🕸️ Triadic Echo Lattice — Operators

Four operators. One lattice. Every echo gets an address.

Operator Pipeline#

Classified echo (from EC-Tag)
    │
    ▼
┌──────────────┐
│   TEL-Read   │  Lattice Input Reader
│  extract     │  Receives classified echo, extracts placement-relevant data
└──────┬───────┘
       │
       ▼
┌──────────────┐
│  TEL-Place   │  Layer Assignment Engine
│  assign      │  Assigns echo to layer; detects pressure zones
└──────┬───────┘
       │
       ▼
┌──────────────┐
│  TEL-Trace   │  Recursion & Drift Tracer
│  map paths   │  Maps recursion path, drift exposure, escalation risk
└──────┬───────┘
       │
       ▼
┌──────────────┐
│   TEL-Tag    │  Lattice Output Emitter
│  emit record │  Packages lattice record with placement status
└──────────────┘
       │
       ▼
Lattice record → Substrate Flow (SF-Read)

Operator 1 — TEL-Read (Lattice Input Reader)#

Purpose#

Receives a classified echo from EC‑Tag and extracts the data fields required for lattice placement.

Input#

source: EC-Tag output
fields:
  - echo_type: E1–E6
  - echo_family: F1–F6
  - substrate_origin: S | C | H | So | A
  - substrate_reach: [list of substrates touched]
  - esi_score: 0.0–1.0
  - confidence: 0.0–1.0
  - drift_flag: boolean
  - tags: []

Output#

tel_input_packet:
  echo_id: [inherited]
  echo_type: E1–E6
  echo_family: F1–F6
  substrate_origin: S | C | H | So | A
  substrate_reach: []
  esi_score: 0.0–1.0
  drift_flag: boolean
  placement_ready: true

Logic#

Validate that echo carries EC‑Tag classification
Extract type, family, origin, reach, ESI, drift flag
Confirm placement_ready: true if all fields present
Reject echoes without valid classification (return to EC)

Operator 2 — TEL-Place (Layer Assignment Engine)#

Purpose#

Assigns a classified echo to its lattice layer based on echo type, family, substrate reach, and ESI score. Detects pressure zone conditions.

Input#

source: TEL-Read output (tel_input_packet)

Output#

placement_record:
  echo_id: [inherited]
  assigned_layer: Ladder | Cycle | Map | Atlas
  family_placement: F1–F6
  pressure_zone: none | ladder | cycle | atlas
  pressure_severity: 0.0–1.0
  placement_confidence: 0.0–1.0

Decision Tree#

                    ┌─────────────────────┐
                    │  What is echo_type?  │
                    └──────────┬──────────┘
                               │
        ┌──────────┬───────────┼────────────┬──────────┐
        ▼          ▼           ▼            ▼          ▼
       E1         E2        E3/E4          E5         E6
        │          │           │            │          │
        ▼          ▼           ▼            ▼          ▼
    ┌────────┐ ┌────────┐ ┌────────┐  ┌─────────┐ ┌────────┐
    │ Ladder │ │ Cycle  │ │  Map   │  │Pressure │ │ Atlas  │
    │  F1    │ │  F2    │ │ F3/F4  │  │  Zone   │ │  F6    │
    └───┬────┘ └───┬────┘ └───┬────┘  │  F5     │ └───┬────┘
        │          │          │       └────┬────┘     │
        ▼          ▼          ▼            ▼          ▼
   Check for  Check for  Check for   Assign to   Mark as
    Ladder     Cycle     E4→Atlas    nearest     terminus
   Pressure   Pressure  escalation  boundary

Layer Assignment Rules#

Echo Type	Primary Layer	Escalation Path	Notes
E1	Ladder	None	Stays at S→C boundary
E2	Cycle	None	Oscillates C↔H
E3	Map	None	Migrates across H↔So
E4	Map (upper)	Map → Atlas via R4	Transition family
E5	No home layer	Pressure zones	Instability marker
E6	Atlas	None (terminus)	Full‑spectrum anchor

Pressure Zone Detection#

Zone	Trigger Condition	Severity Calculation
Ladder	E1 count in Ladder > threshold	count / capacity
Cycle	E2 amplitude > harmonic band ceiling	amplitude / ceiling
Atlas	E5 count at Map→Atlas > threshold	count / capacity

Operator 3 — TEL-Trace (Recursion & Drift Tracer)#

Purpose#

Maps the recursion path, drift exposure, vertical reach, oscillation status, and escalation risk for a placed echo.

