§1, A.1

Statement

Pins are occurrences with two endpoint maps, so parallel pins stay distinct, and partitions are surjections onto [t]

(1.2)

Statement

A second, ordered capacity convention with bound 12(t-1) is defined alongside the paper's unordered one and never used in the main theorem

§1 (Asimow-Roth)

Statement

The cited rank formula is replaced by comparison with the complete graph, and the paper's generic by an open dense set of placements

§1 (Asimow-Roth, regular locus)

Statement

The regular placements are proved open and dense and their complement is not proved Lebesgue-null, and generic is read as simultaneous regularity rather than as algebraic independence of coordinates

§6.4 (necessity)

Necessity

Proved directly rather than by contraposition: no flex is constructed, and grounding fixes one block's twist to zero

§2.1 (addable-edge criterion)

Sparsity

Proved from the induced-edge count alone; supermodularity is never invoked

Lem 2.1, 3.7, 3.8

Sparsity

A 2,811-line construction theorem for (2,2)-tight graphs sits beside them with no paper counterpart, and is not what they rest on

(2.1)-(2.3)

Deletion

Exactness of (2.3) is never asserted; the block-kernel dimension formula is proved directly and gives s = t + u

(2.4)-(2.6)

Deletion

The defect \Delta is not a named quantity anywhere; the inequality \Delta \le 0 appears only as the flagged semismallness budget

§2.2 (certified response edge)

Deletion

The augmentation lemma asks only that the edge be absent and its row in the row space; sparsity of H + xy is a hypothesis of each use, discharged there by the addable-edge lemma

Def 3.1

Flags

Renamed throughout; no standalone one-flag object, and the ghost vertex is the flag index itself

Def 3.2

Flags

Exact types for live vertices and active flags; the completion is an edge set on V \oplus \Gamma, and the variety X_{\mathcal{T}} has no counterpart

Prop 3.3

Flags

Counting halves only: the incidence graph B_{\mathcal{T}} is never constructed, and the geometric half has no counterpart

Thm 1.2

Flags

Never stated standalone; the sole self-stress hypothesis of the assembly theorem is a grounded form over \Q, derived by adjoining three translation variables

Prop 3.3, Prop 6.5

Flags

A rendering convention: the release line has no proposition directive, so the paper's propositions render as lemmas with the word Proposition in the title

§4, Thm 4.2

Strata

Expository: the scheme statements have no Lean counterpart, and Theorem 1.1 does not depend on them

(1.6)/(5.2)

Split–Klein

Two builds of I_F; the load-bearing one is grounded, over \Q, indexed by selected pin occurrences, with the distinct locus as a denominator

Thm 1.3

Split–Klein

Proved for a grounded ideal over \mathbb{Q} indexed by pin occurrences, with the distinct locus a denominator rather than an open set

Cor 5.4

Split–Klein

Neither the ungrounded variety nor the product decomposition has a counterpart; the formalization is grounded from the ring onward

Lem 6.3

Body–pin

No matroid API: the sparse subgraph comes from a maximum sparse subset and the tight-hull partition, with only the constructive half of the min-max load bearing

Lem 6.4

Body–pin

No statement of the lemma's shape exists; a homogeneous prime avoiding a positive-degree denominator drops height, which replaces the orbit argument

§6.4 (sufficiency)

Body–pin

No complex-to-real specialization occurs: the certificates are integer polynomials from the start, and the compatibility-matrix minor f has no counterpart