Pith Number

pith:MJSU7V77

pith:2010:MJSU7V77CTZLUWE2MUN34NTM6V

not attested not anchored not stored refs pending

Almost-isometry between Teichm\"{u}ller metric and length-spectra metric on moduli space

Lixin Liu, Weixu Su

arxiv:1012.1921 v1 · 2010-12-09 · 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{MJSU7V77CTZLUWE2MUN34NTM6V}

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	2026-05-18T04:33:49.345725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62654fd7ff14f2ba589a651bbe366cf56377fdd012d94b5e6f55155ba1d71b62

Aliases

arxiv: 1012.1921 · arxiv_version: 1012.1921v1 · doi: 10.48550/arxiv.1012.1921 · pith_short_12: MJSU7V77CTZL · pith_short_16: MJSU7V77CTZLUWE2 · pith_short_8: MJSU7V77

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/MJSU7V77CTZLUWE2MUN34NTM6V \
  | 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: 62654fd7ff14f2ba589a651bbe366cf56377fdd012d94b5e6f55155ba1d71b62

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "754494c034dafd737788fe9bcf63b4c5de2ee38357588915862db7e49b1bec48",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-12-09T04:48:19Z",
    "title_canon_sha256": "a68ed653113be0fe13b42f010a7c60774e3b2cdc7a0327ad75e6761fa17f15a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.1921",
    "kind": "arxiv",
    "version": 1
  }
}