Angular Time Coordination for Robotics

θ as the angular velocity / phase coordinate

Every /v1/spiral response returns sin(θ) and cos(θ) for each of the Temporal Spiral's 12 nested time scales — from microseconds to millennia. Because θ is encoded as a unit-circle pair rather than a raw angle, phase stays continuous across day, year, and era boundaries — exactly what a control loop needs.

Use atan2(sin, cos) to recover θ ∈ [−π, π] at any granularity. For a 1 Hz control loop, the second-scale rung gives the fractional position of the current second within its minute. For slower planners, the minute- or hour-scale rung gives the same quantity at a coarser resolution. Full θ reference →

// Fetch θ (theta) for the current moment — the angular phase coordinate
// across every time scale from microseconds to years.

const { scales } = await fetch(
  "https://api.temporalblock.com/api/v1/spiral",
  { headers: { "X-API-Key": process.env.TBLK_API_KEY } }
).then((r) => r.json());

// scales[0] is the finest rung (microseconds).
// Each rung exposes sin(θ) and cos(θ) — a unit-circle encoding that
// keeps phase continuous across midnight, year, and era boundaries.
const { sin, cos } = scales[0];

// Use atan2(sin, cos) to recover θ ∈ [−π, π] without discontinuities.
const thetaRad = Math.atan2(sin, cos);

Stamp every sensor frame with a certified Spiral coordinate

Vision Block lets you POST a capture timestamp (hardware PTP or software) and receive back the full Spiral coordinate — including θ — for that exact instant. Every camera frame, LiDAR scan, or IMU sample gets a tamper-evident temporal address you can correlate across nodes without relying on local clock agreement.

// Stamp every camera frame or LiDAR scan with a certified Spiral coordinate.
// The Vision Block API returns the θ phase for the exact capture instant.

const stamp = await fetch(
  "https://api.temporalblock.com/api/v1/vision-block/stamp",
  {
    method: "POST",
    headers: {
      "Content-Type": "application/json",
      "X-API-Key": process.env.TBLK_API_KEY,
    },
    body: JSON.stringify({
      capturedAtUtcMs: Date.now(),   // replace with hardware PTP timestamp
      sensorId: "lidar-front",
    }),
  }
).then((r) => r.json());

// stamp.spiralCoordinate.scales[N].sin / .cos gives sin(θ) and cos(θ)
// for the capture moment across every temporal scale — microseconds to years.
const { sin, cos } = stamp.spiralCoordinate.scales[0];

The stamp is anchored to an NTP/NTS-disciplined server clock. On dedicated deployments, PTP (IEEE 1588) hardware timestamping is available for sub-microsecond envelopes.

Strict event ordering across distributed robot nodes

When multiple compute nodes write joint-angle snapshots, state transitions, or planning events, wall-clock timestamps collide within the same millisecond. Causal Block issues Hybrid Logical Clock tuples that always strictly increase — even across nodes writing concurrently — so your robot's event log has a total order you can replay deterministically.

// Enforce strict event ordering across distributed robot nodes.
// Each node writes to the same Causal Block — no clock-skew collisions.

const event = await fetch(
  "https://api.temporalblock.com/api/v1/causal-block/event",
  {
    method: "POST",
    headers: {
      "Content-Type": "application/json",
      "X-API-Key": process.env.TBLK_API_KEY,
    },
    body: JSON.stringify({
      label: "joint-angle-snapshot",
      payload: { nodeId: "arm-left", joints: [1.57, 0.0, -0.78] },
    }),
  }
).then((r) => r.json());

// event.hlc is a Hybrid Logical Clock tuple that ALWAYS strictly increases —
// even across nodes writing within the same millisecond.
console.log(event.hlc); // { wallMs: 1750000000123, counter: 4, nodeId: "..." }

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