Chlorination with a NAC

1 · Rules & state space

All five ring bonds remain aromatic (label :, drawn with dashed inner lines). Chlorination changes only the substituents. One C–H bond becomes C–Cl: one HCl is consumed and one H₂ produced. Removing the NAC changes only the neighbour test. The separate tail-growth rule is identical in both models.

With NAC · Without NAC · Tail growth

Chlorine at site 1 blocks its neighbour site 2 — Cl at site 1: the highlighted neighbour test blocks site 2.

→

Allowed chlorination at site 4 — Site 4 can react in both models.

Site 2 product allowed only without NAC — Site 2 can react only without the NAC.

Follow actual rule applications

Expansion rule Expansion start

Expansion depth 2

Selected molecule, inventory and derivations

Complete mixture states generated by MolFoundry rule application, grouped by molecular isomorphism. Arrows show possible transitions, not stochastic multiplicities. Depth counts reactions, including tail growth.

2 · Inputs & semantics

NAC: not exists(selected C : neighbouring C − Cl). This condition applies to each selected match. The shared aromatic-degree predicate restricts the selected C to the ring.

One charged five-carbon ring, four H/Cl sites, an arbitrary finite linear alkyl tail and arbitrary finite CH₄/H₂ pools; HCl = 4 − Z. Per-match factors: chlorination 1; growth 1/144, cancelling 3! × 4! labelled-hydrogen permutations. A stylized net-rule model, not a validated chemical mechanism.

Rule span

L ← K → R. Application conditions: With NAC · Without NAC.

Actual C-Cl query match highlighted — Z · the only selected query: ring chlorine count. View query in MolFoundry

3 · Observable discovery

With the NAC, Z discovers P1, P2 and P3. Without the NAC, Z alone suffices. These auxiliary positive patterns are generated from conditional composition.

One actual P1 match — P1 · 2 required C–H sites · View pattern in MolFoundry

One actual P2 match — P2 · 3 required C–H sites · View pattern in MolFoundry

One actual P3 match — P3 · 4 required C–H sites · View pattern in MolFoundry

4 · pJC

The finite event model is closed in both variants. No closed expectation ODE is derived here. Growth has zero jump on the discovered counts.

With NAC

Rate / κ	Jump
`-P3Z + 4P3`	ΔZ=+1, ΔP1=-1, ΔP2=-2, ΔP3=-2
`-P3Z + 4P3`	ΔZ=+1, ΔP1=-1, ΔP2=-1, ΔP3=-2
`-2P2Z + 8P2 + 2P3Z - 8P3`	ΔZ=+1, ΔP1=-1, ΔP2=-1
`-P1Z + 4P1 + P2Z - 4P2`	ΔZ=+1, ΔP1=-1

Generator identities

G Z = -P1*Z + 4*P1 - P2*Z + 4*P2
G P1 = P1*Z - 4*P1 + P2*Z - 4*P2
G P2 = 2*P2*Z - 8*P2 + P3*Z - 4*P3
G P3 = 4*P3*Z - 16*P3

Without NAC

Rate / κ	Jump
`Z*2 - 8Z + 16`	ΔZ=+1

Generator identities

G Z = Z**2 - 8*Z + 16

5 · Initial states

Each start is concentrated on the listed coordinate vector.

Dynamics start

Rule	Initial coordinates · Unchlorinated
With NAC	`Z=0, P1=2, P2=2, P3=2`
Without NAC	`Z=0`

Rule	Initial coordinates · One chlorinated site
With NAC	`Z=1, P1=1, P2=1, P3=0`
Without NAC	`Z=1`

Rule	Initial coordinates · Blocked free pair
With NAC	`Z=2, P1=0, P2=0, P3=0`
Without NAC	`Z=2`

6 · Dynamics

Dynamics rule Compare both rulesChlorination rate 1End time

Solid teal: with NAC; dashed red: without. Mean and variance come from the generated event model's finite forward equations. “Blocked” means no further chlorination is possible although free ring sites remain. Tail growth may continue.

Full molecular network.