Pith Number

pith:ZL36HUZJ

pith:2015:ZL36HUZJP5UDPRFWTUHQYIB7JQ

not attested not anchored not stored refs pending

Small Lefschetz fibrations and exotic 4-manifolds

Mustafa Korkmaz, R. Inanc Baykur

arxiv:1510.00089 v2 · 2015-10-01 · math.GT · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZL36HUZJP5UDPRFWTUHQYIB7JQ}

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	2026-05-18T01:30:07.692232Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

caf7e3d3297f6837c4b69d0f0c203f4c2990cca2215e69b131e83281d6bd8538

Aliases

arxiv: 1510.00089 · arxiv_version: 1510.00089v2 · doi: 10.48550/arxiv.1510.00089 · pith_short_12: ZL36HUZJP5UD · pith_short_16: ZL36HUZJP5UDPRFW · pith_short_8: ZL36HUZJ

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/ZL36HUZJP5UDPRFWTUHQYIB7JQ \
  | 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: caf7e3d3297f6837c4b69d0f0c203f4c2990cca2215e69b131e83281d6bd8538

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "631bcade9bd28366c051b88d831ef2d02e510090d53f8c369b98f4530fa5b239",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-10-01T01:57:10Z",
    "title_canon_sha256": "82bec4d6413b21ddd0c1a7ffcded69d3a5a8c8048219f7a15c94b4647d09084e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.00089",
    "kind": "arxiv",
    "version": 2
  }
}