Hunt R-2AC05F: adjudicate the two conflicting kappa = 2 coefficient tables

Two directories in this laboratory carry a table of the same quantity and disagree from i = 2 onward, with conflicting diagnoses of why:

• hunts/higher_xi/C2_EXACT.json (on main), C_{2,i} = 1, -8, 24, -32, 64/3, ... Diagnosis: Bian's published row is wrong from i = 2 because the weights M(v_l) M(w_k) are dropped between thesis p. 71 and eq (8.1).
• hunts/rogue_frontier/fkappa/ (branch hunts(rogue_frontier) checkpoints, commit 360c545), corrected C_{2,i} = 1, -4, 4, -16, 52/3, ... Diagnosis: Bian's published row is right through i = 4 and wrong from i = 5 because of three implementation defects (a truncated assembly loop, phantom zero slots evaluated as nonzero, and an alpha! overcount in (6.18)).

Both cannot be right. The lab's record on main currently carries only the first. This is a mathematical question and must not be settled by a merge order or by whichever branch lands first.

id: r_2ac05f
question: Which of the two recorded kappa=2 form-factor coefficient tables, hunts/higher_xi/C2_EXACT.json or hunts/rogue_frontier/fkappa/coefficients.json (corrected mode), is the correct C_2,i?
frontier: the two tables agree only at i=1 (both 1); higher_xi gives C_2,2=-8 and fkappa gives C_2,2=-4, and they differ at every index from 2 to 11
proposed_attack: recompute the row from the analytic identity R_kappa = xi'/xi + D log Q_kappa in a formal Dirichlet word algebra written for this adjudication, importing neither disputant, and calibrate the one borrowed ingredient on the externally published kappa=1 row
dead_routes:
  - deciding by merge order or by which branch lands first
  - trusting Bian's Lemma 12 that C_kappa,2 is universal, which is the disputed assertion itself
  - using the kappa=1 row alone as the validation, which fkappa's own RESULTS.md section 5(a) already records as the reason none of its three defects was visible from the literature side
required_oracles:
  - the Farmer-Gonek closed form for the kappa=1 row, arXiv:0803.0425, as published
  - exact rational arithmetic in Python fractions, no floating point anywhere
  - fault injection against the probe's own controls
kill_conditions:
  - the independently written probe fails to reproduce the Farmer-Gonek kappa=1 row exactly at all eleven indices
  - the probe reproduces neither disputed table
  - the planted-defect check shows the kappa=1 control is blind to every plant, leaving the calibration unanchored
agents_may:
  - derive the R_kappa expansion and implement it
  - compare against both recorded tables and against the published Bian figure row
  - plant faults in the probe's own machinery to measure control power
  - record the outcome in harness/departments/review_ledger.py
agents_may_not:
  - edit either disputant's directory or files
  - assign a certainty rung to their own output beyond what the oracles support
  - use the reserved word for anything in this hunt
  - claim novelty; no literature search beyond the two sources already named was run

Scope

Writes only inside hunts/r_2ac05f/, plus the two sanctioned exceptions: one case-log entry in hunts/README.md and one appended AttackOutcome in harness/departments/review_ledger.py.

Nothing in this hunt is evidence for or against the Riemann hypothesis (docs/08).