Pith Number

pith:VMF5XFOW

pith:2012:VMF5XFOWBDA5RIYOXEHY2VXTCO

not attested not anchored not stored refs pending

Collapsing topology of isolated singularities

Alexandre Fernandes, Lev Birbrair, Vincent Grandjean

arxiv:1208.4328 v1 · 2012-08-21 · math.MG · math.AG · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VMF5XFOWBDA5RIYOXEHY2VXTCO}

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	2026-05-18T03:48:23.893759Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab0bdb95d608c1d8a30eb90f8d56f313b7b7b9a7b21e51abae68279c9fbf4384

Aliases

arxiv: 1208.4328 · arxiv_version: 1208.4328v1 · doi: 10.48550/arxiv.1208.4328 · pith_short_12: VMF5XFOWBDA5 · pith_short_16: VMF5XFOWBDA5RIYO · pith_short_8: VMF5XFOW

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/VMF5XFOWBDA5RIYOXEHY2VXTCO \
  | 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: ab0bdb95d608c1d8a30eb90f8d56f313b7b7b9a7b21e51abae68279c9fbf4384

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c046b370f68f32c3859d3e8295662fd3e167520b672ea892c3fbaabbbbe7b433",
    "cross_cats_sorted": [
      "math.AG",
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2012-08-21T18:11:23Z",
    "title_canon_sha256": "ae2a85e7d8abf6f474d152b83ff2216907ec78a7c14609b894a662078cf5459b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.4328",
    "kind": "arxiv",
    "version": 1
  }
}