## Anchored routes explain the shared 4346 hinge

The retained macro family has a source-conditioned placement as well as a common arithmetic shape. Two supplied regular-MT routes reach 4346:

| Source state | Held anchor | Operation on radius | Generated head |
|---|---:|---|---:|
| Standard Creation 4114 | Exodus 1446 | E(2668)=2900 | 4346 |
| Creation 4304, with +60 Terah and +130 Cainan | Conquest 1406 | P(2898)=2940 | 4346 |

The source-state difference 190=60+130 equals the difference in expansion gains, 232−42. The completed radii differ by 40, exactly matching the anchor separation. Those balances explain the convergence. The shared head is a generated parent label for the two operations; its historical transmission is a separate question.

The second route also maps the complete source path 4304→2648→1406 to 4346→2666→1406. Its 1656|1242 partition becomes 1680|1260, retaining the 4:3 ratio. The internal labels are generated seams within that comparison. They do not inherit the identities of unrelated nodes with the same numerical label.

One civil 1470-step ladder then generates 4346 BC→2876 BC→1406 BC→AD65. A five-year forward translation gives 4341 BC→2871 BC→1401 BC→AD70. Enoch’s close 2876 and the Long-pair center 2871 retain different roles. In the source’s wider Danielic path, the retained junctions give

$$
490|1400|70|1470|1400|35|35=4900.
$$

Grouping the four middle parts gives 490|4340|35|35. Its tenth-scale template is 49|434|3.5|3.5; the fine and coarse paths are dependent resolutions of the same supplied object. Their arithmetic does not by itself appoint a literal historical 434-year interval.

The same retained-component law unifies the new macro completion with the earlier Actual–Rounded connection. If a fraction f of a span is converted by k while the rest remains fixed, the effective total ratio is

$$
q=1+(k-1)f.
$$

| Converted portion | Key | Effective total ratio |
|---|---|---|
| 1/6 | E | P |
| 1/26 | E | J |
| 23/30, the upper 9660 of 12600 | P | 91/90 |
| 23/30, the upper 9660 of 12600 | E | 16/15 |

The last two ratios produce 12740 and 13440. Applying those effective ratios uniformly would move the retained junction: the partial and uniform arms differ by 98/3 or 196 respectively, although their totals agree. This extends the Actual–Rounded endpoint lesson to a second complete source family. An effective total ratio describes the evaluation; the retained partition describes the path.

*Sources: Supplement A §§9.1–9.8,10.3,11.1–11.6; File22 owns the dual-route construction. C692–C695, C699–C702, C713–C715.*

## Bounded companion tests distinguish whole families from selected matches

The admitted four-row directional comparison provides a compact example. Its input magnitude is always 690. Forward E/P assignments from held heads 3626/3576 converge at 2876; reverse P/E assignments from 2216/2166 converge at 2916. The common cause is 50=(E−P)690, which balances the supplied 50 offset. Swapping the Keys breaks the pairings. The comparison keeps its existing SKL status and does not extend to new source states.

Its supplied quartet 2946/2916/2906/2876 has gaps 30|10|30 and center 2911. The declared 1470 translation preserves that shape in 1476/1446/1436/1406. Only 2916 and 2876 are direct paired-Key outputs; the other positions retain their distinct source or generated-companion roles.

Supplement A §13 supplies a separate fixed twelve-node phase field, centered at −2921 in its exact civil phase chart. Translation by 5842 sends every node onto the mirror set. The associated affine reflection pairs all twelve nodes in six transpositions. For the four supplied totals 5840/5842/5844/5846, whole-set overlap counts are 8/12/8/4. The conditional placement equation is c+5842=−c, giving c=−2921 after the template and chart have been fixed. The supplied Long center −2871 instead requires 5742.

This is affine reflection of a fixed phase set, distinct from Rounded digit reversal and its mirror convention. Section13 remains a verification-complete, registered working amendment, without separate author Finalization or full-file pressure testing. These bounded reconstructions retain that status. Remote extensions remain outside this cycle.

*Sources: Supplement A §§8.1–8.6,13.1–13.5,13.7,13.9; C696–C709. The source-location and status review is recorded in REVIEW_C692_C709.*