The labour market, as a space of variants
Not a forecast. An instrument for the interaction of the drivers AI opens up — capability speed, recursion, diffusion, robotics, energy, ownership, individual adaptive capacity, collective worldview — and how they drive each other. The public argument moves one factor at a time; this models the coupling. Its worth is in the dependencies it makes explicit, not in any particular number.
How many people are still economically needed to work over 2026–2035? Three scenarios. The solid line is the central estimate; the band around it is the credible range — its width is the genuine disagreement between our formulas (a fixed deployment rate vs the coordination-cost collapse) and the unsettled unknowns, not decorative fuzz. The band’s lower edge is where the AI-agent / coordination-collapse channel takes it. Drag any driver below; switch lenses to add the human and political frictions.
One boundary even the band can’t show: every scenario assumes today’s scientific picture holds. Genuine discontinuities — a breakthrough, a shock, the sideways event no one is modelling — would move all of this, for better or worse, and they sit outside every dial here. We draw the space we can defend and stop at the edge of speculation; why, and where exactly we stop, is set out in the methodology below.
Pure cost-logic — how few people are economically needed once a machine is cheaper (no human or political friction yet). The line is the central estimate; the band’s lower edge is the coordination-cost collapse, its upper edge the conservative fixed-rate reading. A baseline to reason from, not a forecast.
The biggest movers of how much labour is needed are diffusion and the complexity tail θ — both genuinely unpinned. “Tectonic” shows only when the recursion loop crosses ρ(M)>1, never a baked label. Every output variable, the sensitivity ranking, and the falsifiability tests live in expert.
The instrument’s logic, and its caveats
Capability is integrated as a bounded (logistic) frontier whose rate is set by the recursion network’s spectral radius ρ(M) — never raw eigen-growth, so no “singularity” is promised and “tectonic” appears only as ρ(M)>1. A firewall separates the growth regime from the labour regime: a distinct, mid-band transfer maps one to the other, and the ρ=1 boundary is a band, not a line.
The outputs are tracked separately and never summed — necessity, employment, agency, formation, meaning, worldview, redistribution. The soft tiers (individual, political) modulate the hard economic outputs only within a bounded, declared, rendered envelope (the do-not-sum invariant), never collapsing them into one index. The worldview tier is the verified Gavrilets–Seabright replicator (p = the zero-sum frequency; lock-in α(1−a)+β>|s|).
Every constant in the engine carries one of four honesty tags (source-derived · interpretive · arbitrary-exposed · borrowed-formalism). The genuinely-unpinned drivers head the sensitivity sweep because they dominate the outcome and cannot be pinned. Both poles — the reassuring and the transformational — are reachable; the fast-growth premise is a dial the viewer moves, opening from the measured present, not a settled fact.
Why the lines are drawn the way they are
This instrument is not a forecast, and the lines are not an intuition rendered smooth. Each line is the integration over 120 months of a coupled dynamical system whose every Tier-1 dynamic traces to a named formal result — a spectral-radius growth condition, a wage bound, a diffusion law, a replicator equation. What follows is the full specification: the state, the update law, the coupling, every constant with its honesty tag and source, and a reproducibility appendix precise enough to re-implement and recover these exact numbers. It is written for the reader who is right to refuse to take the lines on trust.
1 · What this rejects
The honest failure mode of a model like this is a smooth surface laundering a guess: a few dozen hand-tuned constants with no source, fitted until the curve "looks right." That earlier prototype existed, and it is the thing this version is built against. The discipline here is the opposite: no un-tagged number may enter the engine. Every structural coefficient is declared once, in a registry, with one of four honesty tags and a source; the engine imports them by name and contains no free model literals. The reference table in §8 is that registry, generated from the same file the running model reads — so this document cannot drift from the machine.
2 · The state and the update law
The engine is a deterministic discrete-time dynamical system. A state vector of thirteen quantities is advanced one month at a time, for 120 months (2026 → 2035), by a single update map. Within a step the quantities are computed in a fixed forward order — capability frontiers → the growth→labour transfer → the diffusion layers → necessity → employment and agency — so each downstream quantity reads the freshly-computed upstream value of the same step (the order below in §4 is that order, and is part of the specification). What is held lagged, not instantaneous, is the one place a true cycle would otherwise close: the worldview tier reads a necessity value delayed by six months, and the political loop back to agency is broken the same way — so no quantity ever depends circularly on itself within a step, and the run is deterministic regardless of anything outside this order. Quantities marked ′ in §4 (the prior diffusion layers) are read at their previous-step value; all others are same-step. Initial conditions are first-class declared inputs — with bistable subsystems the starting basin can matter more than any dial, so no default is hidden. The step is monthly, every rate is per-month, and each increment is clamped so growth·Δt cannot manufacture spurious oscillation. The recursion matrix depends only on the dials, not the state, so its spectral radius is computed once per run.
The outputs are tracked separately and never summed into one index — collapsing necessity, employment, agency, meaning, and worldview into a single "score" is precisely the error the companion essay is built against. Necessity falling toward zero is a claim about the marginal economic value of labour; it is not a claim about income, and not a claim that people are unneeded. The model asserts only the first.
