Pith Number

pith:ZG7UQSO7

pith:2013:ZG7UQSO7C224HWZ2ZVDLLYPS6H

not attested not anchored not stored refs pending

Milnor and Tjurina numbers for smoothings of surface singularities

Jonathan Wahl

arxiv:1307.6491 v2 · 2013-07-24 · 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{ZG7UQSO7C224HWZ2ZVDLLYPS6H}

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	2026-05-18T01:18:18.624536Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9bf4849df16b5c3db3acd46b5e1f2f1f896ded8eb7c0d63cd12774efb1076c4

Aliases

arxiv: 1307.6491 · arxiv_version: 1307.6491v2 · doi: 10.48550/arxiv.1307.6491 · pith_short_12: ZG7UQSO7C224 · pith_short_16: ZG7UQSO7C224HWZ2 · pith_short_8: ZG7UQSO7

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/ZG7UQSO7C224HWZ2ZVDLLYPS6H \
  | 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: c9bf4849df16b5c3db3acd46b5e1f2f1f896ded8eb7c0d63cd12774efb1076c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "940b3922ceafd32de2232c386f73d21ca8aa86c67605cac913b700e8dea5311b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2013-07-24T17:01:19Z",
    "title_canon_sha256": "555bab69e2a20d8e9a08c6a60ac422a5611ec098e7f4c494303245045cb0decd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.6491",
    "kind": "arxiv",
    "version": 2
  }
}