Triadicframeworks
Overview

FFF_Gravity · Operators

Canonical path: docs/FFF_Gravity/OPERATORS.md Authority: This document is the single source of truth for all operator symbols in FFF_Gravity. In any conflict between this file and a function file, this file governs. Normative: Yes — all sections except §0 and §10 are normative.

§0 · Session Context#

Active Session#

Field Value
Session ID SES-20260813-OPS-001
Opened 2026-08-13T07:48:00-04:00
Closed — (active)
Editor Nawder
Branch main
Intent Create canonical OPERATORS.md — master symbol authority
Status 🟡 Active

Update Policy#

When to update this file:
  1. A new operator is introduced in any function file         → add to §1 or §2
  2. A new state flag is introduced                            → add to §3
  3. A new primitive is defined in any function file           → add to §4
  4. A new failure mode is defined                             → add to §5
  5. A composition rule is formalized                          → add to §6
  6. A scaffold file is promoted to canonical                  → update §8 freeze status
  7. A version bump occurs                                     → update §9 and CHANGELOG.md

Never:
  - Remove a frozen symbol (deprecate instead)
  - Rename a frozen symbol without a major version bump
  - Add a symbol that conflicts with FFF_Field, FFF_Momentum, or FFF_Resonance namespaces

§1 · Primary Operators#

Primary operators are direct inputs to f_Capture and its sibling functions. They are measured or externally provided — not computed from other operators. All 9 are frozen at v1.0.0.

§1.1 · Full Specification Table#

Symbol Full Name FFF Node Type Domain Range Unit Frozen Defined In
v_approach Approach Vector F_force scalar ℝ≥0 [0, ∞) normalized velocity ✅ f_Capture.md §4.1
v_escape(A) Escape Velocity F_freq scalar ℝ>0 (0, ∞) normalized velocity ✅ f_Capture.md §4.1
ρ(Φ) Field Density F_freq scalar ℝ≥0 [0, 1] dimensionless ✅ f_Field.md §4.1
r_capture Capture Radius Frame scalar ℝ>0 (0, ∞) normalized distance ✅ f_Capture.md §4.1
β Binding Coefficient derived scalar ℝ≥0 [0, ∞) dimensionless ✅ f_Capture.md §4.1
ω_res Orbital Resonance F_freq ratio ℚ ∪ ℝ rational or irrational dimensionless ✅ f_Capture.md §4.1
M_A Attractor Mass F_fluid scalar ℝ>0 (0, ∞) normalized mass ✅ f_Field.md §4.1
M_E Element Mass F_fluid scalar ℝ>0 (0, ∞) normalized mass ✅ f_Capture.md §4.1
r Separation Distance geometry scalar ℝ>0 (0, ∞) normalized distance ✅ f_Capture.md §4.1

§1.2 · Operator Constraints and Guards#

Symbol Hard Constraints Guard Violation Consequence
v_approach Evaluated at r_capture crossing only; not at outer field boundary Premature evaluation → invalid C_thresh
v_escape(A) Must be recomputed if ρ(Φ) changes between entry and encounter Stale value → FM-006 risk
ρ(Φ) 0 = null field — triggers FM-002 immediately; 1 = saturated Unguarded null → undefined P_eff
r_capture Set by Attractor; cannot be modified by Element or engineering primitives Modification → Frame integrity failure
β Must be ≥ 1.0 for capture to proceed; < 1.0 = flyby unconditionally Below floor → CAPTURE_FAILED regardless of all other conditions
ω_res Irrational value = FM-004 at any point — during approach or post-lock Irrational → CAPTURE_DECAYING
M_A Must be finite and positive; M_A ≈ M_E triggers FM-007 check Mass parity → dissolution path
M_E Must be finite and positive Zero or infinite mass → undefined behavior
r r = 0 is undefined (singularity); r > r_capture → short-circuit in evaluate_capture_threshold Zero → ⊥

§1.3 · Node Assignment Summary#

FFF Node Symbols
F_freq (Frequency) v_escape(A), ρ(Φ), ω_res
F_fluid (Fluids) M_A, M_E
F_force (Forces) v_approach
Frame r_capture
Geometry r
Derived (no single node) β

§2 · Derived Operators#

Derived operators are computed from primary operators via defined formulas. Symbols marked ✅ frozen are defined in f_Capture.md v1.0.0 and cannot change. Symbols marked 🔵 pending have formulas in scaffold files awaiting canonicalization.

