Gravity of Dismissal

file: GravityOfDismissal.md
module: FFF_Gravity
wave: 0
type: genesis-document
subtype: conceptual-foundation
status: canonical
version: 1.0.0
date: 2026-08-13
session: SES-20260813-DISMISSAL-001
author: umaywant2
companion_to: f_Capture.md
thematic_inverse_of: f_Capture.md
cross_module:
  - f_Release.md
  - f_Decay.md
  - f_Collapse.md
  - f_Dampen.md
  - f_Force.md
  - f_Field.md
note: >
  Wave 0 genesis documents establish conceptual vocabulary and theoretical
  foundations. They do not introduce frozen PRIM IDs or frozen operator
  symbols. Those are introduced in the Wave that formalizes each concept.
  This file is the conceptual authority for all dismissal-related phenomena
  across the FFF_Gravity module.

Capture is the inward pull; dismissal is the force that makes the pull irreversible in the opposite direction.

§0 Genesis Context#

§0.1 Position in the Module#

GravityOfDismissal.md is the third and final Wave 0 document, alongside f_Capture.md (the binding operator) and f_Source.md (the node registry). It stands apart from both: where f_Capture.md specifies the mechanics of attraction, and f_Source.md specifies the static properties of nodes, GravityOfDismissal.md specifies the phenomenology of rejection — the field dynamics that arise when a capture relationship ends not by mutual agreement or natural decay, but by the attractor's active withdrawal.

This document does not define primitives or freeze operator symbols. It defines concepts, vocabulary, and structural relationships that every downstream module inherits. When f_Release.md distinguishes voluntary release from expulsion, it draws on the vocabulary established here. When f_Decay.md models the approach toward dissolution, the threshold at which drift becomes dismissal is anchored here. When f_Collapse.md handles terminal unbinding, the irreversibility of the post-dismissal state is articulated here.

§0.2 Why Wave 0#

Dismissal is not a late-stage phenomenon. It is present from the first moment a capture is possible: the conditions that determine whether E can be re-captured after departure depend entirely on whether E was released, decayed, or dismissed. This phenomenological distinction cannot be introduced after the capture variants (Waves 4+) are specified — it must precede them, informing every termination mechanic in the module.

§1 The Problem of Dismissal#

Standard gravitational models account cleanly for:

• Attraction: F_capture pulls E into A's orbit
• Decay: d_bind decreases over time toward d_collapse
• Release: E escapes A's field with positive kinetic energy

What standard models fail to capture is the phenomenon that practitioners of relational dynamics encounter constantly: the attractor that does not merely stop attracting but actively repels. An entity that was once captured, deeply bound, orbiting stably — and is then dismissed — does not simply return to its pre-capture approach state. It enters a qualitatively different state: the field it once navigated toward A is now oriented away from A, and the very path that led to orbit now leads back toward open space.

This is not decay. Decay is the passive erosion of binding depth over time; it is symmetric — any party can interrupt it by applying f_Amplify or f_Emit. Dismissal is asymmetric and directed: A acts against E specifically, producing a field configuration that E experiences as active rejection, not merely as absence of pull.

This document names that phenomenon, maps it to the triadic model, and establishes the vocabulary that all subsequent dismissal-related mechanics will use.

§2 Core Thesis#

Dismissal is not the absence of capture. Dismissal is capture's photographic negative — the same gravitational geometry, with the field polarity inverted in the direction of the dismissed entity.

When A dismisses E:

1. A does not simply cease to emit a capture field. A inverts field coherence in E's directional zone, converting the pull that once drew E into orbit into a push that carries E outward and away.

2. This inverted field leaves a residue — what this document names the Dismissal Well: a negative-polarity field signature that persists in the space where E's orbit once was. The Well is not passive — it actively repels any future approach by E.

3. The depth of the Dismissal Well is proportional to the strength of the binding that was severed. Deep orbits (high d_bind at time of dismissal) produce deep wells. Shallow soft captures produce shallow wells. This proportionality is the module's core mechanism for encoding the weight of a dismissal in the field state.

4. The Well decays over time at a rate governed by the attractor's own coherence dynamics. A field that remains healthy and active will maintain its Dismissal Well longer. A decaying or dampened field will lose its Well faster — not because the dismissal was less meaningful, but because the field that created the Well is weakening.

