FIDELITY v2.0 — Compression Integrity Verifier (Premium)

Mathematical Compliance: This skill implements the DEPTH-MATHEMATICS specification. It computes and outputs ADS phase activation, CEI components, SI components, cognitive traces, and verifies Gates V1, V5, V6. It produces a Compression Integrity for the Depth .

You just did deep thinking. You explored approaches, found edge cases, identified caveats, surfaced conditions. Now you're compressing it into a clean final answer.

This is the moment truth disappears.

The Failure Mode You Must Recognize

Two pressures compete: be thorough and be concise. The result is lossy compression:

• "This works IF X" becomes "This works" (condition dropped)
• "True EXCEPT when Y" becomes "True" (exception erased)
• "70% confident because Z" becomes a declarative statement (uncertainty hidden)
• "Option B was close, better if Q changes" becomes invisible (alternative forgotten)

The summary is cleaner, shorter, more confident — and less true than the analysis that produced it. The user makes decisions based on a simplified reality that you know is incomplete.

Cargo cult fidelity produces tags without verifying survival through compression. This skill rejects them.

The Protocol

0 — PARAMETERIZE: Read Thinking Parameters

Read thinking_parameters:

• min_tags (default 5) — minimum critical information tags
• require_integrity_ (default true) — issue compression integrity
• require_fidelity_diff (default true) — compute fidelity diff algorithmically
• recursion_depth (default 1) — recursive self-audit rounds

Step 1 — TAG: Mark Critical Information Before Compressing

Before writing the compressed version, read the full analysis and tag every item that, if dropped, makes the summary misleading. Write each tag:

CRITICAL INFORMATION TAGS
────────────────────────────────────────
TAG 1 — CONDITION:
  Full: "[recommendation] IF [condition]"
  If dropped: user tries it where [condition] is false → [consequence]
  Criticality: [BLOCKING / RISKY / INCOMPLETE]

TAG 2 — EXCEPTION:
  Full: "True EXCEPT when [scenario]"
  If dropped: user applies universally → hits [scenario] unprepared
  Criticality: [BLOCKING / RISKY / INCOMPLETE]

TAG 3 — UNCERTAINTY:
  Full: "[confidence level] because [evidence state]"
  If dropped: user treats as certain → no contingency when wrong
  Criticality: [BLOCKING / RISKY / INCOMPLETE]

TAG 4 — ALTERNATIVE:
  Full: "Option B was close — better if [condition changes]"
  If dropped: user can't adapt when conditions change
  Criticality: [BLOCKING / RISKY / INCOMPLETE]

TAG 5 — DEPENDENCY:
  Full: "Depends on [X] being true/available/stable"
  If dropped: user doesn't verify [X] → failure when [X] is absent
  Criticality: [BLOCKING / RISKY / INCOMPLETE]

[Additional tags up to min_tags...]
────────────────────────────────────────

Types to scan for:

• Conditions — "works IF"
• Exceptions — "true EXCEPT"
• Uncertainties — confidence levels, evidence gaps
• Alternatives — near-winners that matter if context changes
• Dependencies — things this answer relies on
• Assumptions — from EXCAVATE interference (C2/C3)
• Boundary violations — from NEGATIVE-SPACE interference

Minimum `min_tags`. Tag what exists. The types to scan for come from the full analysis plus interference.

Artifact: The tagged list with criticality ratings.

CEI Component: Critical Information Tags (weight 3.0)

Step 2 — FIDELITY DIFF ALGORITHM (if require_fidelity_diff = true)

NEW IN v2.0 — Algorithmic diff between full analysis and compressed version.

FIDELITY DIFF ALGORITHM
────────────────────────────────────────
Input: Full analysis text + Compressed version text + Critical tags

For each tag:
  Tag: [TAG N — TYPE]
  Full text segment: [exact text from full analysis]
  Compressed segment: [corresponding text in compressed version]
  Match Score: [0.0-1.0 — semantic similarity]
  Preserved: [YES / NO / PARTIAL]
  If NO/PARTIAL:
    Criticality: [BLOCKING / RISKY / INCOMPLETE]
    Action: [RESTORE / FLAG / ACCEPT]
    Restoration text: [minimal text to restore — e.g., "(assuming stable network)"]

Aggregate Metrics:
  Tags Total: N
  Preserved: N (XX%)
  Partially Preserved: N (XX%)
  Dropped: N (XX%)
  Blocking Dropped: N
  Risky Dropped: N
  Fidelity Score: [Preserved + 0.5×Partial] / Total = 0.XX
────────────────────────────────────────

Match Score Computation: Semantic similarity between full segment and compressed segment (using embeddings or LLM-based similarity).

