Section 2.1, tableWhat the model captures and does not capture about deployed inference

Informal interpretation Motivation, interpretation or scope; not a formal claim.

1 Paper text

Property of deployed inference	Captured here	Not captured here
Fixed latency / bounded depth	constant depth $L$ (and window $T$ )	depth growing with $n$
Fixed-scale quantisation (bounded range)	weights/thresholds in fixed grid $\Qset_{W,D}$	fan-in dependent scaling or thresholds growing with $n$
Parallel bit operations	unbounded fan-in AND/OR/NOT	exact global counting / exact parity on unbounded inputs
Signed effects	via input negations (Lemma B.1)	large signed dot-product accumulation

Property of deployed inference

Captured here

Not captured here

Fixed latency / bounded depth

constant depth

L

(and window

T

)

depth growing with

n

Fixed-scale quantisation (bounded range)

weights/thresholds in fixed grid

\Qset_{W,D}

fan-in dependent scaling or thresholds growing with

n

Parallel bit operations

unbounded fan-in AND/OR/NOT

exact global counting / exact parity on unbounded inputs

Signed effects

via input negations (Lemma B.1)

large signed dot-product accumulation

Generated from paper_jmlr.tex, lines 336–350.

2 Explain this

The table lines up four properties of deployed inference with what the model captures:

fixed latency: constant depth (and window $T$ ), not depth growing with $n$ ;
fixed-scale quantisation: weights and thresholds on a fixed grid, not fan-in-dependent scaling;
parallel bit operations: unbounded fan-in AND, OR, NOT, but not exact global counting or parity;
signed effects: through input negations, not large signed dot products.

3 How this is formalised

A summary table. The formal content is the gate model and its simulation: Definition 2.1, Lemma B.1 and Theorem 2.4.

Coverage record
Paper anchor	`par-why-fixed-scale-quantisation-suggests-an-ac0-abstraction-table1` (website anchor; the manuscript has no label here)
Displayed as	Section 2.1, table
Claim	What the model captures and does not capture about deployed inference
Coverage category	Informal interpretation
Statement source	paper_jmlr.tex lines 336–350; SHA-256 of the normalised block source `995cbe39b401240a…`
Depends on	Definition 2.1, Theorem 2.4, Lemma B.1
Explanations	`explain/c-model-table`, `formal/c-model-table`
Build evidence	fresh isolated rebuild, audit report

4 Lean statement and source

No Lean statement corresponds to this claim. This is interpretation or motivation, not a formal mathematical claim.

Build evidence: fresh isolated rebuild of all 38 bundled modules with Lean (version 4.26.0, started 2026-10-10T15:21:56Z, finished 2026-10-10T15:27:00Z: 38/38 modules compiled, 1588 axiom reports, no errors. See Build for the commands and the independent audit of 2026-10-10 (dated evidence).