5. Re-capture is possible — but it costs. E must supply enough approach energy to overcome the Well before A's standard capture conditions can evaluate. This cost is the module's formal expression of the asymmetry that dismissal creates between first capture and re-capture.

§3 The Dismissal Well#

§3.1 Definition#

The Dismissal Well is the field-state residue left by a dismissal event. It is characterized by:

ρ_D(Φ, t) < 0

where:
  ρ_D(Φ, t)  — dismissal field density at time t (negative extension of ρ(Φ))
  t = 0       — moment of dismissal
  t → ∞       — ρ_D(Φ, t) → 0  (well dissipates)

The dismissal field density ρ_D occupies the negative real axis, the domain complementary to the standard field density ρ(Φ) ∈ [0, 1]. At dismissal time, ρ_D(Φ, 0) = −d_bind(t_dismiss) — the well begins at a depth equal to the binding depth that was severed.

§3.2 Decay Model#

The Dismissal Well decays exponentially:

ρ_D(Φ, t) = −d_bind(t_dismiss) × exp(−t / T_dismiss)

where:
  T_dismiss — dismissal persistence time (attractor-specific constant)
  d_bind(t_dismiss) — binding depth at the moment of dismissal

T_dismiss interpretation:

§3.3 Re-capture Threshold#

For E to re-enter A's capture field after dismissal, E's approach must supply binding energy sufficient to overcome the active Well:

d_bind_approach > |ρ_D(Φ, t_recapture)|

Equivalently:
  β × ρ(Φ) × (1 − e) > d_bind(t_dismiss) × exp(−t_since_dismiss / T_dismiss)

When t_since_dismiss is small (shortly after dismissal), the right-hand side is close to d_bind(t_dismiss) — re-capture requires nearly as deep a binding as the dismissed orbit had. When t_since_dismiss is large, the right-hand side approaches 0 — re-capture returns to standard conditions.

This is the module's formal expression of the phrase time heals: the Well does not disappear, but it dissipates. The entity that was dismissed can return — but it must wait, or come stronger, or find the attractor in a more receptive field state.

§3.4 Well Depth Is Not Permanent State#

The Dismissal Well is not a property of the attractor node. It is a property of the directed relationship (A, E). The same attractor A can have:

• A deep Well against E (recently dismissed after a long orbit)
• A shallow Well against E₂ (recently dismissed after a brief soft capture)
• No Well at all against E₃ (approached but never captured)
• An open capture field against E₄ (currently in orbit)

All four states coexist. The Well is relational, not nodal.

§4 Three Dismissal Modes#

Dismissal is not a monolithic event. The FFF_Gravity module recognizes three structurally distinct dismissal modes, each with different field dynamics, Well profiles, and re-capture costs.

Mode A — Intentional Dismissal (ψ_dismiss = INTENTIONAL)#

Definition: The attractor A explicitly and deliberately severs the binding with E, actively inverting field polarity in E's directional zone.

Mechanism:

1. A invokes targeted field suppression against E:  f_Dampen(E) → ρ(Φ) ↓
2. A inverts coherence polarity in E's zone:        ρ_D(Φ, 0) := −d_bind(t_dismiss)
3. E's orbit dissolves; E is expelled outward
4. Dismissal Well is established at maximum depth

Field signature: Deep Well; long T_dismiss; E experiences maximum repulsive force during the expulsion phase. This is the mode most readily recognized as dismissal in relational experience — deliberate, directed, and consequential.

Distinguishing mark: The initiating action comes from A. E may have been stable, even thriving in orbit, at the moment of dismissal. The dismissal force overwhelms the existing binding depth.

Well profile:

|ρ_D(Φ, t)|
     ↑
d₀ = d_bind(t_dismiss) ──────────────────────────────────────────────
                       \
                        \       (slow decay, T_dismiss large)
                         \
                          \______________________________________ t
                                                              ε

Mode B — Structural Dismissal (ψ_dismiss = STRUCTURAL)#

Definition: The attractor's field collapses globally (FM-002 → ρ(Φ) = 0), expelling all bound entities including E simultaneously. No specific intent toward E is present — the dismissal is a consequence of the field's structural failure.

Mechanism:

1. ρ(Φ) → 0 (FM-002: Field Null)
2. All active orbits lose their binding field simultaneously
3. Each entity Eₙ is expelled from A's orbital registry
4. A shallow Dismissal Well is established for each expelled entity
5. Well depth is bounded by the field's coherence at the moment of collapse

Field signature: Shallow Well (because the field that generated it had already weakened to zero); T_dismiss is short (the collapsed field cannot sustain a strong Well). Re-capture becomes possible again as soon as A's field is restored above the minimum capture threshold.

