Pith Number

pith:6BJ3TNF4

pith:2012:6BJ3TNF4VBTFA7RBVHDFKZU7FP

not attested not anchored not stored refs pending

Semi-continuity of Complex Singularity Exponents in Singular Central Fiber Cases

Yuchen Liu

arxiv:1211.1450 v2 · 2012-11-07 · math.AG · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6BJ3TNF4VBTFA7RBVHDFKZU7FP}

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	2026-05-18T03:20:58.641376Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f053b9b4bca866507e21a9c655669f2bd21f3baba76b56adc10a9607655a258a

Aliases

arxiv: 1211.1450 · arxiv_version: 1211.1450v2 · doi: 10.48550/arxiv.1211.1450 · pith_short_12: 6BJ3TNF4VBTF · pith_short_16: 6BJ3TNF4VBTFA7RB · pith_short_8: 6BJ3TNF4

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/6BJ3TNF4VBTFA7RBVHDFKZU7FP \
  | 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: f053b9b4bca866507e21a9c655669f2bd21f3baba76b56adc10a9607655a258a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e5038def1773b0508da4e077da85e22976c4a1b6ac5505310b84c8d6bcbad6e4",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-11-07T05:16:32Z",
    "title_canon_sha256": "c0e1ef7505bf76337fb55c5d6428bd0418ac5e7ea18fc23410fe19f80218dca3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.1450",
    "kind": "arxiv",
    "version": 2
  }
}