majiayu000 Docs ACSet Skill
Transform Google Docs/Sheets into an ACSet-condensed system with GF(3) conservation.
Trit: 0 (ERGODIC - coordinator)
Principle: Published Document = Condensed State
Implementation: DocsACSet + CommentTracker + CellSaturation
Overview
Docs ACSet applies category-theoretic structure to documents:
- Transform - Documents/Sheets → GF(3)-typed Interactions
- Track - Comments/Cells → Saturation state
- Detect - All resolved → ANIMA condensed state
- Verify - Narya proofs for consistency
DocsACSet Schema
┌────────────────────────────────────────────────────────────────────┐
│ DocsACSet Schema │
├────────────────────────────────────────────────────────────────────┤
│ │
│ Document ────────┬────▶ Section │
│ ├─ doc_id: String│ ├─ heading: String │
│ ├─ title: String │ ├─ level: Int │
│ └─ published: Bool └─ content_hash: String │
│ │ │
│ Comment ─────────┼────▶ Thread (doc) │
│ ├─ content: String ├─ resolved: Bool │
│ ├─ author: String └─ reply_count: Int │
│ └─ trit: Trit │ │
│ │ │
│ Spreadsheet ─────┼────▶ Sheet │
│ ├─ ss_id: String │ ├─ name: String │
│ └─ locale: String └─ row_count: Int │
│ │ │
│ Cell ────────────┴────▶ Range │
│ ├─ value: String ├─ a1_notation: String │
│ ├─ formula: String └─ dirty: Bool │
│ └─ trit: Trit │
└────────────────────────────────────────────────────────────────────┘
Objects
| Object | Description | Trit Role |
|---|---|---|
Document |
Google Doc with publish state | Aggregate |
Section |
Heading-delimited content block | Node |
Comment |
Review comment with resolution state | Interaction |
Spreadsheet |
Google Sheets workbook | Aggregate |
Sheet |
Individual tab within spreadsheet | Node |
Cell |
Single cell with value/formula | Data |
GF(3) Verb Typing
Docs/Sheets actions assigned trits based on information flow:
VERB_TRIT_MAP = {
# MINUS (-1): Consumption/Reading
"get_doc_content": -1, "read_sheet_values": -1,
"get_spreadsheet_info": -1, "inspect_doc_structure": -1,
"read_document_comments": -1, "debug_table_structure": -1,
# ERGODIC (0): Coordination/Metadata
"modify_doc_text": 0, "find_and_replace_doc": 0,
"update_doc_headers_footers": 0, "resolve_document_comment": 0,
"create_sheet": 0, "reply_to_document_comment": 0,
# PLUS (+1): Generation/Creation
"create_doc": +1, "create_spreadsheet": +1,
"insert_doc_elements": +1, "insert_doc_image": +1,
"create_table_with_data": +1, "modify_sheet_values": +1,
"create_document_comment": +1, "export_doc_to_pdf": +1,
}
MCP Tool → Trit Mapping
| Tool | Trit | Description |
|---|---|---|
get_doc_content |
-1 | Read document (MINUS) |
read_sheet_values |
-1 | Read cells (MINUS) |
read_document_comments |
-1 | Read comments (MINUS) |
modify_doc_text |
0 | Edit text (ERGODIC) |
resolve_document_comment |
0 | Resolve thread (ERGODIC) |
create_doc |
+1 | Create document (PLUS) |
create_spreadsheet |
+1 | Create workbook (PLUS) |
modify_sheet_values |
+1 | Write cells (PLUS) |
Doc-Thread Morphism
Documents and Gmail threads form a natural morphism:
┌─────────────────────────────────────────────────────────────────┐
│ Doc-Thread Morphism │
├─────────────────────────────────────────────────────────────────┤
│ │
│ Document ◀─────────────▶ Thread │
│ ├─ doc_id ├─ thread_id │
│ ├─ published ├─ saturated │
│ └─ all_comments_resolved └─ needs_action │
│ │
│ Functorial mapping: │
│ F(doc) = thread where doc shares via gmail │
│ F(comment) = message in review workflow │
│ F(resolve) = archive/reply │
│ │
└─────────────────────────────────────────────────────────────────┘
Workflow Paths
# Doc → Email (share for review)
share_path = doc_read >> email_compose # -1 + 1 = 0 ✓
# Email feedback → Doc update
feedback_path = email_read >> doc_modify >> comment_resolve
# -1 + 0 + 0 = -1 (needs PLUS balance)
balanced = feedback_path >> doc_export # -1 + 1 = 0 ✓
Saturation Detection
Saturation occurs when all comments are resolved:
def is_saturated(doc_id: str) -> bool:
"""Document is saturated when:
1. All comments resolved (no open threads)
2. GF(3) cycle closure: sum(trits) ≡ 0 (mod 3)
3. Published state stable
"""
comments = get_all_comments(doc_id)
all_resolved = all(c.resolved for c in comments)
cycle_sum = sum(c.trit for c in comments)
return all_resolved and (cycle_sum % 3) == 0
ANIMA Detection
def detect_anima(doc_ids: List[str]) -> Dict:
"""System at ANIMA when:
1. All documents saturated (comments resolved)
2. All spreadsheets consistent (no dirty cells)
3. GF(3) conserved globally
"""
return {
"at_anima": all_docs_saturated and all_sheets_clean,
"condensed_fingerprint": sha256(all_content_hashes),
"published_count": sum(1 for d in docs if d.published),
}
Published Document as ANIMA: When all comments are resolved and document is published, it's in condensed equilibrium.
