Item 21: Signed versus magnitude control of grade error
Deference line — second wave · difficulty open · project deference · closed · node item-21
— answered by Stage II; the magnitude target is retired — see item 24
Answered by Stage II, and the magnitude target is retired. Registered as magnitude.* in projects/deference/CLAIMS.md: the signed error sum is exactly a trader payoff and is controlled under the criterion, while the magnitude functional is not a trader payoff and cannot be made one — every trader averages to zero over a coherent mixture, because net worth is affine in the payout vector and the absolute value is not. The obstruction is intrinsic to cash settlement. Record: prompts/2026-08-11-phase-ii-prediction/REPORT.md §1.
Registered results bearing on this item
- magnitude.mixture-networth-zero: No hypothesis on the trader — not on efficiency, rank, or what it reads. This is the mechanism behind the impossibility below.
- magnitude.not-trader-payoff: An impossibility, and intrinsic to cash settlement rather than to the feature grammar: net worth is affine in the payout vector and the absolute value is not. This is why the magnitude target is retir
- magnitude.sharp-trader-networth: Exactly, in every world, on every day. The first summand is a trader payoff; the second is a function of the assessed agent's own prices.
- magnitude.signed-bounded: Ordinary Logical Induction gives signed calibration, under the emission certificate.
- magnitude.signed-bounded-actual: Stage V's form: invokes the pinned dependency's own no-exploitation theorem and retains only the substantive bounded-downside premise, which the constant-tautology declarations inhabit.
- magnitude.sq-error-split: For binary settlement, exactly; `sq_error_le_of_mem_Icc` gives the inequality that survives the substitution.
- magnitude.unit-trader-networth: No remainder term: the criterion has an instrument for the signed functional.
Where it hangs
- held by deference-and-trust
Rounds and decisions that touch it
None recorded.