C697 — Derive directional convergence from the Key gap

Question

What source offset makes the paired anchored outputs equal?

Inputs

{
  "span": 690,
  "held_forward": [
    3626,
    3576
  ],
  "held_reverse": [
    2216,
    2166
  ]
}

Sources

[
  "C696; Supplement A §8"
]

Opened utc

2026-09-28T01:16:27.059306+00:00

Results

{
  "Key_output_gap": 50,
  "forward_residual": 0,
  "reverse_residual": 0,
  "individual_gains": [
    10,
    60
  ]
}

Finding

The50 source offset equals(E−P)×690. With the declared direction and assignment, that one equality forces both convergences. The four outputs are structured consequences of the offset and operators, not four independent confirmations.

Reassessment

Recover the complete70-wide quartet and its supplied1470 translation.

Checks

{
  "gap": true,
  "residuals": true,
  "gains": true
}

Closed utc

2026-09-28T01:16:27.059594+00:00

Record provenance

Exact record hash: 7d177b1e037e0e89f11da8a55776b08a414cbe3f4868ce0427c15c6c02d11037

Source journal: Research_Cycles/C0632_C0731/journal.json