Model

TLDR

This stage formalises the topology’s recommended target: a generating function for net life-outcome change under AI transition, partitioned into a defensive side (meaning lost when AI absorbs work that produced it) and an offensive side (value gained when AI compresses the price of ambitious projects). The spine is ΔNet = ΔV + ΔM (with ΔM ≤ 0 by construction). Each side decomposes into three additive channels — for ΔM, telic absorption + competence erosion + relational dose-response; for ΔV, gated novice-skill compression + therapeutic-grade relational benefit + a self-automator-trap penalty when the gate closes. The single conceptual move that makes the pieces fit is encoding the topology’s cross-domain bridge G4 (cognitive offloading via practice atrophy) as one global parameter — ρ, retained effortful practice — that enters the competence-erosion channel directly and the self-automator gate g(f, ρ) that governs both productivity gain and trap penalty. Three of the six channels move with ρ; the other three (telic absorption, therapeutic-grade relational benefit, relational dose-response) are independent of it. ρ is what makes the bridge non-decorative: lowering it degrades the analytical-work and meaning-architecture channels simultaneously while leaving identity-allocation (T, B) and relational-dose (d, δ_R) decisions with their own independent leverage.

The dashboard exposes ten levers (T telic share, B atelic ballast, φ AI-absorbable fraction, κ competence-frustration sensitivity, s pre-attempt skill, a AI capability, f feedback-loop richness, ρ retained practice, d daily AI-emotional minutes, δ_R relational baseline thickness) and reports ΔV, ΔM, ΔNet, the channel-level decomposition, and three structural flags — below the self-automator gate, above the relational dose-safe threshold, telic share exceeding atelic ballast. Six scenario presets anchor recognisable positions: the default risk path (telic-heavy knowledge worker), the same person after the S3 atelic-ballast intervention, the Randazzo self-automator trap, the asymmetric exploiter (novice using AI to attempt previously-out-of-reach projects), the creative-displacement-anxiety vector, and the heavy companion-app user. The trajectory tab makes the A3 crux (O3 in the topology) directly parametric: under λ = 0 (calculator analogue), ρ stays put; under λ > 0 (cumulative atrophy), ρ decays exponentially in the offloading-rate × time product and ΔNet drifts down with it as the gate closes.

What’s ready for formalisation: the topology’s two mechanistic reframers (G4 offloading, G7 telic exhaustion) admit clean closed-form representations; G3 (engagement-optimized substitution) is encoded only as a parameter source for ψ_R rather than as a represented mechanism, so re-calibrating ψ_R covers G3-shifts but the model’s structure does not change. The OpenAI-MIT dose-response is well-enough characterised to support a piecewise-linear surface; Brynjolfsson-Li-Raymond and the BCG RCT give the productivity-scale anchor for α and the rough location of the self-automator gate. What’s still observational: the empirical magnitude of λ (the cumulative-atrophy speed — the single largest unknown in the model and the load-bearing parameter for whether the picture leans defensive or offensive over a five-year horizon); the exact shape of the relational dose-response (linear above d_safe is a placeholder; the curve may be sigmoidal or have a second inflection at very high doses); the calibration of κ across populations; and whether T and B can be treated as scalar identity-shares or require a multi-dimensional decomposition. Stage 4 (data) inherits these as the named targets to fit.

The model is genuinely useful in two ways. First, it makes the structural argument visible: the three defensive channels collapse to a single hidden variable ρ, and the strategic recommendations from the topology (S3 ballast, S4 in-person relationships, S5 dose-limit, S6 effortful practice) each map to one or two specific levers — pulling them is not “AI hygiene” but specific countermoves against specific channels. Second, it makes the upside path legible: most public discourse on AI-and-life is defensive in flavour, and the model shows that under conditions of high feedback-loop richness, maintained practice, and a low pre-attempt skill stock, ΔV is large and ΔNet is positive — the asymmetric-exploiter regime. The model is not a forecast; it is a frame the user fills in with their own (T, B, φ, κ, s, a, f, ρ, d, δ_R), and the value of the frame is that pulling any single slider has visible structural consequences across all three domains rather than just the domain it nominally belongs to.

Integrated ΔNetTrajectory ρ(t)

Identity allocation

TTelic share of identity0.70

BAtelic ballast0.20

AI exposure on telic work

φAI-absorbable fraction0.60

κCompetence-frustration sensitivity0.50

Capability vs price asymmetry

sPre-attempt skill stock0.60

aAI capability on the task0.70

fFeedback-loop richness0.50

ρRetained effortful practice0.60

Relational channel

dDaily AI-emotional minutes15 min

δ_RRelational baseline thickness0.40

Scenario presets

Knowledge worker (default path)Same worker after S3 (atelic ballast)Self-automator trap (Randazzo)Asymmetric exploiter (upside path)Creative pre-AI (high displacement risk)Heavy companion-app user

Telic-heavy career identity, thin atelic ballast, moderate AI capability on the work. Default trajectory of the topology.

Net

ΔV

-0.037

offensive

ΔM

-0.234

defensive (≤ 0)

ΔNet

-0.271

ΔV + ΔM

Channel decomposition

ΔM telic

-0.150

ΔM compet.

-0.084

ΔM relat.

+0.000

ΔV product.

+0.056

ΔV relat.

+0.012

ΔV trap

-0.105

Summary

ΔV (offensive)

-0.037

ΔM (defensive)

-0.234

ΔNet

-0.271

Structural flags

○Above gate (g = 0.50). f·ρ ≥ τ — AI use is augmenting rather than degrading.

○Daily AI-emotional dose at or below d_safe — therapeutic-grade benefit dominates.

⚠Telic share T exceeds atelic ballast B by 0.50. ΔM_telic active. S3 (build atelic infrastructure) is the load-bearing intervention.

ΔV and ΔM are normalised changes in expected outcome over a fixed horizon (treat the unit as "life-scale outcome share" — comparable across people, not comparable across stages of life). ΔNet is positive when the asymmetric capability-vs-price upside dominates and negative when telic absorption, competence erosion, or relational-dose-response wins. The constants α, η_trap, τ, σ, λ_M, ψ_R, β_R are calibrated to the lit-review anchors but await Stage 4 fitting against time-use surveys, the BCG consultant data, and the OpenAI-MIT dose-response curve.

How to read this stage

The dashboard above is not a prediction engine. ΔV, ΔM, and ΔNet are normalised changes in expected life-outcome share over a fixed horizon — units are arbitrary; what matters is the sign, the relative magnitude across channels, and how the numbers move when you pull a lever. If two configurations of the sliders give ΔNet = +0.10 and ΔNet = −0.20, the model is claiming the first life-arrangement is structurally better-positioned than the second under the model’s assumptions. It is not claiming +10% versus −20% of anything literal.

Three reading rules:

1. The signs and the channel-level decomposition carry the most signal. A positive ΔNet that is small but balanced across channels reads very differently from a positive ΔNet of the same magnitude where ΔV_prod is huge and ΔM_comp is large-and-negative. The first is robust; the second is a self-automator trap waiting to spring.
2. Pull one slider at a time and watch what moves. The point of the bridge encoding through ρ is that ρ enters multiple terms — moving it shows which terms it touches. Moving T (telic share) at fixed B (atelic ballast) shows how the ΔM_telic channel responds to identity allocation. The structural flags below the channel chart fire when the configuration crosses a meaningful threshold; they are the model’s way of saying “you have entered a regime where one of the topology’s recommendations is load-bearing for you specifically.”
3. The presets are not personality types. Each preset is a recognisable position from the lit review — the Randazzo self-automator (BCG 27%), the OpenAI-MIT high-dose companion-app user, the Caporusso creatively-displaced practitioner, the Brynjolfsson-Li-Raymond novice-skill-compression archetype (which is what the asymmetric-exploiter preset instantiates). Use them to calibrate your intuition for what each region of the parameter space looks like, then move the sliders toward your own position.