§2.1 · Full Specification Table#

Symbol Full Name Formula Depends On Output Range Sign Convention Frozen Defined In
P_eff Effective Pull M_A × ρ(Φ) / r² M_A, ρ(Φ), r [0, ∞) always positive ✅ f_Capture.md §4.2
C_thresh Capture Threshold v_escape(A) − v_approach v_escape(A), v_approach (−∞, ∞) positive = capture possible; negative = escape ✅ f_Capture.md §4.2
d_bind Binding Depth β × ρ(Φ) × (1 − e) β, ρ(Φ), e [0, ∞) higher = more stable ✅ f_Capture.md §4.2
p_res Residual Momentum M_E × (v_approach − C_thresh) M_E, v_approach, C_thresh [0, ∞) always positive post-capture ✅ f_Capture.md §4.2
e Orbital Eccentricity p_res / (p_res + P_eff) p_res, P_eff [0, 1) 0 = circular; approaching 1 = near-parabolic ✅ f_Orbit.md §4.1
T_orb Orbital Period 🔵 pending f_Orbit.md §4.1 d_bind, ω_res (0, ∞) always positive 🔵 f_Orbit.md §4.1
δ Decay Rate Δd_bind / Δt d_bind series (−∞, 0] in decay negative = losing energy 🔵 f_Decay.md §4.1
E_rel Release Energy 🔵 pending f_Release.md §4.1 d_bind, p_res, ρ(Φ) [0, ∞) energy required to achieve release 🔵 f_Release.md §4.1
F_emit Emit Field Strength 🔵 pending f_Emit.md §4.1 M_A, emit energy input [0, ∞) higher = deeper coherence well 🔵 f_Emit.md §4.1
F_damp Dampen Depth 🔵 pending f_Dampen.md §4.1 ρ(Φ), dampen energy input [0, 1] fraction of ρ(Φ) to suppress 🔵 f_Dampen.md §4.1

§2.2 · Supplementary Operators (Engineering Primitives Layer)#

These operators are introduced by engineering primitive files. They extend the derived operator set and are pending canonicalization.

Symbol Full Name Formula Defined In Frozen
F_amp Amplification Factor scalar ≥ 1.0 f_Amplify.md §4.1 🔵
β_max Binding Coefficient Ceiling 🔵 pending f_Amplify.md §4.1 🔵
heading_delta Heading Change angular delta (radians) applied to v_approach f_Deflect.md §4.1 🔵
r_emit Emission Radius bounded region of emit_field effect f_Emit.md §4.1 🔵
r_damp Dampening Radius bounded region of suppress_field effect f_Dampen.md §4.1 🔵
d_warn Decay Warning Threshold d_bind level at which FM-004 is raised f_Decay.md §4.1 🔵
d_collapse Collapse Threshold d_bind level at which FM-005 fires; f_Collapse triggered f_Decay.md §4.1 🔵
m_parity Mass Parity Threshold max ` M_E − M_A ` below which FM-007 fires

§2.3 · Undefined Conditions#

Operator Undefined When Symbol for Undefined
P_eff r = 0 (singularity) or ρ(Φ) = 0 (FM-002) ⊥
C_thresh v_escape(A) undefined (ρ = 0) ⊥
d_bind e ≥ 1 (hyperbolic trajectory — not captured) ⊥
p_res C_thresh ≤ 0 (no capture) ⊥
e P_eff = 0 (FM-002) ⊥
δ Pre-capture (no time series) ⊥
E_rel d_bind = 0 (collapse state; release not viable) ⊥
F_amp β > β_max (runaway — FM-010) ⊥

§3 · State Flags#

State flags represent the discrete relational state of an Element in the FFF_Gravity system. The state machine is deterministic — every transition has a single defined trigger. No state is revisitable once terminal. All 11 flags are frozen at v1.0.0.

