decoy_depthOne_blind
plain-language theorem explainer
The depth-one classical source reading of Loom certificate configurations A and B is identical. Gravity analysts arguing that order-sensitive response needs a depth-two commutator cite this as the decoy: any loop-by-loop amplitude bag conflates the pair. Proof is a one-line wrapper of the Loom separation lemma that the depth-one invariant is blind on A and B.
Claim. The depth-one (loop-by-loop) classical source projection of Loom certificate configuration $A$ equals that of configuration $B$.
background
The module freezes claims G2/G3 of the order-sensitive gravity proposition: an edge-current response on the Freudenthal patch built from the depth-two commutator reading of a Loom Config, seated as an antisymmetric Fin-16 edge current on the generator-(0,2) edge. No metric $H$ and no muCoord table enter.
The depth-one source of a config is the first component of its base invariant: a list of natural numbers, the loop-by-loop amplitude bag. Configurations $A$ and $B$ are the standard Loom certificate pair (door/key duals) that agree on shallow structure and differ deeper in the relation lists.
Upstream, the Loom separation lemma states that this loop-by-loop reading is blind: identical on the pair. Any carrier whose reading of an utterance is a multiset of per-loop quantities therefore conflates $A$ with $B$.
proof idea
One-line wrapper. The depth-one source is defined as the first component of the base invariant, so the claimed equality is exactly the Loom theorem that the depth-one invariant of $A$ equals that of $B$. That upstream result is discharged by decide on the concrete certificate data; this declaration only renames the equality into the gravity analysis vocabulary.
why it matters
Honesty layer for the order-sensitive gravity campaign. The module's THEOREM block is separation, action firing, and metric-image exclusion on the certificate pair; this decoy records that the classical depth-one source cannot be the separating observable. Anyone who treats a bag of per-loop amplitudes as the gravitational source is forced to identify $A$ with $B$, so a physical response that distinguishes them must draw on depth-two content (pair traces / commutator residual), which the sibling seating and history-response constructions supply.
No downstream consumers are wired yet; the declaration stands as a named checkpoint that classical projection is blind before the depth-two edge current is installed. It does not touch the T0–T8 forcing chain or the Recognition Composition Law directly; it is local to the Loom certificate separation used by the gravity analysis.
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