Pith Number

pith:T2HSXLDW

pith:2010:T2HSXLDWHOCKPXJ357MEWUV3KZ

not attested not anchored not stored refs pending

Half-balanced braided monoidal categories and Teichmueller groupoids in genus zero

Benjamin Enriquez

arxiv:1009.2652 v2 · 2010-09-14 · 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{T2HSXLDWHOCKPXJ357MEWUV3KZ}

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	2026-05-18T04:40:54.292196Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e8f2bac763b84a7dd3befd84b52bb565d0628dbde8c31e3d35ed6391dfba867

Aliases

arxiv: 1009.2652 · arxiv_version: 1009.2652v2 · doi: 10.48550/arxiv.1009.2652 · pith_short_12: T2HSXLDWHOCK · pith_short_16: T2HSXLDWHOCKPXJ3 · pith_short_8: T2HSXLDW

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/T2HSXLDWHOCKPXJ357MEWUV3KZ \
  | 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: 9e8f2bac763b84a7dd3befd84b52bb565d0628dbde8c31e3d35ed6391dfba867

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b408d3928a69151bf532782dbe64641ce9bce2160b7a6a3a4f79d45ec33ee554",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2010-09-14T13:18:16Z",
    "title_canon_sha256": "abd5f65f22b83a1381cb492edeff9b88ec4e4c8c3ff81edc982bb540c4502cac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.2652",
    "kind": "arxiv",
    "version": 2
  }
}