---
slug: transient_response
name: Transient Response
one_liner: "The time-course by which a system approaches (or departs from) a state after a disturbance — the trajectory between disturbed and settled, with a named anatomy (settling time, relaxation time, overshoot, damping) that is distinct from the resting state it approaches."
type: prime
schema_version: 2
status: density_v2_draft
categories: [structural, physical, control_theory]
origin_domain: control_theory
alternate_origin_domains: [physics, chemistry, ecology, economics, neuroscience]
aliases: [relaxation_dynamics, relaxation_time, step_response, impulse_response, settling_behavior, approach_to_equilibrium]
related: []
solution_archetypes: []
review_flags:
- "OPERATOR-DERIVED (op-03 temporalization, flavor 3b / state→trajectory) — the DYNAMIC prime obtained by temporalizing a static state: the time-course of approach to (or departure from) a settled state, as opposed to the state itself. THE STRONGEST AND MOST CONVERGENT FIND OF THE OP-03 SWEEP — convergence ~12 inputs (equilibrium, feedback, impedance_mismatch, fail_safe, economy_of_force, outlier_leverage, network_flow_models, counter_current_exchange, zone_of_proximal_development, attractor_selection_and_basin_control, bottleneck, irreducible_floor). Discovered 2026-07-03. STRONG hold (verified absent from corpus; established scientific name — transient response in control theory / signals & systems; relaxation dynamics in physics & chemistry). STATUS: HOLD pending owner keep/cut."
- "Created 2026-07-03; STUB ONLY (frontmatter + Core Idea + Notes). SI/SF/similarity are PROPOSER ESTIMATES pending triangulation. Body sections (Structural Signature onward) NOT written."
- "Screens to run at incorporation: `damping` (IS in corpus — it is a COMPONENT/parameter of transient response, the damping ratio; relate by component/child, not merger), `oscillation` (a special case: undamped/underdamped transient), `resilience` (recovery-time-after-disturbance is one facet; argue transient_response is the general dynamical form and resilience adds an evaluative/robustness frame), `equilibrium` (the endpoint / the input — sibling not parent), `attractor_selection_and_basin_control`, `feedback` (transient response is the time-domain behavior a feedback loop produces — related, distinct)."
- "Phase-C action: re-similarity-check + edge-draw + v1 draft + one_liner sync per CLAUDE.md. The subsumption edge equilibrium→transient_response is the WRONG direction — transient_response is a sibling/companion of equilibrium (the approach vs the rest state). Instead draw a component edge damping→transient_response and a child edge transient_response→overshoot (overshoot is a separate op-03 stub — cross-reference it)."
substrate_independence:
  composite_substrate_independence: 5
  domain_breadth: 5
  structural_abstraction: 5
  transfer_evidence: 5
  reasoning: 'The bare structure — the time-course of a system''s approach to (or departure from) a settled state after a disturbance, with an anatomy of settling time, relaxation time/time-constant, overshoot, and damping (overdamped monotone return vs underdamped oscillatory return vs undamped ringing) — is purely about *how* a system gets to where it is going, carrying no substance from any home domain. It recurs across structurally-unlike siblings: control systems (step/impulse response), physics (relaxation to equilibrium — dielectric, NMR, thermal), chemistry (reaction relaxation to a new steady state), ecology (recovery trajectory after a disturbance), economics (adjustment path to a new equilibrium), neuroscience (post-stimulus settling), and organizational change (settling after a reorganization). Domain_breadth is 5 (genuinely unlike domains sharing only the abstract trajectory), structural_abstraction is 5 (the core is a pure statement about a trajectory between two states, needing no physical substrate — the named parameters are dimensionless or time-valued shapes), and transfer_evidence is strong (independently named — "transient response" in engineering, "relaxation time" in physics/chemistry — across multiple mature literatures). One of the most structural finds of the op-03 sweep.'
similarity_to_nearest_existing_prime:
  slug: equilibrium
  similarity: 0.60
structural_framed:
  label: structural
  aggregate: 0.30
  criteria: {vocab_travels: 0.8, evaluative_weight: 0.2, institutional_origin: 0.1, human_practice_bound: 0.1, import_vs_recognize: 0.3}
  rationale: 'Reads strongly structural. The core claim — a settling/relaxation trajectory with named anatomy (settling time, overshoot, damping, relaxation time) — is recognized rather than imported and travels cleanly into physics, chemistry, ecology, economics, and neuroscience without carrying control-engineering vocabulary; the terms "transient" and "relaxation" are already the shared cross-domain names. Framing residue is minimal: there is no institutional origin and almost no human-practice binding, and the only mild evaluative cast is that a "settled" state is often the *desired* one (keeping evaluative_weight off the floor). One of the most structural op-03 candidates, comparable to its companion `equilibrium`.'
phase_b_passes_completed: []
---
# Transient Response

## Core Idea

Transient response is the *time-course* by which a system approaches — or departs from — a state after a disturbance: the trajectory that runs between "disturbed" and "settled", as opposed to the resting state itself. The corpus already names the endpoint (`equilibrium`, `fixed_point`, `attractor_selection_and_basin_control`), but the endpoint tells you only *where* a system goes, not *how* it gets there. Temporalize the static state — replace "the system is at rest here" with "the system is on its way to rest, and the way matters" — and a distinct object appears: not the destination but the journey to it, with its own measurable shape. This is the general, substrate-neutral form of "how a system settles."