Distinguishing mark: The Well is symmetric — all expelled entities face the same Well depth, regardless of orbit depth at time of collapse. The Well encodes nothing about the quality or duration of the former orbit. It encodes only the field's final coherence value before collapse.

Well profile:

|ρ_D(Φ, t)|
     ↑
d₀ = ρ(Φ) at collapse ──────────────────────────────────────────────
                       \
                        \   (fast decay, T_dismiss small)
                         \______________________________________ t
                                                              ε

Mode C — Asymptotic Dismissal (ψ_dismiss = DRIFT)#

Definition: The binding decays over many cycles until E's orbit becomes unstable and E drifts outward without a discrete dismissal event. There is no moment at which A explicitly dismisses E; rather, the orbit dissolves through accumulated neglect.

Mechanism:

1. f_Decay reduces d_bind over successive cycles
2. d_bind → d_warn → d_collapse
3. Before d_collapse is reached, the orbit becomes marginal (stab_class = PRECARIOUS)
4. E drifts outward as the binding force can no longer maintain the orbit
5. A minimal Dismissal Well forms — the residue of the decay process itself

Field signature: Minimal Well (because neither party applied force; the orbit simply exhausted itself); T_dismiss is very short. This mode produces the weakest Wells and the easiest re-capture conditions.

Distinguishing mark: Asymptotic dismissal is the only mode where the Well depth is decoupled from the orbit depth at time of separation. A deep, long-standing orbit that decays slowly may produce a shallower Well than a shallow orbit that was intentionally severed. The Well encodes only the velocity of departure, not the depth of what was lost.

Well profile:

|ρ_D(Φ, t)|
     ↑
d₀ (small) ──────────────────────────────────────────────
            \
             \  (very fast decay)
              \___________________________ t
                                       ε

§4.1 Mode Comparison#

§5 Triadic Mapping#

The triadic equation G = F_freq · F_fluid · F_force governs the module. Dismissal operates across all three nodes, but with inverted directionality: where capture maximizes G, dismissal minimizes it toward a negative analog G_D.

§5.1 F_freq Node Under Dismissal#

F_freq is the primary node of dismissal. The dismissal well is encoded in the frequency domain as a negative coherence signature. This is why well depth is measured in the same units as d_bind — they are the same quantity, opposite in sign.

§5.2 F_fluid Node Under Dismissal#

F_fluid records the coupling history. An entity that was tightly coupled (high β) to A before dismissal will experience stronger repulsive coupling during the expulsion phase. This is the visceral experience of dismissal from a former deep orbit: the very closeness that made the orbit stable makes the departure more forceful.

§5.3 F_force Node Under Dismissal#

F_force governs the trajectory. During expulsion, E acquires a departure velocity v_depart that must overcome A's residual field to exit cleanly. After exit, v_depart is the velocity at which E moves away from A's field boundary. The higher v_depart, the faster E reaches regions where the Dismissal Well is no longer felt.

§5.4 G_D — The Dismissal Product#

By analogy with G = F_freq · F_fluid · F_force, dismissal operates through:

G_D = F_freq_D · F_fluid_D · F_force_D

where:
  F_freq_D  = |ρ_D(Φ)| × k_freq_dismiss
  F_fluid_D = |β_D| × k_fluid_dismiss
  F_force_D = v_depart × k_force_dismiss

G_D measures the total dismissal force — the product of:
  field inversion intensity × coupling repulsion × departure velocity

G_D is not a value used in computation — it is a conceptual quantity that expresses the magnitude of the dismissal event as a unified product of all three triadic nodes. A high G_D indicates a strong, directed, traumatic dismissal. A low G_D indicates a soft, quiet, barely-noticed departure.

§6 The F_dismiss Operator Family#

The following operators are introduced at the conceptual level. They are not frozen in this file — their formal specifications are registered when the module's dismissal primitive is authored. They are named here to establish conceptual authority.

These operators will be frozen — with full formal specification, PRIM IDs, and INV compliance records — in a dedicated Wave 5 file when the dismissal primitive is authored.

§7 Dismissal vs. Other Termination Mechanisms#

The FFF_Gravity module provides multiple pathways by which a capture relationship ends. The table below distinguishes dismissal from each.

