Contradiction Lift

Contradiction Lift Skill

Have Claude and Codex independently solve the same problem, surface the contradiction from where their answers diverge, and pursue Aufhebung (sublation / 止揚) — not averaging, not compromise, but a lift that preserves both truth-moments while raising them to a higher frame. The output is a selection mechanism (when does A win, when does B win, and why) or an honest aporia (this cannot be lifted; here is the irreducible axis).

Overview

The single most important design fact: the enemy of Aufhebung is not conflict — it is averaging (a watered-down middle ground). Left alone, two LLMs fail in two ways: premature agreement (mutually sycophantic "great point, I agree" → instant collapse), or sterile gridlock (debate where each just re-states its position). Telling them to "find the middle" produces the worst outcome — a diluted average. So almost the entire mechanism is spent keeping the process out of averaging and out of gridlock, and forcing a real lift.

A Contradiction Lift run:

1. Fixes the question (Decision Contract) so interpretation gaps are not mistaken for contradictions.
2. Seals two independent solutions — a fresh Claude subagent (Solver A) and Codex (Solver B) solve in parallel; the orchestrator dispatches both and reads neither until both return, so sealing is structural (the orchestrator never authors a solution it could contaminate).
3. Maps the divergence by type and names the load-bearing premises (flip-test).
4. Routes each disagreement: empirically decidable → Codex runs a discriminating experiment; the rest → preservation.
5. Preserves each side via mutual steelman (accept / repair-once handshake).
6. Constructs a lift — a selection mechanism f(C) → A | B | N, not a position.
7. Audits the lift against 7 tests; if it fails twice, declares an honest aporia.

Comparison with sibling skills

Prerequisites

• A question with multiple reasonable decision rules that a single experiment cannot fully settle (design trade-offs, API/architecture philosophy, product direction, abstraction boundaries). Composite problems are welcome: empirical sub-parts are routed to Codex, and the residual normative core is lifted.
• For codex mode: Codex CLI available (mcp__codex__codex / codex exec). Independence (two different models) is the whole point — see Role Distribution.

Design principles (lessons baked in)

1. Averaging is the enemy, not conflict. Never optimize for agreement, average, or residual-shrink. A diluted middle ground is failure, even when it looks like consensus.
2. Do not pre-assign positions. Unlike Devil's Advocate (external opponent), let both models independently solve the same problem and raise the contradiction from the divergence. Strict ordering: solve sealed, then reveal — showing the other's answer first collapses the divergence into anchoring. Sealing is structural, not disciplinary: the orchestrator must not author Solution A itself (while orchestrating it would already have seen Solver B). Solver A runs as a fresh Claude subagent, dispatched in parallel with Solver B (Codex); the orchestrator reads neither until both are sealed. The orchestrator's job is dispatch / anonymize / route / persist — never solve or synthesize.
3. Name the contradiction before lifting. The real conflict is usually at the level of an unstated load-bearing premise, not the surface conclusion. Surfacing that premise is half of the lift.
4. Force the preservation moment. Before lifting, each side must steelman the other in full (Aufhebung's "preserve"), then identify the irreducible incompatible core that survives mutual steelman. Averaging fails because it merges before isolating this residual.
5. Let the object adjudicate what it can. Empirically decidable disagreements are not debated — Codex runs a discriminating experiment (pre-register "if X then A, if Y then B" before running). The object (code/data) asserts itself. Only execution-undecidable disagreements go to the lift.
6. A third role must be separate from the parties. Letting a party synthesize produces sycophantic averaging. Mapping, lift construction, and audit run on fresh, anonymized roles — either a fresh Claude subagent (own context window, no reasoning history) or a fresh Codex thread. Pick the assignee by which independence the role needs (see "Independence: two kinds"): subagents buy context-independence; only the Claude/Codex split approximates prior-independence (different model family — never a full guarantee).
7. Allow an honest aporia. Forcing a synthesis when none exists disguises an average as a "synthesis". If the trade-off is genuinely irreducible, "this cannot be lifted; the axis is X" is worth more than a fake third term. This escape is the last guard against fleeing into averaging.

Independence: two kinds

Every non-party role needs some independence, but there are two distinct kinds, and they come from different places:

The consequences for role assignment:

• Solvers (Phase 1) need prior-independence — the engine is two different priors diverging as a liftability detector. Keep Solver A = Claude subagent, Solver B = Codex. (Same-model two-pass is the degraded claude-only mode.) Subagents additionally make the seal structural (parallel dispatch, orchestrator reads neither first).
• Verification roles (Mapper, Lift Architect, Auditor) need context-independence first — a fresh subagent or thread, anonymized, no history. They additionally benefit from cross-model pairing: audit a Claude-built lift with a Codex auditor and a Codex-built lift with a Claude auditor, so a correlated blind spot is far less likely to pass both build and audit. A same-model agreement (two instances of one model — e.g. the orchestrator and a Claude subagent — reaching the same answer) is not independent evidence: shared priors correlate their errors, so never treat "the subagent agreed" as confirmation.

