Survey Theoretical Literature

Structured survey on defined topic → synthesis mapping seminal contributions, chronological dev, open problems, cross-domain connections.

Use When

• Start research unfamiliar topic, map landscape
• Lit review for paper/thesis/grant
• ID open probs + gaps in field
• Find connections between result + adjacent fields
• Eval novelty of proposed contribution

In

• Required: Topic desc (specific enough to bound search; e.g. "topological phases in non-Hermitian systems" not just "topology")
• Required: Scope (time, subfields in/out, theoretical vs experimental)
• Optional: Known seed papers (anchor search)
• Optional: Audience + depth (intro overview vs expert)
• Optional: Output format (annotated bib, narrative, concept map)

Do

Step 1: Define Scope + Search Terms

Bound precisely before search.

1. Core topic statement: 1 sentence defining survey scope. Acceptance criterion for paper inclusion.
2. Search terms:
   • Primary: exact tech phrases (Kohn-Sham eqns, Berry phase, RG)
   • Secondary: broader/adjacent (geometric phase = Berry phase synonym)
   • Exclusion: prevent irrelevant ("Berry" botanical)
3. Temporal: Define window. Mature field → seminal decades old, recent narrow to last 5-10y. Emerging → entire history few years.
4. Domain boundaries: Subfields in vs out. e.g. quantum error correction → topological codes IN, classical coding theory OUT.

## Survey Scope
- **Core topic**: [one-sentence definition]
- **Primary search terms**: [list]
- **Secondary search terms**: [list]
- **Exclusion terms**: [list]
- **Time window**: [start year] to [end year]
- **In scope**: [subfields]
- **Out of scope**: [subfields]

Got: Scope tight enough → 2 researchers independently agree on inclusion.

If err: Too broad (>~200 papers) → narrow w/ subfield constraints | tighten time. Too narrow (<~10) → broaden secondary | extend time.

Step 2: ID Seminal Papers + Key Results

Build backbone from most influential.

1. Seed-based: Start from seeds (or most recent review). Trace refs back + citations forward → repeated papers.
2. Citation count heuristic: Rough proxy for influence. Weight recent (5y) more (less time to accumulate).
3. Seminal criteria: ≥1 of:
   • Introduced foundational concept, formalism, method
   • Proved result that redirected field
   • Unified disparate strands
   • Cited by majority of subsequent papers
4. Key result extraction: per seminal:
   • Main result (theorem, eqn, prediction, method)
   • Assumptions/approximations
   • Impact on subsequent work

## Seminal Papers
| # | Authors (Year) | Title | Main Result | Impact |
|---|---------------|-------|-------------|--------|
| 1 | [authors] ([year]) | [title] | [one-sentence result] | [influence on field] |
| 2 | ... | ... | ... | ... |

Got: 5-15 seminal papers = backbone, each w/ result + impact.

If err: No clear seminals → topic too new | too niche. ID earliest + most-cited as anchors, note canonical refs not yet emerged.

Step 3: Map Chronological Development

Trace evolution origins → present.

1. Origin: When + where core ideas first appeared. Within field | imported from another?
2. Growth: Initial generalized, applied, challenged. Key turning points (new proof tech, unexpected counterex, exp confirmation).
3. Branching: Where lit branches → sub-topics. Per branch: focus + relationship to trunk.
4. Current: Mature (consolidating) | active (rapid dev) | stagnant (few recent)?
5. Timeline: Build chronological of most important devs.

## Chronological Development

### Origin ([decade])
- [event/paper]: [description of foundational contribution]

### Key Developments
- **[year]**: [milestone and its significance]
- **[year]**: [milestone and its significance]
- ...

### Branching Points
- **[year]**: Field splits into [branch A] and [branch B]
  - Branch A focuses on [topic]
  - Branch B focuses on [topic]

### Current State ([year])
- **Activity level**: [mature / active / emerging / stagnant]
- **Dominant approach**: [current mainstream methodology]
- **Recent trend**: [direction of latest work]

Got: Narrative timeline → newcomer can read + understand how field arrived current state.

If err: Chronology unclear (multi independent discoveries, disputed priority) → doc ambiguity vs imposing false linear narrative. Parallel timelines OK.

Step 4: ID Open Problems + Frontiers

Catalog unknown/unresolved.

