Pith Number

pith:QK2L346V

pith:2015:QK2L346VTF3TTTSMCYOIJGTMMN

not attested not anchored not stored refs pending

Thurston's metric on Teichm\"uller space and the translation lengths of mapping classes

Athanase Papadopoulos (IRMA), Weixu Su

arxiv:1509.06499 v1 · 2015-09-22 · 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{QK2L346VTF3TTTSMCYOIJGTMMN}

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	2026-05-18T01:32:20.136440Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82b4bdf3d5997739ce4c161c849a6c6364e3597de8f8b83bd0f421073bd98dc9

Aliases

arxiv: 1509.06499 · arxiv_version: 1509.06499v1 · doi: 10.48550/arxiv.1509.06499 · pith_short_12: QK2L346VTF3T · pith_short_16: QK2L346VTF3TTTSM · pith_short_8: QK2L346V

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/QK2L346VTF3TTTSMCYOIJGTMMN \
  | 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: 82b4bdf3d5997739ce4c161c849a6c6364e3597de8f8b83bd0f421073bd98dc9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1da080d7a94eb1011206a8e8e8ba177eaef2da7d17aab5724d15ced0929b3a16",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-09-22T08:33:23Z",
    "title_canon_sha256": "5cd3730fd64fc57a119068b1f90d22326dde8992ddeae2a7d07b679b7956d4ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.06499",
    "kind": "arxiv",
    "version": 1
  }
}