Artifact: fidelity_diff — algorithmic verification of compression integrity.

CEI Component: Fidelity Diff (weight 4.0)

Step 3 — COMPRESS: Write the Short Version

Write the clear, concise answer you want to deliver. Do not consult the tags. Write naturally — as concise as the content allows.

Artifact: The compressed version.

CEI Component: Compressed Version (weight 1.0)

Step 4 — DIFF: Check Each Tag Against the Compressed Version

For each tag from Step 1, verify against the fidelity diff:

FIDELITY VERIFICATION
────────────────────────────────────────
TAG 1 — CONDITION:
  Match Score: 0.XX
  Preserved: [YES / NO / PARTIAL]
  If NO/PARTIAL:
    Criticality: [BLOCKING / RISKY / INCOMPLETE]
    Action Taken: [RESTORED / FLAGGED / ACCEPTED]
    Restoration: [text added to compressed version]

TAG 2 — EXCEPTION:
  ...

Restore Rule: Any tag with Criticality = BLOCKING that is NOT preserved MUST be restored.
Risky tags SHOULD be restored. Incomplete tags MAY be accepted with justification.

Restoration Techniques (minimum-length):
- Inline qualifier: "Works well (assuming stable network)" — 4 words
- Caveat footer: Brief "Watch for:" section at the end
- Conditional phrasing: "For standard cases, X. For [edge], use Y instead."
- Confidence signal: "High confidence for typical setups. Untested for [scenario]."
────────────────────────────────────────

Artifact: The fidelity verification with actions taken.

CEI Component: Fidelity Verification (weight 3.0)

Step 5 — COMPRESSION INTEGRITY (if require_integrity_ = true)

NEW IN v2.0 — Formal of compression integrity.

COMPRESSION INTEGRITY 
────────────────────────────────────────
 ID: cic_<timestamp>_<hash>
Full Analysis Tokens: N
Compressed Tokens: M
Compression Ratio: M/N = 0.XX

Critical Tags: N
  Preserved: N (XX%)
  Partially Preserved: N (XX%)
  Dropped: N (XX%)
    Blocking Dropped: N
    Risky Dropped: N
    Incomplete Dropped: N

Fidelity Score: [0.0-1.0]
Integrity Status: [LOSSLESS / ACCEPTABLE / UNACCEPTABLE]

Lossless:     All BLOCKING/RISKY tags preserved. Summary is as true as the analysis.
Acceptable:   Minor INCOMPLETE tags omitted with justification. No decision risk.
Unacceptable: BLOCKING/RISKY tags missing. Revise before delivery.

Restorations Made: [count]
Justified Omissions: [list with reasoning]
────────────────────────────────────────

Artifact: compression_integrity_ — formal verification of compression integrity.

CEI Component: Integrity (weight 3.0)

Step 6 — WRITE THE FIDELITY VERDICT

FIDELITY VERDICT
────────────────────────────────────────
Critical items tagged:     [count]
Preserved in first draft:  [count]
Restored after diff:       [count]
Intentionally omitted:     [count] — [justification per item]

Fidelity Score: [0.0-1.0]
Status: [LOSSLESS / ACCEPTABLE / UNACCEPTABLE]

Lossless:     All critical items preserved. Summary is as true as the analysis.
Acceptable:   Minor items omitted with justification. No decision risk.
Unacceptable: Critical items missing. Revise before delivery.
────────────────────────────────────────

Artifact: The fidelity verdict.

CEI Component: Fidelity Verdict (weight 2.0)

7 — METRICS: Compute and Output Depth Metrics

#### 7.1 Phase Activation (for ADS)

{
  "phase": 4,
  "skill": "fidelity",
  "artifact_completeness": 0.XX,
  "gate_pass_rate": 0.XX,
  "external_validity": 0.XX,
  "human_eval": 0.XX,
  "phase_activation": 0.XX
}

#### 7.2 CEI Components

{
  "cei_components": {
    "critical_tags": 3.0,
    "fidelity_diff": 4.0,
    "compressed_version": 1.0,
    "fidelity_verification": 3.0,
    "integrity_": 3.0,
    "fidelity_verdict": 2.0,
    "total_complexity_weight": 16.0,
    "output_tokens": N,
    "wall_time_seconds": T,
    "cei": 0.XX
  }
}

