tkersey/fixed-point-driver

Fixed-Point Driver

This skill coordinates implementation, review, adjudication, reduction, verification, parallel read-only adversarial challenge, ablation challenge, and closure until the artifact set reaches Truth-Owner Ablative-Isomorphic Normal Form.

The single rule

Drive toward this state:

Every material invariant has exactly one canonical owner, every witness points back to that owner, every review finding is either discharged or represented as a counterexample, every adversarial or ablation veto is cleared, accepted as risk, or routed, every additive scaffold has been promoted/collapsed/deleted, every dominated/subsumed/vestigial/non-canonical surface has been deleted, collapsed, privatized, decommissioned, or kept with an explicit warrant, and every deletion/collapse/canonicalization has a current behavior-preservation witness, and no duplicate truth surface remains merely because it helped satisfy an intermediate review loop.

A fixed point is not “review is clean.” A fixed point is a normal form of the code and proof system.

Why this skill exists

Frontier coding agents are good at adding code and addressing review comments. They are weaker at noticing that the best fix is to delete a path, collapse duplicate owners, privatize a surface, tighten the one boundary that should have owned the invariant from the start, or let a parallel adversary invalidate the local patch before time is spent implementing it.

This skill converts review churn into an ownership-normalization and surface-ablation problem. It converts adversarial pressure into time-efficient, read-only clearance packets and converts deletion pressure into witness-backed Ablation Ledger rows.

Doctrine alpha driver

This skill owns the conversion from doctrine-rich pressure into normal-form artifacts.

Use doctrine only when it changes the route:

• fixed-point creates a reopenable material fixed-point gate, not a long review loop by default.
• invariant creates or updates a Truth Unit and owner edge.
• canonical selects one owner/representation and retires, privatizes, or justifies shadow owners.
• witness creates proof receipts tied to current head/artifact state.
• adversarial / de novo creates candidate inventory, challenger packets, and no-finding countercases.
• parallel creates independent read-only adversarial lanes when it can reduce elapsed time or prevent wrong action.
• unwitnessed guarantee / illegal inhabitant creates Soundness Ledger rows.
• ablative creates Ablation Ledger rows and prevents additive mutation until deletion, collapse, reuse, privatization, decommissioning, or canonicalization is defeated or selected.
• isomorphic creates Ablative Isomorphism Cards so deletion, collapse, merge, reuse, or canonicalization preserves observable behavior.
• clone-classified prevents accidental-rhyme or semantic-clone merges from being treated as safe simplification.
• abstraction-laddered prevents new helpers/interfaces/generics/wrappers from skipping the evidence rung.
• dominated creates a delete/collapse candidate when an existing path covers the obligation with lower complexity or stronger proof.
• subsumed creates an owner-canonicalization candidate when a local abstraction no longer owns a distinct obligation.
• vestigial creates a decommission/delete candidate when a surface only remains from a retired obligation.
• uninhabited creates a deletion/assertion candidate when a branch/state cannot legally occur under current constructors and invariants.

Overprocessing guard

Do not use this skill for simple bounded tasks where ordinary direct execution plus one focused check fully closes the state space. If the run stays active, the reason must be a material open truth unit, stale proof, unresolved counterexample, unresolved adversarial veto, unresolved ablation veto, unresolved isomorphism gap, shadow owner, addition escrow, route-changing architecture uncertainty, or active warrant that requires fixed-point handling.

Local-validity trap breaker

When several findings are each locally valid, ask whether they are all counterexamples to the same truth unit. If yes, prefer one owner-level rewrite or canonicalizing/ablative move over multiple local patches.

Parallel adversarial and ablative action

This skill is parallel-adversarial by default for material actions and ablative-before-additive for mutation routes, but single-writer for all code changes.