§3.1 · Flag Specification Table#

Flag Entry Condition Set By Exit Condition Valid Next States Terminal
CAPTURE_PENDING E crosses r_capture; outcome unresolved compute_approach_vector C_thresh evaluated CAPTURE_LOCKED, CAPTURE_FAILED No
CAPTURE_LOCKED C_thresh > 0 ∧ β ≥ 1.0 ∧ Frame ok ∧ ω_res ∈ ℚ register_capture d_bind falls below d_warn; or FM-007 CAPTURE_DECAYING, CAPTURE_COLLISION No
CAPTURE_DECAYING FM-004 raised; d_bind decreasing flag_decay d_bind ≤ d_collapse CAPTURE_FAILED, CAPTURE_COLLISION No
CAPTURE_FAILED FM-001/002/003/006 raised; or decay → ejection register_capture — — Yes
CAPTURE_COLLISION FM-005 terminal infall; or FM-007 dissolution execute_collapse — — Yes
ORBIT_STABLE stab_class = stable ∧ e < 0.5 post CAPTURE_LOCKED classify_orbit stab_class drops below stable threshold ORBIT_ECCENTRIC, CAPTURE_DECAYING No
ORBIT_ECCENTRIC e ≥ 0.5 while orbit is still captured classify_orbit e drops below 0.5; or FM-004 ORBIT_STABLE, CAPTURE_DECAYING No
RELEASED f_Release conditions satisfied; clean exit execute_release — — Yes (clean exit)
COLLAPSED f_Collapse infall complete execute_collapse — — Yes
DAMPEN_ACTIVE f_Dampen engaged on Attractor's field suppress_field Dampening removed; ρ(Φ) restored CAPTURE_PENDING, ORBIT_STABLE No
EMIT_ACTIVE f_Emit engaged on Attractor's field emit_field Emission withdrawn ORBIT_STABLE, CAPTURE_DECAYING No

§3.2 · State Transition Diagram#

                          E crosses r_capture
                                  │
                                  ▼
                        ┌─────────────────┐
                        │ CAPTURE_PENDING  │
                        └────────┬────────┘
                                 │
              ┌──────────────────┼──────────────────────┐
              │                  │                       │
    C_thresh > 0             C_thresh ≤ 0           ρ(Φ) = 0
    β ≥ 1.0                  (FM-001)               (FM-002)
    Frame ok                      │                       │
    ω_res ∈ ℚ                     │                       │
              │                   │                       │
              ▼                   ▼                       ▼
   ┌──────────────────┐   ┌───────────────┐       (FM-003 / FM-006)
   │  CAPTURE_LOCKED  │   │ CAPTURE_FAILED│◄──────── all terminal
   └────────┬─────────┘   │   [TERMINAL]  │             FMs
            │             └───────────────┘
            │
     d_bind monitored every cycle via flag_decay
            │
    ┌───────┴────────────────────────┐
    │                                │
d_bind < d_warn               M_E ≈ M_A
(FM-004)                      (FM-007)
    │                                │
    ▼                                ▼
┌──────────────────┐      ┌──────────────────┐
│ CAPTURE_DECAYING │      │ CAPTURE_COLLISION │
└────────┬─────────┘      │    [TERMINAL]    │
         │                └──────────────────┘
    ┌────┴────┐
    │         │
ejection  infall
(FM-005)  (FM-005)
    │         │
    ▼         ▼
CAPTURE_  CAPTURE_
FAILED    COLLISION

