# ENTRY.md — Sequence Dojo Entry Specification (Draft v0.1)
See also:
* [REVEAL.md](./REVEAL.md) (Archive phase produces Entries)
* [SPEC.md](./SPEC.md) (published record format and canonicalization)
* [RULES.md](./RULES.md) (competition context for solver lineage)
## 1. Purpose
An **Entry** is the canonical, archival record of a Sequence Dojo problem after Reveal (the Archive phase in [REVEAL.md](./REVEAL.md)).
Each Entry represents:
* A well-defined integer sequence
* Its generating mechanism (setter program)
* Its mathematical structure and properties
* Its verification hash commitment
* Its reference and solution lineage
An Entry is intended to be:
* Reproducible
* Citable
* Versioned
* Stable
---
## 2. Entry Identification
Each entry must have a unique identifier:
```
SD-Axxxx
```
Example:
```
SD-A0001
```
This identifier must remain permanent once published.
---
## 3. Entry Structure
Each Entry must contain the following sections in order.
---
## 4. Header
```
# SD-A0001 — [Short Descriptive Title]
```
### Metadata Block
```
Entry ID: SD-A0001
Problem Title: Trial 002
Published: YYYY-MM-DD
Reveal Date: YYYY-MM-DD
Version: 1.0
P_hash (SHA-256): <hash>
Platform Environment:
Python: 3.x
sympy: x.y.z
Canonicalization Policy:
UTF-8 + LF normalization + strip trailing blank lines + preserve all other bytes
```
This block must not change across versions except `Version`.
---
## 5. Definition
### 5.1 Primary Mathematical Definition
Provide the cleanest mathematical definition possible.
Example:
`a_n = 2^{floor((n+5)/2)} - 2n - 5`
Or, if recursive:
`a_{n+1} = f(a_n, n)`
If multiple equivalent forms exist, list the simplest first.
---
### 5.2 Program Definition (Canonical Source)
Include the canonical setter source exactly as revealed:
```python
def seq(n: int) -> int:
exponent = (n + 5) // 2
return (1 << exponent) - 2 * n - 5
```
The source must correspond to `P_hash`.
---
## 6. Initial Terms
Provide a verified prefix:
```
a_0 = ...
a_1 = ...
...
a_20 = ...
```
Optionally include:
* First 200 terms inline (or downloadable)
* Link to machine-readable JSON
---
## 7. Structural Properties
Document known properties.
### 7.1 Growth Behavior
* Asymptotic growth
* Order of magnitude
* Dominant term
### 7.2 Recurrence (if any)
### 7.3 Generating Function (if known)
### 7.4 Modular or Divisibility Properties
### 7.5 Relations to Known Sequences
* Linear transforms of Fibonacci?
* Subsequence of another SD entry?
* Corresponding OEIS entry (if applicable)
---
## 8. Derivation / Explanation
A short conceptual explanation:
* Why does this structure arise?
* What is the hidden mechanism?
* Why does the disclosed pattern look misleading (if applicable)?
If a formal proof exists, summarize and optionally link to a longer document.
---
## 9. Solver Lineage
Document representative correct solver approaches.
For each selected solver:
```
Solver ID: user_handle
Method Tag: closed_form / recurrence / matrix / symbolic_guess / other
Program Length (chars): XXXX
Notes: short explanation
```
This section illustrates diversity of reasoning.
---
## 10. Difficulty Statistics
Optional but recommended.
```
Total Solvers: X
Stage Pass (100 correct): Y
Reward Correct (200 correct): Z
Branch Count at 100: K
```
This provides empirical difficulty data.
---
## 11. References
Provide academic references where applicable.
Example:
* Author, Title, Journal, Year
* DOI
* Related OEIS ID
Use standard citation format (BibTeX preferred).
---
## 12. Related Entries
List cross-links:
* SD-A0003 (shared recurrence)
* SD-A0011 (same growth family)
Entries should form a network, not isolated pages.
---
## 13. Revision History
```
v1.0 — Initial reveal publication.
v1.1 — Added generating function.
v1.2 — Corrected asymptotic description.
```
Rules:
* `P_hash` must never change.
* If the generating program changes, it is a new Entry ID.
* Mathematical clarifications increment the version number.
---
## 14. Archival Principles
An Entry must:
* Remain permanently accessible
* Preserve the original setter logic
* Maintain hash-verifiable integrity
* Allow independent reproduction
The Entry is a mathematical object, not merely a competition artifact.
---
## 15. Optional Extensions (Future)
In later versions, entries may include:
* Machine-verifiable proof artifacts
* Symbolic derivation scripts
* Automated property detection reports
* External citation metrics
---
## 16. Philosophy
Each Entry represents:
> A discovered generative structure reconstructed from partial observation.
Sequence Dojo Entries are intended to function as:
* Experimental mathematics artifacts
* Structured sequence encyclopedia objects
* Reproducible generative definitions
---
Version: **ENTRY.md v0.1**