3 · Why this is a coupled system, not a weighted sum
The central question a skeptic should press is: are the fifteen drivers simply added up behind the curtain? They are not. They interact in five structurally distinct ways, none of which is summation:
- Multiplicative gating
- A driver scales another’s effect rather than adding to it: the diffusion flow is rate · diffusion · diffusionAccel · (target−x); the coordination dial enters as a multiplier (1 + gain·coordEff), not a term.
- Eigenvalue threshold
- The growth feedback is the spectral radius ρ(M) of a 6-channel matrix, and the frontier rate scales as ρ raised to an exponent — near-flat below ρ≈1, accelerating above: a threshold nonlinearity, not a linear weight. (The exponent itself, 4, is a labelled modelling choice, not a measured value — the qualitative threshold shape is the claim, not the precise curvature.)
- Closed feedback loops
- Necessity → worldview → redistribution → agency closes a cycle across three tiers; meaning → productivity → necessity is a second. These are real cycles, not a one-pass sum — but deliberately bounded: the worldview→agency reach is squash-limited and the loop is lag-broken, and the meaning→productivity edge ships off by default. The architecture is cyclic; the default run keeps the cycles weak on purpose.
- Relaxation toward moving targets
- Hard outputs do not equal a formula; they RELAX toward a target that is itself moving — necessity toward the W_H ceiling at a migration rate, employment toward max(necessity, policy floor).
- Bistable basins
- The formation reservoir has two attractors separated by an unstable point; the same drivers send it to a virtuous cycle or a human-capital trap depending on where it starts. No sum has two stable outcomes.
The concrete map — every cross-influence in the engine, with its sign (which quantity multiplies, gates, or suppresses which) — is laid out in §4.9 below.
And the claim that the soft tiers (psychology, worldview, politics) do not secretly aggregate into the hard economic outputs is not asserted — it is enforced and tested. Every soft→hard reach passes through a bounded squashing function; the political feedback loop is lag-broken; and a runnable self-test (§7) pins the three worldview inputs at their extremes — confirming no hard output moves by more than the worldview→agency squash bound — and pins the two pure-soft inputs (support, inertia) to confirm they reach no hard output at all. The most speculative reach, meaning → productivity, is not covered by this invariant for a simpler reason: it ships off by default, and when on it is bounded by its own (smaller) squash. If any pinned soft input moved a hard output beyond its bound, a soft tier would be dominating, and the run is flagged. The soft tiers modulate the hard outputs within a declared, rendered envelope; they never collapse the separated quantities into one.
4 · The equations
Normalized quantities live in [0,1]. σ is the logistic function; clamp01 bounds to [0,1]; Δt = 1 month. Constant names in this face are the registry ids in §8.
4.1 · Growth feasibility — the recursion matrix and its spectral radius
Six channels couple, in this index order: S_capability, H_compute, E_energy, Mat_materials, B_robotics, A_rnd (capability/algorithms, compute, energy, materials, robotics, R&D-automation). The diagonal is own-accumulation clip(1 − βi·betaScale, 0, 1) with the six β values beta_S … beta_A in §8 (hardware’s β is lowest — the "dominant lever"); the off-diagonals are the cross-sector spillover edges below. The spectral radius is the explosion condition.
The eleven spillover edges and the dial that modulates each (generated from the engine):
| receiver ← source | driver dial |
|---|---|
| H_compute ← S_capability | speed |
| S_capability ← H_compute | speed |
| H_compute ← Mat_materials | materials |
| H_compute ← E_energy | energy |
| S_capability ← A_rnd | speed |
| H_compute ← A_rnd | — |
| Mat_materials ← S_capability | materials |
| E_energy ← S_capability | energy |
| B_robotics ← S_capability | robotics |
| A_rnd ← S_capability | — |
| A_rnd ← H_compute | — |
ρ is a rate diagnostic, never the integrated state: ρ > 1 of a linear map is geometric, not finite-time, growth. The badge "tectonic" is rendered only as ρ ≥ rho_enter_tectonic, with hysteresis down to rho_exit_tectonic so it cannot chatter — never a baked label, never a promised singularity.
One honest distinction the reproducer needs: the engine integrates the driver-modulated matrix above (each spillover floats with its dial), and at the present default this gives ρ ≈ 0.814. The validation numbers in §7 (present ρ ≈ 0.819, the boundary band) are for the illustrative weight-1 matrix — every driven edge at w = 1 — which is the object the disconfirming-matrix gate was written against. The engine ships its own regime-boundary check for the matrix it actually runs, so the two are never conflated; both are reachable from the construction above (set every wedge = 1 for the gate matrix).
4.2 · Bounded capability frontiers
The rate is set by ρ; the state is always logistic-bounded. Raw eigen-growth is never integrated.
The physical frontier has the same logistic shape but a different, linear rate law — driven by robotics, not by ρ4:
4.3 · The firewall — growth does not transfer to labour
The growth-singularity result is about growth, not the labour market. A separate, explicitly interpretive transfer maps the growth regime to a deployable-automation target; the cognitive/physical value split is a swept degree of freedom, never a fixed weight.
4.4 · The coordination-cost dial — the Coase channel added
The diffusion rate is the engine’s most contestable assumption, because today’s binding constraint is organizational retooling, not capability — exactly the coordination cost an AI agent might collapse. So the rate becomes a function of a coordination dial c, saturating toward the connectedness cap, not unbounded.