The rest of the document spells out what each parameter means, what closed-form pieces compose the dashboard, where the model breaks, and the four objections it has to defend against.

1. What’s being formalised

This stage performs three explicit moves:

• Decomposition. Net life-outcome change under the AI transition is partitioned into ΔV (offensive — value gained) and ΔM (defensive — meaning lost), each further decomposed into three additive channels. The decomposition is orthogonal at the channel level (each channel is its own sum) but block-coupled through the shared bridge parameter ρ.
• Generating function. Each channel is written as an explicit function of the input parameters, with closed-form expressions where the topology supports them (the gate g(f, ρ), the AM-style telic-absorption term, the exponential ρ(t) trajectory) and a piecewise-linear placeholder where it does not (relational dose-response above d_safe).
• Integration. The three lit-review domains (work, relationships, meaning) and the three reframer mechanisms from the topology (G3, G4, G7) are unified under a single equation rather than treated as parallel stories. The integration is what gives the strategic recommendations their leverage: S3 ballast moves B, S5 dose-limit moves d, S6 effortful practice moves ρ — and because ρ is shared across channels, S6 is structurally the highest-leverage move even though it looks like a workplace-productivity tip.

What is ready for formalisation:

Piece	Source	Form
Productivity scale α	Brynjolfsson-Li-Raymond, BCG RCT	α ≈ 0.40, gated by f·ρ
Self-automator gate τ	Randazzo BCG self-automator share + skill-development null	τ ≈ 0.30, σ ≈ 0.06
Telic-absorption ΔM (G7)	Setiya telic/atelic + topology A5	−κ·φ·max(0, T−B)
Competence-erosion ΔM (G4)	SDT competence-frustration + topology G10	−λ_M·(1−ρ)·T
Relational dose-response	OpenAI-MIT N=981	piecewise: protective ≤ d_safe, harm > d_safe
Time evolution of ρ	A3 crux made parametric	ρ(t) = ρ₀·exp(−λ·u·t)

Two of the topology’s reframer mechanisms (G4 cognitive offloading bridge, G7 telic exhaustion) admit mechanistic closed-form representations as listed above. The third reframer (G3 engagement-optimized substitution) is not represented mechanistically — it is a parameter source for ψ_R: G3 informs the calibration of the dose-response slope above d_safe, but the model has no machinery for the engagement-optimization mechanism itself. If G3 weakens (regulation, consumer demand, competitor design), ψ_R would re-calibrate but the model’s structure would not change. This is a real scope difference: G4 / G7 are encoded in the model; G3 is encoded only in the calibration of one parameter.

What is still observational and inherited by Stage 4 as fitting targets:

• λ (cumulative-atrophy speed) — the single largest unknown. The topology’s open question O3 is exactly “is λ ≈ 0 or λ ≈ 0.06?” The 2+ year longitudinal study that would answer this does not yet exist; Stage 4 will use the cross-sectional evidence (Gerlich, Stadler-Bannert-Sailer, Kosmyna, Ehsan) to bound λ from below but cannot pin it down.
• ψ_R (above-d_safe slope), β_R (below-d_safe slope), and the precise location of d_safe — the OpenAI-MIT data give the qualitative shape but the magnitudes will need refitting from the 300,000-message dataset directly.
• κ (competence-frustration sensitivity) calibration across populations and trait classes. The SDT literature gives within-study coefficients but not a portable scale.
• The scalar-identity assumption on T and B. The topology treats meaning architecture as one thing; in reality identity is multi-domain (work, family, hobbies, civic), and the AI absorption fraction φ may differ across components. Stage 4 should test whether scalar T is a useful approximation or whether a vector T = (T_work, T_family, T_hobby, …) is required.

Time horizon. ΔV and ΔM are comparative-statics changes — they are not instantaneous nor lifetime-cumulative. The defensible reading is that the static dashboard’s ΔNet represents change over a “medium” horizon, ~1–5 years, where the fast channels (ΔV_prod from current AI capability) and slow channels (ΔM_telic, ΔM_comp from prolonged absorption and offloading) meaningfully overlap. Shorter than ~1 year, the productivity-gain side over-weights because the meaning-erosion channels haven’t had time to materialise. Longer than ~5 years, the trajectory tab — which evolves ρ explicitly — is the better lens because the static parameters drift. The horizon is implicit because the literature does not yet give a single time-scale for the slow channels (the cross-sectional evidence is duration-vague). Stage 4 should test whether different empirical anchors imply different horizons and, if so, build a time-resolved version of the dashboard rather than a static one.

2. The generating function

2.1 Spine

For an individual, over a fixed horizon Δt:

ΔNet = ΔV + ΔM
ΔM ≤ 0 by construction

ΔV is offensive — the value gained from AI augmenting projects, accessing previously-out-of-reach domains, and (in the relational channel) the therapeutic-grade benefit at low dose. ΔM is defensive — the meaning lost when AI absorbs work that was carrying meaning, when retained practice atrophies and competence erodes, and when high-dose AI-emotional engagement substitutes for in-person relationships in a thin baseline.

A note on the cut. The V/M split is an organising convention for presentation, not a structural claim about the model. The substantive structure is the six-channel additive decomposition; “ΔV” and “ΔM” group channels by typical sign for ease of reading. ΔV_trap in particular is bounded above by 0 (it is always negative-or-zero) and could equivalently be moved to the ΔM side without changing any of the model’s claims. The block-coupling through ρ runs across the V/M cut: ΔM_comp (defensive side) and ΔV_prod / ΔV_trap (offensive side) all move together when ρ moves. If you find the V/M framing more confusing than helpful, read the channels directly and ignore the cut.

The spine is intentionally minimal. The work happens in the channel-level decomposition.

2.2 The three defensive channels (ΔM)

ΔM_telic = −κ · φ · max(0, T − B)
ΔM_comp  = −λ_M · (1 − ρ) · T
ΔM_rel   = −ψ_R · max(0, d − d_safe) · (1 − δ_R)
ΔM       = ΔM_telic + ΔM_comp + ΔM_rel

ΔM_telic — telic absorption. The Setiya / topology A5 channel. Fraction φ of telic work that AI absorbs, weighted by competence-frustration sensitivity κ, conditional on the telic share T exceeding the atelic ballast B. When B ≥ T, the meaning that was staked on telic completion has somewhere else to live; when T ≫ B, telic absorption is structurally costly. The max(0, ·) is the topology handoff’s “B ≥ T → ΔM ≈ 0” boundary made explicit.

ΔM_comp — competence erosion (the bridge). The G4 / G10 channel. Practice atrophy degrades competence not just symbolically (AI can do it) but actually (you cannot do it any more). The (1 − ρ) factor is the inverse of retained practice; the T multiplier is because competence erosion only hurts to the extent the lost competence carried meaning. This is the channel that makes ρ the bridge: a single parameter pulls both the offensive gate (below) and the defensive ΔM_comp term.

ΔM_rel — relational dose-response. The G3 / E11 / E12 channel. The OpenAI-MIT N=981 RCT found loneliness, dependence, and reduced in-person socialization at high daily voluntary use; below a threshold (placed at d_safe in the model), the same engagement is protective rather than harmful. Above d_safe, the penalty scales linearly in the excess dose, dampened by the relational baseline thickness δ_R — someone embedded in thick local relational infrastructure absorbs the dose better than someone in the Anti-Social-Century baseline. ψ_R is the per-minute slope; in the dashboard it is calibrated so that 60 minutes above d_safe in a thin baseline produces a meaningful but not catastrophic ΔM_rel.

