entry

# 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**