Every material action must have an adversarial response:

| phase/action | adversarial response | |---|---| | warrant intake | Is the warrant stale, expired, overbroad, or incompatible with current artifact state? | | truth-unit extraction | Is the invariant split incorrectly? Is the canonical owner wrong? Are there shadow owners? | | route selection | Is delete/reuse/refactor/canonicalize/privatize/no-change/validate-first better than mutation? | | implementation | Does the patch exceed warrant scope or surface budget? Does it add duplicate truth surfaces? | | validation | Does proof exercise the real failure mechanism and current artifact state? | | de novo review | Are there unlisted counterexamples, illegal inhabitants, or unretired scaffolds? | | ablation pass | Are there dominated, subsumed, vestigial, uninhabited, pass-through, or non-canonical surfaces that should be removed or warranted? | | one-change challenge | Is there one remaining impactful change before closure? | | closure handoff | Are proof receipts current and all adversarial/ablation vetoes cleared or explicitly routed? |

Parallelism modes:

• root-equivalent: root performs the adversarial/ablative response inline for narrow, bounded, already-proof-bearing work.
• targeted-parallel: one or two independent read-only lanes challenge distinct uncertainty classes.
• expanded-targeted: three or four lanes for coupled truth units, stale proof, negative evidence, surface-budget risk, or ablation risk.
• swarm: five or more lanes for large, contentious, P2+, invariant-coupled, deletion-sensitive, or likely-to-reopen runs.
• not-required: no safe action exists; block and name missing evidence.

Parallel adversaries may gather evidence, inspect surfaces, challenge proofs, map hazards, test invariants conceptually, and identify deletion/collapse candidates. They must not edit code, alter fixtures, resolve threads, or draft final replies. The root coordinator integrates packets and keeps writes single-threaded.

Companion skills

• review-adjudication decides which review comments matter and issues warrants; this skill decides whether selected work preserves Truth-Owner Ablative Normal Form.
• accretive-implementer performs implementation/remediation when the selected rewrite is narrow, owned, and warrant-scoped.
• adversarial-reviewer challenges the current artifact state and should report normal-form violations, not just bugs.
• verification-closure performs decisive proof and closure gating.
• logophile may sharpen PR-facing summaries, names, and doctrine stacks, but does not own operational policy.

Entry conditions

Use this skill when any of these are true:

• review/fix loops are repeating
• a PR has multiple coupled comments
• review comments are locally valid but may share one governing invariant
• closure proof keeps becoming stale
• a local patch may be inferior to a delete/collapse/canonicalize/privatize move
• additive scaffolding remains after satisfying intermediate review pressure
• a Resolution Warrant routes address, delete-collapse-canonicalize, or validate-only to $fixed-point-driver
• an Adversarial Action Matrix selects full-fanout, swarm, contentious, invariant-level, structural, validation-only, ablation-sensitive, or likely-to-reopen work
• the user asks to drive a branch/changeset to closure or find all impactful issues

Do not use this skill for simple bounded tasks with an obvious check.

Workflow

1. Frame

   • user goal
   • artifact state
   • current review/adjudication inputs
   • active Resolution Warrants and Adversarial Action Matrix rows
   • explicit non-goals
   • proof bar

2. Warrant intake / parallelism plan

   • consume review-adjudication output when present
   • verify each warrant is active for the current artifact state
   • preserve permitted action (mutate-code, delete-collapse-canonicalize, add-validation-only, proof-only, draft-reply, or none)
   • record surface budget and forbidden actions
   • choose root-equivalent, targeted-parallel, expanded-targeted, swarm, or not-required mode for each material action

3. Truth Unit extraction

   • material invariant / contract / semantic fact
   • canonical owner
   • witnesses
   • duplicate or shadow truth surfaces
   • counterexamples / review findings / adversarial vetoes

4. Adjudication intake

   • consume review-adjudication output when present
   • do not redo adjudication unless stale or contradictory
   • promote coupled local comments into a Governing Invariant Candidate
   • preserve ablative clearance and surface-budget obligations
   • do not broaden beyond active warrants or cleared adversarial actions