4.5 · Layered diffusion — the monthly flow
Automation diffuses through three layers (firm → function → task) at different rates, resisting reversal (sticky basins). The task layer is the binding deployed-automation share.
dFirm′, dFunc′ are the previous step’s values — the simultaneous-update discipline.
4.6 · The residual split and the necessity bound split added
Necessity relaxes toward the wage bound WH ≤ λ·k·r_c — an inequality, not an assignment. The residual r_c splits into a hard verifiability floor coordination cannot touch and a collapsible interface-gated part. New-task creation and demand elasticity offset deployed automation; they can only push the bound back up toward 1, never above it.
4.7 · Worldview — the verified replicator
The zero-sum worldview share p evolves by the Gavrilets–Seabright replicator, driven by a selection pressure s our economy→s bridge derives from lagged displacement (the political loop is lag-broken by six months). Assortment reduces effective conformity.
4.8 · The bounded soft→hard squash — the do-not-sum guard
Where a soft tier reaches a hard output, it passes through a squash whose entire low→high swing is bounded by the declared edge bound — the constructive twin of the §7 invariant.
The most speculative edge — meaning → productivity — ships behind a toggle, off by default, bounded by squash_bound_meaning_productivity, with its refuter named on the surface.
4.9 · The influence map — what multiplies what, what suppresses what
§3 named the kinds of interaction in the abstract. This is the concrete map: every place one quantity enters another’s update in the engine, and with what sign. Read it as the directed graph the model actually is. Almost nothing is added; quantities multiply, gate, or suppress one another. The suppressors — the ↓ rows — are where the model’s tensions live: diminishing returns fighting ρ, the complexity tail and the coordination dial eroding the residual, deployed automation eroding necessity, ownership eroding agency, a locked worldview eroding redistribution — and, the one stabilizing one, necessity itself damping the zero-sum pressure that would otherwise feed back on it.
| recursion ↑ ρ(M) | scales every spillover entry: M += recursion · φ · w |
| φ (phiG) ↑ ρ(M) | base spillover strength — a common multiplier on all edges |
| speed / energy / materials / robotics ↑ ρ(M) | each lifts its own edge weight w = phi_driver_base + driver |
| β (diminishing returns) ↓ ρ(M) | diagonal = clip(1 − β); a higher β shrinks self-accumulation, lowering ρ |
| ρ(M) ▲ capCog | frontier rate = base · ρ⁴ — near-flat below ρ≈1, accelerating above |
| robotics ↑ capPhy | physical-frontier rate = phys · (rho_floor + robotics) |
| capCog & capPhy ⊗ autoFrontier | mixed by cogShare: cogShare · capCog + (1 − cogShare) · capPhy |
| autoFrontier ↑ autoTarget (deployable automation) | gain: transfer_bias + transfer_gain · autoFrontier |
| coordination c ↑ diffusion speed | diffusionAccel = 1 + coord_accel_gain · coordEff, coordEff saturating at the cap |
| diffusion dial ↑ layer flow | multiplies the per-layer flow rate |
| stickiness ↓ un-adoption | reverse flow scaled by (1 − stickiness): adoption resists reversal |
| deployed automation ↓ necessity | necessityBound = 1 − deployed · (1 − offset) · (1 − r_c) |
| residual r_c ↑ necessity | enters as (1 − r_c): a thicker human residual defends necessity |
| θ (complexity tail) ↓ residual r_c | r_c base = max(floor, 1 − θ): a thinner tail erodes the residual |
| coordination c ↓ residual r_c | r_c = verif + collapsible · (1 − coordEff): collapses the interface-gated part |
| new tasks & demand elasticity ↑ necessity | via the offset (1 − offset): re-absorb destruction, capped at offset_cap |
| necessity (lagged 6 mo) ↓ zero-sum pressure s | s = gain · (2·(1 − necessity) − 1): more necessity → less displacement → less pressure (a STABILIZING negative feedback) |
| pressure s ↑ worldview p | replicator s · p(1 − p) |
| assortment a ↓ conformity | effective conformity αₑ = α · (1 − a): echo-chamber homogeneity REDUCES the lock-in pull |
| authority β ↑ worldview p | + β(1 − p): pushes toward the zero-sum fixed point |
| necessity ↑ agency | agencyBase = necessity · (…) |
| ownership concentration ↓ agency | · (1 − agency_ownership_suppression · ownership): concentration suppresses bargaining |
| worldview p ↓ redistribution | redist = policy · (1 − lock · p): a locked zero-sum view collapses feasibility |
| redistribution ⊗ agency | + bounded squash((redist − ½)·gain): the only soft→hard political reach |
| policy ↑ employment & redistribution | lifts the employment floor and the redistribution target |
| necessity ↓ meaning-load | load = floor + gain · (1 − necessity): more necessity → less existential load |
| support / tempo / inertia ⊗ formation reservoir | forcing = support·w − tempo-drain; inertia raises the re-grounding rate that offsets the drain |
| meaning ⊗ necessity | optional bounded squash — ships OFF by default (the most speculative edge) |
This is why the do-not-sum invariant (§7) is a real test and not a slogan: the only edges that reach a hard economic output from a soft tier are the two bounded squashes (worldview → agency; the off-by-default meaning → productivity). Every other influence above is inside one tier or runs hard → soft, so no soft quantity can accumulate into the economic line.
