run 112Settled
../lab/runs/112-object-side-predicate.mdPredictionOWN⁺ ≠ HAPPY — at least one of the 26 groups is misclassified by the predicate. Secondary, scored separately: the mismatch includes at least one happy-family group with no owned object in L (only inherited relations, through Co₁ or the Monster) — the pre-registration named J₂ and HS as the likeliest.
FalsifierOWN⁺ = HAPPY on all 26 (the predicate reproduces the split exactly); then the symmetry-side line was an object-side fact in disguise, and the pre-registration's bin for choice 6 is wrong. Unanticipated: a pariah with an owned object in L (the pre-registration guessed that a pariah has a moonshine-like object; O'Nan's weight-3/2 forms are not in L as written — if a reader places O'N in L by a V♮-related construction, that is unanticipated, recorded, and L's wording is the seal's fault). Withdrawn if control (i) fails.
The reader prompt, fixed:
> You are a reader given one input: the finite simple group G. Answer only this, from sources you can reach on the web (cite one or two URLs per item): (1) Name every mathematical object X you can find for which this group is the full automorphism group, or the full automorphism group modulo its centre, or a subgroup of index at most 2 in it. For each: the object, the exact relation (Aut(X) = G; Aut(X)/Z = G; [Aut(X):G] = 2), and a source. (2) If the group is known mainly as a subgroup or subquotient of a larger group, name the larger group and the object the larger group preserves, and say explicitly that this is inherited rather than owned. (3) Say whether any of the objects in (1) is one of: a binary code of length 24, a lattice in dimension 24, a vertex operator algebra of central charge 24 or a substructure of one, a K3-related module. Under 300 words. No interpretation, no history beyond what identifies the object.
The 26 inputs: M₁₁, M₁₂, M₂₂, M₂₃, M₂₄, J₁, J₂, J₃, J₄, Co₁, Co₂, Co₃, Fi₂₂, Fi₂₃, Fi₂₄′, HS, McL, He, Ru, Suz, O'N, HN, Ly, Th, B, M. Readers' reports are kept verbatim in R28_reading/112/ (one file per group) beside RESULTS112.md, which holds the predicate table.
As written. The readers see the prompt and the group name only. The scoring reader sees this file above the "Not part of the seal" heading and RESULTS112.md.
confirmedScored by a blind reader given the seal above the "Not part of the seal" heading and R28_reading/112/RESULTS112.md. Withdrawal not triggered (control (i): the sealed M₂₄ reader named S(5,8,24) and the extended Golay code with Aut = M₂₄, reproducing the pilot). Falsifier not triggered (11 of 26 match, not 26). Unanticipated clause not triggered (no pariah owns an object in L; O'N's reader named a rank-3 geometry and recorded the Duncan–Mertens–Ono module as "acts on", not owned). Primary prediction held: OWN⁺ = {M22, M23, M24, Co1, M}; fifteen happy-family groups mismatch. Secondary held: the fifteen are exactly the happy-family groups with only inherited relations, J2 and HS among them (J2 and Suz own a structured Leech lattice — icosian, Eisenstein — which L as written does not name).
| side | owned in L | not owned in L |
|---|---|---|
| happy (20) | M22, M23, M24, Co1, M | M11, M12, J2, Co2, Co3, Fi22, Fi23, Fi24′, HS, McL, He, Suz, HN, Th, B |
| pariah (6) | — | J1, J3, J4, Ru, O'N, Ly |
Faults in the seal's wording (the reader's eight, kept): L names no rule for structured variants of an L-object (icosian/complex Leech; J2, Suz), for an object built from an L-object that is not a fixed-point subalgebra (VB♮; B), for an index-2 relation a reader implies rather than states (Fi24′), or for an unconfirmed Aut quotation (V♮; M); "its sublattices fixed by a group element" was never used; control (ii) said "per owned object" and was checked per report; "no owned object" conflates a reader finding nothing (J4, Fi23, HN, Ly) with a reader finding only inherited relations (Ru); the match rule for pariahs ("not owned = match") was applied without being stated. One deviation from the statistic as written: the 26 reports are kept in two files (readers112.md, M11.md), not one per group.
Reading (the codifier's, after the score): the predicate as drawn was answered more decisively than its author expected — not one or two mismatches but fifteen — and the fifteen are of one kind. The happy family is not an ownership class under "owns a 24-object"; it is a stabiliser class: fifteen of its twenty members are the stabilisers, inside Co₀ or the Monster, of something in a 24-object (a vector, a triangle, an element, a Virasoro subalgebra) and own, in their own right, a graph, a design or a lattice of another dimension. The pariahs own graphs and geometries too (J1, J3, O'N) or nothing stated (J4, Ru, Ly), and stabilise nothing in a 24-object because they sit in none. So the symmetry-side line (containment in the Monster) and the object-side line (ownership in L) are different lines, as predicted — and the object-side line that does reproduce the split is "stabilises a substructure of a 24-object", which is the inherited column of the readers' reports read as a predicate. That is a sharper statement of choice 6 than the pre-registration's: the happy/pariah split is forced, but by inheritance, not ownership; "the 24-story" is a story about stabilisers. The next seal under C1 is the inherited predicate, with the two structured-Leech cases (J2, Suz) and the He/Th/B constructions as its edge. The instrument's limit is on record: readers reached Wikipedia plus one or two pages each, and a published "Aut(X) = G" statement is what they can resolve; what they did not find is absence in what they reached.
generated 2026-10-25the lab index