---
slug: size_biased_redistribution
name: Size-Biased Redistribution
one_liner: "A population of discrete units evolves toward fewer and larger under a size-dependent cost asymmetry, so mass flows from disfavored small units into favored large ones."
type: prime
schema_version: 2
status: density_v2_draft
categories: [structural, economic, physical]
origin_domain: statistical_physics
alternate_origin_domains: [economics, ecology, materials_science]
aliases: [rich_get_richer_by_cost, boundary_cost_consolidation, size_dependent_coarsening, mass_concentration_asymmetry, unit_amalgamation]
related: []
solution_archetypes: []
review_flags:
- "OPERATOR-DERIVED (op-05 generalization) — the proposed GENUS of `coarsening` (lift: strip the boundary-energy / surface-tension physical frame and generalize to any size-dependent cost asymmetry that redistributes mass from small units to large ones). Discovered in the op-05 remaining-strata sweep 2026-07-03. Tier B candidate (sonnet coinage — genus label not an established term). STATUS: HOLD pending owner keep/cut."
- "COINAGE + ALIAS RISK: 'size-biased redistribution' is a descriptive coinage; the abstracted pattern (mass concentrating in favored units) risks collapsing into a preferential-attachment / rich-get-richer / cumulative-advantage prime if one exists. Verify the *cost-asymmetry MECHANISM* is the distinguishing content, not the outcome (concentration), which is shared by several dynamics."
- "Created 2026-07-03; STUB ONLY (frontmatter + Core Idea + Notes). SI/SF/similarity are PROPOSER ESTIMATES pending triangulation. Body sections (Structural Signature onward) NOT written."
- "Phase-C action: re-similarity-check vs `coarsening` (the input) and any preferential-attachment / Matthew-effect / cumulative-advantage / power-law prime; confirm it is a genuine genus (covers the input AND the wealth-concentration / extinction / market-consolidation siblings) and that the size-dependent COST asymmetry is the load-bearing mechanism, not just the concentration outcome; draw a subsumption edge coarsening→candidate + sibling edges at incorporation; sync one_liner to a v1 draft per CLAUDE.md before merge."
substrate_independence:
  composite_substrate_independence: 4
  domain_breadth: 4
  structural_abstraction: 4
  transfer_evidence: 3
  reasoning: 'The bare structure — a population of discrete units in which per-unit cost scales with the boundary/interface rather than the bulk, so small units pay a higher cost-to-content ratio and mass therefore migrates from small to large until few large units remain — is a clean relational form defined by a size-dependent cost gradient and a conserved (redistributed) mass. It presupposes only discrete units, a conserved quantity, and a cost that disfavors smallness, so it lifts off statistical physics into finance (fixed transaction/overhead cost disfavoring small holdings) and ecology (fragmentation cost disfavoring small populations). It scores above its physical input `coarsening` because the lift discards surface tension and keeps the cost-asymmetry skeleton. Transfer evidence held at 3 because the social/economic instances arguably run on a preferential-attachment mechanism rather than a genuine boundary-cost one, so the identity of mechanism across domains is not yet confirmed.'
similarity_to_nearest_existing_prime:
  slug: coarsening
  similarity: 0.66
structural_framed:
  label: structural
  aggregate: 0.26
  criteria: {vocab_travels: 0.85, evaluative_weight: 0.05, institutional_origin: 0.2, human_practice_bound: 0.2, import_vs_recognize: 0.2}
  rationale: 'The candidate is a bare dynamical structure: discrete units, a size-dependent cost asymmetry, and conserved mass flowing small-to-large. Its vocabulary (unit, boundary cost, bulk, redistribution, consolidation) travels across physics, finance, and ecology; it carries essentially no evaluative content and is recognized as a structure rather than imported as a doctrine. It reads clearly structural.'
phase_b_passes_completed: []
---
# Size-Biased Redistribution

## Core Idea

Size-biased redistribution is the structure in which *a population of discrete units evolves toward fewer and larger units because a cost asymmetry penalizes smallness*, driving a conserved quantity — mass, wealth, energy, individuals — to flow out of disfavored small units and into favored large ones. The genus is reached from its input, `coarsening`, by stripping the specific physical mechanism (boundary energy / surface tension, where small droplets pay a higher surface-to-volume price and evaporate into large ones): what remains when you drop the surface-tension frame is the general pattern of *any* size-dependent cost gradient that makes small units more expensive per unit content and therefore redistributes mass toward the large.

