# Modular Phase Intersection Validator

> Modular Phase Intersection Validator is a paid API for AI agents from detect.halowerk.com, paid per call via x402, $0.002/call, status unknown (last checked 2026-11-04).

Validates whether a claimed first common tick and repeating period are correct for a system of integer congruences with noncoprime moduli (Chinese Remainder Theorem generalization).

## Facts

- Endpoint: POST https://detect.halowerk.com/v1/workflow/workflow-modular-phase-intersection?utm_source=zero.xyz
- Price: $0.002/call
- Payment: x402
- Status: unknown
- Last checked: 2026-11-04
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/modular-phase-intersection-validator-f73d500f
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_qz2ORLwYnncIEpJup8fzF

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability modular-phase-intersection-validator-f73d500f -d '<json body>'
```

Example prompt: I have three independent tick schedules: one fires at residue 3 mod 10, one at residue 5 mod 14, and one at residue 7 mod 21. Someone claims the first common tick is 143 and the period repeats every 210 steps — can you verify that?

## When to prefer this

Use this endpoint when you need to verify or audit a claimed solution to a system of integer congruences where the moduli may share common factors (noncoprime), making standard CRT inapplicable. Ideal for agent scheduling systems, periodic event synchronization, or any scenario where independent tick schedules need their first coincidence and repeat period validated.

## Known failure modes

- Residue exceeds modulus (residue must be < modulus)
- No common intersection exists (system of congruences is inconsistent — no solution)
- Claimed first tick is outside valid range
- More than 32 congruence pairs provided
- Modulus or residue out of allowed bounds (modulus 1–1000000, residue 0–999999)
- claimed_period of 0 when a nonzero period exists

## How this service works

An agent that joins independently phased integer tick schedules needs its claimed first common tick and repeating period checked with noncoprime moduli.

## Output

Returns whether the claimed first common tick and claimed period are correct for the given set of congruences with potentially noncoprime moduli, along with the true first intersection tick and true repeating period (or a counterexample witness if the claim is wrong).

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "artifact": {
   "type": "object",
   "required": [
    "congruences",
    "claimed_first",
    "claimed_period"
   ],
   "properties": {
    "congruences": {
     "type": "array",
     "items": {
      "type": "object",
      "required": [
       "residue",
       "modulus"
      ],
      "properties": {
       "modulus": {
        "type": "integer",
        "maximum": 1000000,
        "minimum": 1
       },
       "residue": {
        "type": "integer",
        "maximum": 999999,
        "minimum": 0
       }
      },
      "additionalProperties": false
     },
     "maxItems": 32,
     "minItems": 1
    },
    "claimed_first": {
     "type": "integer",
     "maximum": 1000000000000,
     "minimum": -1
    },
    "claimed_period": {
     "type": "integer",
     "maximum": 1000000000000,
     "minimum": 0
    }
   },
   "additionalProperties": false
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/modular-phase-intersection-validator-f73d500f/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from detect.halowerk.com](https://www.zero.xyz/host/detect.halowerk.com/llms.txt)