Pith Number

pith:VLXVKXEP

pith:2013:VLXVKXEPX3Q5IW53AVCMXSSTZU

not attested not anchored not stored refs pending

Chart description for hyperelliptic Lefschetz fibrations and their stabilization

Hisaaki Endo, Seiichi Kamada

arxiv:1306.2707 v1 · 2013-06-12 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VLXVKXEPX3Q5IW53AVCMXSSTZU}

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	2026-05-18T03:21:09.664543Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aaef555c8fbee1d45bbb0544cbca53cd0ceda782843e90479e11f9ca2bae4485

Aliases

arxiv: 1306.2707 · arxiv_version: 1306.2707v1 · doi: 10.48550/arxiv.1306.2707 · pith_short_12: VLXVKXEPX3Q5 · pith_short_16: VLXVKXEPX3Q5IW53 · pith_short_8: VLXVKXEP

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/VLXVKXEPX3Q5IW53AVCMXSSTZU \
  | 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: aaef555c8fbee1d45bbb0544cbca53cd0ceda782843e90479e11f9ca2bae4485

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "28666f1e06fb5b3a7fbfbf68949b073827342beac74af3317077708f82558707",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-06-12T04:06:13Z",
    "title_canon_sha256": "94c8def70f5413e1176299e5dd35b4dee845396b9ce5442b7f4fefe328bbcca3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.2707",
    "kind": "arxiv",
    "version": 1
  }
}