# 490d C436 — Source Identity and Direction of the Shem–Flood Return Loop

25 September 2026 UTC. Step 2 of 10, C435–C444.

The additional path3206→3170→3206 is a **source-labelled, mixed-direction affine return**. It is not a chronology running forward and then repeating its history.

| Slot | Source |
|---|---|
|3206 start/end|SP-primary or theoretical LXX-OFF Shem birth, G1/C0/T0/F1|
|3170 intermediate|SP or theoretical LXX-OFF Flood start, G3/C0/T1/F1|
|3620 first pivot|SP companion Noah birth, G1/C1/T0/F0|
|2756 second pivot|SP-primary or theoretical LXX-OFF Noah death, G1/C0/T0/F1|

The16 Cartesian label assignments split into **eight returns to the identical start record** and eight switches between coordinate-equal SP/LXX labels. Exactly one assignment is entirely SP; none preserves one unchanged source context. Source aliases do not supply independent historical witnesses.

The36-year station gap has a direct source derivation. The same-context Flood for Shem3206 is3106, preserving100. Adding the existing Terah60 and G1→G3 shift4 reaches3170. Hence:

`3206−3170=100−60−4=36`.

The first E leg has signed gap414→450; the second has−414→−450. Both use18×23→18×25 in absolute magnitude. Since the full map is E² held at3206, the return is its fixed point; its slope625/529 is not the identity slope1.

A further exact source relationship emerges from this audit:

`(3620+2756)/2=(3206+3170)/2=3188`.

**3188 is already MT Noah birth G2/C1/T0/F1.** The actual pivots sit at3188±432, and the two loop stations at3188±18. Their radii satisfy432=24×18. This is a derived local comparison around an existing record, not adoption of a new global Mirror axis. The source membership of its Gear/Terah family has not yet been tested.

The complete SP source contexts are preserved in the evidence. The first-pivot Noah3620 has companion death2670; the second-pivot Noah death2756 belongs with birth3706. Both retain950. Intermediate3170 belongs to a different Gear/Terah context, with Shem3270 and Noah3770.

Selective comparison with the authenticated C413 synthesis confirms that its earlier E/J/P return graph used the different2531/2533/2535 source menu. C436 does not reopen that census or claim that all possible chronology loops have now been classified. Six current source excerpts support the present records, variants, local rails, Flood distinction and E ratio.

## Verification and scope

17 calculation checks and 20 source/predecessor authentication checks passed. Main result files replay byte for byte. These are root-agent checks, not an independent-agent review or independent historical witnesses.

A fixed-point return is not an identity map or a repeating historical sequence. The midpoint3188 is a local source comparison; the global January-AD1 Mirror is unchanged.

Mirror/529 focus: K=529, E=25/23, P=70/69; J=300/299 remains File02 gap conversion, not a calendar date operator or Residue Protocol. Regular Gears are Noah/Shem/Flood only. SP person companions are local to Noah/Shem; Flood close is an independent event boundary. Both500/100 and502/98 bindings remain valid; SP primary Noah death retains its inclusive/harmonic qualification. LXX native Cainan is ON; OFF is theoretical removal. Global paired Mirror January AD1; local junction January AD2; no civil year zero. No new source point, phase, fitted axis, upstream/cumulative Gear, primer reopening or canonical/graph edit. Capture now; canonize later. Coordinates, source labels, context aliases and derived comparisons remain distinct. Counts are not independent historical witnesses.

## Best next bounded step

**C437, proposed and unexecuted:** Census the six Gear/Terah local midpoint profiles already determined by C434: c=N−518, outer pivots c±432, inner stations c±18. Require every point to remain in the fixed source register and derive the role/context offsets without fitting a center.

The source audit reveals an existing MT Noah record at the common midpoint. Its finite source family is the next structural question before any reflection operation is considered.