Pith Number

pith:JM4QEMS7

pith:2011:JM4QEMS7FTATM6HEZC3CZO3WU3

not attested not anchored not stored refs pending

On the Finsler stucture of the Teichm\"uuller metric and Thurston's asymmetric metric

Athanase Papadopoulos (IRMA), Weixu Su (IRMA)

arxiv:1111.4079 v1 · 2011-11-17 · 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{JM4QEMS7FTATM6HEZC3CZO3WU3}

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	2026-05-18T04:08:12.012516Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b3902325f2cc13678e4c8b62cbb76a6cf8e8b848186df666d2bfd66c525ea04

Aliases

arxiv: 1111.4079 · arxiv_version: 1111.4079v1 · doi: 10.48550/arxiv.1111.4079 · pith_short_12: JM4QEMS7FTAT · pith_short_16: JM4QEMS7FTATM6HE · pith_short_8: JM4QEMS7

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/JM4QEMS7FTATM6HEZC3CZO3WU3 \
  | 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: 4b3902325f2cc13678e4c8b62cbb76a6cf8e8b848186df666d2bfd66c525ea04

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "892fad81702646268673f2bef525c07f4ed516874d1fccfe408c27174d845d7d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-11-17T13:04:34Z",
    "title_canon_sha256": "eae23de67fb498a8986487dac18d106fb48d520b3ba0e30dca3ea71f994c96ce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.4079",
    "kind": "arxiv",
    "version": 1
  }
}