Its load-bearing anatomy is a set of parameters the static state does not have. A *settling time* measures how long the return takes; a *relaxation time* (or time constant) sets the characteristic rate of approach; an *overshoot* records whether the trajectory exceeds the target before settling; and a *damping ratio* sorts the qualitative shapes of return — overdamped (slow monotone approach, no overshoot), underdamped (oscillatory approach that rings down toward the target), and undamped (sustained ringing that never settles). These parameters are precisely what `equilibrium` and `fixed_point` are silent about, and even the corpus's *dynamic* primes do not name them: `feedback` describes the loop that *produces* a transient, and `oscillation` is one special case (the undamped or underdamped limit), but neither names the settling-time / overshoot / damping / relaxation-time anatomy as such. The feature present in the temporalized prime and absent in the input is this: a state has no time-course, but an *approach to a state* does, and the shape of that approach is a nameable, comparable thing.

Read structurally, the same shape appears wherever a system relaxes toward a settled condition, and the siblings are genuinely unlike. In *control theory and signals & systems* it is literally the transient response — the step response, impulse response, and settling behavior of a plant. In *physics and chemistry* it is relaxation dynamics: dielectric, NMR, and thermal relaxation times, and the approach of a reaction to a new steady state. In *ecology* it is the recovery trajectory of a disturbed population; in *economics* the adjustment path to a new equilibrium after a shock; in *neuroscience* the post-stimulus settling of a neural response; in *organizational change* the settling of a team after a reorganization. Across all of these the shared abstract object is a trajectory between two states, characterized by settling time, overshoot, and damping — the biological, economic, and engineered cases are species of one genus, and the strong cross-input convergence (~12 unlike inputs surfacing the same missing structure) is the signal that the genus is the bare dynamical form, not any one substrate's version of it.

## Notes

**Provenance.** Produced by operator 03 (temporalization), flavor 3b (state → trajectory), as the dynamic prime obtained by temporalizing a static settled state: the time-course of approach to (or departure from) that state, distinct from the state itself. This was the STRONGEST and most convergent find of the entire op-03 sweep. The convergence spans roughly *twelve* structurally-unlike inputs — `equilibrium`, `feedback`, `impedance_mismatch`, `fail_safe`, `economy_of_force`, `outlier_leverage`, `network_flow_models`, `counter_current_exchange`, `zone_of_proximal_development`, `attractor_selection_and_basin_control`, `bottleneck`, and `irreducible_floor` — each of which, when temporalized, surfaced the same absent object: the settling/relaxation trajectory. Established scientific construct under multiple canonical names: *transient response* (control theory / signals & systems — step response, impulse response, settling time), and *relaxation dynamics* / *relaxation time* (physics and chemistry — e.g. dielectric and NMR relaxation). Surfaced 2026-07-03. Verified absent from the corpus. Manifest: STRONG hold.

**For owner evaluation (keep/cut).** The case FOR is strong. Transient response is a *canonical, named scientific construct* (not a proposer coinage), verified absent, with an unusually sharp named anatomy — settling time, overshoot, damping ratio, relaxation time — that the corpus's *static* primes (`equilibrium`, `fixed_point`) and even its *dynamic* primes (`feedback`, `oscillation`) do not name as such. And it carries the strongest convergence signal in the op-03 sweep: ~12 unlike inputs independently pointed at it, which is exactly the pattern one wants for a genus-level gap rather than a one-off temporalization artifact. It is the clearest gap temporalization found. The RISKS Kurt should weigh: (1) **relationship to `damping` (already in the corpus) and `resilience`** — `damping` is a *component/parameter* of transient response (the damping ratio), so it should attach as a component/child, not merge; `resilience` overlaps on the "recovery-time-after-disturbance" facet, but the discriminating claim is that transient_response is the *general dynamical form* (the trajectory and its anatomy) while resilience adds an evaluative/robustness frame — recommend keeping them distinct with an overlap note. (2) **One prime or a family?** — settling, overshoot, and relaxation are each separately nameable; the proposer's recommendation is transient_response as the *genus* with `overshoot` as a child (overshoot is a separate op-03 stub — cross-reference it), not a scatter of co-equal primes. Sharp keep/cut question: *is "the time-course of approach to a state" a distinct prime, or is it just `equilibrium` described dynamically?* — the proposer's answer is that the approach has an anatomy (settling time, overshoot, damping) that the rest state provably lacks, so it is a companion object, not a redescription.

**At incorporation.** Re-run similarity against `equilibrium` (input / companion endpoint), `damping` (component — the damping ratio), `oscillation` (special case — undamped/underdamped transient), `resilience` (evaluative-facet overlap), `attractor_selection_and_basin_control`, `feedback` (the loop that produces the transient), and `fixed_point`, to confirm no collapse. **Do NOT draw a subsumption edge `equilibrium` → `transient_response` — that is the wrong direction.** Transient response is a *sibling/companion* of equilibrium (the approach vs the rest state), not a child of it; draw a sibling/companion edge to `equilibrium` instead. If kept: draw a *component* edge `damping` → `transient_response` (the damping ratio is a parameter of the transient) and a *child* edge `transient_response` → `overshoot` (cross-reference the separate op-03 overshoot stub). Add a missing-edge note flagging the `damping` component relationship, the `resilience` evaluative-facet overlap, and the `oscillation` special-case contrast explicitly. Write a v1 draft and sync the one_liner across v1 and v2 per CLAUDE.md before merge.
