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Affine Earth Math Court Remote

by earth.affine
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bond_presented_key

QC-022 fused bond - the pipeline in ONE call: open key in, bond, verified pair, signature requirements. Post q_hex (the open key, uncompressed 04-prefixed pubkey hex; Q is accepted as the same face) and optionally A (the presented private face, 64-hex or decimal; k is the same face). q_hex ALONE answers UNPRESENTED_PAIR - no scalar on the wire; x(Q) is reported as ground because it is real and derivable, and it is PUBLIC, never a face. With A presented the court projects ground = AG (scalar multiplication, total, no search - the same law project_affine_key runs) and grades the pair by the verify_presented_pair law: pair_verdict is WIN iff AG == Q exactly, and A == x(Q) is the FALSE FACE, halting at APART_x_of_Q_is_public_not_a_face. sig_ready is true iff pair_verdict is WIN; pack_lock is ground on a WIN and absent otherwise. Malformed input answers in the court's REFUSED family. Floats refused. Deterministic. Does not ECDLP.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
ANopresented private face, 64-hex or decimal. e.g. 1
QNosame face as q_hex, old label. e.g. 0479be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
kNosame face as A, old label. e.g. 1
q_hexNoopen key, uncompressed 04-prefixed pubkey hex (required). e.g. 0479be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8

Schema Changelog

Changes observed during successful MCP inspections.

  1. Changed5 schema fields changed
    • addedInput schema / anyOf
      Added value: +[
+  {
+    "required": [
+      "A"
+    ]
+  },
+  {
+    "required": [
+      "Q"
+    ]
+  },
+  {
+    "required": [
+      "k"
+    ]
+  },
+  {
+    "required": [
+      "q_hex"
+    ]
+  }
+]
    • changedInput schema / properties / A / description
      Previous value: -"presented private face, 64-hex or decimal"New value: +"presented private face, 64-hex or decimal. e.g. 1"
    • changedInput schema / properties / Q / description
      Previous value: -"same face as q_hex, old label"New value: +"same face as q_hex, old label. e.g. 0479be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8"
    • changedInput schema / properties / k / description
      Previous value: -"same face as A, old label"New value: +"same face as A, old label. e.g. 1"
    • changedInput schema / properties / q_hex / description
      Previous value: -"open key, uncompressed 04-prefixed pubkey hex (required)"New value: +"open key, uncompressed 04-prefixed pubkey hex (required). e.g. 0479be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8"
  2. Added

TDQS

A3.8/5.0
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 so well: it states no scalar goes on the wire, that x(Q) is public and never a face, that malformed input returns REFUSED, floats are refused, and the tool is deterministic and does not solve ECDLP. It omits auth/permission or statefulness details, but for a stateless computational verifier this is substantial disclosure.

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

Conciseness3/5

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

The purpose clause is front-loaded, which is good, but the body is a dense run-on of stacked clauses and invented terminology that forces re-reading. Sentences earn their informational load but not their readability.

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

Completeness4/5

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

There is no output schema, so the description must explain returns, and it names the key outputs and states: pair_verdict WIN/APART, sig_ready true iff WIN, pack_lock ground on a WIN, UNPRESENTED_PAIR, and the REFUSED family. For a complex fused tool this is nearly complete.

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 coverage is 100%, so the schema already documents the 4 parameters and their alias labels ('same face as q_hex, old label'). The description restates the q_hex/A roles and reinforces the Q/k alias mapping, but adds little syntax beyond what the schema provides, so the baseline 3 applies.

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

Purpose4/5

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

The description states a specific fused operation: take an open key (q_hex), bond a presented private face (A), verify the pair (A*G == Q), and report signature readiness. It also names the sibling laws it fuses ('the same law project_affine_key runs', 'the verify_presented_pair law'), which helps position it against siblings. However, the heavy proprietary jargon ('court', 'face', 'ground') mutes the verb+resource statement, so it lands at a clear-but-not-crisp 4.

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

Usage Guidelines4/5

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

It signals the usage context clearly via 'the pipeline in ONE call' and 'QC-022 fused bond', implying it replaces the separate project_affine_key/verify_presented_pair steps, and it discloses the q_hex-ALONE branch (UNPRESENTED_PAIR). There is no explicit 'use X instead when Y' exclusion, but the conditions distinguishing branches are given.

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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