The load-bearing anatomy is threefold. First, a *population of discrete units* holding some conserved quantity that can move between units. Second, a *size-dependent cost asymmetry*: the cost of maintaining a unit does not scale with its content but with something that disfavors smallness — a boundary, an interface, a fixed overhead — so the small unit pays a worse cost-to-content ratio than the large one. Third, *conservative redistribution*: content is not destroyed but transferred, so what the small units lose the large units gain, and the population drifts monotonically toward fewer, larger units. The characteristic payoff of recognizing the pattern is *inevitability without malice*: the concentration is not driven by any preference or agency but falls out of the cost geometry alone, which explains why it recurs and resists piecemeal correction. The characteristic cost/failure is *irreversible consolidation*: because the asymmetry always favors the large, the process runs to a small number of dominant units and does not spontaneously reverse — the diversity of the initial population is ratcheted away, and restoring it requires paying against the cost gradient.

Read structurally, the same size-biased flow recurs across unlike domains. In *finance*, fixed per-transaction and overhead costs disfavor small holdings, so under friction wealth concentrates from many small holders into few large ones. In *ecology*, habitat fragmentation imposes an edge/area cost that disfavors small populations, so mass (surviving individuals) redistributes as small populations wink out and large contiguous ones persist. In *markets*, fixed overhead disfavors small firms, so consolidation flows market share from many small firms into a few large ones. These are structurally unlike in medium (money, organisms, market share) yet share the form: discrete units, a cost that penalizes smallness, and a conserved quantity draining small-to-large — subject to the caveat below about whether the *mechanism* is truly identical.

## Notes

**Provenance.** Produced by operator 05 (generalization / lift) as the proposed genus of the input prime `coarsening`, by stripping the boundary-energy / surface-tension physical frame to reach a general size-dependent cost asymmetry driving mass concentration. Surfaced in the op-05 remaining-strata sweep on 2026-07-03. It claimed the siblings *wealth concentration under transaction friction*, *species extinction under habitat fragmentation cost*, and *market consolidation under fixed overhead*. Logged as a Tier-B (B-rest) candidate in the op-05 remaining-strata manifest.

**For owner evaluation (keep/cut).** The case FOR: the candidate names a *mechanism* for concentration — a size-dependent cost asymmetry — rather than merely the outcome, and that mechanism has a clean physics pedigree (coarsening/Ostwald ripening) with suggestive transfer into economics and ecology. If the transfer is real, it unifies several "big gets bigger" phenomena under a shared cost-geometry cause. The RISKS Kurt should weigh, plainly: (1) **This is a sonnet COINAGE** — "size-biased redistribution" is a built label, not established terminology. (2) **Alias risk vs. preferential attachment / Matthew effect / cumulative advantage** — the corpus may already hold a rich-get-richer / preferential-attachment / power-law prime; concentration-of-mass is the *shared outcome* of several distinct dynamics, so this candidate is only distinct if the *boundary-cost mechanism* is truly its own thing. (3) **Cross-domain mechanism mismatch (the sharpest risk)** — coarsening's driver is genuine boundary energy, but the wealth/market siblings arguably run on preferential attachment (returns scale with size), not on a per-unit boundary cost; if so, the operator has grouped structurally-different mechanisms under a superficially-shared outcome, which would be a false lift. **The sharp keep/cut question: is the size-dependent COST asymmetry actually the same mechanism in all four exemplars, or has the operator conflated boundary-cost coarsening with preferential attachment because both end in concentration?** If the latter, cut and keep `coarsening` scoped to genuine boundary-cost cases.

**At incorporation.** Re-run similarity against `coarsening` (the input) and against any preferential-attachment, Matthew-effect, cumulative-advantage, or power-law prime; the decisive check is *mechanism identity*, not outcome similarity. If kept, draw a subsumption edge `coarsening` → `size_biased_redistribution` and sibling edges only to those exemplars whose mechanism is genuinely boundary-cost; route preferential-attachment exemplars to their own genus instead. Write a v1 draft and sync the one_liner across v1 and v2 per CLAUDE.md before merge.
