CBOR-LD-ex

Compact Binary Linked Data with Semantic Reasoning for Constrained IoT Networks

CBOR-LD-ex extends CBOR-LD with bit-packed Subjective Logic primitives — compliance status, opinion tuples, operator provenance, temporal decay, and security metadata — enabling edge IoT devices to exchange semantically-rich compliance annotations at a fraction of the cost of JSON-LD.

Built on jsonld-ex and its compliance algebra (Syed et al. 2026).

Key Properties

• 4-byte semantic annotations on constrained devices (1-byte header + 3-byte opinion)
• 37× smaller than JSON-LD, >10× smaller than standard CBOR-LD for the same semantic content
• 93% bit efficiency — almost every wire bit carries Shannon information
• Tiered encoding adapts to device capability: 1-byte headers on MCUs, 4-byte+ on gateways/cloud
• Temporal extensions — bit-packed decay metadata, log-scale half-life (1s to 388 days in 8 bits), compliance triggers
• Security primitives — annotation digests, Byzantine fusion metadata, chained provenance (16 bytes per entry, zero waste)
• Transport-agnostic — identical payloads over MQTT and CoAP
• Three formal axioms — backward compatibility, algebraic closure, quantization correctness
• 282 tests including exhaustive 8-bit verification (32,896 pairs) and Hypothesis property tests

6-Way Encoding Benchmark

CBOR-LD-ex is not just smaller — it carries more semantic information in fewer bytes than any alternative encoding.

#	Encoding	Payload size	Annotation overhead	Semantic fields
1	JSON-LD (raw text)	~280 bytes	~148 bytes	data + verbose annotation
2	jsonld-ex CBOR-LD (context-only compression)	~85 bytes	0	data only
3	Our CBOR-LD (full key+value compression)	~22 bytes	0	data only
4	jsonld-ex CBOR-LD + annotation	~210 bytes	~125 bytes	data + annotation as JSON
5	Our CBOR-LD + standard CBOR annotation	~70 bytes	~49 bytes	data + CBOR k/v annotation
6	CBOR-LD-ex (bit-packed)	~30 bytes	4 bytes	data + compliance + opinion + provenance

Key findings:

• CBOR-LD-ex annotation: 4 bytes vs CBOR-LD's 49 bytes for the same semantic content (>10× smaller)
• Our ContextRegistry (full key+value compression) beats jsonld-ex's context-only compression
• CBOR-LD-ex is the only encoding that fits compliance + opinion in a single 802.15.4 frame (127 bytes)
• Annotation bit efficiency: 93% (Shannon information / wire bits)

Run cbor_ld_ex.transport.full_benchmark() to reproduce these numbers for your own documents.

Installation

pip install cbor-ld-ex

Or with Poetry:

poetry add cbor-ld-ex

Quick Start

from cbor_ld_ex.opinions import quantize_binomial
from cbor_ld_ex.headers import Tier1Header, ComplianceStatus, PrecisionMode
from cbor_ld_ex.annotations import Annotation, encode_annotation
from cbor_ld_ex.codec import encode, decode, ContextRegistry

# Quantize an opinion: 85% belief, 5% disbelief, 10% uncertainty
b_q, d_q, u_q, a_q = quantize_binomial(0.85, 0.05, 0.10, 0.50, precision=8)
# (217, 13, 25, 128) — SL constraint preserved exactly: 217 + 13 + 25 = 255

# Build a Tier 1 annotation (constrained device)
header = Tier1Header(
    compliance_status=ComplianceStatus.COMPLIANT,
    delegation_flag=False,
    has_opinion=True,
    precision_mode=PrecisionMode.BITS_8,
)
ann = Annotation(header=header, opinion=(b_q, d_q, u_q, a_q))

# Encode annotation: 4 bytes total (1 header + 3 opinion; û not on wire)
wire_bytes = encode_annotation(ann)
assert len(wire_bytes) == 4