5. Ablative preflight

   • identify surfaces that may be dominated, subsumed, vestigial, uninhabited, unreachable, pass-through, duplicate truth surfaces, non-canonical, additive scaffolds, or temporary proof scaffolds
   • run ablation_auditor or root-equivalent packet when a deletion/collapse route could materially change implementation or closure
   • classify candidates as delete, collapse, canonicalize, privatize, decommission, validate-first, or keep-with-warrant
   • compute Ablation Opportunity Scores for non-trivial candidates
   • classify clone/collapse candidates before merging or reusing them
   • run an abstraction-ladder check before introducing or expanding an abstraction
   • require an Ablative Isomorphism Card for selected deletion/collapse routes

6. Adversarial preflight

   • run read-only challengers in the calibrated parallelism mode
   • challenge owner, route, proof, scope, surface budget, ablative route, and no-change cases
   • reject stale, wrong-scope, wrapper-leaking, acknowledgement-only, or no-evidence packets
   • block, reroute, or narrow on unresolved/vetoed material findings

7. Route selection

   • validate-first
   • accretive implementation
   • owner-level rewrite
   • delete/collapse/canonicalize/privatize/decommission
   • proof-only / no-change
   • blocked / needs decision

8. Implementation pass

   • delegate mutation to accretive-implementer when the selected rewrite is narrow and owned
   • root may perform root-equivalent edits only with an active mutate-code or delete-collapse-canonicalize warrant, current adversarial clearance, current ablative clearance, and passing Surface Budget Preflight
   • keep writes single-threaded
   • subagents may gather read-only evidence
   • emit Surface Delta Receipts and Ablation Ledger rows after material patch groups
   • emit Ablative Isomorphism Cards for any deletion, collapse, merge, reuse, canonicalization, privatization, or decommissioning performed

9. De novo adversarial review

   • use adversarial-reviewer or root-equivalent challenge
   • require candidate inventory, no-finding countercases, Soundness Ledger, and Change Agenda
   • record adversarial findings in the Adversarial Action Ledger

10. One-change challenge Ask:

    If you could change one thing about this changeset, what would you change?

    Then ask the ablative variant:

    If you could delete, collapse, privatize, decommission, or canonicalize one thing in this changeset without weakening the live contract, and with behavior-preservation proof, what would it be?

    If either answer is impactful and in-scope, route it to accretive-implementer or root-equivalent single-writer implementation, then rerun de novo review. If structural and outside constraints, mark needs-decision or blocked. If no impactful remaining change exists, proceed to verification closure.

11. Material fixed-point test A candidate fixed point exists only when:

    • no open material findings remain
    • no unresolved material soundness rows remain
    • no unresolved adversarial vetoes remain
    • no unresolved ablation vetoes remain
    • no duplicate truth owner remains unretired
    • no additive scaffold remains without explicit justification
    • no dominated, subsumed, vestigial, uninhabited, pass-through, or non-canonical surface remains without a keep warrant
    • no selected deletion, collapse, reuse, or canonicalization lacks an Ablative Isomorphism Card or explicit validate-first blocker
    • no semantic clone or accidental rhyme was merged without equivalence proof
    • no review counterexample remains unresolved
    • surface budgets are satisfied or expansion is explicitly granted
    • proof receipts are tied to current artifact state

12. Verification closure Hand off to verification-closure with a closure packet. If closure reopens a gate, resume at route selection.

Required ledgers

Warrant Intake / Parallelism Plan

| warrant id | claim id | permitted action | permitted scope | expiry check | surface budget | adversarial plan | ablation plan | parallelism mode | intake status |
|---|---|---|---|---|---|---|---|---|---|

Rules:

• intake status is active, stale, blocked, consumed, or not-applicable.
• Active mutate-code warrants must have surface budget and adversarial clearance.
• Active delete-collapse-canonicalize warrants must have ablation proof or a validate-first gate.
• Active add-validation-only warrants must forbid production mutation.
• Stale or blocked warrants may not be consumed for writes, validation, thread resolution, or replies.

