erdos-problems

Maintained by SproutSeeds. Research stewardship: Fractal Research Group (frg.earth).

CLI and workspace for Paul Erdos problems.

Browse the atlas, scaffold a dossier, and keep public status, local route state, and verification records separate.

erdos-problems
atlas -> dossier -> pack -> checkpoint -> archive

erdos-problems is a CLI for working with Paul Erdos problems. It bundles problem records, local dossiers, workspace scaffolding, and pack-specific views for the problems that already have more structure in this repo.

Links: GitHub · npm

Watch It Run

A short example from the first minute:

What It Includes

• a bundled external atlas import snapshot for provenance and seeding
• local dossiers and workspace bundles
• separate surfaces for public status, local route state, and verification records
• pack-specific views where this repo already has enough structure to support them
• an ORP-based workflow for claims, checkpoints, and run artifacts
• an integrated research stack surface that ties canonical imports, ORP, theorem loops, compute lanes, and writeback commands together
• a paper writer bundle mode for public-safe, citation-safe, agent-friendly drafting

Repo, npm, and External Imports

• SproutSeeds/erdos-problems is the canonical public home for this project's atlas, dossiers, packs, and contribution workflow
• the npm package is the installable CLI plus the bundled import snapshot, packaged dossiers, and packaged pack assets
• the GitHub repo is the broader public collaboration space for dossiers, pack packets, docs, issues, discussions, PRs, and future deep research bundles
• .erdos/ is local workspace state created by the CLI; it is not canonical repo truth
• erdos import show reports whether you are using the bundled import snapshot or a workspace-local refreshed import snapshot
• erdos import sync currently refreshes an external atlas import snapshot from teorth/erdosproblems without mutating the canonical local dossier layer
• erdos import sync --write-package-snapshot is the maintainer path for intentionally updating the bundled import snapshot in this repo
• most deep-research directories such as formal/, paper/, imports/, and analysis/ remain repo-only and are intentionally kept out of npm
• research/frontier-engine is the current exception: it ships as an optional bundled subsystem so users can opt into GPU-oriented frontier search without making base npm install heavier
• repo-only public research can live in this GitHub repo without shipping in the npm tarball; see the contribution guide: https://github.com/SproutSeeds/erdos-problems/blob/main/CONTRIBUTING.md

Start In 60 Seconds

Install:

npm install -g erdos-problems

If you already know the problem you want, the fastest path is:

erdos bootstrap problem 857
erdos sunflower frontier 857
erdos sunflower ready 857
erdos workspace show --json

If you want the optional frontier-engine runtime, keep it explicit:

erdos frontier doctor
erdos frontier setup --base
erdos frontier setup --cpu
erdos frontier setup --cuda --torch-index-url <url>
erdos frontier create-brev erdos-h100 --gpu-name H100 --dry-run
erdos frontier create-brev-fleet erdos-h100x2 --type hyperstack_H100 --count 2 --dry-run
erdos frontier attach-brev --instance <name> --apply
erdos frontier sync-fleet erdos-h100x2 --lane p848_anchor_ladder --apply
erdos number-theory dispatch-fleet 848 --fleet erdos-h100x2 --apply --action gpu_profile_sweep --strategy ladder_cover_v1

The Brev path is meant to be a native frontier rung: preview hardware with create-brev --dry-run, then create, attach, and sync a lane into the same SSH-backed frontier loop used by local and fixed remote boxes.

To see how the whole stack connects for the active problem:

erdos workspace show
erdos preflight

Those views now summarize:

• canonical source and import provenance
• ORP/checkpoint workflow
• theorem-loop entry and refresh commands
• compute entrypoints and hardware setup
• canonical writeback surfaces

If you want to start from a new local seed:

erdos seed problem 25 --cluster number-theory
erdos problem show 25
erdos checkpoints sync

Beginner Flow

This is the zero-assumption path for a new user.

1. Install the CLI once

npm install -g erdos-problems

This gives you a global erdos command. The workspace state it creates is local to the folder you are in.

2. Make a clean working folder

mkdir erdos-work
cd erdos-work

Later, the CLI will create a local .erdos/ directory here for workspace state, checkpoints, ORP files, and pulled artifacts.

