Pith Number

pith:OWK4SSKG

pith:2022:OWK4SSKGKTU5UX4PZBPKYMMHUL

not attested not anchored not stored refs pending

The worst approximable rational numbers

Boris Springborn

arxiv:2209.15542 v3 · 2022-09-30 · math.NT · math.GT · math.MG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OWK4SSKGKTU5UX4PZBPKYMMHUL}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Cited by

1 paper in Pith

Plane geometry of $q$-rationals and Springborn Operations

Receipt and verification

First computed	2026-07-05T08:23:51.776123Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7595c9494654e9da5f8fc85eac3187a2d241b545c38688dc9dced84d004a9493

Aliases

arxiv: 2209.15542 · arxiv_version: 2209.15542v3 · doi: 10.48550/arxiv.2209.15542 · pith_short_12: OWK4SSKGKTU5 · pith_short_16: OWK4SSKGKTU5UX4P · pith_short_8: OWK4SSKG

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/OWK4SSKGKTU5UX4PZBPKYMMHUL \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 7595c9494654e9da5f8fc85eac3187a2d241b545c38688dc9dced84d004a9493

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5982ae6726cbc92820c15d2f90dc524deeef10968f37ef1e60e94885978739af",
    "cross_cats_sorted": [
      "math.GT",
      "math.MG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2022-09-30T15:45:47Z",
    "title_canon_sha256": "ffff0760ee188335cd929e273ec256fa6a5f2717e79bdfa9c65b775b7fc47ef0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2209.15542",
    "kind": "arxiv",
    "version": 3
  }
}