Pith Number

pith:F7RTYXB5

pith:2010:F7RTYXB5W5TMHJJFGSW3EFOWIB

not attested not anchored not stored refs pending

Minimal Diagrams of Free Knots

Alexander Leaf, Allison Henrich, Tomas Boothby

arxiv:1008.3163 v4 · 2010-08-18 · math.CO · cs.DM · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{F7RTYXB5W5TMHJJFGSW3EFOWIB}

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.

Receipt and verification

First computed	2026-05-18T02:42:39.906557Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2fe33c5c3db766c3a52534adb215d6405f32394b72b6f0c0b78fc3b6880a24ff

Aliases

arxiv: 1008.3163 · arxiv_version: 1008.3163v4 · doi: 10.48550/arxiv.1008.3163 · pith_short_12: F7RTYXB5W5TM · pith_short_16: F7RTYXB5W5TMHJJF · pith_short_8: F7RTYXB5

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/F7RTYXB5W5TMHJJFGSW3EFOWIB \
  | 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: 2fe33c5c3db766c3a52534adb215d6405f32394b72b6f0c0b78fc3b6880a24ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f56ffff767249061b4f4c3571e9185b290cca4317ecd5410d10022f9dc657f5",
    "cross_cats_sorted": [
      "cs.DM",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-08-18T20:01:04Z",
    "title_canon_sha256": "662d1d207e107a44125ca947d731780e5e8ab9cd75201a79b2c1fca5650f758d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.3163",
    "kind": "arxiv",
    "version": 4
  }
}