3. Browse everything first

erdos problem list

Use this when you do not yet know a problem number or cluster.

4. Inspect one problem in plain English

erdos problem show 857

This shows the title, status, cluster, short statement, and research-state posture for that problem.

5. Learn the families only after that

erdos cluster list
erdos cluster show sunflower

Once you know what a cluster is, you can narrow the atlas:

erdos problem list --cluster sunflower

6. Start a workspace on a well-packaged problem

erdos bootstrap problem 857

What this does:

• creates .erdos/ in the current folder
• activates the problem locally
• syncs the ORP kit
• scaffolds the workspace for the next research move

7. Orient yourself immediately

erdos workspace show
erdos state show
erdos problem artifacts 857 --json

Use these to understand the workspace layout, current route/frontier state, and the artifact surface that already exists for the problem.

8. Run the first honest-state sync

erdos orp sync
erdos state sync
erdos preflight

This refreshes the protocol kit, recomputes local research state, and checks whether the workspace is in a sane posture to continue.

9. Set your continuation mode

erdos continuation show
erdos continuation use route

For most new users, route is the right default. It keeps the loop focused on the current route instead of bouncing between surfaces.

10. Sync checkpoints before doing real work

erdos checkpoints sync

This writes the checkpoint shelf and keeps the workspace history honest.

11. Look at the actual frontier

erdos sunflower status 857
erdos sunflower frontier 857
erdos sunflower ready 857

This is where the problem becomes actionable instead of just descriptive.

12. Drill down to the next unit of work

erdos sunflower routes 857
erdos sunflower ticket 857 T10
erdos sunflower atom 857 T10.G3.A2

That is the real research loop:

• inspect route
• inspect ticket
• inspect atom
• do the next honest move

13. Close the loop cleanly

erdos state sync
erdos checkpoints sync
erdos workspace show

If the problem is not already deeply packaged, use one-step local seeding instead of bootstrapping:

erdos seed problem 25 --cluster number-theory
erdos preflight
erdos continuation use route
erdos checkpoints sync
erdos workspace show

In that flow, the seeded dossier is written under .erdos/seeded-problems/<id>/ and enters the same state/checkpoint loop as packaged dossiers.

Daily Loop

Once a workspace already exists, this is the main operating loop:

erdos state sync
erdos preflight
erdos continuation use route
erdos checkpoints sync
erdos workspace show

Then inspect the current frontier and active unit of work:

erdos sunflower frontier 857
erdos sunflower atom 857 T10.G3.A2

After a real step, sync checkpoints again:

erdos checkpoints sync

The guiding rule is simple:

• inspect frontier
• work the next honest move
• checkpoint at honest boundaries

Initialize or resume a paper bundle:

erdos paper init 857
erdos paper show 857

Archive a solved problem:

erdos graph-theory status 1008
erdos archive scaffold 1008 --json

Current Coverage

Surface	Coverage
Bundled external atlas snapshot	1183 problems
Native packaged dossiers	18
Sunflower pack	20, 536, 856, 857
Number-theory pack	1, 2
Graph-theory archive pack	19, 22, 1008
Most developed pack problems	20, 857

Seeded problems today:

• 1, 2, 3, 4, 5, 6, 7, 18, 19, 20, 21, 22, 89, 536, 542, 856, 857, 1008

Example Output

$ erdos sunflower frontier 857
Erdos Problem #857 sunflower frontier
Active route: anchored_selector_linearization
Active ticket: T10
First ready atom: T10.G3.A2
Checkpoint focus: keep the board packet honest around T10 while preserving the open-problem / active-route / route-breakthrough ladder.

$ erdos graph-theory status 1008
Erdos Problem #1008 graph-theory harness
Family role: c4_free_lean_archive
Harness profile: lean_archive_workspace
Archive mode: method_exemplar
Problem solved: yes
First ready atom: G1008.G1.A1 — Freeze the primary Lean-facing archive hook for the `C_4`-free density result

Core Flows

1. Bootstrap a seeded problem

erdos bootstrap problem 857
erdos problem artifacts 857 --json
erdos checkpoints sync

What this does:

• sets the active workspace problem
• syncs the bundled ORP kit into .erdos/orp/
• scaffolds the dossier into .erdos/scaffolds/<id>/
• pulls in pack-specific context where available
• prepares the workspace for the next step

2. Seed a new problem

erdos seed problem 25 --cluster number-theory

What this does:

• pulls external public metadata into a workspace bundle
• includes live site review and an agent websearch brief by default
• seeds a local dossier into .erdos/seeded-problems/<id>/
• syncs state, checkpoints, and ORP automatically

3. Pull artifacts without seeding

erdos pull problem 857
erdos pull literature 857 --include-crossref --include-openalex --json

Use this when you want a research bundle first and a canonical dossier later.