# Full CBOR-LD-ex message with context compression
registry = ContextRegistry(
    key_map={"@context": 0, "@type": 1, "value": 2, "unit": 3},
    value_map={"https://schema.org/": 100, "Observation": 101, "celsius": 102},
)
doc = {
    "@context": "https://schema.org/",
    "@type": "Observation",
    "value": 22.5,
    "unit": "celsius",
}
cbor_ld_ex_bytes = encode(doc, ann, context_registry=registry)

# Decode round-trip
recovered_doc, recovered_ann = decode(cbor_ld_ex_bytes, context_registry=registry)
assert recovered_doc["value"] == 22.5
assert recovered_ann.opinion[:3] == (217, 13, 25)  # b̂, d̂, û (û derived)

Transport (MQTT / CoAP)

from cbor_ld_ex.transport import (
    to_mqtt_payload, from_mqtt_payload, derive_topic, derive_qos,
    to_coap_payload, from_coap_payload,
)

# MQTT — same CBOR-LD-ex payload + protocol metadata
payload = to_mqtt_payload(doc, ann, context_registry=registry)
topic = derive_topic(doc, ann)         # "cbor-ld-ex/Observation/temp-042/compliant"
qos = derive_qos(doc, ann)            # 2 (high confidence → exactly-once)

# CoAP — identical payload, different transport
coap_payload = to_coap_payload(doc, ann, context_registry=registry)
assert coap_payload == payload         # Transport-agnostic encoding

Temporal Decay

from cbor_ld_ex.temporal import (
    TemporalBlock, ExtensionBlock, encode_half_life, decode_half_life,
    compute_decay_factor, apply_decay_quantized, DECAY_EXPONENTIAL,
)

# Encode a 1-hour half-life in 8 bits (log-scale, ~7% granularity)
encoded = encode_half_life(3600.0)
decoded = decode_half_life(encoded)  # ≈ 3600 seconds

# Apply decay to a quantized opinion (dequantize → decay → re-quantize)
factor = compute_decay_factor(DECAY_EXPONENTIAL, half_life=3600.0, elapsed=3600.0)
# factor ≈ 0.5 (one half-life elapsed)
b2, d2, u2, a2 = apply_decay_quantized(*ann.opinion, factor, precision=8)
assert b2 + d2 + u2 == 255  # Axiom 3 preserved through decay

Security

from cbor_ld_ex.security import (
    compute_annotation_digest, verify_annotation_digest,
    ProvenanceEntry, CHAIN_ORIGIN_SENTINEL,
    encode_provenance_entry, verify_provenance_chain, compute_entry_digest,
)

# Annotation digest (truncated SHA-256, 8 bytes)
digest = compute_annotation_digest(wire_bytes)
assert verify_annotation_digest(wire_bytes, digest)

# Provenance chain entry (16 bytes, 128 bits, zero waste)
entry = ProvenanceEntry(
    origin_tier=0, operator_id=0, precision_mode=0,
    b_q=217, d_q=13, a_q=128,
    timestamp=1710230400,
    prev_digest=CHAIN_ORIGIN_SENTINEL,
)
entry_bytes = encode_provenance_entry(entry)
assert len(entry_bytes) == 16  # Every bit carries information

Architecture

Tier 1 (Constrained)     Tier 2 (Edge Gateway)      Tier 3 (Cloud)
┌─────────────────┐      ┌─────────────────────┐    ┌──────────────────────┐
│ 1-byte header   │      │ 4-byte header        │    │ 4-byte + extensions  │
│ 3-byte opinion  │─────>│ Fused opinion         │──>│ Provenance chain     │
│ = 4 bytes total │ MQTT │ Operator provenance   │    │ Full audit trail     │
│                 │ CoAP │ Byzantine filtering   │    │ Chained digests      │
└─────────────────┘      └─────────────────────┘    └──────────────────────┘
     ~85% smaller              Temporal decay             Full reasoning
     than JSON-LD              + spatial fusion            reconstruction

Formal Guarantees

Axiom	Property	Guarantee
Axiom 1	Backward Compatibility	Strip annotations → valid CBOR-LD → valid JSON-LD
Axiom 2	Algebraic Closure	Every SL operator produces valid annotations
Axiom 3	Quantization Correctness	b̂ + d̂ + û = 2ⁿ − 1 exactly

All three axioms are verified by cross-cutting property tests including exhaustive enumeration of all 32,896 valid 8-bit opinion pairs, and Hypothesis property tests through all operators (fusion, meet, decay).

