Pith Number

pith:LRFAL5ZP

pith:2010:LRFAL5ZPAFZGNNPST5GAERGI5H

not attested not anchored not stored refs pending

Entropy, Weil-Petersson translation distance and Gromov norm for surface automorphisms

Sadayoshi Kojima

arxiv:1004.2109 v2 · 2010-04-13 · 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{LRFAL5ZPAFZGNNPST5GAERGI5H}

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	2026-05-18T04:11:31.925506Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5c4a05f72f017266b5f29f4c0244c8e9e48fdf487089306fe6c0d203b328384b

Aliases

arxiv: 1004.2109 · arxiv_version: 1004.2109v2 · doi: 10.48550/arxiv.1004.2109 · pith_short_12: LRFAL5ZPAFZG · pith_short_16: LRFAL5ZPAFZGNNPS · pith_short_8: LRFAL5ZP

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/LRFAL5ZPAFZGNNPST5GAERGI5H \
  | 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: 5c4a05f72f017266b5f29f4c0244c8e9e48fdf487089306fe6c0d203b328384b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e670cc9e0bdbb4c101160ad26427b9c1db54d2aa8539deb29143824dd845051a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-04-13T05:19:25Z",
    "title_canon_sha256": "6bbd4fdee2cec849c276e6f50638bba7239d8521a3d2ed442a7b74c5716f5986"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.2109",
    "kind": "arxiv",
    "version": 2
  }
}