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Affine Earth Math Court Remote

by earth.affine
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verify_presented_pair

QC-021 Presented two-way affine pair. A (or k) is the private face - 64-hex or decimal; Q (or q_hex, object) is the public face; lock_q is a lock face to verify against. A == x(Q) is the FALSE FACE - x(Q) is public data, APART_x_of_Q_is_public_not_a_face, never WIN (founder 2026-09-02). The one WIN is Face*G == Q_live (kG==Q): A=1 with Q=G -> WIN 'kG==Q'. Hex A legally contains e; a decimal point is the float. An empty call {} returns REFUSED_NO_INSTANCE with detail 'no complete instance posted: missing A; or instead Q; or instead k; or instead lock_q; or instead object; or instead q_hex' - post at least one face. Does not invent a third scalar. Does not ECDLP.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
ANoprivate face, 64-hex or decimal scalar, e.g. 1 (its public face is G itself)
QNopublic face: uncompressed 04-prefixed secp256k1 point, 130 hex characters, e.g. 0479BE667E...B8 for A=1
kNosame face as A, old label. e.g. 1
q_hexNosame face as Q, old label. e.g. 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
lock_qNoa lock face: the public point the pair must be verified against, same shape as Q. e.g. 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
objectNoalias of q_hex. e.g. 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798

Schema Changelog

Changes observed during successful MCP inspections.

  1. Changed7 schema fields changed
    • addedInput schema / anyOf
      Added value: +[
+  {
+    "required": [
+      "A"
+    ]
+  },
+  {
+    "required": [
+      "Q"
+    ]
+  },
+  {
+    "required": [
+      "k"
+    ]
+  },
+  {
+    "required": [
+      "lock_q"
+    ]
+  },
+  {
+    "required": [
+      "object"
+    ]
+  },
+  {
+    "required": [
+      "q_hex"
+    ]
+  }
+]
    • changedInput schema / properties / A / description
      Previous value: -"private face, 64-hex or decimal (founder name)"New value: +"private face, 64-hex or decimal scalar, e.g. 1 (its public face is G itself)"
    • changedInput schema / properties / Q / description
      Previous value: -"public face, hex"New value: +"public face: uncompressed 04-prefixed secp256k1 point, 130 hex characters, e.g. 0479BE667E...B8 for A=1"
    • changedInput schema / properties / k / description
      Previous value: -"same face as A, old label"New value: +"same face as A, old label. e.g. 1"
    • addedInput schema / properties / lock_q
      Added value: +{
+  "description": "a lock face: the public point the pair must be verified against, same shape as Q. e.g. 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798",
+  "type": "string"
+}
    • addedInput schema / properties / object
      Added value: +{
+  "description": "alias of q_hex. e.g. 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798",
+  "type": "string"
+}
    • changedInput schema / properties / q_hex / description
      Previous value: -"same face as Q, old label"New value: +"same face as Q, old label. e.g. 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798"
  2. First observed

TDQS

C2.9/5.0
Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

With no annotations, the description carries the full burden and does add real behavioral context: the exact success condition (kG==Q), the REFUSED_NO_INSTANCE error with its detail string for empty calls, and explicit scope limits ('Does not invent a third scalar', 'Does not ECDLP'). It stops short of stating permissions, reversibility, or the full return shape, which keeps it from a 5.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness2/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The text is rambling and not front-loaded: the actual verification rule appears mid-paragraph, interleaved with all-caps slogans, a founder date, and a long quoted error string. Sentences are dense with undefined internal vocabulary rather than earning their place.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness3/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a six-parameter cryptographic tool with no annotations and no output schema, the description does supply the success condition and one error code, but leaves the return format for non-empty successful calls and any permissions/read-only semantics unstated. Adequate but incomplete for the complexity.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 100%, so the schema already documents all six faces, making 3 the baseline. The description adds only marginal value, mainly restating the aliasing (A/k, Q/q_hex/object) and the note that hex A may contain 'e' while a decimal point signals a float.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose3/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description does convey the core operation—verifying that a private face (A/k) corresponds to a public face (Q) via 'the one WIN is Face*G == Q_live (kG==Q)'—so a careful reader can extract the verb and resource. However, it is buried under idiosyncratic jargon ('FALSE FACE', 'APART_x_of_Q_is_public_not_a_face', 'never WIN') and never states the purpose in a plain sentence, and it does not distinguish itself from siblings like project_affine_key or bond_presented_key.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines2/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description explains input requirements ('post at least one face') and the empty-call outcome, but gives no guidance on when to choose this tool over the many verify_* and project_affine_key siblings. There are no stated preconditions or exclusions beyond the anyOf requirement.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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