows have $D=5289-d$, $X=3704+d$, and MT cumulative ON $A=5291+d$. Their five retained rows occupy d = 1,2,3,4,5, while the five direct 13K source edges occupy d = 0,1,2,3,4.

Consequently the common domain is precisely d = 1–4. These are also the four fully sourced C10 17K squares. “Five” in the two outer registers counts different selections. The C10/C12 column concerns its retained Noah-bearing 3K+17K routes; it is not an exhaustive count of every possible bare cumulative 20K endpoint equality.

The domain calculation can be stated without a new search. Native Creation has bases 4414–4421 and ordinary MT Flood has bases 2455–2460. Requiring $b+f=6877$ leaves f = 2456–2460: five direct pairs. Requiring an admitted $q=f-1058$ leaves f = 2457–2460: four mediated pairs. Flood 2455 would require Creation 4422, outside the native field. At the other boundary, Conquest 1403 requires Flood 2461, outside the held ordinary MT field.

Corrected P6 attribution

P6's actual graph nodes remain A5296, D5284, SP Noah X3709. Its 20K endpoint, 3K+17K route, single 17K diagonal and sourced opening bracket 5296→5290→5284 = 6+6 remain valid. Preserving the links above gives

The first two nodes already exist as C5_creation and C5_conquest, joined by the existing native11_5 edge. C122 explicitly excludes their Flood continuation because 2461 is outside the held field. The full P6 square separately lacks cumulative ON 6342 BC and alternate MT 2651n BC, as C10 records.

By comparison, placing opening Creation 4421 and Flood 2456 into P6 changes the required links to 5284−4421 = 863 and 2651−2456 = 195. Although those altered gaps still add to 1058, they are not the retained 868/190 source-profile links. Equal total length did not justify that cross-family binding. C133 supersedes that attribution in C131/C132; their separate endpoint arithmetic and four-row core remain valid.

Checkpoint

The bounded checker passes 56 assertions covering frozen inputs, current attached controls, all five direct typed edges, four exact path decompositions, the two source-domain intersections, and the P6 attribution correction. The graph remains the inherited 208 nodes/rank 208; no graph node, edge, canonical source or Gear application was added. Original interrupted Reports 11–25 remain unestablished. The evidence packet includes the selected C05 provenance and the explicit correction certificate.

Best next bounded step: test P6's equal 3K comparisons using its correctly aligned, admitted Creation 4416 / Conquest 1403 nodes. Determine whether the C129 equal-3K comparison extends to this boundary despite its missing Flood continuation. This retains the 529 focus and Noah/Shem/Flood Gear scope.