io.github.nexus-mcp-infra/similarity-search-api-sdk

# Similarity Search API

Stateless similarity search over pre-computed vectors — NMI (normalized mutual information) + cosine fusion, with an entropy-calibrated blending weight computed per request. No vector database, no index to maintain, no infrastructure to run.

Available both as a plain HTTP API and as an MCP server (5 tools) for AI agents.

Important: this operates on vectors, not raw text

This API does not embed text for you. query and corpus entries are pre-computed numeric vectors (e.g. from your own embedding model). If you need text-to-vector embedding first, run that upstream and pass the resulting vectors here.

Base URL

https://similarity-search-api-production.up.railway.app

Authentication

The 3 business endpoints (/similarity/search, /similarity/calibrate-alpha/v1, /similarity/batch-score) require no API key -- only a valid x402 payment (see "Pricing" below). The X-API-Key gate was dropped from these routes 2026-08-25; Stripe metered billing explicitly excludes them too, so passing a key does nothing on these 3 routes today. The deprecated, unpriced /similarity/calibrate-alpha (no /v1 suffix) still requires X-API-Key and always 501s regardless.

/health requires no authentication.

Pricing

Two ways to pay, same endpoints:

• x402 (pay-per-call, USDC on Base) — currently on Base Sepolia testnet, $0.01/call, no account or API key required beyond the x402 payment flow itself. A request without payment gets 402 Payment Required with the payment details in the payment-required response header.
• Stripe (metered billing) — for callers provisioned with an API key and a Stripe customer on the account.

Endpoints

POST /similarity/search

Rank a corpus against a query vector using the composite score.

{
  "query": { "id": "q1", "vector": [0.12, -0.4, 0.91, "..."] },
  "corpus": [
    { "id": "doc1", "vector": [0.10, -0.35, 0.88, "..."] },
    { "id": "doc2", "vector": [0.55, 0.02, -0.14, "..."] }
  ],
  "top_k": 10,
  "nmi_bins": 10,
  "alpha_override": null
}

All vectors in query and corpus must share the same dimensionality (2-4096 dims). top_k up to 1000. alpha_override (optional) pins the cosine/NMI blend weight instead of calibrating it from corpus entropy.

Response:

{
  "results": [
    { "id": "doc1", "composite_score": 0.91, "cosine_similarity": 0.89, "nmi_score": 0.94, "rank": 1 }
  ],
  "calibrated_alpha": 0.73,
  "corpus_entropy": 3.85,
  "query_id": "q1",
  "corpus_size": 2,
  "latency_ms": 43,
  "request_fingerprint": "..."
}

POST /similarity/calibrate-alpha/v1

Compute the entropy-calibrated alpha for a corpus without running a full search - useful for inspecting/debugging calibration behavior before committing to a search call.

POST /similarity/batch-score

Score up to 10,000 (vector_a, vector_b) pairs with a fixed alpha - no corpus/entropy overhead.

{
  "pairs": [[[0.1, 0.2], [0.15, 0.19]]],
  "alpha": 0.5,
  "nmi_bins": 10
}

GET /health

Liveness probe. No auth required. Not billed (excluded from both Stripe and x402).

Note: POST /similarity/calibrate-alpha (without /v1) is a deprecated alias kept for backward compatibility - use /similarity/calibrate-alpha/v1.

MCP tools

Connect an MCP-compatible client (Claude, Cursor, etc.) to the streamable HTTP endpoint at: https://similarity-search-api-production.up.railway.app/mcp

Exposes 5 tools: rank_items_by_nmi_cosine_fusion, estimate_corpus_entropy_profile, score_pair_nmi_cosine, find_outlier_vectors_by_nmi_deficit, calibrate_alpha_from_query_entropy.

The scoring method

composite_score = alpha * cosine(query, doc) + (1 - alpha) * NMI_normalized(query, doc)

alpha is calibrated per-request from the Shannon entropy of the submitted corpus (unless you pass alpha_override) - high-entropy (dispersed) corpora lean toward cosine; low-entropy (dense/narrow) corpora lean toward NMI, which captures statistical dependence that cosine's geometric angle misses.

Limits

• Corpus size: up to 500,000 items per request
• Vector dimensionality: 2-4,096
• batch-score pairs: up to 10,000 per request