4. Promote a pulled bundle into a canonical dossier

erdos maintainer review problem 25 --from-pull .erdos/pulls/25
erdos maintainer seed problem 25 --from-pull .erdos/pulls/25 --cluster number-theory

5. Initialize a paper writer bundle

erdos paper init 857
erdos paper show 857

What this does:

• creates or resumes a paper bundle for the problem
• writes machine-readable public evidence and section indexes
• scaffolds claim-safe section drafts, a citation ledger, and a privacy review
• defaults to paper/problems/<id>/ when run inside this repo and to .erdos/papers/<id>/ elsewhere

Packs

Sunflower Pack

The sunflower pack currently covers this quartet:

• 20: strong / uniform sunflower core
• 857: weak / non-uniform sunflower core
• 536: natural-density LCM analogue
• 856: harmonic-density LCM analogue

Useful commands:

erdos sunflower status 857
erdos sunflower board 857
erdos sunflower frontier 857
erdos sunflower routes 857
erdos sunflower tickets 857
erdos sunflower route 857 anchored_selector_linearization
erdos sunflower atom 857 T10.G3.A2
erdos sunflower compute run 857

What is included here:

• public board packets
• route / ticket / atom views
• checkpoint and report packets
• governed local-scout compute posture where a packet exists

Number-Theory Pack

The number-theory pack currently includes:

• 1: open route-oriented starter pack around a distinct-subset-sum lane
• 2: counterexample / archive pack

Useful commands:

erdos number-theory status 1
erdos number-theory frontier 1
erdos number-theory routes 1
erdos number-theory route 1 distinct_subset_sum_lower_bound
erdos number-theory ticket 1 N1
erdos number-theory atom 1 N1.G1.A1

Graph-Theory Archive Pack

The graph-theory archive pack currently includes:

• 19: decision archive pack
• 22: proof archive pack
• 1008: Lean-facing proof archive pack

Useful commands:

erdos graph-theory status 19
erdos graph-theory frontier 22
erdos graph-theory routes 1008
erdos graph-theory tickets 19
erdos archive scaffold 1008 --json

Design rule:

• no fake live frontier for solved or decided problems
• keep the archive usable as a method exemplar
• preserve public status discipline instead of inflating pressure where none exists

Using It With Agents

If you are using Codex, Claude Code, or another coding agent, the package provides:

• canonical dossier files
• external import provenance when available
• pack-aware context where it exists
• .erdos/ workspace state
• ORP templates and protocol guidance
• checkpoint shelves
• explicit next-step framing
• machine-readable JSON on the main public surfaces

Useful commands for agent workflows:

erdos problem artifacts 857 --json
erdos workspace show --json
erdos pull literature 857 --include-crossref --include-openalex --json
erdos import drift 857 --json

ORP And Truth Hygiene

erdos-problems ships a bundled Open Research Protocol kit:

• PROTOCOL.md
• AGENT_INTEGRATION.md
• templates/CLAIM.md
• templates/VERIFICATION_RECORD.md
• templates/FAILED_TOPIC.md

When the global orp CLI is available, erdos-problems can also broker ORP research runs for source audits, discovery questions, and breakthrough scouting:

erdos orp research status --json
erdos orp research ask 848 --question "Check whether this source changes the current proof route" --json
erdos orp research ask 848 --question "Check whether this source changes the current proof route" --execute --allow-paid --json
erdos orp research openai-check --json
erdos orp research openai-check --execute --allow-paid --json
erdos orp research usage --json