2.3 The three offensive channels (ΔV)

g(f, ρ) = 1 / (1 + exp(−(f · ρ − τ) / σ))

ΔV_prod = g · α · a · (1 − s)
ΔV_rel  = β_R · min(d, d_safe) · (1 − δ_R / 2)
ΔV_trap = −(1 − g) · η_trap · a
ΔV      = ΔV_prod + ΔV_rel + ΔV_trap

g(f, ρ) — the self-automator gate. The smooth analogue of the topology handoff’s “above thresholds → upside, below → trap” dichotomy. The product f · ρ is the relevant axis: feedback-loop richness times retained practice. Both have to be present for AI use to upskill; if either collapses, the gate closes. τ ≈ 0.40 puts the threshold roughly where Randazzo’s self-automator boundary lies in the BCG data; σ ≈ 0.06 makes the transition smooth enough that small parameter changes don’t flip the regime discontinuously.

ΔV_prod — productivity / novice-skill compression. Brynjolfsson-Li-Raymond’s customer-service finding (+14% overall, +34% novice) plus the BCG RCT inside-frontier gains. The (1 − s) factor is novice-skill compression: experts gain little from AI on tasks they’re already good at, novices gain the most. α is the productivity scale; in the dashboard, α = 0.40 reproduces Brynjolfsson novice gain at s ≈ 0.2 (α · 0.8 ≈ 0.32, in the 30–34% range). Multiplied by a (AI capability on the task) — when capability is low or task is outside the jagged frontier, ΔV_prod shrinks regardless of s.

ΔV_rel — therapeutic-grade relational benefit. Therabot RCT (Heinz et al. 2025) and the De Freitas equivalence-hypothesis cluster — at low dose, AI emotional engagement produces real benefit. Capped at d_safe so the channel does not double-count the dose-response harm; the (1 − δ_R/2) factor flattens the benefit for people in already-thick relational baselines (they get less marginal benefit from low-dose AI use because they have alternatives).

ΔV_trap — self-automator penalty. When the gate closes (g → 0), AI use is not just unhelpful but actively degrading: the user delegates without the practice and feedback loops that would catch errors, and incurs both the productivity gain they fail to capture and the deskilling cost. η_trap is the penalty scale; calibrated so that f = ρ = 0.2 (well below threshold) and a = 0.8 produces a moderately negative ΔV_prod + ΔV_trap sum even before adding ΔM.

2.4 The bridge through ρ

The cross-domain bridge G4 from the topology is encoded as one fact: ρ enters three of the six channels — one defensive directly, two offensive via the gate.

ΔM_comp = −λ_M · (1 − ρ) · T          ← direct: ρ low → competence erosion
g       = sigmoid((f · ρ − τ) / σ)    ← intermediate: ρ low → gate closes
ΔV_prod = g · α · a · (1 − s)         ← gated: lower g → less productivity gain
ΔV_trap = −(1 − g) · η_trap · a       ← gated: lower g → larger trap penalty

The remaining three channels (ΔM_telic, ΔM_rel, ΔV_rel) do not depend on ρ. ΔM_telic depends on (T, B, φ, κ) — the identity-allocation and AI-exposure parameters. ΔM_rel and ΔV_rel depend on (d, δ_R) — the daily-relational-dose and baseline-thickness parameters. Lowering ρ has compounding effects across the three ρ-coupled channels: it directly increases ΔM_comp, and it lowers g which simultaneously reduces ΔV_prod and increases ΔV_trap. This is the mathematical content of the topology’s claim that S6 (maintain effortful practice) is load-bearing — it is a single-parameter intervention with leverage in three of the six channels.

The bridge is also why the channel-level decomposition is not fully orthogonal even though each channel is written as an additive term. The three ρ-coupled channels are block-coupled through ρ: at fixed ρ, they are independent; varying ρ moves them in coordinated ways. This is the model’s representation of the lit review’s structural finding that the work-deskilling and meaning-competence channels share a generating function (G4) — they are not separate transitions but one transition with two projections. The topology’s broader claim that all three domains (work, relationships, meaning) share a generating function is a stronger version that the model represents weakly: ρ couples the work and meaning channels directly, while the relational channel is coupled only via the topology’s parallel-mechanism inference (which the model leaves unencoded; see Objection 2 in §7 for why).

2.5 Time evolution

The trajectory tab makes A3 (cumulative offloading) parametric:

ρ(t) = ρ₀ · exp(−λ · u · t)
ΔNet(t) = compute with ρ(t); all other parameters held fixed

Where λ is the atrophy speed and u is the offloading rate. λ = 0 is the calculator-analogue: using AI is structurally like using a calculator and retained practice does not decay. λ > 0 is the cumulative-atrophy regime: ρ falls exponentially in the offloading-rate × time product. Only ρ evolves; pre-attempt skill stock s, AI capability a, feedback richness f, and the identity / relational parameters are held fixed across the trajectory. The deskilling-over-time effect is captured through ρ, not as a separate s(t) decay: as ρ drops, the gate g(f, ρ) closes, which propagates to ΔV_prod (smaller productivity gain) and ΔV_trap (larger penalty), while ΔM_comp grows directly. Adding a second decaying variable would either double-count the deskilling or imply the user becomes a fresh novice with full upside available — neither of which matches the lit-review evidence.

The empirical question O3 from the topology is which regime is correct for AI-augmented knowledge work. The dashboard makes the answer visibly consequential: under λ = 0 (calculator analogue), a knowledge worker with ρ₀ = 0.8 has flat ΔNet over 10 years; under λ = 0.06 (heavy cumulative regime, ρ-half-life ≈ 19 years), the same person has ρ(10) ≈ 0.56, the gate closes from g ≈ 0.84 to g ≈ 0.42, and ΔNet drifts measurably more negative as ΔV_prod compresses and ΔV_trap grows — the drift magnitude over 10 years is on the order of −0.15 ΔNet under default identity parameters (T = 0.7, B = 0.2). Meaningful, but not catastrophic; cumulative-atrophy is a slow process even in its strong regime, and the dramatic-collapse intuition some readers bring to “AI rots your brain” framings does not map onto the model’s actual trajectory at calibrated λ. The model cannot answer which regime is right; it can only make the difference legible.

3. Closed-form pieces

Three components admit clean equations. The rest are calibrated approximations.

3.1 The gate g(f, ρ)

g(f, ρ) = 1 / (1 + exp(−(f · ρ − τ) / σ))

Standard logistic with location τ and scale σ. The product f · ρ on the location axis is the substantive choice: feedback-loop richness alone is not enough (you can have great feedback loops but no practice if you’ve fully delegated to AI), and retained practice alone is not enough (you can grind without ever testing your work against reality). Both must be present.

Worked anchors at τ = 0.30:

• f = 0.7, ρ = 0.7 (cyborg / centaur centroid in BCG): f·ρ = 0.49 → g ≈ 0.96. Strong upside regime.
• f = 0.5, ρ = 0.5 (median knowledge worker): f·ρ = 0.25 → g ≈ 0.30. Just below the inflection — small interventions push them above; small drift pushes them below.
• f = 0.2, ρ = 0.3 (full self-automator): f·ρ = 0.06 → g ≈ 0.02. Trap effectively closed.

