Pith Number

pith:DJMPNMGV

pith:2011:DJMPNMGVRQUSWIIOOTNI26OIMW

not attested not anchored not stored refs pending

Bi-Lipschitz extension from boundaries of certain hyperbolic spaces

Anton Lukyanenko

arxiv:1112.2684 v1 · 2011-12-12 · math.GT · math.CV · math.DG · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DJMPNMGVRQUSWIIOOTNI26OIMW}

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	2026-05-18T03:25:14.759449Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1a58f6b0d58c292b210e74da8d79c865a37379170ee0a8a207887c1771bea55d

Aliases

arxiv: 1112.2684 · arxiv_version: 1112.2684v1 · doi: 10.48550/arxiv.1112.2684 · pith_short_12: DJMPNMGVRQUS · pith_short_16: DJMPNMGVRQUSWIIO · pith_short_8: DJMPNMGV

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/DJMPNMGVRQUSWIIOOTNI26OIMW \
  | 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: 1a58f6b0d58c292b210e74da8d79c865a37379170ee0a8a207887c1771bea55d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eefedde37d5ed869392c9eddca56fc02e49d95dd60a8b69f00094579e8302ab0",
    "cross_cats_sorted": [
      "math.CV",
      "math.DG",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-12-12T20:23:47Z",
    "title_canon_sha256": "47d0c28b70391fe9d84f97d2a63960038b775469020d3f2281b5dcb0dddc5163"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.2684",
    "kind": "arxiv",
    "version": 1
  }
}