     ORBIT_STABLE ↔ ORBIT_ECCENTRIC  (reclassified each cycle)
     RELEASED [TERMINAL]             (clean exit via f_Release)
     COLLAPSED [TERMINAL]            (infall confirmed)
     DAMPEN_ACTIVE / EMIT_ACTIVE     (engineering overlay flags)

§3.3 · Flag Ownership#

Flag Owned By Written By Primitive
CAPTURE_PENDING Element E compute_approach_vector
CAPTURE_LOCKED Element E + Attractor A registry register_capture
CAPTURE_DECAYING Element E flag_decay
CAPTURE_FAILED Element E register_capture
CAPTURE_COLLISION Both E and A (or composite) execute_collapse
ORBIT_STABLE Element E classify_orbit
ORBIT_ECCENTRIC Element E classify_orbit
RELEASED Element E + Attractor A registry execute_release
COLLAPSED Composite node C (or A post-absorption) execute_collapse
DAMPEN_ACTIVE Attractor A suppress_field
EMIT_ACTIVE Attractor A emit_field

§4 · Engineering Primitives#

§4.1 · Call Order and Dependencies#

Primitives must be called in the order defined in §7 (Evaluation Order). Side-effecting primitives write to external registries and are not idempotent. Pure primitives may be called in any order relative to each other within their group.

§4.2 · Full Primitive Specification Table#

# Primitive Source File Pure Reads Writes Call Timing Frozen
1 compute_approach_vector f_Capture.md §7.2 Yes E.state, A.position v_approach Once · Step 1 ✅
2 resolve_escape_velocity f_Capture.md §7.2 Yes M_A, ρ(Φ) v_escape(A) Once · Step 2 ✅
3 evaluate_capture_threshold f_Capture.md §7.2 Yes v_approach, v_escape, r C_thresh Once · Step 5 ✅
4 lock_orbit f_Capture.md §7.2 No E, A, Φ orbital_parameters Once · Step 8 ✅
5 register_capture f_Capture.md §7.2 No orbital_parameters FFF_Registry, E.registry, A.registry, A.field_curvature Once · Step 9 ✅
6 flag_decay f_Capture.md §7.2 / f_Decay.md §7 No d_bind_delta E.state_flag, decay_status Every cycle post CAPTURE_LOCKED ✅
7 classify_orbit f_Orbit.md §7 Yes p_res, d_bind, ω_res orbital_parameters.orbit_class, .stab_class Once post lock; then each cycle 🔵
8 compute_release_vector f_Release.md §7 Yes E.state, d_bind v_release Once · on release attempt 🔵
9 execute_release f_Release.md §7 No v_release FFF_Registry, E.registry, A.registry Once · on release 🔵
10 execute_collapse f_Collapse.md §7 No d_bind, E, A composite node, both registries Once · on FM-005 or FM-007 🔵
11 initialize_composite_node f_Collapse.md §7 No M_E, M_A new composite node C Once · on FM-007 only 🔵
12 purge_registry f_Collapse.md §7 No E.id, A.id FFF_Registry (deletion) Once · on FM-007; partial on FM-005 🔵
13 emit_field f_Emit.md §7 No F_emit, A, r_emit ρ(Φ) local, A.field_curvature On demand 🔵
14 suppress_field f_Dampen.md §7 No F_damp, ρ(Φ), r_damp ρ(Φ) local On demand 🔵
15 amplify_coupling f_Amplify.md §7 No F_amp, M_A, ρ(Φ) β, P_eff On demand 🔵
16 redirect_force_node f_Deflect.md §7 No heading_delta, r_deflect v_approach heading component On demand 🔵

Note: Primitive 16 (redirect_force_node) was added from scaffold review. Corrected total: 16 primitives. INDEX.md §2 to be updated at next session.