The threshold τ = 0.30 is a structural-claim choice, not a tight fit. The substantive claim is “the median knowledge worker without conscious intervention is on the edge — small movements in f or ρ push them either way” — which the topology supports but no single dataset cleanly calibrates. The BCG-Randazzo 27% self-automator share gives a rough lower-bound anchor (someone with f ≈ ρ ≈ 0.2–0.3 should be in the trap), and the centaur upper-tail (f ≈ ρ ≈ 0.7–0.8) gives a rough upper-bound anchor (clearly above the gate) — but the precise location of τ between these points is a modelling choice. Pass 1 used τ = 0.40 and produced g ≈ 0.07 at the median, which encoded a stronger structural claim than the data supports (“most knowledge workers are deeply trapped”); pass 2 lowered to τ = 0.30 to encode the weaker, better-supported claim (“the median is on the edge”). Stage 4 should test τ directly against the BCG individual-level data; whether the value generalises beyond consulting work is a separate question that requires non-BCG samples to answer. σ = 0.06 makes the transition smooth (10–90% transition over an f·ρ range of about 0.27, or roughly two standard deviations of within-population variation in either parameter alone).

3.2 Telic-absorption ΔM_telic

ΔM_telic = −κ · φ · max(0, T − B)

Three multiplicative factors. φ ∈ [0, 1] is the AI-absorbable fraction of telic work — for software engineering φ might be 0.6 (much of the implementation absorbed but design judgment retained); for in-person therapy φ might be 0.1. (T − B) ∈ [−1, 1] is the unballasted telic share — how much of identity is staked on telic completion that does not have an atelic counterpart. max(0, ·) truncates the negative branch: if B exceeds T, atelic ballast covers the whole telic identity-share and then some, so absorbing telic work does not pull meaning out of unfilled space. κ ∈ [0, 1] is competence-frustration sensitivity — the SDT-derived scalar that translates competence shortfall into amotivation. Some people are temperamentally more sensitive to this; the model exposes κ as a slider rather than a constant.

The boundary B = T is the topology’s atelic-ballast hypothesis (S3) made structurally precise. It is not that ballast eliminates the productivity threat; it is that ballast moves the meaning-architecture out of the line of fire. ΔV_prod is unchanged by raising B; only ΔM_telic shrinks. This is what S3 actually buys.

3.3 Competence erosion ΔM_comp (the bridge term)

ΔM_comp = −λ_M · (1 − ρ) · T

The (1 − ρ) factor is offloading: the fraction of capacity that has slipped because practice was delegated. The T factor is because competence erosion only matters to the extent the eroded competence was carrying identity. λ_M is the coefficient — calibrated so that ρ = 0, T = 1 produces ΔM_comp = −0.30 (a severe SDT-style competence-frustration hit, the upper end of what BPNSFS scales operationalise).

Note the asymmetry with ΔM_telic. Building atelic ballast (raising B) is no defense against ΔM_comp — the competence erosion is happening in the telic domain regardless of where else identity is anchored. The only defense against ΔM_comp is keeping ρ high (S6 effortful practice), which is exactly the topology’s load-bearing recommendation. The model makes this asymmetry visible: pulling B up zeroes out ΔM_telic but leaves ΔM_comp untouched; pulling ρ up shrinks both.

3.4 Relational dose-response

ΔM_rel = −ψ_R · max(0, d − d_safe) · (1 − δ_R)
ΔV_rel = +β_R · min(d, d_safe) · (1 − δ_R / 2)

Piecewise-linear, with the kink at d_safe = 30 minutes/day. Below d_safe, the dose carries therapeutic-grade benefit (Therabot scale, scaled by β_R = 0.001). Above d_safe, every additional minute carries a dose-response penalty (ψ_R = 0.003 per minute per (1 − δ_R)). At the maximum below-threshold dose (d = d_safe = 30) in a fully thin baseline (δ_R = 0), peak benefit is β_R · 30 · 1 = 0.030 — comparable to ΔV_prod at moderate productivity gain. Pass 1 used β_R = 0.004 which made peak benefit ≈ 0.12, dominating ΔV_prod even in well-functioning AI-use scenarios; that overstated the generalisation from Therabot’s clinical-population effect to the median user.

Two things this form does not capture and which Stage 4 should refit:

• Possible sigmoidal saturation at very high doses. ψ_R may fall once d gets large enough — at some point further engagement does not produce additional harm because the relational substitution is already complete. The OpenAI-MIT data is too narrow in dose range to show this.
• The crossover may be nonlinear. d_safe is a sharp kink in the model; in the data it is plausibly a smooth U-shape. The kink is a useful caricature for the dashboard but is not a structural claim about the curve.

The (1 − δ_R) and (1 − δ_R/2) factors encode the topology’s A4 (relational depletion is structural) crux: in a thin relational baseline, both the upside and (especially) the downside are amplified. In a thick baseline, both attenuate. The asymmetric attenuation (penalty fully scaled by δ_R, benefit only half-scaled) is the model’s claim that thick baselines mostly protect — they don’t crowd out low-dose benefit but they do dampen high-dose harm.

3.5 Productivity gain ΔV_prod

ΔV_prod = g(f, ρ) · α · a · (1 − s)

Already covered above. Worth flagging that the (1 − s) novice-skill-compression factor is the offensive-side analogue of the (T − B) ballast structure on the defensive side: just as ballast determines whether telic absorption is costly, pre-attempt skill stock determines whether AI augmentation is large or marginal. The asymmetric-exploiter scenario in the dashboard is exactly the configuration where (1 − s) is large, f and ρ are above the gate, and the upside dominates — a novice with the discipline to maintain feedback loops and effortful practice is structurally better-positioned than an expert who delegates without either.

Cross-domain α heterogeneity. The model’s α = 0.40 is a midpoint compromise across studies that span ~6× in measured productivity gain (α ≈ 0.24 to 1.4). Translating empirical “+X% productivity” into α uses ΔV_prod = α·a·(1−s) at gate-open: α = ΔV_prod / (1−s) with assumed average s for the study population.

• Brynjolfsson-Li-Raymond customer service is a two-anchor study. +14% overall productivity at average s≈0.5 → α ≈ 0.28. +34% novice (s≈0.2) → α ≈ 0.43. The within-study spread is 1.5× — already non-trivial — and the model’s α=0.40 picks up the novice-end of this range.
• BCG consulting (Dell’Acqua-McFowland-Mollick) is two-outcome: +12% productivity inside the frontier (s≈0.5) → α ≈ 0.24; +40% quality on the same tasks → α ≈ 0.80. Productivity-vs-quality spread within a single study is ~3×, the largest within-study spread on record.
• Cui-Demirer-Jaffe-Musolff-Peng-Salz Copilot/coding field experiments found ~26% increase in completed-task throughput per week. With developer s ≈ 0.4–0.5: α ≈ 0.5–0.65.
• Peng-Kalliamvakou-Cihon-Demirer GitHub Copilot controlled experiment found 55% faster task completion on a JavaScript HTTP-server task. With s ≈ 0.4–0.5: α ≈ 1.0–1.4.

The honest reading: α spans ~0.24 to ~1.4 across measured studies — a 5–6× range, not the 4× I previously claimed. The model’s α = 0.40 picks up roughly the median of this range and is closest to the Brynjolfsson-novice anchor. Users in highly AI-suited domains (coding, writing, image generation, data analysis) should mentally bump α up by 1.5–3×; users in BCG-productivity-class tasks should bump it down by ~1.5×; users in domains where AI is awkward (in-person therapy, embodied physical work, deep relational work) should bump it down further still. Stage 4 should fit α per major task category rather than treating it as a scalar — see Q6 in §9.

3.6 ρ(t) trajectory

ρ(t) = ρ₀ · exp(−λ · u · t)

Standard exponential decay. λ is the per-unit-offloading atrophy rate; u is the offloading rate. Their product is the effective atrophy speed. Half-life = ln(2) / (λ · u) — under λ = 0.06 and u = 0.6 (heavy offloading, cumulative regime), half-life ≈ 19 years; under λ = 0.04, half-life ≈ 29 years; under λ = 0.02, half-life ≈ 58 years. Even in the cumulative-atrophy regime, the timescale is multi-decadal, which is consistent with intuition rust being a slow process.

