{PROBLEM_NAME}¶
Source: {wikipedia URL section / list of unsolved problems entry} Status: open / (a) SURVIVES / (b) REFINED / © FALSIFIED Cascade dispatched: YYYY-MM-DD or "awaiting dispatch" Class cascade: {e.g., A∘L∘N∘M∘I}
1. Problem statement¶
Formal statement of the problem, in its standard mathematical form. Cite the canonical source (Hilbert's lecture, Riemann's 1859 paper, etc.) at OA / textbook level only per [[feedback_paywalled_doi_cannot_be_attested]].
2. Why it is open¶
Brief historical context: what's been tried, where the difficulty has been located, what the current best known bound / partial result is. Cite OA references with arXiv IDs where available.
3. Framework reading¶
What is this problem AS A CASCADE-SHAPE QUESTION? Reframe the statement so the 14-class operators (A-N) can address it. The reframe is the load-bearing step — most open problems become tractable once expressed in cascade-vocabulary.
Per [[user_stance_identity_not_implementation_discipline]]: the framework READS what the problem IS at substrate-level; it does not OVERWRITE the mathematical statement.
4. Cascade composition¶
The proposed cascade of primitive classes. Each step names: - Which class operates - What input it consumes (from previous step or from data) - What output it produces (input to next step or final result) - Why this composition is structurally appropriate (NOT result-driven)
Per [[feedback_dont_pre_commit_spike_query_operators]]: design the cascade for broad-query enumeration; don't lean the composition toward an expected verdict; let null findings count.
| Step | Class | Operation | Input | Output |
|---|---|---|---|---|
| 1 | A | content-address | … | hash |
| 2 | L | Laplacian + eigendecompose | … | spectrum |
| 3 | N | rationalize ratio | … | exact integer bound |
| 4 | M | HDC encode + check | … | feasibility |
| 5 | I | cyclic homomorphism verify | … | yes/no |
5. Configuration data needed (AMSC catalog)¶
What records does the catalog need? List the schema fields and any reference data the cascade consumes. Link to descriptor.toml + schema.json + *.ndjson in this directory.
6. Cascade execution¶
Reference generate_catalog.py in this directory. Run with:
Or via AMSC bridge:
from srmech.amsc.catalog import register_attested_root, get_attested_dataset
register_attested_root("docs/unsolved-maths", source="unsolved_maths_research")
ds = get_attested_dataset("{source_key}")
7. Findings¶
What does the cascade reveal? Report verdict-tier honestly per [[feedback_dont_pre_commit_spike_query_operators]]:
- (a) SURVIVES: cascade composition is internally consistent; no structural obstruction found. NOT a "proof" — just absence of falsification on the dispatched test set.
- (b) REFINED: cascade reveals a sharper reformulation. State the refined claim and what changed.
- © FALSIFIED: cascade finds a counter-example or structural inconsistency. State exactly what falsifies.
- (open): cascade dispatched but inconclusive. State the open fermata.
8. Open fermatas¶
What remains open after the cascade runs? List specific testable sub-questions for future dispatches. Use spike-research numbering if dispatched.
9. Citations¶
Per [[feedback_pdf_extraction_citation_discipline]]: all citations PDF-verified at dispatch time. Per [[feedback_paywalled_doi_cannot_be_attested]]: OA / arXiv / open textbook only.
- Author Year Journal vol:pages — arXiv:XXXX.XXXXX (description)
- ...
10. Cross-references¶
- srmech catalog:
<source_key>(registered viaregister_attested_root) - Related canonical stances:
[[user_stance_...]] - Related spike research: Spike-research #...
- Related MFO / srmech notebook sections: §...