The construction
An agent acts in two contexts, A and B, with targets a and b, D = |a − b|. As in CASE-115, one shared output cannot meet both. Its output is y_k = x + s_k·u·z with s_A = +1, s_B = −1, a shared level x and a differentiating command z ∈ [−1, 1]. How far it can differentiate is u = σ(S)σ(G), σ(c) = c/(1 + c), where S is its capacity to tell A from B, a sensor, and G its capacity to act differently on them, a channel. With x and z adapting fast, its residual frustration is F(u, D) = max(0, D/2 − u)².
The capacities are slow:
- Ṡ = αF + βP(G) + e_S(t) − (1 + d)S
- Ġ = αF + βP(S) + e_G(t) − (1 + d)G
- P(c) = 3c²/(1 + c²)
αF is production driven by the agent’s own frustration, the “own activity on a discrepancy” of CLAIM-532. βP is the mutual production by which sensor and channel maintain each other, CASE-189’s Construction 1. e(t) is any outside supply, and d damage on turnover.
Results
All from scratch/formal/self_formation.py (scipy’s solve_ivp, rtol 10⁻⁹).
The maintained state. With no frustration, S = G = (3 + √5)/2 ≈ 2.618 is stable, with a saddle at (3 − √5)/2 ≈ 0.382 and extinction at 0. There u ≈ 0.5236, so the formed capacity resolves any D ≤ 1.0472.
Formation, persistence and transfer. Discrepancy D = 1 on t < 20, none on 20–60, a new discrepancy of the same class, D = 0.8, on 60–80.
| system | S(20) | S(59) | ∫F on [0, 20] | ∫F on [60, 80] |
|---|---|---|---|---|
| self-forming (α = 1, β = 1) | 2.618 | 2.618 | 0.794 | 0.000 |
| no maintenance cycle (β = 0) | 0.219 | 0.000 | 4.406 | 2.955 |
| same agent, never exposed | 0 | 0 | 0 | 0.876 |
The self-forming agent meets the later conflict with no frustration. An agent of the same kind that was never exposed must form the capacity first, at a cost of 0.876. Without the maintenance cycle the capacity only tracks the frustration that drives it, never resolves the conflict, and is gone once the conflict ends.
Thresholds. At D = 1, formation needs α > 0.390. At α = 1 it needs D > 0.645: smaller discrepancies are tolerated, at a standing frustration, and form nothing.
The class is bounded. A later D = 1.6 exceeds what was formed. The capacity stretches, S from 2.618 to 2.712, but frustration stays at 0.071, and S returns to 2.618 when the conflict ends.
Provenance. Three agents reach the same maintained state, S = 2.618 at t = 29:
- own, formed by its frustration;
- pulse, with no frustration-driven production (α = 0) and an outside supply of 3 on t < 2, then its own maintenance;
- upheld, with no internal maintenance (β = 0) and an outside controller supplying P(G) and P(S) as feedback; its trajectory equals own’s to machine precision (CLAIM-522).
| knockout | own | pulse | upheld |
|---|---|---|---|
| internal maintenance, from t = 30 | 0 | 0 | 2.618 |
| outside supply, from t = 30 | 2.618 | 2.618 | 0 |
| frustration-driven production, from t = 0 | 0 | 2.618 | 0 |
Upheld is told apart afterwards. Own and pulse are not: after formation they are the same organization, and only a knockout made during formation separates them.
Damage. With constant damage on turnover after formation, the capacity settles at 1.730 for d = 0.3 and 1.299 for d = 0.45. At d = 0.5 it approaches the fold at 1 (critical slowing, 1.003 at t + 400), and at d = 0.55 it is lost, as in CASE-189’s Construction 1.
What it shows and does not
It shows CLAIM-532’s account working in a model. A discrepancy the agent cannot meet drives production of a distinction and a channel. The capacity outlasts the discrepancy because sensor and channel maintain each other (CLAIM-516’s productive cycle), and it serves later discrepancies of the same class, which the claim’s first test detects.
It qualifies the claim’s second test. Interventions on the processes that produce and maintain a capacity tell an agent that formed it from one in which it is upheld from outside. But they tell it from one in which it was installed from outside and then self-maintained only if made during formation. After the fact the history leaves no trace, which is QUESTION-071’s point for self-formation.
Why the provenance result matters
That a self-maintained capacity’s origin leaves no trace in its present organization would be idle if nothing turned on origin. The record holds several entries on which something does.
- Responsibility and freedom. On structural accounts of free agency, a condition stated only in present psychological structure is met by an agent whose structure a manipulator installed (THEORY-040; McKenna and Coates, THEORY-1118). The “pulse” agent here is that agent in miniature: installed once, then self-maintaining, indistinguishable afterwards. So the construction is a case for the historical condition those entries say such accounts need. Fischer and Ravizza’s ownership is historical, by taking responsibility (THEORY-121). Kane’s ultimate responsibility is the strongest such condition (CLAIM-022’s note of 2026-11-02). And Pereboom’s four-case argument (THEORY-328) is the warning that a historical condition may not separate the installed agent from an ordinarily caused one either.
- Whose the will is. Explaining efficacy does not settle whose the will is (CLAIM-022), and what makes a will-organization the agent’s own is QUESTION-011. Both hold only with a historical condition, and this construction shows the present cannot supply one.
- Reflexive control. An outside pulse that leaves the agent maintaining what was installed is CLAIM-404’s informational route and CASE-123’s one-time-perturbation variant, interpretive capture (TERM-066) that needs no continued control. This is the dynamics that makes it undetectable after the fact. CLAIM-545’s domination clause, another’s capacity to govern one’s governing relations whether used or not, is the standing form of the same vulnerability.
- Autonomy as psychology measures it. Self-determination theory holds that how a regulation was taken in, under controlling or supportive conditions, shapes how autonomous acting on it is (THEORY-047). If that is right, an outside-installed and a self-formed capacity must differ somewhere this model lacks, for instance in how the capacity is integrated with the agent’s other demands (THEORY-054). The construction locates where to look: not in the capacity, which is identical, but in its relations to the rest.
- Endorsement in advance. The voluntary delegation of CASE-128 differs from an imposed restriction only in how it came about. The record already counts that difference as one of self-governance.
- The counterweight. An objective that originates outside a learning system can still become its goal (CLAIM-356). Exogenous origin does not by itself disqualify; the entries above say what more, on each view, would.
- Persistence. For collectives the record already holds that what persists is what is causally transmitted, not what resembles (CLAIM-329, QUESTION-118). Whether a self-formed capacity continues the agent’s will is the same question asked of a capacity (QUESTION-364).
The view it qualifies. Juarrero (LIT-1995, NOTE-1532) holds that coherent dynamics “carry their history on their backs” (p. 75) and “make manifest the context and the moment in which they were created” (p. 76). Her examples, graphite and diamond, are different attractors reached by different routes. Here one attractor is reached by two routes and keeps no trace of which, so the construction limits her general claim without contradicting her examples. Her self-determination is closure, a present, maintenance-provenance notion with no formation condition (pp. 93–94).
It does not show a new variable coming to be. S and G are in the model from the start, and formation raises them from zero, so this is a bistable system pushed across a separatrix, as CASE-189 says of itself. The “class” is fixed by the stipulated cue: the sensor tells A from B and nothing else. The production terms are not paid for thermodynamically (CASE-189’s notes of 2026-10-31).