Pith Number

pith:J7HK4CO3

pith:2011:J7HK4CO377OZTPCBTUJ2U3H5F4

not attested not anchored not stored refs pending

Dynnikov coordinates on virtual braid groups

Andrei Vesnin (AOSSI), Bert Wiest (IRMAR), Valerij G. Bardakov (AOSSI)

arxiv:1103.4441 v2 · 2011-03-23 · math.GT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{J7HK4CO377OZTPCBTUJ2U3H5F4}

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	2026-05-18T04:17:04.304042Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4fceae09dbffdd99bc419d13aa6cfd2f2a9039727e8423ad4489286004f0b7ac

Aliases

arxiv: 1103.4441 · arxiv_version: 1103.4441v2 · doi: 10.48550/arxiv.1103.4441 · pith_short_12: J7HK4CO377OZ · pith_short_16: J7HK4CO377OZTPCB · pith_short_8: J7HK4CO3

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/J7HK4CO377OZTPCBTUJ2U3H5F4 \
  | 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: 4fceae09dbffdd99bc419d13aa6cfd2f2a9039727e8423ad4489286004f0b7ac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b95c2e1029ae345007d6964842b8abf2740d27756f523714a567c126cacd71e7",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-03-23T05:56:24Z",
    "title_canon_sha256": "fbac32a52c88e4de48641699055579176be4b55d89fde294594060556b926273"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.4441",
    "kind": "arxiv",
    "version": 2
  }
}