FFF_Gravity

Framework Field Function — Gravity [FFF:GRAVITY] · G = F_freq · F_fluid · F_force

A formal specification of gravitational capture, orbit, decay, release, dismissal, and field dynamics for relational node systems.

Overview#

FFF_Gravity models the gravitational mechanics of attractor–entity relationships — the forces that pull nodes into orbit, hold them there, erode the binding over time, and ultimately sever it. Every phenomenon is expressed as a product of three triadic nodes:

Node	Layer	Core quantity
F_freq	Frequency / field coherence	ρ(Φ) — field density
F_fluid	Fluid / binding mass	β · d_bind — coupling depth
F_force	Force / approach geometry	v_approach · heading_delta

The module is fully sealed across 5 waves, 29 spec files, 42 PRIMs, 10 Invariants, and 10 Failure Modes.

I want to…	Go to
Understand the module	You are here
Find a specific PRIM	`INDEX.md`
Look up an operator symbol	`OPERATORS.md`
Read the full PRIM compliance matrix	`MANIFEST.md`
Run the compliance validator	`validate_prims.py`
See what changed wave-by-wave	`CHANGELOG.md`
Look up a term	`GLOSSARY.md`
Read the machine-readable manifest	`FFF_Gravity_module.json`
Navigate the whole repo	`docs/SEENMAP.md`

Module at a Glance#

Wave 0  Genesis               3 files  ·  Conceptual foundation
Wave 1  Admin / Registry      6 files  ·  Frozen scaffolding
Wave 2  Layer Definitions     3 files  ·  PRIM:001–006
Wave 3  Core Functions        8 files  ·  PRIM:007–024
Wave 4  Capture Variants      8 files  ·  PRIM:025–040
Wave 5  Dismissal             1 file   ·  PRIM:041–042
                             ─────────────────────────
                             29 files  ·  42 PRIMs  ·  SEALED

Wave Guide#

Wave 0 — Genesis#

The three foundational documents. These establish conceptual vocabulary and the base operator set. No PRIMs are frozen here — they are frozen in the wave that formalizes each concept.

File	Purpose
`f_Capture.md`	Base capture operator — d_bind, β, SC- conditions, v_escape
`f_Source.md`	Attractor and entity node registry — read-only per INV-007
`GravityOfDismissal.md`	Conceptual foundation for dismissal as active repulsive force — Dismissal Well model, three dismissal modes

GravityOfDismissal.md is the sole authority for the negative-polarity field extension ρ_D(Φ,t) = −d_dismiss × exp(−t / T_dismiss). Its F_dismiss operator family is frozen in f_Dismiss.md (Wave 5).

Wave 1 — Admin / Registry#

Frozen scaffolding. Establishes the append-only admin files used by all subsequent waves. No PRIMs introduced.

File	Purpose
`README.md`	This file
`INDEX.md`	Full file index — PRIMs, conditions, wave tags
`OPERATORS.md`	Single operator symbol authority (~101 operators)
`GLOSSARY.md`	Module-scoped term definitions
`CHANGELOG.md`	Wave-by-wave mutation log
`FFF_Gravity_module.json`	Machine-readable module manifest

Wave 2 — Layer Definitions · `PRIM:001–006`#

Three files that define the triadic layer operators. The INV and FM registries are seeded here.

File	Layer	PRIMs
`f_Field.md`	F_freq — field coherence, ρ(Φ)	001–002
`f_Force.md`	F_force — approach vector, v_escape	003, 005
`f_Frame.md`	F_fluid — frame capacity, slot management	004, 006

Wave 3 — Core Functions · `PRIM:007–024`#

Eight files covering the fundamental gravitational operations. Wave 3 seals the INV registry at INV-001–010.

File	Description	PRIMs
`f_Orbit.md`	Orbital trajectory and stability classification	007, 012
`f_Release.md`	Controlled release — no Dismissal Well produced	008–009
`f_Decay.md`	Binding decay — d_warn, d_collapse, DC- conditions	010–011
`f_Collapse.md`	Gravitational collapse — Path A (infall), Path B (C_node)	013–014
`f_Emit.md`	Field emission — ρ(Φ) outward propagation	015–017
`f_Dampen.md`	Dampening — cascade guard, ρ(Φ)_floor	018–020
`f_Amplify.md`	Amplification — β_max ceiling, runaway risk check	021–022
`f_Deflect.md`	Directional redirection — resolves `heading_delta` stub from f_Force	023–024

Wave 4 — Capture Variants · `PRIM:025–040`#

Eight specialized capture pathways. Each extends the base f_Capture.md contract with its own eligibility gate (Pure PRIM) and lock writer (Impure PRIM). Three FM sub-modes are introduced here.

