Pith Number

pith:XMTF3KD4

pith:2012:XMTF3KD4K3SYGK5AO56H2WN3QQ

not attested not anchored not stored refs pending

Variation of extremal length functions on Teichmuller space

Lixin Liu, Weixu Su

arxiv:1210.0743 v3 · 2012-10-02 · 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{XMTF3KD4K3SYGK5AO56H2WN3QQ}

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	2026-05-18T01:07:52.704597Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bb265da87c56e5832ba0777c7d59bb841d2915f1a46d8b500dfe15e1d5857211

Aliases

arxiv: 1210.0743 · arxiv_version: 1210.0743v3 · doi: 10.48550/arxiv.1210.0743 · pith_short_12: XMTF3KD4K3SY · pith_short_16: XMTF3KD4K3SYGK5A · pith_short_8: XMTF3KD4

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/XMTF3KD4K3SYGK5AO56H2WN3QQ \
  | 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: bb265da87c56e5832ba0777c7d59bb841d2915f1a46d8b500dfe15e1d5857211

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "05310901f4610a0ec68ee7b4a2b8f7e3bbaa804dc09a98a96f5ffe45360c3f54",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-10-02T12:19:22Z",
    "title_canon_sha256": "e7eac1ef071fcda553fd6974acfc6426985bb23ded2801a08ec2d27dcb2602c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.0743",
    "kind": "arxiv",
    "version": 3
  }
}