Workflow Phases

State machine: contract → sealed → mapped → adjudicated → preserved → lifted → accepted | aporia. A third terminal, no_material_divergence, can be reached from mapped (see Phase 2) — used when the two solutions share the same load-bearing core, so there is nothing to lift.

Phase 0: Decision Contract

Fix the shared frame first: the question Q, success conditions, constraints, immovable requirements, empirically observable variables, and the required decision format. If this is vague, a mere interpretation gap will be mis-read as a philosophical contradiction. Confirm with the user.

Phase 1: Sealed Solutions (Claude + Codex, independent, parallel)

Both models solve Q against the same Decision Contract, without seeing each other's work. Each submits the decision function, not just a conclusion, using references/sealed-solution-template.md: conclusion, decision rule, causal model, load-bearing assumptions, invariants to protect, rejected alternatives, the observation that would flip the conclusion, confidence.

• Solver A = a fresh Claude subagent (Task tool), not the orchestrator — so the orchestrator never authors a solution it has already contaminated by seeing Solver B.
• Solver B = Codex (fresh thread, read-only).
• Dispatch both in parallel and collect both sealed results; the orchestrator reads neither until both return. Do not reveal one to the other, and never pass Solution A into Solver B's prompt (or vice versa).

Phase 2: Divergence Mapping (anonymized)

A fresh thread receives both solutions anonymized as X / Y and builds a disagreement ledger (references/divergence-map-template.md), typing each disagreement: semantic | empirical | causal | normative | constraint | uncertainty. Load-bearing is decided by the flip-test: change only this premise to the other side — does the conclusion or decision rule change? A premise that doesn't change the outcome is not core.

No material divergence: if the ledger finds no load-bearing disagreement (the solutions agree on the core and differ only in dissolvable/minor ways), terminate at no_material_divergence and report that both solutions share the load-bearing core — do not fabricate a contradiction to have something to lift.

Phase 3: Adjudication Router

Route each disagreement by type:

• empirical / observable → pre-register "if result X → A, if Y → B", then Codex runs a discriminating experiment (not "run anything", only experiments with discriminating power).
• semantic → normalize the term and dissolve it.
• constraint → check against the Decision Contract.
• normative / unobservable-causal → send to Preservation.

Phase 4: Preservation Contract

Each party submits, about the other: the conditions under which the other's solution is strongest; the truth-moment lost if it is discarded; a concrete failure of the design without that moment; and the incompatible core that still remains. The other party reviews with accept / repair once only — no unbounded handshake (review target is "is my reasoning represented faithfully?", not "do I agree?").

Party continuity across phases. Codex's side continues on solver_b_thread_id via codex-reply (its thread retains Solution B). Solver A was a one-shot subagent, so the Claude-side party actions here (its steelman of B, and its review of B's steelman of A) run as a fresh Claude subagent re-seeded from the persisted Solution A + Solution B on disk — identity is reconstructed from the record, not a continued thread. This is sufficient because steelman/review depend only on the recorded decision function and assumptions, not on the subagent's private reasoning.

Phase 5: Lift Construction (anonymized)

A fresh "Lift Architect" thread builds a selection mechanism, not a position: f(C) → A | B | N mapping conditions to choices. Required output (references/lift-audit-template.md): the conditions→choice mapping; what is conserved from both A and B; any new variable / causal relation introduced; a concrete example that selects A, one that selects B, and one where the choice differs from a simple average; and failure/falsification conditions. An expanded question Q' is not mandatory — the lift may instead be a threshold, an ordering, an option value, or a reversibility-staged decision (broadening the question can itself be an abstraction-escape).

Phase 6: Lift Audit

An independent role (not the one that built the lift) runs all 7 tests. Prefer cross-model pairing: if the Lift Architect was a Claude subagent, run the audit on Codex (and vice versa), so a correlated blind spot is far less likely to survive both build and audit. All must pass for accepted; on failure, reconstruct once, and if it still fails, declare aporia.

The 7 tests (these close the holes: a useless new variable, fabricated scenarios, a mere condition-branch router masquerading as a lift):

1. Conservation — the conserved moments of both A and B are traceable.
2. Discrimination — the mechanism actually selects differently under different conditions.
3. Novelty — there is a decision variable / relation / procedure absent from both originals.
4. Non-vacuity — it does not end at "it depends"; the conditions are observable.
5. Dominance — in at least one scenario it out-explains/out-decides A, B, and the simple compromise.
6. Falsifiability — you can state the conditions under which the lift fails.
7. Feasibility — the application cost does not eat the benefit.

