Pith Number

pith:CU5KOLTH

pith:2019:CU5KOLTHR6QWTB3GBITL4SPTCL

not attested not anchored not stored refs pending

Null-homologous unknottings

Charles Livingston

arxiv:1902.05405 v2 · 2019-02-14 · 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{CU5KOLTHR6QWTB3GBITL4SPTCL}

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

Untwisting 3-strand torus knots

Receipt and verification

First computed	2026-07-05T02:58:32.947949Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

153aa72e678fa16987660a26be49f312f9729159e056d1d28692c22d15e40028

Aliases

arxiv: 1902.05405 · arxiv_version: 1902.05405v2 · doi: 10.48550/arxiv.1902.05405 · pith_short_12: CU5KOLTHR6QW · pith_short_16: CU5KOLTHR6QWTB3G · pith_short_8: CU5KOLTH

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/CU5KOLTHR6QWTB3GBITL4SPTCL \
  | 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: 153aa72e678fa16987660a26be49f312f9729159e056d1d28692c22d15e40028

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "542b29f77002fb3e1b37ba9fe773ee45a91c2774a96f415df7b51193d7689b3f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2019-02-14T15:02:00Z",
    "title_canon_sha256": "63f463080ff56c9001a2532b8a44945ed4161e45764adc2d5b6c4efd6f476c09"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1902.05405",
    "kind": "arxiv",
    "version": 2
  }
}