5 · What was added, and what keeps each bounded
Five mechanisms were added on top of the validated baseline. Each names its grounding and — crucially — the firewall that prevents it from buying an unbounded result. Adding a dial is honest; turning arithmetic into geometry by fiat is not.
what Collapsing coordination/transaction cost does two things, both saturating: it accelerates the diffusion rate along an S-curve toward a connectedness cap (χ≤½), and it erodes the interface-gated part of the human residual (the next card). Makes the standing Coase concern a declared degree of freedom instead of an unmodelled gap.
grounding Direction + within-frame slope from nber_w35314; the precise Coasean-margin elasticity is unmeasured, so the gain/steepness are labelled guesses that HEAD the sensitivity sweep.
firewall Two hard limits, not one. The diffusion acceleration saturates at the connectedness cap — never unbounded. And the residual it erodes is only the interface-gated part: c cannot touch the hard reward-verifiability floor and never rewrites θ — so by Corollary 4 (nber_w35155), below the θ-dependent threshold the bottleneck re-imposes itself and growth self-arrests. "Honest" here is a dial with two floors, not a claim that c changes nothing but the rate.
what The permanently-human residual r_c splits into a HARD reward-verifiability floor coordination cannot touch, plus an interface-gated part that collapses as coordination cost falls.
grounding arxiv_2605.02598: reward-verifiability is the first principal component (65% of variance) and is distinct from exposure. The hard floor here (0.08) is the reward-verifiability residual — tasks with no constructible verifiable reward. It is NOT the paper’s 40.7% physical-embodiment floor, which is a larger, different residual carried separately in the θ band’s lower edge (next card).
firewall r_c is floored at the verifiability term regardless of the dial, so necessity can never be driven below that hard residual — and note this floor binds only on the thin-residual side of the swept θ band; elsewhere the thicker θ residual is the binding constraint.
what θ faces opposite-signed pressure (codification recedes ↑, but constitutive metis + physical floor ↓), so the band is WIDENED rather than re-centred. The line does not move; the doubt around it grows.
grounding Lower edge grounded at the corpus floor (40.7% physical ⇒ θ≈0.6, plus metis + information-rent tail ⇒ 0.55); upper edge at full-delegation. NOT the old 0.2, which overstated even the floor.
firewall θ is swept as a band ensemble, never chosen as a point; it enters both the wage bound and the stability claim as the same object (role-separation).
what On the board, each scenario’s band is not a statistical fan but the spread between two corner runs of the engine: a collapse corner (coordination→1, thin θ, full spillover) and a conservative corner (coordination→0, thick θ, no spillover). The drawn line is the MIDPOINT of the two corners; the band is their disagreement. (The expert view uses a different, wider construction for the same doubt — a quantile ensemble that sweeps every unpinned degree of freedom.)
grounding A measure of justified doubt: the width comes from the genuine spread between two defensible corner formulas + the parameter ranges, not from fitting an intuition. The two constructions agree on the principle and differ only in how they sample it.
firewall Neither corner is a forecast and the line is neither — it is their midpoint, so the catastrophic corner never becomes the headline. Separately, each scenario is seeded with a MODEST central coordination prior (the corpus rule "do not move the median"), so the default scenarios are not pre-dialled toward collapse.
what The board’s "share still economically engaged" base is the cost-rational extreme (fewest people needed); each lens — human adaptation, then collective response — RESTORES a retention cushion the pure cost-logic ignores, lifting the band.
grounding Additive retention ABOVE the firewalled economic floor — a human-presence premium scaled by support, a job-preservation premium scaled by policy.
firewall These cushions never feed back into the hard economic outputs (necessity, employment, agency). The firewall stands: engaged ≥ necessityBound always, and the economic line is untouched.
6 · The named formal results — and the one role each plays
Composing results from different underlying models in one recursion is the chief inconsistency risk. The discipline: each result plays one declared role, and the model respects it.
