Robert Putnam (2000) distinguished bonding social capital (dense ties within groups) from bridging capital (links across groups). Fukuyama and others tied trust to economic coordination. In FPE terms, social capital is stored coordination capacity — a component of \(\Phi\) at the collective layer and a precondition for cheap \(\Psi\) between nodes.

Classical description

Concept	What it names
Bonding capital	Strong in-group ties — family, ethnic network, tight team
Bridging capital	Weak ties across difference — cross-class, cross-firm, civic associations
Generalised trust	Default expectation that strangers will cooperate under norms
Social trust collapse	When coordination requires constant verification

High social capital does not mean “everyone likes each other.” It means lower cost to run operations 1 and 2 — honesty and repair are cheap because defection is visible and punished by the graph.

FPE mapping

Term	Social-capital reading
\(\Phi\) (collective)	Trust stock, reciprocity history, shared language, reputation
\(\eta(I)\)	Transactions completed without lawyers; projects shipped without politics
\(\mathcal{D}_{KL}\)	“We are a trusting culture” vs observed backstabbing
\(\Gamma\)	Unpaid favours, broken promises, feud lines between subgroups
\(\Psi\)	Civic institutions, rule of law, professional norms that extend trust beyond kin
Low bridging	\(\mathcal{E}_\Sigma\) spikes at group boundaries — every outsider interaction expensive

Bonding vs bridging

Bonding lowers \(\Gamma\) inside the blanket — fast repair, shared rituals, dense monitoring.
Bridging lowers \(\mathcal{E}_\Sigma\) between blankets — trade, hiring across networks, democratic stability.

Pathology: bonding without bridging → high in-group \(\mathcal{R}\), predatory out-group treatment, corruption rings. Bridging without bonding → atomised individuals, no \(\Phi\) to voice with.

Generalised trust as \(\Phi\) amortisation

When generalised trust is high, agents spend less \(P_{in}\) on verification (contracts, surveillance, reputation checks). That freed numerator is available for actual work — a measurable \(\eta\) boost. Trust collapse is denominator inflation by other means: every interaction requires costly proof.

Putnam’s civic decline

Putnam documented falling association membership and bowling alone. In FPE: bridging \(\Phi\) depleted → households and firms face higher \(\mathcal{E}_\Sigma\) from isolation; politics becomes bonding-only (tribal) because cross-cutting ties atrophied.

Why trust erodes

Trust stocks deplete when:

\(\mathcal{D}_{KL}\) exposed — institutions preach fairness while members witness extraction.
\(\Gamma\) unresolved — grievances between subgroups never settled; feud lines harden.
\(\Phi\) drained — precarious labour, commuting grind, no time for associations.
Predatory \(\Psi\) — platforms or employers capture bonding ties for profit without reciprocity.

Each is measurable harm, not vague “polarisation.”

Interruption

1. Lower \(\mathcal{D}_{KL}\)

Institutions model reality members witness — especially elite vs median experience.
Transparency that predicts — open books, audit trails, not PR.

2. Lower \(\Gamma\)

Truth and reconciliation at group boundaries; clear settlement of historical debts.
Anti-corruption as \(\Gamma\) reduction, not moral theatre.

3. Invest in bridging \(\Phi\)

Third places, mixed-income housing, cross-functional teams, universal services.
Time sovereignty — bonding and bridging require spare \(P_{in}\); exhausted members cannot build capital.

Fractal note

Trust at \(L+2\) (firm) and \(L+3\) (state) uses the same variables. A nation with low social trust pays \(\omega\) everywhere — more police, lawyers, compliance. Geopolitics essays track \(\Phi\) including “social trust” at state scale (comparison.md).

Social capital and trust