To propose a format for knowledge encoding using elliptic curve encoding in ECAI, we follow a structured approach that ensures deterministic, cryptographically secure, and elliptically mappable knowledge states.

Here’s a clean and practical format:

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ECAI Knowledge Encoding Format (EKEF v0.1)

1. Input Format

{

"subject": "Gravity",

"predicate": "is proportional to",

"object": "mass",

"context": "Newtonian physics",

"timestamp": "2025-04-07T12:34:56Z"

}

This is a human-structured knowledge tuple:

(Subject, Predicate, Object, Context, Timestamp)

This tuple is the minimal atomic form of knowledge in ECAI, similar to RDF triples but with deterministic encoding.

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2. Preprocessing

Concatenate the tuple into a single string for hashing:

Gravity | is proportional to | mass | Newtonian physics | 2025-04-07T12:34:56Z

Apply canonical formatting (e.g., remove excess whitespace, enforce lowercase if desired).

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3. Hashing

Use a cryptographically secure hash (e.g., SHA-256):

import hashlib

def hash_knowledge(data: str):

return hashlib.sha256(data.encode()).digest()

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4. Mapping to Elliptic Curve

Using a secure curve (e.g., secp256k1, SECP256R1), map the hash onto a valid curve point. One common technique is try-and-increment to find a valid x-coordinate whose y satisfies the curve equation.

Example with Python ecdsa:

from ecdsa import SECP256k1, ellipticcurve

curve = SECP256k1.curve

def map_to_curve(hash_bytes):

x = int.from_bytes(hash_bytes, 'big') % curve.p()

while True:

try:

y = curve.y_values(x)

return (x, y[0]) # Use first valid y

except Exception:

x = (x + 1) % curve.p()

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5. Final Encoded Knowledge Point

{

"x": "0xabc123...",

"y": "0xdef456...",

"curve": "secp256k1",

"original_data": {

"subject": "...",

...

}

}

This structure is now a cryptographic representation of deterministic knowledge that can be stored, verified, and retrieved without interpretation or AI "guesswork".

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Why This Format Works

Determinism: No randomness—same input always yields same curve point.

Cryptographic Integrity: Secured by elliptic curve cryptography.

Post-Quantum Ready: Can evolve to SIDH or lattice schemes in the future.

Composable: Complex structures can be encoded recursively.

Retrievable: Knowledge can be verified and retrieved across subfields.

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Would you like me to generate a full implementation in Python or Erlang?