Pairing-Preserving Radical Repairs Form a Hom-Complex Torsor
Epistemic-graph event: 1348.
When Ledger 1328's radical obstruction vanishes and one correction C_0
exists, every other pairing-preserving repair is
C_0+Z, with Z a radical-valued chain map.
Thus literal repairs form a torsor under
Z^0(Hom(C(G),R)); modulo radical chain homotopy, repair classes form a
torsor under H^0(Hom(C(G),R)). Uniqueness up to homotopy holds exactly
when the latter group vanishes.
The one-term control C(G)=R=Z has zero differential and zero defect, yet
admits one repair for every integer multiplication. Hence a degenerate
pairing can leave a genuine canonicity obstruction after existence is
settled.
A physical five-site repair would therefore need both obstruction vanishing and either radical Hom-rigidity or an independently sourced normalization selecting one torsor point.
Research note:
research/grothendieck/radical-repairs-form-hom-torsor.md.