Pith Number

pith:WFZXIYXV

pith:2011:WFZXIYXVKEHVJDK4YRDYXBP4FN

not attested not anchored not stored refs pending

Jacobian discrepancies and rational singularities

Roi Docampo, Tommaso de Fernex

arxiv:1106.2172 v5 · 2011-06-10 · 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{WFZXIYXVKEHVJDK4YRDYXBP4FN}

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	2026-05-18T01:30:49.609032Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1737462f5510f548d5cc4478b85fc2b6fc3768b37c0dd3597ed4010af6ee5d5

Aliases

arxiv: 1106.2172 · arxiv_version: 1106.2172v5 · doi: 10.48550/arxiv.1106.2172 · pith_short_12: WFZXIYXVKEHV · pith_short_16: WFZXIYXVKEHVJDK4 · pith_short_8: WFZXIYXV

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/WFZXIYXVKEHVJDK4YRDYXBP4FN \
  | 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: b1737462f5510f548d5cc4478b85fc2b6fc3768b37c0dd3597ed4010af6ee5d5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "60ea0553ac84a83d02e9e72377eac443eb0aad8cd0aa67e520a8e02b562346bd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-06-10T20:45:51Z",
    "title_canon_sha256": "1c7a64b851bd07fa9bedc96521650be3c3af124ed11dd3e276f732fb8cacc851"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.2172",
    "kind": "arxiv",
    "version": 5
  }
}