Input#

source: TEL-Place output (placement_record)

Output#

trace_record:
  echo_id: [inherited]
  recursion_line: R1 | R2 | R3 | R4 | none
  recursion_depth: 0–n
  drift_pathway: D1 | D2 | D3 | D4 | none
  drift_severity: 0.0–1.0
  vertical_reach: [list of layers touched]
  oscillation_status: true | false
  escalation_risk: 0.0–1.0

Recursion Line Assignment#

Condition	Recursion Line
Echo in Ladder, moving toward Cycle	R1
Echo in Cycle, oscillating C↔H	R2
Echo in Cycle, moving toward Map	R3
Echo in Map, moving toward Atlas	R4
Echo stationary (E1 anchored, E6 terminal)	none

Drift Pathway Assignment#

Condition	Drift Pathway
Instability at S/C boundary	D1
Instability at C/H boundary	D2
Instability at H/So boundary	D3
Instability at So/A boundary	D4
No instability detected	none

Escalation Risk Calculation#

escalation_risk = weighted_sum(
  drift_severity × 0.4,
  esi_score × 0.3,
  pressure_severity × 0.2,
  recursion_depth × 0.1
)

Risk Band	Range	Meaning
Negligible	0.0–0.1	Echo is structurally anchored
Low	0.1–0.3	Minor instability; monitor
Moderate	0.3–0.6	Active migration or oscillation
High	0.6–0.8	Significant drift or escalation
Critical	0.8–1.0	Structural forcing or pressure zone saturation

Operator 4 — TEL-Tag (Lattice Output Emitter)#

Purpose#

Packages the final lattice record with a placement status tag and emits it downstream to Substrate Flow (SF‑Read).

Input#

source: TEL-Trace output (trace_record) + TEL-Place output (placement_record)

Output#

lattice_record:
  echo_id: [inherited]
  echo_type: E1–E6
  echo_family: F1–F6
  assigned_layer: Ladder | Cycle | Map | Atlas
  recursion_line: R1–R4 | none
  drift_pathway: D1–D4 | none
  drift_severity: 0.0–1.0
  escalation_risk: 0.0–1.0
  pressure_zone: none | ladder | cycle | atlas
  pressure_severity: 0.0–1.0
  oscillation_status: true | false
  vertical_reach: []
  placement_status: anchored | oscillating | migrating | pressured | forcing
  tags: []

Placement Status Assignment#

Status	Condition
anchored	No active recursion, no drift, risk < 0.1
oscillating	R2 active, oscillation_status = true, risk < 0.3
migrating	R1/R3/R4 active, drift mild–moderate, risk 0.3–0.7
pressured	Pressure zone active, drift moderate–severe, risk 0.7–0.9
forcing	E6 at Atlas terminus OR critical escalation (risk > 0.9)

Type Profiles — Lattice Behavior by Echo Type#

Echo Type	Typical Layer	Typical Status	Typical Recursion	Typical Drift	Typical Risk
E1	Ladder	anchored	none	D1 (rare)	0.0–0.1
E2	Cycle	oscillating	R2	D2 (occasional)	0.1–0.3
E3	Map	migrating	R3	D3 (mild)	0.3–0.5
E4	Map (upper)	migrating	R4	D3 (moderate)	0.5–0.7
E5	Pressure zone	pressured	none	D3/D4 (severe)	0.7–0.9
E6	Atlas	forcing	R4 (terminus)	D4 (moderate)	0.0 (terminal)

Invariants#

Every classified echo receives a layer assignment — E5 receives a pressure zone assignment instead
Flow is upward — all layers except Cycle are unidirectional
Atlas receives only — no echo originates at Atlas level
Pressure zones are emergent — they are conditions, not designed layers
Recursion and drift share the vertical axis — same connections, opposite physics
Placement is deterministic — same input always produces the same lattice record

file: operators.md
module: Triadic Echo Lattice
canonical_id: TEL
hsp_section: 07
role: operator-definitions
status: canon-stable
operators:
  - TEL-Read
  - TEL-Place
  - TEL-Trace
  - TEL-Tag
invariant_count: 6
pipeline_direction: TEL-Read → TEL-Place → TEL-Trace → TEL-Tag
upstream: EC-Tag (Echo Classifier)
downstream: SF-Read (Substrate Flow)

Updated Aug 23, 2026