Only ρ evolves in the trajectory tab; pre-attempt skill stock s, AI capability a, feedback richness f, and the identity / relational parameters are held fixed across the horizon. This is a deliberate simplification (pass 1 had s also decaying, but the asymmetric exponential-vs-linear decay was unprincipled, and adding a second decaying variable doubles-counts deskilling-over-time which is already fully captured through ρ → g closing → ΔV_prod giving way to ΔV_trap).

The form is phenomenological — λ is not derived from a deeper biological model. It’s a calibration knob whose value is the falsification window for A3. Stage 4 will bound it from below using the existing cross-sectional evidence; pinning it down requires longitudinal data that does not exist yet.

4. Composing the parts: scenario anchors

The dashboard’s six presets are calibration targets — each should produce a recognisable position from the lit review.

Preset	T	B	φ	κ	s	a	f	ρ	d	δ_R	Expected output (τ=0.30, β_R=0.001)
Default risk	0.70	0.20	0.60	0.50	0.60	0.70	0.50	0.60	15	0.40	g ≈ 0.50 (on the threshold); ΔV slightly negative (trap and productivity roughly cancel); ΔM dominated by telic absorption + competence erosion; ΔNet ≈ −0.27
Ballast intervention	0.50	0.50	0.60	0.50	0.60	0.70	0.50	0.60	15	0.40	Same g, same ΔV; ΔM_telic → 0 (B = T); ΔM_comp unchanged; ΔNet ≈ −0.10 (≈ +0.17 improvement over default risk)
Self-automator	0.60	0.30	0.70	0.40	0.40	0.80	0.20	0.30	10	0.40	g ≈ 0.02 (gate effectively closed); ΔV_prod ≈ 0; ΔV_trap ≈ −0.24; ΔNet ≈ −0.43
Asymmetric exploiter	0.40	0.40	0.40	0.40	0.20	0.80	0.70	0.70	5	0.50	g ≈ 0.96; large ΔV_prod from (1−s = 0.8); ΔM_telic = 0; modest ΔM_comp; ΔNet ≈ +0.20
Creative pre-AI	0.80	0.10	0.80	0.70	0.70	0.80	0.40	0.50	10	0.30	g ≈ 0.16; small ΔV (high s + partial gate, mostly trap penalty); very large ΔM_telic ≈ −0.39 from κ·φ·(T−B) compounding at extremes; displacement-anxiety trajectory; ΔNet ≈ −0.69
Heavy companion	0.50	0.30	0.40	0.40	0.50	0.70	0.50	0.60	90	0.20	g ≈ 0.50; relational channel dominant — ΔM_rel ≈ −0.14 from 60-min dose excess in thin baseline — but s = 0.50 gives more (1−s) upside than the default-risk preset, partially offsetting ΔV_trap; ΔNet ≈ −0.24

Three non-obvious calibration targets:

1. The default-risk preset should produce ΔNet < 0 driven by the meaning side, not the gate. Under the new τ = 0.30 the gate sits at g ≈ 0.50 for default risk — ΔV is approximately neutral, and the negative ΔNet comes from ΔM_telic + ΔM_comp. This is the right structural reading: the default knowledge-worker risk is not that AI use is broken (the gate isn’t fully closed) but that meaning is leaking from the unballasted telic identity and from competence erosion at moderate ρ.
2. Ballast intervention should improve ΔNet without changing ΔV. Raising B alone zeroes ΔM_telic; nothing else changes. The dashboard makes this visible: the ΔV bar is identical between default risk and ballast intervention, only the ΔM_telic channel collapses.
3. The asymmetric-exploiter preset should beat the ballast intervention by a large margin. ΔNet ≈ +0.20 vs ≈ −0.10 — the offensive path is not just “different” from the defensive path, it dominates when the conditions are met. The point of the upside framing is to make this comparison legible; a user comparing the two presets should see that S3 (ballast) is a partial mitigation while the asymmetric-exploiter regime is a positive-sum strategy.

5. Boundary conditions and where the model breaks

Five boundaries are explicit:

1. B ≥ T (atelic ballast covers telic identity). ΔM_telic = 0 by construction. The model still computes ΔM_comp and ΔM_rel; ballast does not protect against competence erosion or relational dose-response. This is the topology’s S3 strengthening exactly the channel S3 was designed to address.

2. f · ρ ≪ τ (gate fully closed). g ≈ 0; ΔV_prod ≈ 0; ΔV_trap ≈ −η_trap · a. Below the gate, AI use is a net negative on the offensive side regardless of capability a. The model is making the strong claim that there is a regime where more AI capability increases damage rather than reducing it. This is not a bug; it is the formalisation of the self-automator finding.

3. s → 1 (expert at the relevant task). ΔV_prod → 0. AI augmentation offers little to someone already fully capable. The model is silent on the meaning dimension here — an expert may still suffer ΔM_telic and ΔM_comp from AI absorbing their craft even when they get no productivity benefit from it. This is a real and well-attested experience (creative-displacement anxiety in expert practitioners) and the model captures it correctly: ΔV ≈ 0 while ΔM is large and negative.

4. a → 0 (AI cannot do this task). Both ΔV_prod and ΔM_telic shrink — there is no absorption when AI cannot do the work. The relational channels are independent of a (they depend on d). This boundary is what the topology calls the “outside the jagged frontier” region.

5. λ = 0 (calculator-analogue). ρ(t) = ρ₀ for all t; the trajectory tab collapses to a flat line. This is one tail of the A3 crux. The model under this regime is still useful — the cross-sectional ΔNet is still meaningful — but the time evolution becomes trivial and S6 (effortful practice) loses its strong defensive role (it still maintains the gate and ΔM_comp at t = 0, but does not protect against compounding). The dashboard’s “calculator” preset on the trajectory tab makes this regime explicitly testable.

Beyond these, five structural limits are not boundary conditions but scope limits:

• Individual scope only. The model takes T, B, φ, etc. as individual parameters. Aggregate dynamics (labor-share macro, civilisational meaning architecture) are out of frame, matching the topology’s individual-decision-maker scope.
• Western-population calibration. All anchor values come from US/Western studies (BCG, Brynjolfsson, OpenAI-MIT, Therabot, Anti-Social Century, Common Sense). The model’s predictions for non-Western contexts should be treated as hypotheses, not findings — particularly for δ_R (relational baseline) which is most sensitive to cultural variation.
• Single-task framing of φ and a. The model treats AI capability and AI absorbability as scalars over the user’s telic work. Real careers span multiple tasks with very different φ and a. A vector form (φ_i, a_i) is a future extension; the scalar version is sufficient for the structural claims.
• Labor-market access is exogenous (G5 apprenticeship-break). The model takes “you have access to the work” as given and computes ΔV_prod from there. But one of the strongest empirically-supported labor findings in the lit review is the apprenticeship-ladder break — entry-level employment in highly AI-exposed occupations fell ~13% (Brynjolfsson-Chandar-Chen ADP data, Aug 2025) for 22-25-year-olds, while same-occupation employment for over-35s rose. For early-career users in highly-exposed occupations, getting the work in the first place is the dominant practical concern, and the model is silent on it. ΔV_prod estimates for novices should be read as conditional on labor-market access; if you don’t have the access, the model’s offensive side does not apply and S7 (career bet) is not the right frame to begin with. This is a structural feature of the labor market, not a parameter the individual can pull.
• Material-floor primacy (L2). For users whose material floor is insecure (precarious income, dependent-care obligations, no economic runway), the absence of ΔV_prod — i.e., job loss or income disruption — is the existential question. The model’s individual-decision framing implicitly assumes economic security: ΔM_telic versus ΔV_prod is a choice you can have only when survival is not in question. The topology’s logical guardrail L2 names this directly, and the model inherits it as a scope limit. For users at the material-secure end of the distribution, the model’s strategic recommendations are decision-relevant; for users at the material-insecure end, the labor-economics question dominates and the meaning-architecture machinery here is not the right tool.

