decoy_depthOne_blind_on_discovery
plain-language theorem explainer
The depth-one bag projection returns identical lists of naturals on the discovery certificate pair. Anyone treating classical source readings as the conventional half of the order-sensitive gravity discriminator would cite this decoy. The proof is a one-line application of the loom lemma that the loop-by-loop invariant is blind on that pair.
Claim. The depth-one (loop-by-loop amplitude bag) projection of the discovery configuration $A$ equals that of configuration $B$: both yield the same list of natural numbers from the first component of the base invariant.
background
The module freezes the classical-source half of the order-sensitive gravity campaign. A classical source projection is a typed reading of a Loom Config allowed to stand in for the conventional source in the discovery discriminator. Only readings already proved equal on the gauge-separated certificate pair may sit at theorem grade; identifying any such reading with continuum stress-energy remains model-level.
The depth-one source is the loop-by-loop amplitude bag: the first component of the base invariant of a configuration, a list of natural numbers. Configurations $A$ and $B$ are the standard discovery pair (every door has a key that opens it with one master lock, versus every door has a key that locks it with one master open). Upstream, the loom separation result states that the loop-by-loop reading is blind: identical on the pair, so any carrier whose reading is a multiset of per-loop quantities conflates $A$ with $B$.
proof idea
One-line term wrapper. The depth-one source is definitionally the first component of the base invariant, so the claim is exactly the loom theorem that the loop-by-loop reading is blind on the discovery pair. That upstream result is discharged by decide on the concrete certificate data; no further algebra is needed here.
why it matters
This is decoy D2 in the classical source projection module: additive, occupation-style bag readings cannot separate the discovery pair. Together with the sibling equalities for abelianised projections and the depth-two separations on both certificate pairs, it inhabits the classical-equal / recognition-unequal shape required by the frozen world G0 plan for order-sensitive gravity.
No downstream theorems currently depend on it (used_by is empty); it is a named instantiation of the general blindness fact at the depth-one projection itself, so the decoy is visible at the gravity-analysis layer rather than only inside Loom. It does not claim a continuum Einstein equation, a seating into Fin 16, or that the depth-two residue is gravitational. Continuum $T_{\mu\nu}$ identification remains model-level honesty.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.