# Bracketed Polynomial Root Finder

> Bracketed Polynomial Root Finder is a paid API for AI agents from www.mahastrategies.com, paid per call via x402, $0.009/call, status unknown (last checked 2026-09-14).

Bisects a sign-changing rational bracket for a polynomial of degree 1–8 to certify a root bracket or exact rational root within up to 64 iterations.

## Facts

- Endpoint: POST https://www.mahastrategies.com/api/v1/micro/bracketed-polynomial-root
- Price: $0.009/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-14
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/bracketed-polynomial-root-finder-76b7d881
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_ELd-r4aY4Am2yZ33K5aBO

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 bracketed-polynomial-root-finder-76b7d881 -d '<json body>'
```

Example prompt: Find a certified root of the polynomial 1 + 0x - 6x² + x³ (coefficients ascending: [1, 0, -6, 1]) between lower bound -3 and upper bound -2, with tolerance 1e-9 and at most 64 iterations, using public data.

## When to prefer this

Choose this endpoint when you need a numerically certified, audit-traceable root bracket for a univariate polynomial of degree 1–8, and you have a known sign-changing interval. It is ideal for deterministic, reproducible numerical results with rational arithmetic guarantees — not for finding all roots, roots of higher-degree polynomials, or complex roots. Prefer it over general-purpose computer algebra systems when certified bracketing and receipt-level auditability matter.

## Known failure modes

- No sign change detected between lower and upper bounds — bisection cannot proceed
- Polynomial degree exceeds 8 (more than 9 coefficients) — rejected
- Max iterations exceeds 64 — rejected by schema validation
- Tolerance or bound values malformed or too long (>21 chars) — schema rejection
- Lower bound equals upper bound — degenerate bracket
- Payment failure via x402 protocol — call not executed

## How this service works

Get a checked rational bracket for a degree 1-8 polynomial root. Bisect a sign-changing rational bracket for at most 64 iterations; return a certified bracket or exact rational root. No arbitrary code, all-roots or uniqueness claim.

## Output

Returns a JSON object containing the certified bracket or exact rational root, the offer ID, version string, input and receipt digests, amount in base units, and an array of boundary points accumulated during bisection — providing an auditable, certified numerical result.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "required": [
  "input"
 ],
 "properties": {
  "input": {
   "type": "object",
   "required": [
    "type",
    "method",
    "bodyType",
    "body"
   ],
   "properties": {
    "body": {
     "type": "object",
     "required": [
      "dataClass",
      "coefficientsAscending",
      "lower",
      "upper",
      "tolerance",
      "maxIterations"
     ],
     "properties": {
      "lower": {
       "type": "string",
       "maxLength": 21
      },
      "upper": {
       "type": "string",
       "maxLength": 21
      },
      "dataClass": {
       "enum": [
        "public",
        "synthetic"
       ],
       "type": "string"
      },
      "tolerance": {
       "type": "string",
       "maxLength": 21
      },
      "maxIterations": {
       "type": "integer",
       "maximum": 64,
       "minimum": 1
      },
      "coefficientsAscending": {
       "type": "array",
       "maxItems": 9,
       "minItems": 1
      }
     },
     "additionalProperties": false
    },
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "enum": [
      "POST"
     ],
     "type": "string"
    },
    "bodyType": {
     "enum": [
      "json",
      "form-data",
      "text"
     ],
     "type": "string"
    }
   },
   "additionalProperties": false
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "type": "string"
    },
    "example": {
     "type": "object",
     "required": [
      "version",
      "offerId",
      "amountBaseUnits",
      "inputDigest",
      "result",
      "boundaries",
      "receiptDigest"
     ],
     "properties": {
      "result": {
       "type": "object"
      },
      "offerId": {
       "enum": [
        "bracketed-polynomial-root"
       ],
       "type": "string"
      },
      "version": {
       "enum": [
        "maha-microproducts/0.1"
       ],
       "type": "string"
      },
      "boundaries": {
       "type": "array",
       "maxItems": 128,
       "minItems": 0
      },
      "inputDigest": {
       "type": "string",
       "maxLength": 71
      },
      "receiptDigest": {
       "type": "string",
       "maxLength": 71
      },
      "amountBaseUnits": {
       "enum": [
        "9000"
       ],
       "type": "string"
      }
     },
     "additionalProperties": false
    }
   }
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/bracketed-polynomial-root-finder-76b7d881/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from www.mahastrategies.com](https://www.zero.xyz/host/www.mahastrategies.com/llms.txt)