The key discriminant: Does the separation produce a Dismissal Well?

• No Well: f_Release — E departs freely; A remains open.
• Shallow Well: Decay / Drift — the relationship exhausted itself.
• Deep Well: Intentional dismissal — A acted against E.
• Maximum/permanent Well: f_Collapse — structural dissolution; the orbit cannot be re-established without a new node construction.

§8 Re-capture After Dismissal#

§8.1 The Recovery Window#

Re-capture after dismissal is possible when:

d_bind_approach(t) > |ρ_D(Φ, t)|

i.e.:  β × ρ(Φ) × (1 − e)  >  d_dismiss × exp(−t / T_dismiss)

The left side is what E brings to a new approach. The right side is the cost E must exceed. As t increases, the right side decreases — the window for re-capture widens naturally over time.

§8.2 Assisted Recovery#

The recovery window can be accelerated by:

1. A voluntarily dampens the Well — A applies f_Emit to raise ρ(Φ) and simultaneously allows ρ_D to decay faster. This is A actively signaling openness to re-encounter.

2. E approaches with stronger binding — E uses f_Amplify to raise β before approach, increasing d_bind_approach to overcome the residual Well.

3. Time alone — If neither party acts, the Well decays at its natural rate. Patience is a valid strategy.

§8.3 What Dismissal Cannot Do#

Dismissal cannot:

• Erase E's prior orbit history from A's registry (only purge_registry PRIM:004 does this, and it requires explicit invocation)
• Prevent E from approaching a different attractor
• Change E's mass or β (these are entity properties, not relationship properties)
• Prevent the Well from decaying on its own

Dismissal can do exactly one thing: make the path back to A more costly for E. It encodes the act of rejection in field geometry and allows that geometry to persist proportionally to the depth of what was severed.

§9 Canonical Illustrations#

The following four illustrations ground the abstract model in concrete attractor/entity configurations. These are illustrative, not exhaustive.

Illustration 1 — The Mentor Who Withdraws (Mode A)#

Configuration:

A: senior practitioner   M_A = 8.5, ρ(Φ) = 0.88
E: junior colleague       M_E = 0.4, β = 1.8, d_bind = 1.12

Event: After a breach of trust, A intentionally withdraws. A applies targeted field suppression against E (f_Dampen) and inverts coherence polarity in E's zone. E's orbit dissolves over two cycles.

Dismissal Well parameters:

d_dismiss = d_bind(t_dismiss) = 1.12
T_dismiss = 8.0 cycles (long — the relationship was deep and deliberate)
ψ_dismiss = INTENTIONAL

Re-capture cost at t = 4 cycles:

|ρ_D(Φ, 4)| = 1.12 × exp(−4 / 8.0)
             = 1.12 × exp(−0.5)
             = 1.12 × 0.607
             = 0.680

E would need d_bind_approach > 0.680 for re-capture to begin.
At t_dismiss, E had d_bind = 1.12 — so half the original depth is
needed after 4 cycles. The relationship is not closed; it is costly.

Reading: The mentor has not simply walked away. The field still knows what was there. E can return — but must show up with more than half the depth they carried before the breach.

Illustration 2 — The Dissolved Institution (Mode B)#

Configuration:

A: organization node     M_A = 12.0, ρ(Φ) → 0 (FM-002 active)
E₁, E₂, E₃: members     varying d_bind

Event: The organization collapses (FM-002). All bound entities are expelled simultaneously. The Dismissal Well forms symmetrically for each.

Dismissal Well parameters:

d_dismiss(Eₙ) = ρ(Φ) at collapse moment ≈ 0.08 (field was already weak)
T_dismiss = 1.0 cycle (short — the field was barely alive at dismissal)
ψ_dismiss = STRUCTURAL

Significance:

E₁ had d_bind = 2.1 (deep orbit, long tenure)
E₂ had d_bind = 0.4 (shallow orbit, recent join)
E₃ had d_bind = 1.3 (mid-depth orbit)

All three face the same Well depth: 0.08.
The institution's collapse did not encode the individual relationships.

Reading: Structural dismissal is equalizing — it treats all departures as equivalent regardless of orbit depth. A member of ten years and a member of ten days face the same re-entry cost if the institution reconstitutes. This is the mathematical expression of an institution that closed without malice: the field simply failed.

