Pith Number

pith:BH3G4L43

pith:2012:BH3G4L435KM2H5R7SLISY5NOCS

not attested not anchored not stored refs pending

Polar actions on complex hyperbolic spaces

Andreas Kollross, J. Carlos Diaz-Ramos, Miguel Dominguez-Vazquez

arxiv:1208.2823 v3 · 2012-08-14 · 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{BH3G4L435KM2H5R7SLISY5NOCS}

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	2026-05-18T00:48:21.220223Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

09f66e2f9bea99a3f63f92d12c75ae14b39fe6f3b2e2c4dab47cc868419d7e49

Aliases

arxiv: 1208.2823 · arxiv_version: 1208.2823v3 · doi: 10.48550/arxiv.1208.2823 · pith_short_12: BH3G4L435KM2 · pith_short_16: BH3G4L435KM2H5R7 · pith_short_8: BH3G4L43

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/BH3G4L435KM2H5R7SLISY5NOCS \
  | 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: 09f66e2f9bea99a3f63f92d12c75ae14b39fe6f3b2e2c4dab47cc868419d7e49

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "acc967b0adca426c199f013a2d100704586b82dadfd9ffcd3f2c461313c1ae1a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-08-14T10:37:01Z",
    "title_canon_sha256": "49e2828284d799ad66a7d57d81035388feb8d80aea0fdec5b96f7e96bc598f2a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.2823",
    "kind": "arxiv",
    "version": 3
  }
}