Pith Number

pith:VRAQBVMF

pith:2015:VRAQBVMF7WWZIU5HWYECWOYIXT

not attested not anchored not stored refs pending

The density property for Gizatullin surfaces of type $[[0,0,-r_2,-r_3]]$

Frank Kutzschebauch, Pierre-Marie Poloni, Rafael B. Andrist

arxiv:1510.08771 v2 · 2015-10-29 · math.CV · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VRAQBVMF7WWZIU5HWYECWOYIXT}

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	2026-05-18T01:17:00.098017Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac4100d585fdad9453a7b6082b3b08bcfc08a1c380be3e07726ec1d998eef169

Aliases

arxiv: 1510.08771 · arxiv_version: 1510.08771v2 · doi: 10.48550/arxiv.1510.08771 · pith_short_12: VRAQBVMF7WWZ · pith_short_16: VRAQBVMF7WWZIU5H · pith_short_8: VRAQBVMF

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/VRAQBVMF7WWZIU5HWYECWOYIXT \
  | 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: ac4100d585fdad9453a7b6082b3b08bcfc08a1c380be3e07726ec1d998eef169

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "51dee923439f4d1c075212e2cda9c5f3275f71caa5f10624ba7c5d832d67a379",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2015-10-29T16:39:47Z",
    "title_canon_sha256": "9710bce704d406e04c1a187eaf0c47d5cb77a970aca1080c3b26a9078c9b76c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.08771",
    "kind": "arxiv",
    "version": 2
  }
}