Pith Number

pith:F5ZPACYY

pith:2016:F5ZPACYYOOXLR2HRW4JFZSLOVU

not attested not anchored not stored refs pending

Unrestricted virtual braids, fused links and other quotients of virtual braid groups

Celeste Damiani, Paolo Bellingeri, Valeriy Bardakov

arxiv:1603.01209 v1 · 2016-03-03 · 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{F5ZPACYYOOXLR2HRW4JFZSLOVU}

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	2026-05-18T01:19:39.401273Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f72f00b1873aeb8e8f1b7125cc96ead14a993ee1281d94c2f15633feb3fec52

Aliases

arxiv: 1603.01209 · arxiv_version: 1603.01209v1 · doi: 10.48550/arxiv.1603.01209 · pith_short_12: F5ZPACYYOOXL · pith_short_16: F5ZPACYYOOXLR2HR · pith_short_8: F5ZPACYY

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/F5ZPACYYOOXLR2HRW4JFZSLOVU \
  | 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: 2f72f00b1873aeb8e8f1b7125cc96ead14a993ee1281d94c2f15633feb3fec52

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "17f4f5d608e783379ce569a93113ed970c0aaf0f86cd733bad9bac5b0c000ac8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-03-03T18:17:46Z",
    "title_canon_sha256": "33cca08f02c01c3ce30252a2d64c7f52582e1a91ba012ca6ebbac548f3b4575f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.01209",
    "kind": "arxiv",
    "version": 1
  }
}