Precision	Max error (b,d)	Max error (u)	Wire bytes
8-bit	~0.002	~0.004	3
16-bit	~0.000008	~0.000015	6
32-bit	IEEE 754	IEEE 754	12

API Overview

Module	Purpose
opinions.py	Constrained quantization codec (Theorems 1–3)
headers.py	Tier-dependent header encoding/decoding (§5)
annotations.py	Annotation assembly + CBOR Tag(60000) + extensions
temporal.py	Bit-packed decay, log-scale half-life, expiry/review triggers
security.py	Annotation digests, Byzantine metadata, provenance chains
codec.py	Full encode/decode pipeline, ContextRegistry, Shannon bit analysis
transport.py	MQTT + CoAP adapters, 6-way full_benchmark() engine

Development

git clone https://github.com/jemsbhai/cbor-ld-ex.git
cd cbor-ld-ex
poetry install
poetry run python -m pytest tests/ -v

TDD Methodology

This project follows strict test-driven development. Every module has comprehensive tests including property-based testing via Hypothesis. Tests are never weakened to pass — the code or design is fixed instead.

Project Structure

cborldex/
├── src/cbor_ld_ex/
│   ├── opinions.py       # Quantization codec (Theorems 1–3)
│   ├── headers.py        # Tier-dependent header codec (§5)
│   ├── annotations.py    # Annotation assembly + CBOR tagging + extensions
│   ├── temporal.py       # Temporal extensions — decay, triggers, BitWriter/BitReader
│   ├── security.py       # Digests, Byzantine metadata, provenance chains
│   ├── codec.py          # Full codec, ContextRegistry, bit-level analysis
│   └── transport.py      # MQTT + CoAP adapters, 6-way benchmark engine
├── tests/
│   ├── test_opinions.py      # 38 tests — quantization, Hypothesis properties
│   ├── test_headers.py       # 28 tests — Tier 1/2/3 header roundtrips
│   ├── test_annotations.py   # 15 tests — assembly, CBOR tag, wire format
│   ├── test_temporal.py      # 65 tests — bit-packed extensions, decay, triggers
│   ├── test_security.py      # 33 tests — digests, Byzantine, provenance chains
│   ├── test_codec.py         # 46 tests — full pipeline, payload comparison
│   ├── test_axioms.py        # 19 tests — cross-cutting axiom verification
│   └── test_transport.py     # 24 tests — MQTT, CoAP, 6-way benchmark
├── spec/
│   ├── FORMAL_MODEL.md       # Formal specification v0.2.0-draft
│   └── IMPLEMENTATION_PLAN.md
├── pyproject.toml
└── LICENSE

282 tests total, all passing.

References

• Syed, M., Silaghi, M., Abujar, S., and Alssadi, R. (2026). A Compliance Algebra: Modeling Regulatory Uncertainty with Subjective Logic. Working paper.
• Jøsang, A. (2016). Subjective Logic: A Formalism for Reasoning Under Uncertainty. Springer.
• Shannon, C.E. (1948). A Mathematical Theory of Communication. Bell System Technical Journal.
• Bormann, C. and Hoffman, P. (2020). RFC 8949: CBOR. IETF.
• Shelby, Z. et al. (2014). RFC 7252: CoAP. IETF.
• Selander, G. et al. (2019). RFC 8613: OSCORE. IETF.
• CBOR-LD Specification (W3C Community Group Draft).
• JSON-LD 1.1 (W3C Recommendation).

License

MIT — see LICENSE.