Pith Number

pith:SFNGUWGX

pith:2011:SFNGUWGXO5Q6JY4PF46BK5LG7E

not attested not anchored not stored refs pending

On Virtual Crossing Numbers for Virtual Knots

Vassily Olegovich Manturov

arxiv:1107.4828 v1 · 2011-07-25 · 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{SFNGUWGXO5Q6JY4PF46BK5LG7E}

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	2026-05-18T04:16:54.538603Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

915a6a58d77761e4e38f2f3c157566f9121a86bed2ff73e1fc48ba88959dd4f0

Aliases

arxiv: 1107.4828 · arxiv_version: 1107.4828v1 · doi: 10.48550/arxiv.1107.4828 · pith_short_12: SFNGUWGXO5Q6 · pith_short_16: SFNGUWGXO5Q6JY4P · pith_short_8: SFNGUWGX

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/SFNGUWGXO5Q6JY4PF46BK5LG7E \
  | 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: 915a6a58d77761e4e38f2f3c157566f9121a86bed2ff73e1fc48ba88959dd4f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c7f2e63baf8a8fb6bc712d87928aa830f9029e1dc07629fa8fdf46a6bf38b439",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-07-25T02:44:20Z",
    "title_canon_sha256": "e4e0321bdf0e94176cc897836aeb19b7f4924bdd30f75801fe9813b6cd2ae850"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.4828",
    "kind": "arxiv",
    "version": 1
  }
}