§4.3 · Side-Effect Classification#

Class Primitives Consequence of Repeat Call
Pure (safe to repeat) 1, 2, 3, 7, 8 No side effects; produces same output for same inputs
Single-write (idempotent-safe) 4, 6 Overwrites same fields; safe to repeat
Registry-write (non-idempotent) 5, 9, 10, 11, 12, 13, 14, 15, 16 Repeat call creates duplicate records or double-applies effect

§4.4 · Primitive Guards Summary#

Primitive Guard Consequence of Violation
evaluate_capture_threshold r ≤ r_capture Returns C_thresh < 0 immediately if r > r_capture
lock_orbit C_thresh > 0 Must not be called if threshold not met
register_capture lock_orbit completed Undefined behavior if orbital parameters absent
flag_decay Post CAPTURE_LOCKED only No-op if called pre-capture
execute_collapse FM-005 or FM-007 active Must not be called outside terminal FM context
initialize_composite_node FM-007 path only Must not be called on asymmetric collapse
emit_field ρ(Φ) < 1.0 No-op at saturation; runaway risk if β → β_max
suppress_field ρ(Φ) > ρ(Φ)_floor FM-009 risk if floor breached
amplify_coupling β < β_max FM-010 if ceiling exceeded
redirect_force_node heading_delta within bounds Over-deflection → FM-001 equivalent

§5 · Failure Mode Registry#

§5.1 · Full Failure Mode Table#

ID Name FFF Node Trigger Condition Operators Involved State Transition Outcome Severity Recoverable Defined In
FM-001 Overshoot F_force C_thresh ≤ 0; v_approach ≥ v_escape(A) v_approach, v_escape, C_thresh CAPTURE_PENDING → CAPTURE_FAILED Element escapes error No f_Capture.md §6
FM-002 Field Null F_freq ρ(Φ) = 0 at moment of encounter ρ(Φ), P_eff, v_escape CAPTURE_PENDING → CAPTURE_FAILED No pull transmitted error No f_Capture.md §6
FM-003 Frame Saturation Frame Attractor registry at MAX capacity Frame.registry_capacity, β CAPTURE_PENDING → CAPTURE_FAILED Element deflected at boundary error No f_Capture.md §6
FM-004 Resonance Drift ω_res ω_res → irrational; d_bind < d_warn ω_res, d_bind, δ CAPTURE_LOCKED → CAPTURE_DECAYING Orbit destabilizing warn Yes — via f_Emit or f_Amplify f_Capture.md §6
FM-005 Decay Spiral d_bind d_bind ≤ d_collapse; energy exhausted d_bind, δ, p_res CAPTURE_DECAYING → CAPTURE_FAILED or CAPTURE_COLLISION Ejection or infall fatal No f_Decay.md §6
FM-006 Phantom Capture ρ(Φ) β ≥ 1.0 met; ρ(Φ) locally structured; lock dissolves at field boundary β, ρ(Φ), P_eff CAPTURE_PENDING → CAPTURE_FAILED Apparent capture resolves to escape warn No f_Capture.md §6
FM-007 Mutual Dissolution F_fluid |M_E − M_A| < m_parity; collision threshold crossed M_E, M_A, β, C_thresh CAPTURE_LOCKED → CAPTURE_COLLISION Composite node created; both registries purged fatal No f_Collapse.md §6
FM-008 Release Overshoot F_force v_release too high; trajectory becomes hyperbolic v_release, E_rel CAPTURE_LOCKED → CAPTURE_FAILED Uncontrolled ejection error No f_Release.md §6
FM-009 Dampen Cascade F_freq suppress_field propagates beyond r_damp; ρ(Φ) → 0 region-wide F_damp, ρ(Φ), r_damp multiple CAPTURE_LOCKED → CAPTURE_DECAYING Gravity null zone; uncontrolled releases fatal Partial — if caught before propagation f_Dampen.md §6
FM-010 Amplify Runaway F_fluid β > β_max under sustained f_Emit or f_Amplify β, F_amp, F_emit, β_max ORBIT_STABLE → CAPTURE_COLLISION Collapse or singularity fatal No f_Amplify.md §6

