Pith Number

pith:PCWCXVDN

pith:2015:PCWCXVDNGDH53GYNYAX4L6XTO4

not attested not anchored not stored refs pending

Formal descriptions of Turaev's loop operations

Gwenael Massuyeau

arxiv:1511.03974 v3 · 2015-11-12 · math.GT · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PCWCXVDNGDH53GYNYAX4L6XTO4}

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

Drinfeld associators and Kashiwara-Vergne associators in higher genera

Receipt and verification

First computed	2026-05-18T00:24:40.056397Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78ac2bd46d30cfdd9b0dc02fc5faf37732159bc7f6d041e3cc61cfca5c86ca80

Aliases

arxiv: 1511.03974 · arxiv_version: 1511.03974v3 · doi: 10.48550/arxiv.1511.03974 · pith_short_12: PCWCXVDNGDH5 · pith_short_16: PCWCXVDNGDH53GYN · pith_short_8: PCWCXVDN

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/PCWCXVDNGDH53GYNYAX4L6XTO4 \
  | 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: 78ac2bd46d30cfdd9b0dc02fc5faf37732159bc7f6d041e3cc61cfca5c86ca80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e2fcd1f5b18ed95f92dd54fdfe8c393a05d9257a94d4015cd84f9a324aa17c9",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-11-12T17:20:12Z",
    "title_canon_sha256": "b008c03be43ea9b2cb2857f1d6943a567ecda4c777d5cdbecdd69bf63b36f841"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.03974",
    "kind": "arxiv",
    "version": 3
  }
}