| Result | Source | The one role it plays |
|---|---|---|
| Spectral-radius explosion condition ρ(M) > 1recursive self-improvement / growth-singularity analysis | nber_w35155 | Growth-feasibility diagnostic: sets the RATE into a bounded frontier — never the integrated state. Supplies the diminishing-returns β vector and Corollary-4 task-complementarity stabilizer. |
| Wage bound W_H ≤ λ·k·r_cprice-setter / political-economy of automation | arxiv_2605.05558 | The necessity ceiling. An inequality the wage RELAXES toward at a migration rate — a target+bound, not an assignment. r_c is the permanently-human residual. |
| Two-equilibria learning-by-doinghuman-capital accumulation under automation | nber_w35157 | The formation reservoir’s two basins (virtuous cycle vs human-capital trap). A basin label set by initial conditions + pipeline, not re-derived monthly. |
| Layered diffusion (firm / function / task), sticky basinsempirical AI adoption | nber_w35141 | The genuine month-to-month FLOW: automation diffuses through three layers at different rates; adoption resists reversal. |
| Replicator dp/dt = s·p(1−p); lock-in α(1−a)+β > |s|cultural evolution of zero-sum thinking | Gavrilets–Seabright, PNAS 2025 | Worldview dynamics. p = the zero-sum share; verified against the primary source (a backwards sign + a fabricated rate were corrected). |
| CES complexity-tail θ (weakest-link bottleneck)task-automation limits | Korinek–Suh + corpus | Gates the necessity collapse. θ is how far the residual erodes: LOW θ keeps a thick un-automatable residual and necessity high; HIGH θ thins the residual and lets necessity fall (engine: residual = max(floor, 1−θ)). Swept across a corpus-grounded band, never a point. |
| New-task creation vs destruction (post-1980 ≈ 2:1)labour-share decomposition | Autor, Chin, Salomons, Seegmiller (QJE 2024) | The offset SPEED: sustained new work re-absorbs displaced labour; it never manufactures necessity from nothing. |
| Productivity → labour-demand elasticitymacro of automation | Acemoglu (NBER 32487); Penn Wharton | A second offset channel — how far productivity feeds labour demand vs displaces it. |
| Entry-employment −13–16% (junior rung first)AI-exposure labour micro-data | Brynjolfsson; nber_w35141 | The entry-employment diagnostic — the apprenticeship break. |
| Coordination-cost slope 0.570pp / 1pp (elasticity 1.6); connectedness χ ≤ ½transaction-cost / coordination empirics | nber_w35314 | Anchors the ADDED §3.6 coordination dial within-frame; the cross-frame effect is null, which becomes the dial’s firewall (a bounded cap). |
| Reward-verifiability PC1 (65% var); 40.7% physical-embodiment floorRL-feasibility of tasks | arxiv_2605.02598 | The ADDED residual split: tasks with no constructible verifiable reward stay human regardless of coordination cost — a hard floor. |
| Durability pillars + constitutive vs operational metiswhich tasks resist automation | arxiv_2605.14407 | Says WHICH tasks sit in the residual, and which floor is permanent vs moving — grounding the θ band. |
| Youth-wellbeing U-curve breakpresent-trend wellbeing | Blanchflower–Bryson | The meaning-load present floor — the existential load is already rising, pre-AI. |
| Task-horizon doubling (≈4–7 mo)capability measurement | METR | The capability/autonomy SPEED driver (V1). |
7 · Validation & reproducibility
The instrument ships its own checks as runnable assertions, not prose claims:
- The do-not-sum invariant. Pin the three worldview inputs at 0 vs 1 and confirm no hard output (necessity, employment, agency) shifts by more than the worldview→agency squash bound; pin support and inertia and confirm they reach no hard output at all. A larger shift means hidden aggregation, and the run is flagged. (The off-by-default meaning→productivity edge is bounded by its own squash, separately.)
- The disconfirming-matrix gate (β-conditional). Under the source-motivated β (hardware lowest) a non-collapse world is reachable without bottoming the growth dial, and the tectonic regime is also reachable — so the dial is real, not rigged toward the scary answer. The gate fails under a degenerate all-equal β that contradicts the source; it is re-run whenever β is re-derived, not passed once. It reproduces the published numbers for the illustrative weight-1 matrix (§4.1): present ρ ≈ 0.819, ρmax ≈ 2.127, non-tectonic fraction ≈ 67%, boundary band [0.35, 0.90].
- Primary-source verification of the worldview model corrected a backwards sign and a fabricated rate inherited from a secondary summary before either entered the engine.
- Independent re-derivation (a committed test). A test re-implements, from the §4 construction and the §8 constants alone, both the recursion matrix (recovering the engine’s ρ) and the necessity trajectory — using no engine internals — and asserts each reproduces the running model to nine decimal places. It runs in the suite, so the document and the engine cannot silently drift: if a future change moves one without the other, the test fails. The specification here is, demonstrably, sufficient to reconstruct the lines.
Reproduction recipe: initialise the declared state (§4.1 channel order, the §8 constants); each month, in order, build M and compute ρ once (§4.1), then run §4.2 → §4.8 in that order, reading the previous step’s value only for the quantities marked ′ (the prior diffusion layers) and the six-month-lagged necessity in §4.7; record the output vector; repeat 120×. The genuinely-unpinned degrees of freedom that are swept to render the band are the coordination dial, θ, the cog/phys split, the spillover strength φ, and the borrowed β; note that several modelling-rate constants (the frontier base rate, the necessity migration rate, the offset cap) are held fixed at their declared value rather than swept — a limit named honestly in §11, not hidden.
8 · The constant registry — every structural coefficient
The complete set the engine imports, in build order, each with its value, honesty tag, and source. This table is generated from the same file the engine reads; there are no others, and there are no free literals in the engine beyond loop indices and 0/1 clamps. One thing the gradient makes plain once you scan it: none of these structural coefficients is a direct measurement — a rate or a gain rarely is. The measured empirical anchors of the model are the driver bands (METR doubling, robotics cost, adoption rates), not the engine’s coefficients; so every constant here is reasoned, a labelled guess, or a borrowed scaffold. That is the honest state of any structural model — shown here rather than hidden under a smooth surface.
