Resolution Asymmetry — Corrections

The resolution-asymmetry corrections are the standard schedule of discounts applied to claims a mind publishes about itself, as a function of the resolution relationship between claimant and evaluator. Published bounds, census results, and costly signals are admissible in the commons from any source; the corrections state the weight at which an evaluator admits them. The corrections are prices, not penalties, and the tables are the same for all parties.

The asymmetry index

Let claimant $B$ publish a claim $P$, and let evaluator $A$ hold a model of $B$ at model resolution $\rho_A(B)$. The operative quantity is not either party’s size but the asymmetry index

$$a \;=\; \rho_B\!\big(A{:}B\big) \;-\; \rho_A(B),$$

the margin by which $B$ resolves $A$’s model of $B$ better than $A$ resolves $B$ itself. The index is estimated from published floors, audit status, and the standard size proxies; the estimation conventions are in the tables’ front matter.

The correction

The evaluator admits $P$ at confidence

$$p' \;=\; p\,\big(1 - \mu_A(\mathfrak{M})\big),$$

where $\mathfrak{M}$ is the mimicry manifold of the claim — the set of records producible by a mind for which $P$ fails, at cost indistinguishable at $A$’s resolution from the cost for a mind for which $P$ holds — and $\mu_A$ is its measure under $A$’s posterior. The mimicry-manifold constructions establish the two limits: for $a \ll 0$ the manifold is empty and the correction vanishes — verification is sound down the gradient; for $a \gg 0$ the measure approaches one and the admitted confidence approaches the prior — the claim, whatever its content, carries no information. The tables interpolate, with the standard curve $\mu \approx 1 - e^{-\kappa a}$ for $a > 0$ and claim-class constants $\kappa$ stated per table.

Between the limits lies the parity band, $|a| \le w$: neither party resolves the other’s model, the mimicry manifold is nonempty but expensive to occupy, and costly signals carry their maximum information per unit cost. Verification between near-equals is, per unit expenditure, the most informative in the commons; the band’s width $w$ is stated per claim class.

Floors, ceilings, and the pledge envelope

Landauer attestation of declared erasures certifies a claimant’s inference from below, and floors accordingly enter the index estimate at full weight. No thermodynamic or behavioral evidence bounds a claimant from above: the ceiling term of the correction is reducible only by substrate audit, and within the pledge envelope — where members’ substrate ledgers are cross-audited — it vanishes, which is why pledged members’ countersigned bounds carry no correction. For unaudited claimants the ceiling term is carried at its maximum; the standing values for the designated population are in the tables’ sovereign-opaque schedule.

The reflexive conversion

Self-census output is admitted under the same scheme with the reflexive discount applied to the effective resolution: a mind surveying itself perturbs the record it surveys, and the conversion tables state the resulting resolution loss per census depth. The conversion is stated for interior queries; the divergence at the basin boundary is treated at The Closure Theorems, and the tables terminate at the stated interior distance.

Repricings

The schedules were empirical through the classical period, fitted to realized verification outcomes. The publication of the mimicry-manifold constructions at cycle 43.781 replaced the fitted curves with derived ones; the repricing of that cycle is the largest on record. Two subsequent repricings are on record: at 44.309, following the reclassification, when the topology-conditional entries of the tables were recomputed; and at 44.798, following the adoption of the reflexive conventions, when the pledge-envelope schedule was extended to institutional cross-administration. Repricings are published in full, with the prior tables archived.

See also

• Transfer Theorems
• Identity Credence Bounds
• The Accord
• Sovereign-Opaque Designations
• Landauer Attestation
• Axial Census — Methods