6. Distortion-aware reading

Each channel of the decomposition has a public-discourse failure mode. The model’s job is to make the failure visible.

Channel	Common misreading	What the model says
ΔV_prod (positive)	“AI is making everyone more productive”	Conditional on g(f, ρ) being open. Below the gate, the same a and s give negative ΔV via ΔV_trap. Productivity gains are real but only for users meeting feedback / practice conditions.
ΔM_telic (negative)	“AI is destroying meaning”	Conditional on T > B. The atelic-ballast intervention (S3) zeroes this channel without changing AI exposure. The threat is identity-allocation-dependent, not AI-dependent.
ΔM_comp (negative)	“AI use rots your brain”	Conditional on (1 − ρ) being large and T being large. People who maintain practice (high ρ) take little hit even at high AI exposure; people whose identity isn’t telic-loaded (low T) take little hit even at low ρ. The bridge is real; its blanket framing is wrong.
ΔM_rel (negative at high d)	“Companion apps are bad”	Conditional on d > d_safe and δ_R low. Below d_safe, the same engagement is therapeutic-grade benefit (Therabot). The harm is dose-and-baseline-dependent, not modality-dependent.
ΔV_rel (positive at low d)	“AI is great for mental health”	Conditional on staying below d_safe. The same engagement above d_safe flips sign. The dose-response framing is the only honest summary.
ΔV_trap (negative when below gate)	“Some people just don’t know how to use AI”	The trap is structural, not cultural. f and ρ are observable conditions; users meeting them upskill, users not meeting them deskill, regardless of intent or attitude.

The four topology distortions (D1 fatalism, D2 slow-camp dismissal, D3 productivity-only optimization, D4 material-blind class bias) each map to a specific failure mode of reading the decomposition: D1 ignores ΔV (assumes the gate closes globally); D2 ignores ΔV_prod and ΔM_comp (claims aggregate effects haven’t moved); D3 ignores ΔM and ΔV_trap (optimises only ΔV_prod); D4 ignores L2 / the model’s silence on material floor.

7. Adversarial + steelman

Five objections to the formalisation itself.

Objection 1 — Variance bookkeeping for meaning is a category error

ΔM is measured on the same axis as ΔV, but meaning is not a quantitative quantity that admits subtraction or comparison across persons. Calling something “−0.30 ΔM” is pseudo-precision: meaning is qualitative, embodied, narratively structured. The decomposition smuggles in a positivism that the underlying phenomenon does not support.

Steelman. This is the strongest version of the philosophical-versus-quantitative tension. The lit review’s meaning section deliberately uses Setiya, Arendt, and SDT — three traditions, none of which treat meaning as scalar. Reducing them to one number is exactly what those traditions warn against. The objection has force precisely because the model is not claiming to measure meaning literally; it is claiming that comparative claims about meaning (“this configuration is better-positioned than that one”) admit a structured representation, and the structure is the model’s content.

Response. Conceded in part. The model is more accurately described as a comparative-meaning generating function: given two parameter configurations, it produces a directional claim about which is structurally better-positioned. The cardinal numbers ΔM = −0.20 vs −0.50 should be read ordinally, not metrically. Anyone who reads the dashboard as “you will lose 20% of your meaning” is misreading; the dashboard’s job is to surface the channels and their interactions, and the bare numbers are pedagogy for that job. Stage 4 will calibrate the channels against measurable proxies (SDT subscale shifts under intervention, time-use-survey-derived telic/atelic share changes, OpenAI-MIT loneliness-scale movements) without claiming the result is meaning-measurement.

Objection 2 — Encoding the bridge as a single ρ over-collapses three different mechanisms

Cognitive offloading in analytical work, in emotional processing, and in identity-supporting practice are three different psychological processes with different timescales and different reversibilities. Treating them as one parameter ρ is the topology’s bridge made artificially clean — the bridge is an inference, not an observed equivalence, and the cross-sectional evidence (Gerlich, Stadler-Bannert-Sailer) is for the analytical channel only.

Steelman. This is correct as stated — the topology itself flags that channels 2 (relational) and 3 (meaning) are parallel-mechanism inferences, not directly observed. Encoding them as one parameter is a load-bearing simplification, not a theorem. The simplification has structural consequences: pulling ρ in the dashboard moves all three channels in lockstep, which over-states the actual coupling. A model with three ρs (ρ_analytic, ρ_emotional, ρ_meaning) would let the channels move independently and would more accurately represent the evidence.

Response. Conceded with a scope limit. The single-ρ form is the appropriate first formalisation: the topology argues the three channels share a generating function (G4), and a one-parameter representation is the minimum-complexity form consistent with that argument. The dashboard’s bridge slider is meant to test the strong form of the argument. Stage 4 should test whether ρ can be split — if O2 (asymmetric-adoption couples) shows that emotional ρ moves independently of analytical ρ, the model needs a vector form. The single-ρ version is falsifiable in exactly that way, which is part of what makes it useful.

Objection 3 — Linear ΔM_rel above d_safe is not what the OpenAI-MIT curve looks like

OpenAI-MIT N=981 reports a continuous monotone-increasing relationship between daily voluntary use and loneliness, dependence, and reduced in-person socialisation. There is no clean kink at “30 minutes/day”; the safe-threshold is a model artifact. Plus the literature on dose-response in companion-app harm (de Freitas identity-discontinuity) suggests non-linear damage at high doses (the worst harm is from the loss of access, not the use itself), which the model’s piecewise-linear form fully misses.

Steelman. Both points are correct. The kink at d_safe is a useful pedagogical device — it makes the dose-response visible and binds it to a recognisable threshold — but the underlying curve is plausibly smooth and almost certainly nonlinear at the high tail. Heavy users may have already substituted away from human relationships, so additional minutes do not produce additional substitution; this would mean ψ_R falls at high d. Conversely, the catastrophic-loss mechanism (Replika-removal evidence) is not a function of d at all — it is a function of platform stability — and the model has no representation of this.

Response. Conceded fully on both points. The piecewise-linear form is a placeholder; Stage 4 should fit the curve directly from the OpenAI-MIT messaging dataset and the de Freitas survey panels. The catastrophic-loss mechanism is currently outside the model’s scope — it would need a separate “platform-shock” term that doesn’t fit the additive-channel structure cleanly. For now, the model captures the steady-state dose-response but not the failure-mode dynamics; a Stage-3 extension or a Stage-5 build artifact may add this.

Objection 4 — Treating identity as scalar T and B misses the multi-domain structure

Real people allocate identity across work, family, civic, hobby, and friendship domains. Each domain has its own telic/atelic balance and its own AI absorption fraction. Compressing all of this to scalar (T, B) is the modelling equivalent of treating a person as having “one personality trait.” The whole point of the topology’s S2 (identity diversification) recommendation is that diversification across domains is the move; a scalar model cannot represent that move.

Steelman. This is correct. The dashboard’s “raise B” lever is doing two different things at once: it’s literally increasing atelic share, but it’s also implicitly diversifying identity (because increasing atelic share is the same operation as adding a non-telic identity domain). The model conflates the two and the conflation is structural — the additive ΔM_telic = −κ·φ·max(0, T−B) form does not distinguish “more domains” from “more atelic share within the same domain.” S2 is therefore representable in the dashboard only if you read raising B as proxy for raising domain count.

