Pith Number

pith:CEKNL4Y4

pith:2013:CEKNL4Y4XHLHLI5VKP6OAM5U3L

not attested not anchored not stored refs pending

Graph-valued invariants of virtual and classical links and minimality problem

Vassily Olegovich Manturov, Vladimir Krasnov

arxiv:1312.0180 v1 · 2013-12-01 · 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{CEKNL4Y4XHLHLI5VKP6OAM5U3L}

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	2026-05-18T03:05:46.512391Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1114d5f31cb9d675a3b553fce033b4dad2e35a22dc9d5d631abe8083d18236ca

Aliases

arxiv: 1312.0180 · arxiv_version: 1312.0180v1 · doi: 10.48550/arxiv.1312.0180 · pith_short_12: CEKNL4Y4XHLH · pith_short_16: CEKNL4Y4XHLHLI5V · pith_short_8: CEKNL4Y4

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/CEKNL4Y4XHLHLI5VKP6OAM5U3L \
  | 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: 1114d5f31cb9d675a3b553fce033b4dad2e35a22dc9d5d631abe8083d18236ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "925b4cfea64a8202aa48ba9de2c565fd783aeb309c9e53bdf953c127effffc19",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-12-01T05:40:02Z",
    "title_canon_sha256": "f82007e2d9a3ad2ee9bdc4d4482e0a87eb8c72b42bb8cf13a89acbe5b93d139d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.0180",
    "kind": "arxiv",
    "version": 1
  }
}