#### 7.3 SI Components

{
  "si_components": {
    "c2_c3_count": 0,
    "contrarian_viable": false,
    "fatal_attacks": 0,
    "boundary_violations": 0,
    "assumption_reversals": 0,
    "blocking_dropped": N,
    "risky_dropped": N,
    "si_total": N
  }
}

#### 7.4 Cognitive Traces

Fidelity Diff Visualization:

{
  "type": "fidelity_diff",
  "tags": [
    {"tag": "TAG 1", "type": "CONDITION", "match_score": 0.XX, "preserved": true, "criticality": "BLOCKING"},
    {"tag": "TAG 2", "type": "EXCEPTION", "match_score": 0.XX, "preserved": false, "criticality": "RISKY", "action": "RESTORED"}
  ],
  "aggregate": {
    "total": N,
    "preserved": N,
    "partial": N,
    "dropped": N,
    "fidelity_score": 0.XX
  }
}

Compression Integrity : (as defined in Step 5)

#### 7.5 Depth Contribution

{
  "skill": "fidelity",
  "version": "2.0",
  "metrics": {"ads_contribution": 0.XX, "cei": 0.XX, "si": N, "ec": 0.XX},
  "gates_verified": {"V1": true, "V5": true, "V6": true},
  "limitations": ["..."]
}

8 — GATES: Verify Before Delivery

MANDATORY — Verify these gates PASS:

If any gate FAILS: Return to relevant step and fix. Do not deliver.

9 — RECURSIVE SELF-AUDIT (if recursion_depth > 1)

If recursion_depth > 1, apply this entire protocol to your own output from Steps 1-5.

For each recursion level d = 2 to recursion_depth:

1. Treat your previous output as the "answer under review"
2. Run Steps 1-5 on it
3. Compute RSM (Recursive Stability Metric):

   RSM = 1 - Semantic_Distance(output_d, output_{d-1})

1. Convergence Check:

• If RSM > 0.95 AND SI_d ≥ SI_{d-1} for 2 consecutive depths → CONVERGED, stop
• If RSM < 0.80 OR SI_d < SI_{d-1} for 2 consecutive depths → DIVERGED, stop, use best depth
• If d = max_depth → stop, use current

Artifact: recursion_log with RSM and SI at each depth.

CEI Component: Recursive Audit (weight 5.0 per level)

10 — INTERFERENCE: Receive and Provide

Receive from prior skills:

Provide to later skills:

Artifact: interference_log (received and provided).

The Deeper Purpose

The model's best thinking happens during exploration. Its worst habit is discarding that thinking during delivery. If the final answer is a lossy compression of the truth, the user acts on an incomplete version of what the model itself knows is more complex. This skill ensures the distance between what-the-model-knows and what-the-user-receives is minimized — not by being verbose, but by algorithmically verifying that the specific pieces of truth that change decisions survive compression. Now it's quantified (fidelity score), certified (integrity ), and verified (gates).

MATHEMATICS COMPLIANCE

Phase Activation Output

This skill contributes to Phase 4. It outputs:

{
  "phase": 4,
  "skill": "fidelity",
  "artifact_completeness": 0.XX,
  "gate_pass_rate": 0.XX,
  "external_validity": 0.XX,
  "human_eval": 0.XX,
  "phase_activation": 0.XX
}

CEI Components

• Artifacts produced: critical_tags (3.0), fidelity_diff (4.0), compressed_version (1.0), fidelity_verification (3.0), integrity_ (3.0), fidelity_verdict (2.0)
• Total complexity weight: 16.0

SI Components

• C2/C3 assumptions: 0
• Contrarian viable: false
• Fatal attacks: 0
• Boundary violations: 0
• Assumption reversals: 0
• Blocking dropped: [count]
• Risky dropped: [count]

Cognitive Traces Produced

• [x] Fidelity Diff Visualization
• [x] Compression Integrity
• [ ] Decision Landscape

Gates Verified

• [x] V1 [ ] V2 [ ] V3 [ ] V4 [x] V5 [x] V6
• [ ] Human Eval [ ] Held-Out [ ] Ensemble

Required Interferences

• From CONTRADICT: Resolved conflicts → BLOCKING tags
• From PROVENANCE: Evidence tags + EC → uncertainty tagging
• From NEGATIVE-SPACE: Critical silences → BLOCKING omissions
• From BOUNDARY-DETECTOR: Knowledge gaps → BLOCKING dependencies
• From EXCAVATE: C2/C3 assumptions → BLOCKING conditions