| id | value | tag | what it is · source |
|---|---|---|---|
| beta_S | 1 | borrowed scaffold | diminishing-returns β, capability/softwarenber_w35155 (software ~1) |
| beta_H | 0.2 | borrowed scaffold | diminishing-returns β, compute/hardware — the "dominant lever" (lowest β)nber_w35155 |
| beta_E | 1.5 | borrowed scaffold | diminishing-returns β, energynber_w35155 (higher) |
| beta_Mat | 2 | borrowed scaffold | diminishing-returns β, materialsnber_w35155 (higher) |
| beta_B | 1.2 | borrowed scaffold | diminishing-returns β, roboticsnber_w35155 (higher) |
| beta_A | 3.1 | borrowed scaffold | diminishing-returns β, R&D/TFPnber_w35155 (TFP ~3.1) |
| phi_g_max | 0.8 | labelled guess | max base spillover strength g the φ-sweep ranges over (UNPINNED — no empirical φ exists)illustrative (disconfirming-matrix test) |
| frontier_base_rate | 0.16 | labelled guess | base per-month logistic rate, scaled by ρ(M)^k; never integrates raw eigen-growthmodelling choice (bounded-frontier guardrail) |
| frontier_rho_exponent | 4 | labelled guess | the eigenvalue-threshold nonlinearity: rate ∝ ρ^k so the frontier is near-flat below ρ≈1 and accelerates above it (§3.1 "near-flat until the recursion loop crosses its eigenvalue threshold")modelling choice (the §3.1 nonlinearity) |
| frontier_growth_clamp | 0.25 | labelled guess | per-step clamp on growth·Δt to avoid spurious period-doublingnumerical-stability guardrail (§7) |
| rho_floor | 0.05 | labelled guess | floor so a near-zero ρ still yields a tiny positive frontier ratenumerical guardrail |
| rho_enter_tectonic | 1.05 | reasoned | enter "tectonic" at ρ ≥ 1+ε_hinber_w35155 explosion condition ρ>1 + hysteresis |
| rho_exit_tectonic | 0.97 | reasoned | exit "tectonic" at ρ ≤ 1−ε_lo (badge cannot chatter near ρ=1)hysteresis guardrail (§7) |
| transfer_gain | 0.85 | reasoned | gain of the growth-regime→labour-regime transfer (mid-band, NOT a hard edge)interpretive (firewall §3.2) |
| transfer_bias | 0.05 | reasoned | floor of deployable automation even at low frontierinterpretive |
| diffusion_firm_rate | 0.07 | reasoned | per-month firm-layer adoption flow toward targetnber_w35141 (firm 18%); rate interpretive |
| diffusion_func_rate | 0.05 | reasoned | per-month function-layer flow (slower)nber_w35141 (function layer) |
| diffusion_task_rate | 0.09 | reasoned | per-month task-layer flow (the binding deployed-automation layer)nber_w35141 (task 23%); rate interpretive |
| diffusion_stickiness | 0.5 | reasoned | two-sticky-basin retention: adoption resists reversalnber_w35141 (sticky basins); value interpretive |
| necessity_migration_rate | 0.05 | labelled guess | rate the wage/necessity RELAXES toward the W_H ceiling — "the interesting unknown"arxiv_2605.05558 (the rate is unspecified by the result) |
| residual_r_c_floor | 0.06 | reasoned | ε floor on the permanently-human residual r_c (also nber_w35155 Cor-4 stabilizer)arxiv_2605.05558 / nber_w35155 Cor-4 |
| cogShare_low | 0.45 | labelled guess | low end of the swept cognitive-task value sharemust be sourced or swept — NOT a fixed weight |
| cogShare_high | 0.75 | labelled guess | high end of the swept cognitive-task value sharemust be sourced or swept — NOT a fixed weight |
| employment_stick_rate | 0.04 | reasoned | per-month stickiness of employment toward its targetinterpretive |
| policy_floor_gain | 0.6 | reasoned | how much policy (V7) lifts the employment floor above necessityK28 (policy can hold employment above necessity); gain interpretive |
| agency_ownership_suppression | 0.6 | reasoned | ownership concentration (V8) suppression of bargaining powerK27 comparative-advantage breakdown; coefficient interpretive |
| formation_basin_pull | 0.05 | reasoned | pull toward the nearest formation attractor per monthnber_w35157 two-equilibria; rate interpretive |
| formation_separatrix | 0.5 | reasoned | the unstable fixed point separating virtuous-cycle from human-capital-trap basinsnber_w35157; location interpretive |
| meaning_load_gain | 0.5 | reasoned | rate meaning-load rises as employment's 3 non-money functions withdraw (K15)K10/K15; Blanchflower–Bryson present-trend; gain interpretive |
| worldview_s_gain | 0.6 | reasoned | maps economic displacement → q → s (our economy→s bridge; Gavrilets s ≠ economic tempo)gavrilets-seabright-verification §5 (direction supported, no functional form) |
| worldview_dt_gain | 0.4 | reasoned | replicator timestep gain on dp/dt = s·p(1−p) — the Gavrilets Eq.3 STRUCTURE is formal, but this per-step gain is a discretization choice, so the tag marks reasoning, not measurementGavrilets–Seabright Eq.3 (structure formal; the 0.4 timestep gain is ours) |
| redistribution_lock_suppression | 0.7 | reasoned | how far a high zero-sum p collapses redistribution feasibilityK28; coupling to p interpretive |
| entry_lead_factor | 1.6 | reasoned | entry roles automate ahead of the aggregate — a constructed multiplier calibrated so the entry line resembles the observed −13–16%, not itself a measured ratioBrynjolfsson −13–16% (the effect is measured; the 1.6 multiplier is our calibration) |
| squash_bound_worldview_agency | 0.15 | labelled guess | max influence of worldview→redistribution→agency on a hard outputdo-not-sum squash bound (§6/§7) |
| squash_bound_meaning_productivity | 0.1 | labelled guess | max influence of meaning→productivity on a hard output (edge OFF by default)do-not-sum squash bound (§6/§7) |
| lag_break_months | 6 | reasoned | months the T3→T1 loop is lag-broken (worldview reads a delayed economic state)loop discipline (§6); horizon interpretive |
| wildcard_fusion_boost | 0.25 | labelled guess | fusion wildcard: lifts the energy channel (no deployed commercial fusion)arbitrary-exposed wildcard |
| wildcard_quantum_boost | 0.2 | labelled guess | quantum wildcard: speculative compute/algorithm multiplierarbitrary-exposed wildcard |