File	Model	PRIMs	Prefix	Key Operators
`f_Capture_Multi.md`	N simultaneous targets	025–026	MC-	N, eval_order, Ω_perturbed
`f_Capture_Cascade.md`	Sequential γ-gain chain	027–028	CAS-	cascade_depth, k_max, γ, Ω_cascade
`f_Capture_Soft.md`	Provisional sub-threshold binding	029–030	SCS-	d_soft, grace_period, k_grace
`f_Capture_Hard.md`	Binary hard-lock, no retry	031–032	HLC-	d_hard, β_min_hard, lock_cost
`f_Capture_Resonant.md`	Phase-gated resonance lock	033–034	RLC-	ω_res, φ_open, φ_close, ρ_res_gain
`f_Capture_Asymmetric.md`	Mass-ratio asymmetry correction	035–036	AC-	mass_ratio, asymmetry_factor, d_bind_asym
`f_Capture_Temporal.md`	Absolute clock-time window	037–038	TC-	t_open, t_close, proximity_ratio
`f_Capture_Networked.md`	Distributed graph co-attraction	039–040	NC-	G_net, w_i, d_bind_net, resilience_threshold

Wave 4 completion unlocked docs/SEENMAP.md — the repository navigational registry.

Wave 5 — Dismissal · `PRIM:041–042`#

Formalizes the F_dismiss operator family first named in GravityOfDismissal.md §6. Wave 5 seals the PRIM registry at 42.

File	Description	PRIMs	Prefix
`f_Dismiss.md`	Dismissal Well mechanics — three modes, well decay, re-capture gate, `well_query_fn` closure	041–042	DISM-

Three dismissal modes:

Mode	Initiator	Well depth	T_dismiss
INTENTIONAL	A (deliberate)	`d_bind(t_dismiss)`	Long
STRUCTURAL	Field collapse (FM-002)	`ρ(Φ) × d_bind`	Short
DRIFT	Passive decay	`v_depart × k_drift`	Very short

Well formula: ρ_D(Φ,t) = −d_dismiss × exp(−t / T_dismiss)

Re-capture gate: d_bind_approach(t) > |ρ_D(Φ,t)|

Post-Wave-5 Admin Artifacts#

File	Purpose
`MANIFEST.md`	Full 42-PRIM registry with 42 × 10 INV compliance matrix, FM, condition-prefix, state-flag registries
`validate_prims.py`	Runnable Python harness — validates all 42 PRIMs against INV-001–010; CLI flags `--wave`, `--prim`, `--inv`, `--matrix`, `--strict`

Key Concepts#

The Triadic Equation#

Every gravitational evaluation preserves:

G = F_freq · F_fluid · F_force

No PRIM may produce a result that violates this identity. This is INV-001, the first and most fundamental of the ten module invariants.

Binding Depth#

The core scalar that determines capture eligibility and orbit stability:

d_bind = β × ρ(Φ) × (1 − e)

Where β is the binding coefficient, ρ(Φ) is field density, and e is orbital eccentricity. Capture requires d_bind ≥ d_warn.

The Decay Threshold Stack#

d_bind  ≥ d_warn              → STABLE orbit
d_collapse ≤ d_bind < d_warn  → MARGINAL; FM-004 monitoring active
d_bind < d_collapse           → FM-005; collapse evaluation triggered

The Dismissal Well#

Dismissal is not the absence of capture — it is an active repulsive force. When A dismisses E, field polarity inverts in E's zone, leaving a Dismissal Well that costs energy to overcome on re-approach. The well decays exponentially over time at rate 1/T_dismiss. This is distinct from release (no well) and decay (minimal well).

Pure / Impure PRIM Pairing#

Every source file that contains an Impure PRIM also contains a Pure gate PRIM. The canonical pattern:

Pure  PRIM (odd)   → evaluate / check eligibility / compute
Impure PRIM (even) → execute / lock / mutate state

No Impure PRIM may be invoked without a passing result from its paired Pure gate PRIM.