Truth Units

| truth unit id | invariant | canonical owner | witnesses | duplicate/shadow owners | review/adversarial counterexamples | status | proof refs | next action |
|---|---|---|---|---|---|---|---|---|

Ablation Ledger

| id | surface | kind | current obligation | obligation status | canonical owner | replacement path | action | deletion/collapse proof | keep warrant | status |
|---|---|---|---|---|---|---|---|---|---|---|

Allowed kind values:

• dominated
• subsumed
• vestigial
• uninhabited
• unreachable
• pass-through
• duplicate-truth-surface
• non-canonical
• additive-scaffold
• temporary-proof-scaffold

Allowed obligation status values:

• live
• expired
• moved
• duplicate
• unproven
• unknown

Allowed action values:

• delete
• collapse
• canonicalize
• privatize
• decommission
• validate-first
• keep-with-warrant

Ablation Opportunity Matrix

| id | candidate | kind | surface removed | confidence | ownership clarity | risk | score | decision | proof needed |
|---|---|---|---:|---:|---:|---:|---:|---|---|

Use:

Ablation Score = (Surface Removed × Confidence × Ownership Clarity) / Risk

Do not let LOC savings dominate semantic-surface reduction. A small deletion can score high when it removes a duplicate truth surface, obsolete flag, public symbol, state variant, or proof obligation.

Ablative Isomorphism Cards

| card id | surface | action | behavior preserved | public contract preserved | error semantics preserved | ordering/side effects preserved | clone classification | abstraction-ladder check | compatibility risk | proof signal | status |
|---|---|---|---|---|---|---|---|---|---|---|---|

Allowed status values: pass, validate-first, missing, not-applicable.

Adversarial Action Ledger

| action id | phase | target | challenger lanes | parallelism mode | strongest adversarial finding | veto status | clearance | proof ref | decision impact |
|---|---|---|---|---|---|---|---|---|---|

Allowed veto status values: cleared, preserved-no-change, unresolved, vetoed, blocked, not-required.

Allowed clearance values: cleared, preserved, rerouted, downgraded, blocked.

Surface Delta Receipts

| receipt id | warrant id | patch/pass | production insertions | production deletions | net production loc | public symbols added | helpers added | duplicate paths added | budget status | proof ref |
|---|---|---|---|---|---|---|---|---|---|---|

If budget status is expansion-needed or violation, stop implementation until an Expansion Warrant Request is granted or the patch is redesigned.

Closure handoff packet

Before invoking verification-closure, compile:

closure_handoff_packet:
  artifact_state_id: "..."
  goal: "..."
  warrant_intake:
    - warrant_id: "..."
      claim_id: "..."
      permitted_action: "mutate-code | delete-collapse-canonicalize | add-validation-only | resolve-thread | draft-reply | defer | none"
      intake_status: "active | consumed | stale | blocked | not-applicable"
      adversarial_clearance: "cleared | preserved | rerouted | downgraded | blocked"
      ablative_clearance: "clear-additive | select-ablative-route | validate-first | veto-additive | unresolved | not-required"
  parallelism_plan:
    lane: "root-equivalent | targeted-parallel | expanded-targeted | swarm | not-required"
    reason: "..."
    read_only: yes
    write_owner: root-or-delegate
  truth_units:
    - id: "TU1"
      invariant: "..."
      canonical_owner: "..."
      witnesses: ["..."]
      duplicate_truth_surfaces_retired: ["..."]
      open_counterexamples: []
  review_agenda:
    act_on: []
    validate_first: []
    proof_only: []
    delete_collapse_canonicalize: []
    no_change: []
    blocked: []
  ablation_ledger:
    open_candidates: []
    closed_candidates: []
    keep_warrants: []
    unresolved_ablation_vetoes: []
  ablation_opportunity_matrix:
    top_candidates: []
    rejected_candidates: []
  ablation_isomorphism_cards:
    - card_id: "..."
      surface: "..."
      action: "delete | collapse | reuse | canonicalize | privatize | decommission"
      behavior_preserved: "..."
      public_contract_preserved: "yes | no | unknown"
      error_semantics_preserved: "yes | no | unknown | not-applicable"
      ordering_side_effects_preserved: "yes | no | unknown | not-applicable"
      proof_signal: "..."
      status: "pass | validate-first | missing | not-applicable"
  adversarial_action_ledger:
    open_vetoes: []
    cleared_vetoes: []
    accepted_risks: []
  soundness_ledger:
    open_rows: []
    closed_rows: []
  surface_delta_receipts:
    - warrant_id: "..."
      budget_status: "within-budget | expansion-needed | violation | not-applicable"
      proof_ref: "..."
  proof_receipts:
    - command_or_check: "..."
      result: "..."
      artifact_state_match: yes | no
  one_change_challenge:
    answer: "..."
    ablative_answer: "..."
    routed: yes | no
    reason: "..."
  unresolved_adversarial_vetoes: []
  unresolved_ablation_vetoes: []