Source Files
| File | Description | Trit |
|---|---|---|
| docs_acset.py | ACSet schema + comment tracking | 0 |
| sheet_saturation.py | Cell dirty state + formula deps | 0 |
| doc_thread_morphism.py | Functorial Doc↔Gmail mapping | 0 |
Workflows
Workflow 1: Document Review to Saturation
from docs_acset import DocsACSet
acset = DocsACSet("user@gmail.com")
# MINUS: Read document and comments
doc = acset.get_doc_content(doc_id) # trit=-1
comments = acset.read_document_comments(doc_id) # trit=-1
# ERGODIC: Process each comment
for comment in comments:
acset.reply_to_document_comment(doc_id, comment.id, "Addressed")
acset.resolve_document_comment(doc_id, comment.id) # trit=0
# PLUS: Export final version
acset.export_doc_to_pdf(doc_id) # trit=+1
# GF(3): -1 + -1 + 0 + 1 = -1 (needs one more PLUS)
Workflow 2: Spreadsheet Update Cycle
# MINUS: Read current state
values = acset.read_sheet_values(ss_id, "A1:Z100") # trit=-1
# PLUS: Write updates
acset.modify_sheet_values(ss_id, "A1:B10", new_data) # trit=+1
# ERGODIC: Add new sheet for audit
acset.create_sheet(ss_id, "Audit Log") # trit=0
# GF(3): -1 + 1 + 0 = 0 ✓
Workflow 3: Cross-Document Sync
# Read source doc
source = acset.get_doc_content(source_id) # -1
# Create target from template
target = acset.create_doc("Derived Document", source.content) # +1
# Link via comment
acset.create_document_comment(target.id, f"Derived from {source_id}") # +1
# Balance needed: -1 + 1 + 1 = 1 → add MINUS
acset.read_document_comments(target.id) # -1 → total = 0 ✓
Integration with Other Skills
| Skill | Trit | Integration |
|---|---|---|
| google-workspace | 0 | MCP tool provider |
| gmail-anima | 0 | Thread↔Doc morphism |
| gay-mcp | +1 | SplitMixTernary RNG |
| sheaf-cohomology | -1 | Section consistency |
| acsets-algebraic-databases | 0 | Schema foundation |
GF(3) Triadic Conservation
docs-acset (0) ⊗ gmail-anima (0) ⊗ sheaf-cohomology (-1) + gay-mcp (+1) = 0 ✓
read (-1) ⊗ modify (0) ⊗ create (+1) = 0 ✓
comment (-1) ⊗ reply (0) ⊗ resolve (0) + export (+1) = 0 ✓
Skill Name: docs-acset
Type: Document Management / ACSet Framework
Trit: 0 (ERGODIC - coordinator)
GF(3): Conserved via verb typing
ANIMA: Published Document = Condensed State
Scientific Skill Interleaving
This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:
Annotated Data
- anndata [○] via bicomodule
Bibliography References
general: 734 citations in bib.duckdb
SDF Interleaving
This skill connects to Software Design for Flexibility (Hanson & Sussman, 2021):
Primary Chapter: 10. Adventure Game Example
Concepts: autonomous agent, game, synthesis
GF(3) Balanced Triad
docs-acset (+) + SDF.Ch10 (+) + [balancer] (+) = 0
Skill Trit: 1 (PLUS - generation)
Secondary Chapters
- Ch7: Propagators
- Ch3: Variations on an Arithmetic Theme
- Ch6: Layering
- Ch1: Flexibility through Abstraction
Connection Pattern
Adventure games synthesize techniques. This skill integrates multiple patterns.
Cat# Integration
This skill maps to Cat# = Comod(P) as a bicomodule in the equipment structure:
Trit: 0 (ERGODIC)
Home: Prof
Poly Op: ⊗
Kan Role: Adj
Color: #26D826
GF(3) Naturality
The skill participates in triads satisfying:
(-1) + (0) + (+1) ≡ 0 (mod 3)
This ensures compositional coherence in the Cat# equipment structure.