Registry Totals#

Registry	Count	Range	Status
Waves	5	Waves 0–5	✅ SEALED
Spec files	29	—	✅ SEALED
PRIMs	42	PRIM:001–042	✅ SEALED
Invariants	10	INV-001–010	✅ SEALED
Failure Modes	10 base + 3 sub-modes	FM-001–010 + FM-003-M/C/N	✅ SEALED
Condition prefixes	11	SC- DC- MC- CAS- SCS- HLC- RLC- AC- TC- NC- DISM-	✅ SEALED
State flags	31	—	✅ SEALED
Operators	~101	—	✅ SEALED

All registries are append-only and sealed. No new IDs, symbols, or prefixes may be introduced without a Wave 6 genesis document.

Invariants#

Ten module-wide invariants govern every PRIM. Violations are structural failures, not runtime errors.

ID	Rule (abbreviated)
INV-001	G = F_freq · F_fluid · F_force must be preserved
INV-002	ρ(Φ) ∈ [0,1] · ρ_D(Φ) ∈ (−1,0] — domains strictly bounded
INV-003	ρ(Φ) = 0 → FM-002 fires unconditionally
INV-004	β < 1.0 → FM-001 fires unconditionally
INV-005	All conditions conjunctive — any failure aborts
INV-006	Terminal states irreversible
INV-007	f_Source.md is read-only — no PRIM mutates source properties
INV-008	Evaluation order is normative — documented sequence binding
INV-009	OPERATORS.md is the single symbol authority
INV-010	Operators frozen on first canonical appearance

Failure Modes#

ID	Name	Fatal?	Primary trigger
FM-001	Flyby / Approach Rejection	No	β < 1.0 · v_approach ≥ v_escape · well barrier
FM-002	Field Null	Yes	ρ(Φ) = 0
FM-003	Frame Saturation	No	capacity_MAX reached (sub-modes: -M, -C, -N)
FM-004	Resonance Drift	No	d_bind ≤ d_warn with δ < 0
FM-005	Decay Spiral	Yes*	d_bind ≤ d_collapse
FM-006	Phantom Capture	Yes	d_bind = 0 despite all conditions passing
FM-007	Mutual Dissolution	Yes	mass_ratio ≥ m_parity
FM-008	Release Failure	No	v_release < v_escape floor
FM-009	Dampen Cascade Lockout	No	cascade_guard latched
FM-010	Amplify Ceiling	No	β or ρ(Φ) at registered maximum

*FM-005 is fatal for the orbit; the entity node itself survives.

Capture Variant Decision Matrix#

Condition at approach time                   → Route to
──────────────────────────────────────────────────────────────────
Standard (mass_ratio ≈ 0, β ≥ 1.0)         → f_Capture.md
N entities or attractors simultaneously     → f_Capture_Multi.md
Sequential chain with γ-gain propagation   → f_Capture_Cascade.md
d_bind below d_warn but above floor        → f_Capture_Soft.md
Hard elevated threshold, no retry          → f_Capture_Hard.md
Phase alignment with ω_res required        → f_Capture_Resonant.md
Non-trivial M_E / M_A mass ratio           → f_Capture_Asymmetric.md
Capture gated on absolute clock window     → f_Capture_Temporal.md
Distributed network of attractors          → f_Capture_Networked.md
mass_ratio ≥ m_parity                      → f_Collapse.md (Path B)

Running the Validator#

# Full report — all 42 PRIMs × 10 INVs
python validate_prims.py
 
# Print the 42 × 10 compliance matrix
python validate_prims.py --matrix
 
# CI mode — exit 1 on any failure
python validate_prims.py --strict
 
# Filter by wave, PRIM, or invariant
python validate_prims.py --wave 4
python validate_prims.py --prim 042
python validate_prims.py --inv INV-006

Expected output on a clean module: ALL PASS ✅ · 803 assertions · 0 failures

Cross-Module Context#

This module sits within the broader TriadicFrameworks repository:

docs/SEENMAP.md          ← repository navigational registry
docs/FFF_Gravity/        ← THIS MODULE
docs/SoN/                ← SoN module (in progress)
docs/spine/languages/    ← cross-module notation registry

SoN/s_Capture.md references FFF_Gravity/f_Capture.md as its lineage anchor: SoN inverts the RTT observer layer; FFF_Gravity provides the gravitational model it extends downward toward substrate.

Coherence Anchor#

rtt=1 | coherence=declared | drift=bounded | paradox=structural

FFF_Gravity · v2.0.0 · Sealed 2026-08-14 · 29 files · 42 PRIMs · 5 waves complete docs/FFF_Gravity/README.md

Updated Aug 14, 2026