| tail_theta_default | 0.5 | labelled guess | thin-complexity-tail thickness gating necessity-collapse — CITED-NOT-CORPUS (no work-frame for w32255)Korinek–Suh NBER w32255 (cited only; not in corpus/work_frames) |
| phys_frontier_rate | 0.04 | labelled guess | base per-month logistic rate of the physical-task frontier, scaled by robotics (V3)modelling choice (bounded-frontier guardrail) |
| newtask_buffer_gain | 0.35 | reasoned | fraction of deployed automation OFFSET by sustained new-task creation (a speed offsetting destruction, not a free necessity bonus)Autor et al. QJE 2024; gain interpretive |
| demand_elasticity_gain | 0.25 | reasoned | fraction of deployed automation re-absorbed by high sector-demand elasticityAcemoglu / Penn Wharton; gain interpretive |
| formation_tempo_weight | 0.5 | borrowed scaffold | weight of the tempo×inertia drain on the formation reservoir (rates borrowed-formalism, re-derive)K20 timescale formal; Janus inertia rates borrowed |
| formation_support_weight | 0.5 | reasoned | weight of the capacity×support lift on the formation reservoir (Track B)Track B "deep-but-configurable"; weight interpretive |
| soft_relax_rate | 0.05 | labelled guess | per-month relaxation rate of soft outputs (agency, redistribution, meaning) toward their targetsmodelling choice (numerical smoothing) |
| meaning_present_floor | 0.2 | reasoned | present youth-wellbeing load floor — Blanchflower–Bryson establish the rising trend (U-curve broke; suicide +45% F / +21% M 2011–22); the 0.2 intercept on the synthetic [0,1] load axis is our calibrationBlanchflower–Bryson "Not Flourishing" (trend measured; the 0.2 intercept is interpretive) |
| phi_driver_base | 0.5 | reasoned | base of the per-edge driver weight w = phi_driver_base + driver (driver=0.5 reproduces the validation weight 1)engine construct (disclosed deviation from the weight-1 validation matrix) |
| squash_input_gain | 4 | labelled guess | logistic input slope on the bounded soft→hard squash edgesmodelling choice |
| newtask_ramp_years | 10 | reasoned | years over which sustained new-task creation ramps to full offsetAutor et al. (compensation builds over a decade); horizon interpretive |
| offset_cap | 0.9 | labelled guess | cap on the combined new-task + demand offset of deployed automationmodelling choice |
| fan_inertia_jitter | 0.6 | labelled guess | ensemble jitter width on the borrowed-formalism inertia rate (wide — it is unpinned)modelling choice (band width) |
| fan_support_jitter | 0.3 | labelled guess | ensemble jitter width on the support distribution shape (unpinned)modelling choice (band width) |
| fan_beta_lo | 0.7 | borrowed scaffold | low end of the β perturbation in the confidence fan (β is borrowed-formalism)nber_w35155 β re-calibration range |
| fan_beta_hi | 1.3 | borrowed scaffold | high end of the β perturbation in the confidence fannber_w35155 β re-calibration range |
| epistemic_base_half_width | 0.03 | labelled guess | base half-width the hardness factor scales into the visible epistemic floor (formal→0, interpretive→~0.021, soft→~0.048)rendering choice (band width) |
| retention_psych_gain | 0.3 | reasoned | psychological / human-presence retention: fraction of the displaced kept because a human is preferred (the barista-for-presence), scaled by supportinterpretive (no direct measurement; a modelling premise) |
| retention_pol_gain | 0.45 | reasoned | political job-preservation retention: fraction of the displaced kept employed by collective/policy choice, scaled by policyK28 (employment can be held above necessity); gain interpretive |
| coord_central | 0.15 | reasoned | central value of the coordination-cost dial c — a MODEST within-frame prior, so the central line stays near the conservative median (corpus: "do not move the median") and the coordination-collapse lives in the band's lower edgenber_w35314_2026 (within-frame slope modest; cross-frame null; χ≤1/2) |
| coord_cap | 0.5 | reasoned | connectedness cap on the collapse (chi<=1/2): cross-frame coordination collapse is bounded, not global — the firewall on the dialnber_w35314_2026 (chi in [0,1/2]; cross-frame effect insignificant/wrong-signed) |
| coord_steepness | 3 | labelled guess | S-curve steepness of the coordination-cost collapse (geometric early, saturating late) — §3.6 behavioral-interface floormodelling choice (no importable coordination-cost elasticity exists) |
| coord_accel_gain | 1.2 | labelled guess | how much a fully-collapsed coordination layer accelerates diffusion (the §3.6 dial on g_f); UNMEASURED — heads the sensitivity sweeparbitrary-exposed (the standing empirical gap on the Coasean margin) |
| rc_verifiability_floor | 0.08 | reasoned | the reward-verifiability-gated residual: tasks with no constructible verifiable-reward environment stay human regardless of coordination cost — a hard floor on r_carxiv_2605.02598 (PC1 reward-verifiability 65.0% var; 40.7% physical floor; verifiability != exposure) |
| theta_band_lo | 0.55 | reasoned | low end of the swept complexity-tail θ band — the thick-residual / defend side. Grounded at the corpus floor: the 40.7% physical residual ⇒ θ≈0.6, plus headroom for the metis pillars + information-rent long tail ⇒ θ≈0.55. NOT 0.2 (80% human), which overstated even the corpus floor and inflated the band.arxiv_2605.02598 (40.7% physical floor ⇒ rc≈0.4); arxiv_2605.14407 (metis pillars); arxiv_2605.01214 (information-rent tail) |
| theta_band_hi | 0.95 | reasoned | high end of the swept complexity-tail θ band — the thin-residual / erode side (codification recedes, full delegation beats human+AI)nber_f227495_2025 (codification limit receding); essays (full-delegation) |
9 · The cross-tier couplings — each with its refuter
The couplings are the product. Every edge carries the observation that would kill it (the refuter rule binds every edge, not just the convenient ones), and a loop discipline that keeps the cycles from running away.
