Pith Number

pith:TTNNL5Z5

pith:2013:TTNNL5Z5CVGQJNGRO7JD2TNDZI

not attested not anchored not stored refs pending

Generators of the Gauss-Picard modular groups in three complex dimensions

Baohua Xie, Jieyan Wang, Yueping Jiang

arxiv:1307.2113 v1 · 2013-07-08 · math.CV · 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{TTNNL5Z5CVGQJNGRO7JD2TNDZI}

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	2026-05-18T03:19:02.368166Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9cdad5f73d154d04b4d177d23d4da3ca21b38b1ddaaff2f78ff12c09884f63e2

Aliases

arxiv: 1307.2113 · arxiv_version: 1307.2113v1 · doi: 10.48550/arxiv.1307.2113 · pith_short_12: TTNNL5Z5CVGQ · pith_short_16: TTNNL5Z5CVGQJNGR · pith_short_8: TTNNL5Z5

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/TTNNL5Z5CVGQJNGRO7JD2TNDZI \
  | 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: 9cdad5f73d154d04b4d177d23d4da3ca21b38b1ddaaff2f78ff12c09884f63e2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "699fbfdfb49ec037d83c2fcd7d89358b615dd13db2190218d1fbd2b8a11178c4",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2013-07-08T14:52:57Z",
    "title_canon_sha256": "1c537655b99f01be1715cd9b097fc4eb988431a6f6df1b744c82902686cfc74b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.2113",
    "kind": "arxiv",
    "version": 1
  }
}