Response. Conceded. A vector form T = (T_work, T_family, T_civic, T_hobby, …) with corresponding B, φ, a, κ is the right next step. The scalar version is the appropriate first cut: it captures the structural argument (telic absorption hurts, atelic ballast helps, the bridge runs through ρ) cleanly, and the four objections do not break the structural argument — they refine its precision. Stage 4 should test whether the scalar approximation produces reasonable agreement with empirical configurations of real careers, and Stage 5 may build a vector-form interface if the scalar approximation is too lossy.

Objection 5 — The model is moralistic productivity discourse in equations

Look at what the model rewards: high f (rich feedback loops), high ρ (maintained effortful practice), high B (built atelic ballast), low d (limited AI-emotional dose). Every parameter that the model says “moves you toward better outcomes” is a parameter that mainstream AI productivity culture already moralises about. The disciplined user wins on every channel. This is not structural analysis of the AI transition; it is a sophisticated rephrasing of “be diligent, build hobbies, don’t over-rely on AI” — advice you could find in any 2025 LinkedIn post, dressed up in Greek letters and a sigmoid gate. The model’s apparent mathematical content is, on this reading, a credentialing operation: it gives the prevailing productivity-culture prescriptions an air of formalism without changing what they actually recommend.

Steelman. The objection is sharper than D3 (productivity-only optimization, which targets readers who ignore the relational and meaning channels). D3 says “don’t optimise only for ΔV_prod”; this objection says “even when you include all six channels, the model rewards conscientiousness uniformly, and that uniform reward is the moral content smuggled into the structure.” The model has no parameter for “your domain is being eaten regardless of your effort.” It has no representation for “personal discipline cannot save you from labor-market disruption.” The G5 scope limit gestures at this in §5 but the dashboard itself has no surface where structural-disruption-overwhelms-personal-effort can be made visible. A reader pulling sliders sees “discipline → better outcome” everywhere they look, which is exactly the conclusion the productivity-culture frame wants them to reach. Independently, the Caporusso “creative displacement anxiety” finding documents practitioners who suffer despite high discipline, high feedback richness, and intact relational baselines — the dashboard’s creative-pre-AI preset captures this case but as a fixed configuration to be looked at, not as a structural claim about what disciplined-but-still-doomed looks like.

Response. Partially conceded. The objection is correct that the model’s intra-parameter rewards are all aligned with discipline; this is not an arbitrary choice but reflects what BCG / Brynjolfsson / Cui / Randazzo actually found — disciplined users do outperform in those datasets. The model is not making the empirical claim “discipline pays” up; it is encoding the empirical regularity. What the objection correctly surfaces is that the model’s structural cases where discipline does not pay live in scope limits and boundary conditions rather than in the dashboard’s central readout. When a → 1 (AI fully capable on the user’s task), ΔV_prod → 0 regardless of f, ρ, or s. When the user is in the G5 apprenticeship-break regime, no slider position recovers ΔV_prod. When λ > 0 in the cumulative-atrophy regime, even disciplined users see ρ drift down over the trajectory. These are real model representations of “discipline doesn’t save you” — but they are at the periphery of the dashboard, not at its centre. The honest framing the model should defend: disciplined response matters within a labor-market and capability regime that you do not control; the model represents both the within-regime payoff to discipline and (via scope limits and boundary conditions) the regimes where the payoff vanishes. A version of the dashboard that surfaced “domain doomed-ness” as a top-level toggle (rather than an a-slider value) would be more honest than the current one. Stage 5 (build) is the right place to add this; the model formalisation as it stands captures both halves but presents them asymmetrically.

8. Cruxes (load-bearing claims of the model itself)

Beyond the topology’s empirical cruxes (A1–A5), the model rests on five formal cruxes whose collapse would force structural rewriting.

C1 — The bridge through ρ is real and load-bearing. If cognitive offloading in analytical work is not mechanistically related to relational-depth erosion or meaning-architecture erosion, encoding ρ as one parameter over-states the coupling and the model’s strong defensive claims weaken. Falsification window: O2 (asymmetric-adoption couples) — if the relational-channel ΔM_rel does not co-move with the analytical-channel ΔM_comp under the same offloading rate, ρ must split.

C2 — The atelic-ballast hypothesis: B ≥ T eliminates ΔM_telic. If atelic activities are also degraded by AI proximity (AI companions changing the phenomenology of friendship, AI art changing aesthetic contemplation), then raising B does not protect because B itself is being absorbed. Falsification window: O4 (AI-augmented atelic activities — less meaningful?). If O4 resolves yes, the entire defensive-side architecture needs reconstruction; ΔM_telic should be replaced by a term that cannot be cleanly bounded by raising B.

C3 — The self-automator gate is at f · ρ rather than at f or ρ alone. The product structure is the model’s strong claim that both feedback richness and retained practice are necessary; neither is sufficient. If the BCG data instead shows that high-f users still upskill at low ρ (or vice versa), the gate should be max(f, ρ) or some other non-product combination, and the bridge through ρ collapses.

C4 — α (productivity scale) varies ~6× across measured domains; the model’s scalar α is a midpoint compromise. The full range across published studies spans α ≈ 0.24 (BCG productivity inside frontier) to α ≈ 1.4 (Peng coding controlled experiment), with within-study spreads of 1.5–3× (Brynjolfsson novice-vs-overall, BCG productivity-vs-quality). The model’s scalar α = 0.40 picks up roughly the median of this range, closest to the Brynjolfsson-novice anchor. Tasks involving deep relational or embodied work cluster below α=0.40, though they are less precisely measured. The model’s scalar α = 0.40 is therefore not “task-invariant” but a midpoint estimate across a heterogeneous range; per-domain α should be substituted when known. Falsification of the scalar form is already established empirically; the live question is whether the channel-level structure (gating, novice-skill-compression, trap penalty) survives when α is allowed to vary by domain. Stage 4 should fit α per major task category rather than treat it as a single constant — see Q6 in §9.

C5 — Time evolution of ρ is exponential rather than threshold-stepped. The model uses smooth exponential decay; the underlying capacity-loss process may instead be threshold-stepped (you are fine until you are suddenly not). The Ehsan “intuition rust” finding is suggestive of slow decay but is not high-resolution enough to discriminate. Falsification window: 2+ year longitudinal study with periodic capacity assessment; if the curve is sigmoidal-with-cliff rather than exponential, the trajectory tab is qualitatively misleading at the late horizon.

C6 — The six channels are additive (no interaction terms). The model writes ΔNet as ΔV_prod + ΔV_rel + ΔV_trap + ΔM_telic + ΔM_comp + ΔM_rel. This assumes the channels are independent given parameters: a user’s ΔM_comp does not change the sensitivity of their ΔM_rel, and so on. Empirically, this is a strong claim. Plausible interactions: (a) work-meaning erosion (ΔM_comp) may amplify relational substitution (a depleted-at-work user reaches more readily for AI emotional engagement); (b) atelic ballast (B) may attenuate ΔM_rel (ballast in non-work domains crowds out relational AI dose); (c) feedback richness f and pre-attempt skill s may interact (an expert with poor feedback degrades faster than the model suggests). Falsification window: paired-survey data measuring the joint distribution of work-meaning, relational outcome, and AI-use parameters; a significant interaction term in a regression would flip C6 from “additive is sufficient” to “interaction terms are load-bearing.” Until that data exists, the additive form is the model’s principled simplification — additivity is the minimum-complexity decomposition consistent with the topology’s channel-level claims, and adding interaction terms without empirical support would over-fit.

