Pith Number

pith:4UXW7DWK

pith:2007:4UXW7DWKAJBPLF47MLF6OG5KR2

not attested not anchored not stored refs pending

Bounding surface actions on hyperbolic spaces

Josh Barnard

arxiv:0709.2722 v4 · 2007-09-17 · math.GR · 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{4UXW7DWKAJBPLF47MLF6OG5KR2}

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	2026-05-18T03:51:36.407835Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e52f6f8eca0242f5979f62cbe71baa8ea20bd349d7ce0dceba9ef314a05da6e4

Aliases

arxiv: 0709.2722 · arxiv_version: 0709.2722v4 · doi: 10.48550/arxiv.0709.2722 · pith_short_12: 4UXW7DWKAJBP · pith_short_16: 4UXW7DWKAJBPLF47 · pith_short_8: 4UXW7DWK

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/4UXW7DWKAJBPLF47MLF6OG5KR2 \
  | 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: e52f6f8eca0242f5979f62cbe71baa8ea20bd349d7ce0dceba9ef314a05da6e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9abc239210916c5440824cce3d0e5ad962f78ec54346462d661c8300674f5f70",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2007-09-17T20:52:51Z",
    "title_canon_sha256": "2a235381dc21a089ab34166e76643bb1fd2bdb4a882dbdf6a3cdc3031b884295"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.2722",
    "kind": "arxiv",
    "version": 4
  }
}