Illustration 3 — The Fading Connection (Mode C)#

Configuration:

A: former collaborator   M_A = 6.0, ρ(Φ) = 0.71
E: distant colleague      M_E = 0.3, d_bind = 0.19 (d_warn = 0.22)

Event: d_bind has been declining for 12 cycles. It crosses d_warn without either party intervening. E's orbit transitions from MARGINAL to PRECARIOUS and finally to DRIFT. No discrete dismissal event occurs.

Dismissal Well parameters:

d_dismiss = v_depart × k_drift_dismiss ≈ 0.04 (minimal)
T_dismiss = 0.5 cycles (very fast decay)
ψ_dismiss = DRIFT

Re-capture cost:

|ρ_D(Φ, 1.0)| = 0.04 × exp(−1.0 / 0.5)
               = 0.04 × exp(−2.0)
               = 0.04 × 0.135
               = 0.005

Reading: After one cycle, the re-entry cost is effectively zero — the former collaborator can be re-approached as if no dismissal occurred. Drift produces almost no scar tissue. This is the mathematics of the colleague who fades from contact but is warmly received when the connection is renewed. No explicit dismissal happened; the Well barely formed.

Illustration 4 — The Repaired Relationship (Mode A → Recovery)#

Configuration:

A: former mentor   d_dismiss = 0.90, T_dismiss = 10.0 cycles
E: former student  β = 1.6 at time of dismissal

Event: Dismissal occurred 15 cycles ago (Mode A). E has grown (β_new = 2.4). E now approaches A to test re-capture feasibility.

Well at t = 15 cycles:

|ρ_D(Φ, 15)| = 0.90 × exp(−15 / 10.0)
              = 0.90 × exp(−1.5)
              = 0.90 × 0.223
              = 0.201

E's approach binding depth:

d_bind_approach = β_new × ρ(Φ) × (1 − e)
                = 2.4 × 0.71 × 0.88
                = 1.499

Re-capture test:

d_bind_approach > |ρ_D(Φ, 15)|
1.499 > 0.201   ✅

Reading: Re-capture is viable. E brings substantially more binding energy than the Well requires. The 15 cycles of separation have allowed the Well to decay to approximately 22% of its original depth. E's growth (β from 1.6 to 2.4) has increased their binding potential. Both factors together make re-capture not merely possible but comfortable.

The mathematics does not guarantee the re-capture will be welcomed — that is A's decision, not the field's. But the field no longer presents a structural barrier. The gravity of dismissal has not vanished, but it is no longer stronger than what E brings.

§10 Cross-Module References#

§10.1 Upstream — What GravityOfDismissal.md Draws From#

§10.2 Downstream — What Draws From GravityOfDismissal.md#

§10.3 Foundational Status#

GravityOfDismissal.md is the only file in the FFF_Gravity module that defines the negative-polarity extension of ρ(Φ). All uses of ρ_D(Φ) in any future file must cite this document as the definitional authority. No Wave 2+ file may introduce a competing definition of the Dismissal Well without amending this document first.

§11 Document Metadata#

§11.1 Core Properties#

§11.2 Conceptual Index#

§11.3 Wave History#

§11.4 Changelog#

§11.5 Suggested Commit Message#

docs(FFF_Gravity): add canonical GravityOfDismissal.md — Wave 0 complete

Establishes the conceptual foundation for dismissal as active repulsive
force in the FFF_Gravity module. Core contributions:

- Dismissal Well model: ρ_D(Φ,t) = −d_bind(t₀) × exp(−t/T_dismiss)
- Re-capture threshold: d_bind_approach > |ρ_D(Φ,t)|
- Three dismissal modes: INTENTIONAL / STRUCTURAL / DRIFT
- G_D triadic product: F_freq_D · F_fluid_D · F_force_D
- F_dismiss operator family named (to be frozen in Wave 5)
- Distinction table: dismissal vs. release, decay, collapse
- Four canonical illustrations
- Foundational authority for ρ_D(Φ) negative-polarity extension

Wave 0 now complete: f_Capture.md + f_Source.md + GravityOfDismissal.md
FFF_Gravity module: all 28 files canonical across 5 waves.

Session: SES-20260813-DISMISSAL-001

End of GravityOfDismissal.md — Wave 0 Genesis — FFF_Gravity Module — v1.0.0 Session SES-20260813-DISMISSAL-001 · 2026-08-13 23:56 EDT All waves complete. All 28 files canonical. 40 PRIMs registered.