§5.2 · Failure Mode Groupings#

Group IDs Common Cause Common Outcome
Approach failures FM-001, FM-002, FM-003, FM-006 Conditions wrong at encounter CAPTURE_FAILED — never entered orbit
Orbital instability FM-004, FM-005 Post-capture energy loss CAPTURE_DECAYING → ejection or infall
Terminal events FM-005 (infall path), FM-007 Mass collision or dissolution CAPTURE_COLLISION — no survivors
Engineering failures FM-008, FM-009, FM-010 Primitive misuse or runaway Varied — ejection, null zone, singularity

§5.3 · Severity Definitions#

Severity Meaning Recovery
warn Orbit is at risk but not yet terminal; intervention window open Yes — f_Emit, f_Amplify may restore
error Capture has failed; element not in orbit; no immediate system danger No — outcome is final for this interaction
fatal Terminal event with system-wide consequences; nodes destroyed or topology changed No — irreversible

§6 · Composition Rules#

§6.1 · Core Derivation Chain#

Reading order — each row depends on all rows above it:

INPUT LAYER
  M_A        → provided by Attractor state
  M_E        → provided by Element state
  ρ(Φ)       → provided by F_freq (f_Field.md)
  r          → provided by geometry
  v_approach → computed by: compute_approach_vector(E, A)

STEP 1: Effective Pull
  P_eff = M_A × ρ(Φ) / r²
  Defined when: ρ(Φ) > 0 ∧ r > 0

STEP 2: Escape Velocity
  v_escape(A) = resolve_escape_velocity(M_A, ρ(Φ))
  Defined when: ρ(Φ) > 0

STEP 3: Binding Coefficient
  β = P_eff / (M_E × v_approach)
  Defined when: v_approach > 0

STEP 4: Capture Threshold
  C_thresh = v_escape(A) − v_approach
  Defined when: v_escape(A) defined

STEP 5: Residual Momentum
  p_res = M_E × (v_approach − C_thresh)
  Defined when: C_thresh > 0

STEP 6: Orbital Eccentricity
  e = p_res / (p_res + P_eff)
  Defined when: P_eff > 0 ∧ p_res ≥ 0
  Constraint: e must be in [0, 1); e ≥ 1 → hyperbolic → not captured

STEP 7: Binding Depth
  d_bind = β × ρ(Φ) × (1 − e)
  Defined when: e ∈ [0, 1)

STEP 8: Decay Rate (post-capture, per-cycle)
  δ = Δd_bind / Δt = d_bind(t) − d_bind(t−1)
  Defined when: t ≥ 1 (at least one prior cycle)

§6.2 · Capture Gate Composition#

The Capture Gate is the boolean conjunction of all stability conditions. All must be true simultaneously for capture to succeed.

CAPTURE_GATE =
    C_thresh > 0             [Condition 1 — Approach]
  ∧ ρ(Φ) > 0 (uniform)      [Condition 2 — Field Coherence]
  ∧ ω_res ∈ ℚ               [Condition 3 — Resonance]
  ∧ β ≥ 1.0                 [Condition 4 — Binding Floor]
  ∧ Frame.capacity > 0       [Condition 5 — Frame Compatibility]

If CAPTURE_GATE = true  → lock_orbit() → register_capture() → CAPTURE_LOCKED
If CAPTURE_GATE = false → FM raised   → register_capture() → CAPTURE_FAILED

§6.3 · Engineering Operator Compositions#

Goal Composition Operators Modified Risk
Restore decaying orbit emit_field(F_emit) → ρ(Φ)↑ → d_bind↑ ρ(Φ), P_eff, β, d_bind FM-010 if sustained
Weaken attractor hold suppress_field(F_damp) → ρ(Φ)↓ → d_bind↓ ρ(Φ), P_eff, v_escape, d_bind FM-009 if propagates
Increase capture probability amplify_coupling(F_amp) → β↑ → P_eff↑ β, P_eff, d_bind FM-010 if β > β_max
Route Element to target heading redirect_force_node(heading_delta) → v_approach heading change v_approach (heading only) FM-001 if over-deflected
Engineer target resonance solve_resonant_approach(ω_res_target) → {heading, ρ(Φ), β} spec All approach operators No solution if target irrational