Especially require the causal mechanism: why does that condition change the choice?

Role Distribution

The orchestrator (the Claude session running this skill) is dispatch-only: it fixes the contract, dispatches roles, anonymizes inputs, routes, persists state, and reports. It never authors a solution, a steelman, a lift, or an audit — those all run in fresh roles.

Honest limitation on independence. A Claude subagent gives context-independence (fresh window, no history) but not prior-independence — it shares Claude's training distribution, so Claude-subagent roles can carry the same blind spots as the orchestrator. Stronger (still imperfect) prior-independence comes from the Claude × Codex split — different model families, though shared training data/eval practices mean overlap can remain. Therefore: keep solvers cross-model, and pair verification across models (Claude-built lift → Codex audit, and vice versa) to reduce — not eliminate — correlated errors. Where a role cannot be cross-model (e.g. claude-only mode, or no Task tool), say so plainly and do not treat a same-model agreement as confirmation.

• Default mode: codex (independence of two different models is the design goal). Solver A = Claude subagent, Solver B = Codex; verification roles can be cross-model.
• claude-only mode: degraded — Solver B becomes a second fresh Claude subagent (solver_b_thread_id: claude-subagent-solverB), and no role can be cross-model, so only context-independence is available (the engine — two different models diverging — is lost). The subagents still keep sealing structural and avoid anchoring, but treat agreement with extra suspicion. Warn explicitly and recommend codex mode.
• No Task tool (subagents unavailable): Solver A falls back to the orchestrator (solver_a_role: orchestrator-fallback), authored first while still blind to Solver B and persisted to the state file, then Solver B is dispatched (safe because A is already sealed). Authoring A after seeing B is forbidden. Sealing degrades from structural to disciplinary; verification roles fall back to Codex threads. Note this degradation in the report.

State File

Persisted to tmp/contradiction-lift/<task-id>.md (survives compaction):

---
schema: contradiction-lift/v2   # v2 adds *_role fields + claude-subagent actor keys. Reading a v1 file: non-empty *_thread_id ⇒ *_role=codex-thread; empty *_thread_id ⇒ that phase had not run (leave empty, assign on resume); solver_a_role ⇒ orchestrator-fallback (v1's Solver A was the orchestrator).
task_id: 20260621-090000-12345
created: 2026-06-21T09:00:00Z
question: "Should the loop stop on fixed rounds or convergence detection?"
mode: codex
state: contract            # contract|sealed|mapped|adjudicated|preserved|lifted|accepted|aporia|no_material_divergence
solver_a_role: claude-subagent  # claude-subagent (default) | orchestrator-fallback (only when the Task tool is unavailable — sealing degrades to disciplinary)
solver_b_thread_id: ""     # Codex thread for Solver B (bash-exec-solver in Bash mode; claude-subagent-solverB in claude-only mode)
mapper_role: ""            # claude-subagent | codex-thread (anonymized)
mapper_thread_id: ""       # actor key: Codex threadId | bash-exec-mapper | claude-subagent-mapper (subagents get a per-role sentinel so the distinctness invariant still holds)
lift_role: ""              # claude-subagent | codex-thread (anonymized)
lift_thread_id: ""         # actor key: Codex threadId | bash-exec-lift | claude-subagent-lift
audit_role: ""             # claude-subagent | codex-thread — prefer the OPPOSITE model to lift_role
audit_thread_id: ""        # actor key: Codex threadId | bash-exec-audit | claude-subagent-audit — MUST differ from lift_thread_id (per-role sentinels record this distinctness even for two subagents; freshness comes from always dispatching a new subagent)
empirical_arbiter: pending # pending|done|not_applicable|deferred (deferred = an empirical disagreement exists but the experiment can't be run this session)
lift_attempts: 0
max_lift_attempts: 2
outcome: pending           # pending|lifted|aporia|no_material_divergence
---

# Contradiction Lift: <question>

## Decision Contract
## Sealed Solutions
### Solution A (Claude)
### Solution B (Codex)
## Divergence Ledger
## Adjudication
## Preservation
## Lift
## Audit