Output contract

Use tail-weighted sections:

1. Goal / Artifact State
2. Warrant Intake / Parallelism Plan
3. Truth Units
4. Ablation Ledger
5. Ablative Isomorphism Cards
6. Route Selection
7. Work Performed / Routed
8. Adversarial Action Ledger
9. Review, Soundness, and Ablation Results
10. Surface Delta Receipts
11. Proof Receipts
12. Fixed-Point Test
13. Closure Handoff
14. Final State
15. Do Next

Do Next must be the final section.

Fixed-Point Gate

Before closure handoff, emit a gate summary with these fields:

• artifact_state_match: pass / fail
• warrant_intake: pass / fail
• parallelism_calibration: pass / fail
• adversarial_action_coverage: pass / fail
• ablation_coverage: pass / fail / not-applicable
• ablation_isomorphism: pass / fail / not-applicable
• open_truth_units: 0 or named blockers
• duplicate_truth_owners: 0 or named blockers
• open_review_counterexamples: 0 or named blockers
• unresolved_soundness_rows: 0 or named blockers
• unresolved_adversarial_vetoes: 0 or named blockers
• unresolved_ablation_rows: 0 or named blockers
• unresolved_isomorphism_cards: 0 or named blockers
• dominated_surfaces: 0 or named blockers
• unwarranted_keep_surfaces: 0 or named blockers
• unretired_additive_scaffolds: 0 or named blockers
• surface_budget_status: pass / fail / not-applicable
• proof_receipts_current: pass / fail
• one_change_challenge_status: pass / fail
• ablative_one_change_challenge_status: pass / fail
• verification_closure_ready: yes / no

Hard rules

• Do not mutate outside an active mutate-code or delete-collapse-canonicalize warrant.
• Do not turn add-validation-only into production mutation.
• Do not let parallel adversaries or ablation auditors write files, mutate fixtures, resolve threads, or draft final replies.
• Do not treat parallel agreement as proof; require current artifact evidence.
• Do not claim fixed point with unresolved material adversarial vetoes.
• Do not claim fixed point with unresolved material ablation vetoes.
• Do not claim fixed point with unresolved or missing Ablative Isomorphism Cards for selected deletion, collapse, reuse, or canonicalization routes.
• Do not preserve duplicate truth owners unless they are explicitly justified.
• Do not leave additive scaffolding unretired merely because it helped pass an intermediate review loop.
• Do not keep dominated, subsumed, vestigial, uninhabited, pass-through, or non-canonical surfaces without a keep warrant.
• Do not hand off closure with stale proof receipts.
• Do not broaden beyond the permitted scope, forbidden actions, and surface budget consumed from review adjudication.

Resources

• doctrine-alpha.md
• tail-proof.md
• truth-owner-normal-form.md
• one-change-challenge.md
• ablation-ledger.md
• isomorphic-ablation.md
• lane-and-specialist-budget.md
• common-ledgers.md