Pith Number

pith:2747UQLS

pith:2011:2747UQLSDOT6X5YYQLB4LHUFV6

not attested not anchored not stored refs pending

Polar actions on the complex hyperbolic plane

J. Carlos Diaz-Ramos, Jurgen Berndt

arxiv:1108.0543 v1 · 2011-08-02 · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2747UQLSDOT6X5YYQLB4LHUFV6}

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	2026-05-18T04:16:30.234214Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7f9fa41721ba7ebf71882c3c59e85af80155115277a0e7c10d54b689eaa6814

Aliases

arxiv: 1108.0543 · arxiv_version: 1108.0543v1 · doi: 10.48550/arxiv.1108.0543 · pith_short_12: 2747UQLSDOT6 · pith_short_16: 2747UQLSDOT6X5YY · pith_short_8: 2747UQLS

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/2747UQLSDOT6X5YYQLB4LHUFV6 \
  | 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: d7f9fa41721ba7ebf71882c3c59e85af80155115277a0e7c10d54b689eaa6814

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "92a0bdd4255e69547d42c25302d2a238e2425ee785f87884c9a15844edc9d99f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-08-02T11:11:33Z",
    "title_canon_sha256": "0f5fe46c5aa27306df6abab4586e51231a61d2221fa72293ab7925319834841b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.0543",
    "kind": "arxiv",
    "version": 1
  }
}