The safe default is planning-only: live OpenAI API calls require both --execute and --allow-paid unless ERDOS_ORP_RESEARCH_ALLOW_PAID=1 is set for an intentional paid-call session. A workspace-local daily live-run guard defaults to 10 and can be lowered with ERDOS_ORP_RESEARCH_DAILY_LIMIT=0 to disable live calls. A local daily research API budget defaults to $5 via ERDOS_ORP_RESEARCH_DAILY_USD_LIMIT; set it to 0 to disable paid research spend. The guard reserves $1 for normal research asks and $0.05 for smoke checks unless ERDOS_ORP_RESEARCH_ESTIMATED_COST_USD overrides the estimate. This is a local agent/workspace budget guard, not an upstream provider billing hard cap. Use live research for high-leverage source audits, theorem wedges, external reference checks, or repeated local stalls; avoid it for routine tests or deterministic local compute. ORP resolves OPENAI_API_KEY from the environment or the local openai-primary Keychain secret, and secret values are not written to research artifacts.

The package keeps these layers separate:

• canonical repo truth
• external imported public truth
• workspace bundle truth
• pack-specific route / checkpoint / run truth
• ORP research-run truth

Command Gallery

erdos problem list --cluster sunflower
erdos problem show 857
erdos problem artifacts 857 --json

erdos cluster list --json
erdos cluster show graph-theory

erdos workspace show --json
erdos checkpoints sync
erdos preflight

erdos sunflower frontier 857
erdos sunflower ready 857
erdos sunflower compute run 857

erdos number-theory route 1 distinct_subset_sum_lower_bound
erdos graph-theory status 1008

erdos pull problem 857
erdos pull literature 857 --include-crossref --include-openalex --json

erdos seed problem 25 --cluster number-theory
erdos maintainer review problem 25 --from-pull .erdos/pulls/25
erdos archive scaffold 1008 --json

Canonical Home And External Inputs

• canonical repo: https://github.com/SproutSeeds/erdos-problems
• local dossier truth: problems/<id>/problem.yaml
• bundled external import snapshot: data/upstream/erdosproblems/
• workspace external import snapshot: .erdos/upstream/erdosproblems/
• external atlas import repo: https://github.com/teorth/erdosproblems
• external public site: https://www.erdosproblems.com/

Docs

• docs/ERDOS_PROBLEMS_REPO_SPEC.md
• docs/ERDOS_PROBLEMS_PROBLEM_SCHEMA.md
• docs/ERDOS_SUNFLOWER_CLUSTER_SEED_PLAN.md
• docs/RESEARCH_LOOP.md
• docs/LAUNCH_KIT.md

Launch Assets

If you are preparing a public post, start here:

• docs/LAUNCH_KIT.md
• assets/social-card.svg
• assets/terminal-demo.gif

FAQ

What is the difference between this and erdosproblems.com?

erdosproblems.com is an external public problem source. erdos-problems imports from public sources when helpful, but keeps its canonical dossiers, packs, workflow, and contribution surface in this repo.

Can I use this with Codex, Claude Code, or another agent?

Yes. The package can scaffold a local .erdos/ workspace, expose machine-readable JSON on the main public surfaces, and keep public status, local route state, and verification records separate.

Which problems are most developed right now?

The sunflower pack is currently the most developed. Problems 20 and 857 have the deepest public pack surface. Problems 536 and 856 are included as bridge-oriented sunflower dossiers. The number-theory and graph-theory packs are lighter.

Does it only cover open problems?

No. The bundled upstream atlas covers open, solved, and decided problems. Open problems can be seeded into active workspaces. Solved or decided problems can be scaffolded in archive mode and used as method exemplars.

What is a dossier?

A dossier is the local canonical folder for one problem. It usually includes problem.yaml, STATEMENT.md, REFERENCES.md, EVIDENCE.md, and FORMALIZATION.md.

Do I need Lean or ORP to start using it?

No. You can start with erdos bootstrap problem <id> or erdos seed problem <id>. ORP files are bundled into the workspace for structured claims and checkpoints, and some packs include formalization-specific surfaces, but the first step does not require Lean.

Why is the npm package called erdos-problems and not erdosproblems?

erdos-problems is the canonical npm package name and it is already live on npm. The compact unscoped alias erdosproblems is not publishable because npm rejects it as too similar to erdos-problems.