# Erdős Problems 1–100 prospective resolution cohort

- **Series role:** primary outcome
- **Construct:** verified mathematical resolution
- **Cohort:** all integer-numbered Erdős Problems 1–100
- **Freeze:** 19 August 2026
- **Frozen upstream commit:** `881735e82124ab8ad7adea9b7d0aeb3c026dcb95`
- **Current status:** monitoring; prospective baseline only; causality unresolved

## Why this cohort exists

A mathematical-discovery series needs a denominator fixed before the outcomes are observed. Selecting only famous solved problems after the fact would make the measured rate depend on editorial hindsight.

This panel therefore freezes one simple membership rule:

> Include all and only integer-numbered Erdős Problems 1 through 100 at the named upstream commit.

Every problem stays in the register. The cohort is not expanded when an interesting new problem appears, and an existing member is not removed because its status becomes awkward.

## Baseline

At the freeze, the 100 problems contain:

- **54 at-risk problems**;
- **46 resolved-before-freeze problems**;
- **0 verified resolutions after the freeze**;
- **40 prize problems**;
- **69 formally stated problems**;
- **15 problems with a formalized solution**.

The human-reviewed informal statuses are:

| Status | Problems | Baseline role |
|---|---:|---|
| Open | 49 | At risk |
| Falsifiable | 3 | At risk |
| Verifiable | 1 | At risk |
| Decidable | 1 | At risk |
| Proved | 31 | Resolved before freeze |
| Disproved | 12 | Resolved before freeze |
| Solved | 3 | Resolved before freeze |

Formalization is retained as a quality dimension. It does not silently replace the human-reviewed mathematical status.

## What becomes an event

A prospective resolution event must contain:

1. the frozen problem number;
2. the baseline and new human-reviewed status;
3. a defensible solution date;
4. a defensible verification date;
5. a named primary result source;
6. a named verification source or checking basis;
7. a separate AI-attribution assessment.

The event is added to `events.json` only after review. A change in the upstream YAML is merely a candidate for review.

## Dates

**Catalogue-maintenance date:** the upstream field `informal_status.last_update` records catalogue maintenance. It is not assumed to be the date when the mathematics was discovered, announced, published, or verified.

The frozen catalogue dates in this cohort range from 17 February 2025 to 7 June 2026. They are retained for auditability but are not turned into a historical discovery curve.

This rule is the central epistemic safeguard of the panel. Without it, an old theorem entered into a database in 2026 could be misreported as a 2026 discovery.

## Prospective risk set

The at-risk baseline consists of problems whose human-reviewed informal status is:

```text
open
falsifiable
verifiable
decidable
```

The risk set begins at 54 and declines only when a prospective event passes the verification rule. Problems already marked proved, disproved, or solved remain visible in the cohort but do not enter the post-freeze risk set.

The primary future rate is:

```text
verified resolutions / unresolved problem-time at risk
```

The first release reports the exact zero-event baseline. It does not annualize a partial zero-event period or call it stagnation.

## AI attribution

**No AI exposure is assigned at baseline.**

A future event may receive AI attribution only when the method evidence supports it. The intended bands distinguish:

- documented model transcripts, logs, or artifacts;
- explicit author reports of material AI assistance;
- weaker public statements;
- affiliation or tool availability alone;
- unknown attribution.

An AI-attempt link, an AI-company affiliation, or the existence of a formalized statement does not by itself establish that AI contributed to the resolution.

## Source, license, and changes

The source is the community-maintained [`teorth/erdosproblems`](https://github.com/teorth/erdosproblems) database. Its `data/problems.yaml` file is described by that project as its ground truth.

This repository vendors the exact source snapshot at:

```text
Commit: 881735e82124ab8ad7adea9b7d0aeb3c026dcb95
SHA-256: 69719796f01fbe3a33913d14d1307502fa4361a307fa8e4674d20163a745eb0c
```

The source is licensed under Apache License 2.0. A copy is included in `SOURCE-LICENSE.txt`; `SOURCE-NOTICE.md` records the transformation and attribution.

## Rebuild and monitoring

Refresh the frozen source-derived files:

```sh
python3 -m pip install PyYAML==6.0.2
python3 series/fixed-mathematics-problem-cohorts/fetch.py
python3 series/fixed-mathematics-problem-cohorts/fetch.py --from-snapshot
python3 series/fixed-mathematics-problem-cohorts/apply.py
python3 series/fixed-mathematics-problem-cohorts/check.py
```

Compare the current upstream state with the frozen cohort:

```sh
python3 series/fixed-mathematics-problem-cohorts/monitor.py
```

For a read-only freshness check:

```sh
python3 series/fixed-mathematics-problem-cohorts/monitor.py --check
```

The comparison writes field-level differences to `candidate-changes.json`. It never rewrites the baseline and never creates a resolution event automatically.

## Files

- `raw/problems.yaml` — exact upstream snapshot.
- `cohort.json` — normalized register of all 100 problems.
- `summary.json` — baseline counts, tags, source hash, and interpretation.
- `candidate-changes.json` — current upstream differences awaiting review.
- `events.json` — verified prospective resolution events; empty at the freeze.
- `fetch.py` — source snapshot and baseline builder.
- `monitor.py` — prospective upstream comparison.
- `apply.py` — tracker registry and baseline-observation updater.
- `check.py` — independent consistency and public-claim checker.

## Limitations

- Problems 1–100 form a fixed and intelligible cohort, not a representative random sample of mathematics.
- Problem difficulty and importance vary sharply.
- Status updates can lag the underlying mathematical work.
- The panel begins prospectively and cannot reconstruct a trustworthy historical rate from catalogue update dates.
- Zero post-freeze events provide no evidence yet about acceleration.
- Even a later increase in resolution rate would not identify an AI effect without structured attribution or a credible comparison.

## Methodological inspiration

The fixed-risk-set design and the insistence on rebuildable source records were inspired in part by METR's [“LLMs' Contribution to Discoveries”](https://metr.org/notes/2026-08-14-llm-contribution-to-discoveries/) and Thomas Cunningham's public [`ai-discovery-data`](https://github.com/tecunningham/ai-discovery-data) repository.

The cohort definition, source snapshot, status policy, prospective event rule, checks, and presentation in this tracker are independently implemented.