| Coupling | tag | loop discipline | refuter — what would kill the edge |
|---|---|---|---|
| Tempo × Inertia → formationspeed → formation | borrowed scaffold | lag-broken | longitudinal cohorts show formation intact even where tempo outruns re-grounding |
| Capacity × Support → formation inequalitysupport → formation | reasoned | feed-forward | the outcome-by-support gradient is flat once ability is controlled |
| Displacement → worldview (economy→s)necessity → worldview | reasoned | lag-break | zero-sum prevalence does NOT track stagnation/displacement across regions/time (controlling for the Chinoy-et-al. predictors) |
| Worldview → redistribution → agencyworldview → agency | reasoned | clamp; Jacobian sub-critical | redistribution feasibility moves independently of zero-sum prevalence |
| Meaning / cohesion → productivitymeaning → necessity | reasoned | clamp; squash to [0,1] | removal-test / longitudinal evidence shows meaning-load does not move measured productivity → then this edge does NOT ship |
10 · What would prove it wrong
The instrument opens at the present, non-tectonic world; a skeptic dials up from there — the honest direction. And it commits in advance to observations that fire against the thesis, rather than being explained away:
- T1 METR doubling < 4 mo sustained 4 quarters. doubling stays ≥ 7 mo → the speed premise (V1-high) is retired
- T1 entry-employment −20% spread beyond software/CS. entry employment holds outside CS → the apprenticeship-break reading weakens
- T1 labour-share −2 pp with stable employment. labour share holds → the necessity-collapse mechanism is not yet operating
- T1 humanoid cost < $50k. cost stays > $100k → robotics (V3) stays in the low band
- T2 youth-flourishing / deaths-of-despair trend. youth flourishing recovers → the meaning-load mechanism (V13) over-stated
- T2 retention-gap / removal-test effect sizes. removal-tests show formation intact while the economy shifts → the anti-advocacy falsifier fires (§11): the essay over-stated the economic-shadow claim
- T3 zero-sum-thinking survey prevalence. zero-sum prevalence flat under displacement → the economy→s bridge is refuted
- T3 the 2025–27 "lock-in window" as a refutable tripwire. if 2027 passes without observable lock-in, the hypothesis is RETIRED, not rescued
11 · The honest limits
The biggest swept levers — the coordination collapse, the complexity tail, the spillover strength — are labelled guesses or borrowed scaffolds, not measurements. That is much of why the band is wide and no single line is a forecast: a large part of the width is doubt drawn to scale. But the band understates total doubt in one honest way: several modelling-rate constants (the frontier base rate, the necessity migration rate, the offset cap) are held fixed at their declared guess rather than swept, so their uncertainty is not in the band at all. The width is a lower bound on the doubt, not the whole of it.
Two more caveats a careful reader is owed. First, the honesty tag marks where a constant’s structure comes from, not always its exact value — and where those diverged we moved the tag down, not up. Three constants whose formal structure is sourced but whose scalar is our discretization or calibration (the replicator timestep gain, the entry-employment lead factor, the wellbeing-load intercept) are tagged reasoned, not measured, precisely so the gradient does not flatter them. Second, the growth β vector is imported from a model calibrated for a different question and carries that source’s own qualifier — its dramatic quantitative claims are "illustrative intuition pumps rather than forecasts" — and because ρ(M) is built from those numbers, the prominent tectonic / non-tectonic badge inherits that provenance. We surface it rather than bury it.
And there is a residue engineering only mitigates, never dissolves: a model whose native act is to resolve to a state is companion to an essay whose achievement is refusing to resolve. The instrument renders a space of variants and marks every landmark with its conditioning assumption; it does not tell you which one will happen, because it cannot, and any version that claimed to would be the laundered intuition this one was built to replace.
Full design specification and the corpus study grounding every constant are kept in the project record. The validation gates above run in the browser — the two self-tests are the live PASS/PASS shown in the expert section’s transparency panel.