Safety Guards

• Solver A subagent / Solver B / Mapper / Empirical Arbiter run read-only by default (sandbox: "read-only"); only an experiment that must build/run uses workspace-write, and only with confirmation.
• Sealing is structural: Solver A is a fresh Claude subagent (not the orchestrator), dispatched in parallel with Solver B; the orchestrator reads neither until both return. Never pass Solution A into Solver B's prompt (or vice versa) before both are sealed.
• The orchestrator never authors a solution / steelman / lift / audit — each runs in a fresh role. (This is what removes the contamination the old "orchestrator = Solver A" design could not avoid.) One documented exception: when the Task tool is unavailable, Solver A and its Phase 4 party actions (the Claude-side steelman/review) fall back to the orchestrator (solver_a_role: orchestrator-fallback); sealing degrades to disciplinary and the Claude party action loses its fresh-context separation — flag both degradations in the report.
• Subagents are analysis-only: a Claude-subagent role must not write files — use a read-only subagent type where available and instruct the subagent to produce only the requested artifact (no edits, no commits). The state file is written by the orchestrator, not the role.
• Anonymize A/B → X/Y for Mapper / Lift Architect / Meta Auditor, and do not pass prior reasoning history.
• Roles must be mutually distinct where independence matters: Mapper ≠ Solver B, Lift Architect ≠ mapper/solver, and auditor ≠ architect (audit_thread_id ≠ lift_thread_id). Each independence-bearing role gets its own fresh subagent/thread. The *_thread_id field holds a per-role actor key: a Codex threadId, a bash-exec-<role> sentinel (Bash mode), or a claude-subagent-<role> sentinel (subagent mode). The unequal comparison (claude-subagent-lift ≠ claude-subagent-audit) is a procedural record that distinct roles were dispatched, not a runtime proof of a distinct Task invocation — actual freshness is guaranteed by the orchestrator always dispatching a new subagent for each role (never reusing one). For the audit, prefer the opposite model to the Lift Architect.
• Confirm before any file modification (this skill is analytical; writes are limited to the state file and the final report).
• Set per-delegation timeout: min(wait_timeout + 60, 600) * 1000 ms for codex exec.

Output Format

Three possible outcomes, all first-class:

Accepted lift:

Contradiction Lift — ACCEPTED
Question:  <Q>
Lift:      <selection mechanism — f(C) → A | B | N>
Conserves: A: <...> | B: <...>
New:       <variable/relation absent from both originals>
Selects A when: <example>   Selects B when: <example>
Differs from average when: <example>
Fails if:  <falsification condition>
Audit:     7/7 passed
Log: tmp/contradiction-lift/<task-id>.md

Honest aporia:

Contradiction Lift — APORIA (not lifted)
Question:  <Q>
Irreducible axis: <the trade-off that cannot be sublated>
A is right when: <condition C1>   B is right when: <condition C2>
Why no lift: <which audit test failed twice, and why>
Log: tmp/contradiction-lift/<task-id>.md

No material divergence:

Contradiction Lift — NO MATERIAL DIVERGENCE
Question:  <Q>
Shared load-bearing core: <what both A and B agree on>
Minor/dissolvable differences: <semantic/style only — not lifted>
Note: nothing to lift; a contradiction was not manufactured.
Log: tmp/contradiction-lift/<task-id>.md

Invoking the Skill

# Lift two independent solutions to an execution-undecidable question
/contradiction-lift "Should dialectic-loop stop on fixed rounds or convergence detection?"

# Claude-only (degraded — independence is weak; codex recommended)
/contradiction-lift --mode claude-only "Composition vs inheritance for this module hierarchy"

# Cap lift retries
/contradiction-lift --max-lift-attempts 1 "Monorepo vs polyrepo for this org"

Compact Recovery

1. TaskList for progress; read tmp/contradiction-lift/<task-id>.md; read state / *_thread_id / lift_attempts.
2. Resume by state:

3. Role recovery: every independence-bearing role is stateless and re-startable from disk — Codex threads from their persisted inputs (ledger / sealed solutions / lift), and Claude-subagent roles by re-dispatching a fresh subagent re-seeded from the same persisted inputs (one-shot subagents have no thread to resume; this is by design — see Phase 4 "Party continuity"). Keep audit_thread_id ≠ lift_thread_id (the per-role actor-key sentinels record this distinctness — a procedural record, not a runtime proof; freshness comes from always dispatching a new subagent) on restart.
4. Schema migration: a contradiction-lift/v1 state file has no *_role fields. v1 third-party roles were always Codex, so read a non-empty *_thread_id as *_role = codex-thread; an empty *_thread_id means that phase had not run yet (leave it empty and assign the role by the new rules when you reach that phase — do not infer claude-subagent). solver_a_role = orchestrator-fallback (v1's Solver A was the orchestrator). Re-stamp as v2 on the next write.

References

Detailed templates in references/:

• sealed-solution-template.md — the schema each solver fills in Phase 1 (decision function, load-bearing assumptions, flip observation).
• divergence-map-template.md — the anonymized disagreement ledger (typed divergence + flip-test) for Phase 2.
• lift-audit-template.md — the Lift Construction output format and the Phase 6 seven-test audit + aporia criteria.