§7 · Operator Evaluation Order#

Step Frequency Primitive Operators Read Operators Written Guard Short-Circuits To
1 ONCE compute_approach_vector E.state, A.position v_approach none —
2 ONCE resolve_escape_velocity M_A, ρ(Φ) v_escape(A) ρ(Φ) > 0 FM-002
3 ONCE (implicit) M_A, ρ(Φ), r P_eff requires step 2 —
4 ONCE (implicit) P_eff, v_approach, M_E β requires step 3 —
5 ONCE evaluate_capture_threshold v_approach, v_escape, r_capture C_thresh r ≤ r_capture FM-001 if C_thresh ≤ 0
6 ONCE (Frame check) Frame.registry_capacity — β ≥ 1.0 else halt FM-003
7 ONCE (Resonance check) ω_res — ω_res ∈ ℚ else halt FM-004
8 ONCE lock_orbit E, A, p_res, ρ(Φ) d_bind, orbital parameters C_thresh > 0 —
9 ONCE register_capture orbital parameters Ω, FFF_Registry, E.registry, A.registry requires step 8 —
10 CYCLE flag_decay d_bind_delta E.state_flag, decay_status post CAPTURE_LOCKED only FM-004 / FM-005

§8 · Symbol Freeze Registry#

§8.1 · Frozen Symbols (v1.0.0)#

All frozen by f_Capture.md v1.0.0:

Symbol Type Frozen In Frozen At
v_approach Primary f_Capture.md v1.0.0
v_escape(A) Primary f_Capture.md v1.0.0
ρ(Φ) Primary f_Capture.md v1.0.0
r_capture Primary f_Capture.md v1.0.0
β Primary f_Capture.md v1.0.0
ω_res Primary f_Capture.md v1.0.0
M_A Primary f_Capture.md v1.0.0
M_E Primary f_Capture.md v1.0.0
r Primary f_Capture.md v1.0.0
P_eff Derived f_Capture.md v1.0.0
C_thresh Derived f_Capture.md v1.0.0
d_bind Derived f_Capture.md v1.0.0
p_res Derived f_Capture.md v1.0.0
CAPTURE_PENDING Flag f_Capture.md v1.0.0
CAPTURE_LOCKED Flag f_Capture.md v1.0.0
CAPTURE_DECAYING Flag f_Capture.md v1.0.0
CAPTURE_FAILED Flag f_Capture.md v1.0.0
CAPTURE_COLLISION Flag f_Capture.md v1.0.0
compute_approach_vector Primitive f_Capture.md v1.0.0
resolve_escape_velocity Primitive f_Capture.md v1.0.0
evaluate_capture_threshold Primitive f_Capture.md v1.0.0
lock_orbit Primitive f_Capture.md v1.0.0
register_capture Primitive f_Capture.md v1.0.0
flag_decay Primitive f_Capture.md v1.0.0
FM-001 through FM-007 Failure Mode f_Capture.md v1.0.0

