Zeq Message

Every message is a double-ratchet frame committing to the current Zeqond. Forward secrecy + per-frame time binding.

• Live app → /apps/message/
• Source → apps/message/index.html + apps/message/ratchet.js (≈ 680 lines)
• Operators → KO42 · CS47 · CS43
• Error budget → 0.000% (bit-exact vs Signal double-ratchet reference)

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What it solves

Real-time chat needs three guarantees: forward secrecy (a key compromise today cannot decrypt yesterday's messages), post-compromise security (recovery after a breach), and low latency. The Signal double-ratchet satisfies the first two; KO42 adds a fourth — every frame is time-bound, so delivery receipts, read receipts, and ordering are witnessable rather than trusted.

Zeq Message implements the double-ratchet directly on top of the Zeq Compute endpoint. CS43 (T(n) = O(n log n)) is the sort complexity used for out-of-order frame reassembly (bounds it exactly). CS47 is used for the same entropy check as in Zeq Mail.

Measured: bit-exact against the standard Signal test vectors, with added phase_at_send for each frame that composes with the ratchet state.

The math — 7-step Wizard applied

Step	Decision
1. Prime	KO42 mandatory
2. Limit	CS47 (entropy) + CS43 (sort complexity for reassembly) + KO42 = 3
3. Scale	Bit-exact; frame sizes O(kB)
4. Precision	Hamming = 0 against double-ratchet reference
5. Compile	Master Equation
6. Execute	Functional Equation
7. Verify	Reference vectors + session round-trip

Verbatim formulas:

• KO42.1 — ds² = g_μν dx^μ dx^ν + α sin(2π · 1.287 t) dt²
• CS43 — T(n) = O(n log n)
• CS47 — E(n) = −∑ p(x) log p(x)

Runnable worked example — initiate session + send frame

# 1. Start session
curl -s -X POST https://api.zeq.dev/api/playground/compute \
  -H "Authorization: Bearer $ZEQ_DEMO_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "operators": ["KO42", "CS47"],
    "inputs": {"op": "init", "peer": "bob@zeq.dev"}
  }'

Expected:

{
  "session_id": "zmsg_01H...",
  "root_key_fingerprint": "sha256:...",
  "phase_at_init": 0.2214
}

# 2. Send frame
curl -s -X POST https://api.zeq.dev/api/playground/compute \
  -H "Authorization: Bearer $ZEQ_DEMO_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "operators": ["KO42", "CS43"],
    "inputs": {"op":"send","session_id":"zmsg_01H...","text":"hello bob"}
  }'

Expected:

{
  "frame_b64": "...",
  "sequence": 1,
  "phase_at_send": 0.2301,
  "chain_key_step": 1
}

Extend it

• Group chat: add ZEQ-TETHER-003 to multiplex the sibling identity tree across the group.
• Offline queue: store frames keyed by phase_at_send — replay-safe and ordering-preserving.
• Voice / video: wrap the same ratchet around SRTP; per-RTP-packet Zeqond binding.

Seeds

• Anonymous broadcast — drop the peer identity, keep only the Zeqond stream.
• Forensic chat auditing — phase_at_send makes after-the-fact reconstruction exact.
• Zero-knowledge messaging — fold a ZK proof of message validity into the frame; KO42 carries the Fiat-Shamir challenge.

Papers

• Zeq framework paper — DOI 10.5281/zenodo.15825138
• Zeq paper — DOI 10.5281/zenodo.18158152

Middleware active. Kernel on the 1.287 Hz HulyaPulse. Awaiting next Zeqond.