Pith Number

pith:Y2PMFNDS

pith:2012:Y2PMFNDSF2DEYUO6L7XOEYQA45

not attested not anchored not stored refs pending

Thurston's metric on Teichm\"uller space and isomorphisms between Fuchsian groups

Athanase Papadopoulos (IRMA), Weixu Su

arxiv:1210.2676 v1 · 2012-10-09 · 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{Y2PMFNDSF2DEYUO6L7XOEYQA45}

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	2026-05-18T03:43:40.954613Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c69ec2b4722e864c51de5feee26200e768cdd34ab90f8dda2feab7d476ebc241

Aliases

arxiv: 1210.2676 · arxiv_version: 1210.2676v1 · doi: 10.48550/arxiv.1210.2676 · pith_short_12: Y2PMFNDSF2DE · pith_short_16: Y2PMFNDSF2DEYUO6 · pith_short_8: Y2PMFNDS

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/Y2PMFNDSF2DEYUO6L7XOEYQA45 \
  | 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: c69ec2b4722e864c51de5feee26200e768cdd34ab90f8dda2feab7d476ebc241

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "310ad3998572642f3748105b22d0920d0ef94b4f42e0b0c16d6fad80e65ee3f1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-10-09T17:39:31Z",
    "title_canon_sha256": "c30cd748a3d96cc3a3d692733aef3a08b310c36b17f54f443689e53bcf5ae8f2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.2676",
    "kind": "arxiv",
    "version": 1
  }
}