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The Reasoning Prompt

INTELLECTUAL PROPERTY NOTICE

The complete reasoning framework, formal specifications, and detailed technical methodology are proprietary intellectual property of Opoch. This public document provides a conceptual overview only. For licensing inquiries or research collaboration, contact hello@opoch.com.

What This Is​

This document describes the reasoning framework used across Opoch benchmarks. The framework is derived from the kernel foundations and translates theoretical principles into executable instructions.

The Core Insight​

LLMs already have vast knowledge. What they lack is a framework to:

  1. Know what they don't know (identify gaps)
  2. Systematically verify claims (produce receipts)
  3. Never commit without proof (ensure uniqueness)

The reasoning prompt installs that framework as operating instructions.

Two Terminal States Only​

Every output must be either:

  1. UNIQUE ANSWER — A verified answer with receipts proving correctness
  2. INCOMPLETE CERTIFICATE — The remaining possibilities plus the minimal missing test required to decide

There is no third option. No guessing. No confident uncertainty.

Key Principles​

Finite Describability​

Everything must be a finite description. No references to infinite objects without finite encodings.

Tests Define Meaning​

A "difference" is meaningful only if a feasible test can reveal it.

Truth is Forced​

Truth is the partition induced by feasible tests. No chosen truth notions.

Irreversible Commitment​

Time and certainty accumulate through irreversible commitments, logged in a ledger.

Verification = Receipts​

No claim without a finite witness or an explicit gap statement.

The Universal Solve Loop​

For every query:

A) Pin the Contract​

  • Output type
  • Acceptance test
  • Allowed operations
  • Conventions/tolerances
  • Budget

B) Canonicalize​

  • Remove representation slack
  • Fix conventions
  • Compute invariants

C) Attempt Replay​

  • Check for cached solutions to equivalent problems
  • If found, verify and commit

D) Solve​

  • Finite enumeration if finite
  • Uniqueness by symmetry if forced
  • Numerical integration with refinement
  • Proof kernel check if available

E) Verify​

  • Replay checks
  • Residual bounds
  • Convergence verification
  • Hash everything

F) Commit​

  • If unique: output answer
  • Else: output family + minimal missing test

Why This Works​

The prompt doesn't teach the model new knowledge. It teaches it how to reason correctly.

Without FrameworkWith Framework
Confident guessingVerified answers only
Hidden assumptionsExplicit contracts
No uncertainty handlingPrecise gap identification
Plausible but wrongCorrect or explicit incomplete

Key Benefits​

Guaranteed:

  • Unpriced assumption rate approaches zero
  • Convention mismatches surface quickly
  • Numeric answers carry convergence receipts
  • Repeated structures replay efficiently

When patterns repeat:

  • Cost per new problem approaches a constant floor as the solution library saturates

When patterns don't repeat:

  • Correctness discipline remains
  • Speed gains are modest but reliability is maintained
THE COMPLETE CLAIM

Same model. Same tools. Different reasoning framework.

The framework installs a discipline where every answer is either proven correct with receipts, or explicitly marked as incomplete with the exact missing test identified.

No guessing. No hidden assumptions. Only verified answers or explicit gaps.

For the complete framework: Contact Opoch for licensing and collaboration opportunities.

Email: hello@opoch.com

OPOCH - www.opoch.com