1. Explicitly open: Search reviews, problem lists, surveys w/ open questions. Many fields → canonical lists (Clay Millennium, Hilbert's, open probs in QI).
2. Implicitly open: Conjectured-not-proven, numerical observations w/o theory, theory-vs-experiment discrepancies.
3. Active frontiers: Topics most attention last 2-3y. High preprint rate, conf sessions, funding calls.
4. Barriers: Per major problem, why hard? What math/conceptual obstacle?
5. Potential impact: Resolution → incremental (gap fill) | transformative (changes field thinking)?

## Open Problems and Frontiers

### Explicitly Open
| # | Problem | Status | Barrier | Potential Impact |
|---|---------|--------|---------|-----------------|
| 1 | [statement] | [conjecture / partial / open] | [why hard] | [incremental / significant / transformative] |
| 2 | ... | ... | ... | ... |

### Active Frontiers
- **[frontier topic]**: [what is happening and why it matters]
- ...

### Implicit Gaps
- [observation without theoretical explanation]
- [conjecture without proof]
- ...

Got: Cataloged ≥3-5 open problems w/ difficulty assessments + characterization of most active frontiers.

If err: No open problems apparent → scope too narrow (sub-topic solved) | search missed relevant reviews. Broaden | search "open problems in [topic]" + "future directions in [topic]".

Step 5: Cross-Domain Connections + Final Survey

Connect to adjacent + assemble.

1. Cross-domain:

   • Shared math structures (same eqn in optics + QM)
   • Analogies + dualities (AdS/CFT → gravity + field theory)
   • Methodological imports (ML applied to theoretical physics)
   • Experimental connections (predictions testable in cold-atom | photonic)

2. Connection quality: per connection:

   • Deep (structural equiv, proven duality)
   • Promising (suggestive analogy, active investigation)
   • Superficial (surface similarity, no proven relationship)

3. Gap analysis: Connections that should exist but unexplored = research opportunities.

4. Survey assembly: Compile Steps 1-5 → structured doc:

   • Exec summary (1 para)
   • Scope + methodology (Step 1)
   • Historical dev (Step 3)
   • Key results + seminal (Step 2)
   • Open probs + frontiers (Step 4)
   • Cross-domain (this step)
   • Bibliography

## Cross-Domain Connections
| # | Connected Field | Type of Connection | Depth | Key Reference |
|---|----------------|-------------------|-------|---------------|
| 1 | [field] | [shared math / analogy / method import] | [deep / promising / superficial] | [paper] |
| 2 | ... | ... | ... | ... |

## Unexplored Connections (Research Opportunities)
- [potential connection]: [why it might exist and what it could yield]
- ...

Got: Complete structured survey doc mapping topic origins → frontiers w/ cross-domain ID + assessed.

If err: Disjointed → revisit chronological timeline (Step 3) as organizing spine. Every seminal, open prob, cross-domain locatable on timeline.

Check

• Scope precisely defined w/ in+out criteria
• Seminal papers ID'd w/ main results + impact
• Chronological dev traced w/ key milestones
• ≥3-5 open problems cataloged w/ difficulty + impact
• Cross-domain ID'd + depth assessed
• Bib has all cited papers w/ complete ref info
• Newcomer can read + understand landscape
• Survey distinguishes established vs conjectures vs open
• Time of writing stated → readers assess currency

Traps

• Scope creep: Started focused → expanded to everything tangential. Core topic sentence (Step 1) = acceptance criterion. Enforce ruthless.
• Recency bias: Over-rep recent at expense of foundational. 2024 w/ 10 citations may < 1980 w/ 5000. Weight influence not novelty.
• Citation count worship: Sole measure of importance. Highly cited can be methodological tools (widely used, not conceptually deep). Transformative in niche fields may be less cited.
• Missing negative results: Failed attempts + disproven conjectures = part of history. Omitting → misleadingly smooth narrative.
• Superficial cross-domain: Claim connection because same word ("entropy" in thermo + info theory related; "gauge" in physics + knitting NOT). Assess depth before include.
• Presentism: Judging historical by modern standards. 1960 paper → eval given known in 1960, not what failed to anticipate.

→

• formulate-quantum-problem — formulate specific problems ID'd during survey
• derive-theoretical-result — derive | re-derive key results found
• review-research — eval individual papers encountered