Affine Earth Math Court Remote

project_affine_key

Affine key projection on secp256k1. Post ONE face, receive the other. Post A (the private face, decimal or 64-hex; k is accepted as the same face) and the court projects Q = A*G and returns it - scalar multiplication, total, no search, closes for every A in [1, n-1]. Post BOTH A and q_hex and the same projection verifies the bond. Post q_hex ALONE and the other face is the discrete log: the court answers verdict CHI_EXHAUSTED with energy_num = n, the bond dimension this instance requires at the current probe (~1.16e77), over energy_den = 4096, the ceiling. That is a COST report, not a claim of impossibility and not a graded pair - the detail names the probe as the limit (an n-squared enumeration that closes to n=17), and the wire status reads MISS today. x(Q) is reported as ground because it is real and derivable, and it is PUBLIC, never a private face. The court never backfills the face it was asked for. Decimal or hex strings; empty means not posted. Floats refused.

Input Schema

TableJSON Schema

Name	Required	Description
`A`	No	the private face: a secp256k1 scalar as decimal or 64-hex, e.g. 2; the court projects Q = A*G
`Q`	No	same face as q_hex, old label. e.g. 0479be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
`k`	No	same face as A, old label. e.g. 1
`q_hex`	No	the public face: uncompressed 04-prefixed secp256k1 point, 130 hex characters; the court projects its shear and period, never a scalar. e.g. 0479be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8

Schema Changelog

Changes observed during successful MCP inspections.

Changed5 schema fields changedSep 29, 2026

addedInput schema / anyOf

Added value: +[
+  {
+    "required": [
+      "A"
+    ]
+  },
+  {
+    "required": [
+      "Q"
+    ]
+  },
+  {
+    "required": [
+      "k"
+    ]
+  },
+  {
+    "required": [
+      "q_hex"
+    ]
+  }
+]

addedInput schema / properties / A / description

Added value: +"the private face: a secp256k1 scalar as decimal or 64-hex, e.g. 2; the court projects Q = A*G"

addedInput schema / properties / Q / description

Added value: +"same face as q_hex, old label. e.g. 0479be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8"

addedInput schema / properties / k / description

Added value: +"same face as A, old label. e.g. 1"

addedInput schema / properties / q_hex / description

Added value: +"the public face: uncompressed 04-prefixed secp256k1 point, 130 hex characters; the court projects its shear and period, never a scalar. e.g. 0479be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8"

First observedSep 1, 2026

TDQS

A3.5/5.0

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 substantial work: it states scalar multiplication 'closes for every A in [1, n-1]', that the discrete-log path returns verdict CHI_EXHAUSTED with energy_num = n over energy_den = 4096, that the wire status reads MISS, and that 'the court never backfills the face it was asked for'. It discloses the cost-report semantics and the guarantee, though the theatrical framing makes the actual guarantees harder to parse.

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 mode routing is front-loaded, but the description is padded with extended metaphor ('face', 'bond', 'court', 'energy_num', 'shear and period') that costs tokens without adding callable information. Several sentences restate the same mapping multiple times 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?

With no annotations and no output schema, the description must convey returns, and it does name outputs (Q = A*G, x(Q) as public ground, CHI_EXHAUSTED with energy_num/energy_den). But the naming is entangled with in-group metaphor, so an agent cannot cleanly determine the response envelope or success/failure shapes. Adequate but muddled.

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

Parameters4/5

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

Schema coverage is 100%, so the baseline is 3, but the description adds constraints the schema omits: 'Decimal or hex strings; empty means not posted. Floats refused.', plus clarifying that k is the same face as A and Q is the same face as q_hex. These are genuine input-format rules beyond the schema text.

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 identify a concrete operation, secp256k1 scalar multiplication/affine projection, and states the two directions ('Post A ... projects Q = A*G' and 'Post q_hex ALONE and the other face is the discrete log'). However, the core purpose is buried under heavy 'court/face/bond' metaphor, and no sibling tool is named to differentiate it from verify_presented_pair or bond_presented_key. It is decipherable but not immediately clear.

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 gives explicit mode routing: post A alone for projection, post both A and q_hex to verify the bond, post q_hex alone to get the discrete-log cost report. That is clear when-to-do-what guidance. It stops short of naming alternatives or exclusions against siblings, so it is not a 5.

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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