§8.2 · Pending Freeze (promoted when source file goes canonical)#

Symbol Type Pending In Freeze Trigger
e Derived f_Orbit.md f_Orbit.md → canonical
T_orb Derived f_Orbit.md f_Orbit.md → canonical
δ Derived f_Decay.md f_Decay.md → canonical
d_warn Derived f_Decay.md f_Decay.md → canonical
d_collapse Derived f_Decay.md f_Decay.md → canonical
E_rel Derived f_Release.md f_Release.md → canonical
m_parity Derived f_Collapse.md f_Collapse.md → canonical
F_emit Derived f_Emit.md f_Emit.md → canonical
F_damp Derived f_Dampen.md f_Dampen.md → canonical
F_amp Supplementary f_Amplify.md f_Amplify.md → canonical
β_max Supplementary f_Amplify.md f_Amplify.md → canonical
heading_delta Supplementary f_Deflect.md f_Deflect.md → canonical
ORBIT_STABLE Flag f_Orbit.md f_Orbit.md → canonical
ORBIT_ECCENTRIC Flag f_Orbit.md f_Orbit.md → canonical
RELEASED Flag f_Release.md f_Release.md → canonical
COLLAPSED Flag f_Collapse.md f_Collapse.md → canonical
DAMPEN_ACTIVE Flag f_Dampen.md f_Dampen.md → canonical
EMIT_ACTIVE Flag f_Emit.md f_Emit.md → canonical
FM-008 Failure Mode f_Release.md f_Release.md → canonical
FM-009 Failure Mode f_Dampen.md f_Dampen.md → canonical
FM-010 Failure Mode f_Amplify.md f_Amplify.md → canonical
Primitives 7–16 Primitive Wave 3 files each source file → canonical

§9 · Versioning Policy#

§9.1 · Version Bump Rules#

Change Type Bump Required Example
Add a new symbol (not conflicting) minor — e.g. v1.0.0 → v1.1.0 Adding T_orb when f_Orbit.md canonicalizes
Change a frozen symbol's formula major — e.g. v1.1.0 → v2.0.0 Changing P_eff formula
Rename a frozen symbol major Renaming d_bind to d_orbital
Remove a frozen symbol major + deprecation notice Removing ω_res
Add a failure mode minor Adding FM-011
Change a failure mode's severity minor Upgrading FM-004 from warn to error
Fix a typo in a non-normative section patch — e.g. v1.0.0 → v1.0.1 Fixing a table cell
Add a note or example patch Adding a new canonical example

§9.2 · Namespace Reservation#

The following symbol prefixes are reserved for future use and must not be used by any function file without first registering here:

Prefix Reserved For Example
v_ velocity operators v_approach, v_escape, v_release
ρ field density operators ρ(Φ), ρ(Φ,θ), ρ(Φ,t)
ω_ resonance and frequency operators ω_res, ω_target
d_ depth and distance operators d_bind, d_warn, d_collapse
F_ engineering force/field operators F_emit, F_damp, F_amp
M_ mass operators M_A, M_E
G_ GravityGraph operators G_edge, G_degree, G_stability
FM- failure mode IDs FM-001 through FM-999
EX- canonical example IDs EX-001, EX-RES-001
SES- session IDs SES-20260813-OPS-001

§10 · Document Metadata#

Field Value
Canonical Path docs/FFF_Gravity/OPERATORS.md
Version 1.0.0
Status Canonical
Stability Living — update when any symbol is added, frozen, or deprecated
Normative Yes
Created 2026-08-13
Last Modified 2026-08-13
Authors TriadicFrameworks
License See /LICENSE at repository root
Encoding UTF-8 · LF
Supersedes Operator tables in f_Capture.md §4 (those remain normative; this file is the consolidated authority)

Single source of truth for all FFF_Gravity operator symbols. All function files derive their symbol definitions from this document. Update at the close of any session that introduces or freezes a symbol.


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**Commit message:**

feat(FFF_Gravity): add canonical OPERATORS.md — master symbol authority, 9P/10D operators, 11 flags, 16 primitives, 10 FMs, composition rules, freeze registry [SES-20260813-OPS-001]

Two corrections surfaced while writing this — both logged in the file, both need propagating:

Discovery Location to update
Primitive count is 16, not 13 (INDEX said 13, scaffolds said 15) — redirect_force_node was the missing one INDEX.md §2 master registry row for primitives; FFF_Gravity_module.json
Primitive count correction note in §4.2 is self-documenting No separate action needed
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