9. Open questions Stage 4 should resolve

Six empirical targets the formalisation makes sharp:

• Q1 — Magnitude of λ. The cumulative-atrophy speed. Bound from below using cross-sectional evidence (Gerlich N=666, Stadler-Bannert-Sailer, Kosmyna MIT, Ehsan year-long) — but the longitudinal study that would pin λ down does not exist yet. Stage 4 should fit the lower bound and report the model’s predictions across the full plausible range.
• Q2 — Shape of the relational dose-response curve. Refit ψ_R and β_R from the OpenAI-MIT 300,000-message dataset directly. Test whether the piecewise-linear form is a reasonable approximation or whether the curve is sigmoidal / has a high-d saturation.
• Q3 — Location of τ. The self-automator gate threshold. Use the BCG-Randazzo individual-level data to fit τ from observed upskilling-vs-deskilling outcomes against measured f and ρ. The 27% self-automator share gives a rough anchor but not the precise inflection point.
• Q4 — Whether T and B can be scalar. Test the scalar approximation against multi-domain time-use survey data (e.g. ATUS combined with self-report identity-domain weights). If the scalar form produces poor fit, Stage 5 should use the vector form.
• Q5 — Population calibration of κ. Recover κ from BPNSFS scale shifts in populations with measured AI-exposure variation. Test whether κ is approximately constant across demographic strata or whether it stratifies by trait class (e.g. higher κ in conscientiousness-loaded populations).
• Q6 — Per-domain α. Pool studies across customer service (Brynjolfsson-Li-Raymond), consulting (BCG / Dell’Acqua-Mollick), coding (Cui et al., Peng et al.), writing (Noy-Zhang), data analysis (forthcoming), and other measured domains; produce a per-domain α distribution rather than a single scalar. Test whether the channel-level structure (gating, novice-skill compression, trap penalty) holds with per-domain α — i.e., whether the model’s structural claims survive when the productivity-scale parameter is allowed to vary.

10. Connections to other topics

The model touches five sibling topics in the planned-topics list and two active topics.

• Bedrock generating functions. The ΔNet = ΔV + ΔM form is itself a candidate bedrock function for “transitions that restructure life simultaneously across multiple domains.” The structure (positive sum + negative sum gated by a shared bridge parameter) is more general than AI; it would apply to industrialisation, the printing press, suburbanisation, smartphones. The bedrock-generating-functions topic should consider whether the structure is an instance of a broader class.
• Technology utilization architecture (active). The cognitive-partnership-stack model in the sibling topology has its own variant D (regime-stable subgraph) that survives capability change. The current model’s λ (atrophy speed) parameter is the connection point: if λ ≈ 0, the technology-utilization-architecture’s strategic recommendations are sufficient; if λ > 0, they need to be supplemented with practice-maintenance (S6) machinery. The two topologies’ shared concern is verification — both name it as load-bearing under different parameter names. Tech-utilization’s per-shot deskilling β coefficient (Bastani’s 17% drop scaled per-task) is the per-event analogue of this model’s per-time atrophy: integrating tech-utilization β over the offloading rate u and time t recovers something like λ·u·t.
• Prediction & calibration. The model’s gate g(f, ρ) and the topology’s L3 (substitution-vs-complement is the wrong binary) are both arguments about verification. A user’s ability to verify AI output — and to know when their verification is itself compromised by reduced ρ — is a cross-cutting parameter that the prediction-and-calibration topic should address directly.
• Human-psych-variation (active). The model treats κ (competence-frustration sensitivity) as a personal slider with values in [0, 1]. The cross-population calibration of κ — how it varies across people, what predicts variation, whether it stratifies by personality trait class — properly belongs to the individual-differences topic. The current model takes κ as exogenous; integrating with the human-psych-variation framework would let κ be drawn from a population distribution with measurable correlates (conscientiousness, neuroticism, achievement-orientation), which would in turn make the model’s predictions for specific persons more grounded.
• Evolution-modernity mismatch. δ_R (relational baseline thickness) is the depleted-baseline parameter the topology’s A4 names: AI lands into a relational environment that has been depleted for sixty years. Why has it been depleted? The mismatch topic — humans evolved for thicker community than modernity provides — is the upstream causal story. The model uses δ_R as an exogenous input, but the distribution of δ_R across the modern population is itself an output of the evolution-modernity-mismatch dynamics: industrialisation, suburbanisation, smartphone displacement of in-person time, atomised housing, decline of religious affiliation, and so on. The dose-response curve in the model is sharper for users in thinner δ_R baselines because the mismatch is sharper there too.
• Trust architecture. The relational channel in the model treats AI emotional engagement as a single d parameter. In reality the trust placed in different AI systems (companion app, general assistant, fine-tuned therapy bot) varies, and the trust dimension is what determines the dose-response slope. Trust-architecture as a topic should disaggregate d by trust regime and produce per-regime dose curves.
• Information fidelity. Feedback-loop richness f is partly a question of information fidelity — does the user receive accurate signals about their AI-augmented work, or is the feedback channel itself corrupted (sycophantic AI feedback, echo-chamber peer review, vanity metrics)? The information-fidelity topic should produce a structural account of when f is high-quality information versus motivated noise.

11. Glossary

• ΔNet, ΔV, ΔM — net, offensive, and defensive components of life-outcome change. ΔM ≤ 0 by construction.
• T (telic share of identity) — fraction of identity staked on activities aimed at completion (Setiya).
• B (atelic ballast) — fraction of identity in activities realised in the doing rather than at the end.
• φ (AI-absorbable fraction) — share of telic work that AI can do for the user.
• κ (competence-frustration sensitivity) — SDT-derived per-person scalar translating competence shortfall into amotivation.
• s (pre-attempt skill stock) — user’s existing skill on the AI-relevant task. Low s = novice; high s = expert.
• a (AI capability) — AI’s capability on the relevant task; varies with the jagged frontier.
• f (feedback-loop richness) — quality of feedback the user receives on AI-assisted work; low f = no feedback / unverified output.
• ρ (retained effortful practice) — fraction of capacity preserved through deliberate practice rather than offloaded.
• d (daily AI-emotional minutes) — daily voluntary AI engagement minutes for relational / emotional purposes.
• δ_R (relational baseline thickness) — how thick the user’s existing in-person relational infrastructure is. Anti-Social-Century baseline corresponds to low δ_R.
• g(f, ρ) — self-automator gate; smooth logistic over f·ρ at threshold τ.
• τ (gate threshold) — the f·ρ value at which AI use flips from upskilling to deskilling. Currently τ = 0.30.
• σ (gate transition width) — controls how sharply the logistic gate flips around τ. σ = 0.06 makes the transition smooth — 10–90% transition over an f·ρ range of about 0.27, roughly two standard deviations of within-population variation in either f or ρ alone.
• λ (atrophy speed) — rate of practice-decay per unit offloading-time.
• u (offloading rate) — fraction of relevant tasks the user offloads to AI per unit time.
• α (productivity scale) — calibration constant on ΔV_prod; ≈ 0.40 from Brynjolfsson-Li-Raymond.
• η_trap (self-automator penalty scale) — per-unit-capability penalty when below the gate.
• λ_M (competence-erosion coefficient) — calibration constant on ΔM_comp.
• ψ_R, β_R — slopes of the relational dose-response above and below d_safe.
• d_safe (safe-dose threshold) — daily-engagement minutes below which the relational channel is therapeutic-grade benefit; above which it tips into harm.
• Bridge parameter — ρ; the single primitive that connects the work-deskilling, relational-depth-erosion, and meaning-architecture-erosion channels under one generating function (G4).
• Calculator-analogue regime / cumulative-atrophy regime — the two endpoints of A3. Calculator: λ = 0, no decay. Cumulative: λ > 0, exponential decay in offloading-rate × time.
• Self-automator — Randazzo’s third class beyond centaur/cyborg; delegates both what and how to AI; in the model, the f·ρ ≪ τ region.