Pith Number

pith:3KZMNNJM

pith:2012:3KZMNNJMKT7COOETG4QM5AOJBG

not attested not anchored not stored refs pending

Iterated fibre sums of algebraic Lefschetz fibrations

M. J. D. Hamilton

arxiv:1209.2653 v2 · 2012-09-12 · 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{3KZMNNJMKT7COOETG4QM5AOJBG}

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	2026-05-17T23:52:19.508156Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dab2c6b52c54fe2738933720ce81c909b454e1db88c673f6a4ed9860c01aec2f

Aliases

arxiv: 1209.2653 · arxiv_version: 1209.2653v2 · doi: 10.48550/arxiv.1209.2653 · pith_short_12: 3KZMNNJMKT7C · pith_short_16: 3KZMNNJMKT7COOET · pith_short_8: 3KZMNNJM

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/3KZMNNJMKT7COOETG4QM5AOJBG \
  | 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: dab2c6b52c54fe2738933720ce81c909b454e1db88c673f6a4ed9860c01aec2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a298216a75bbcbab1fb5c0f864286868942d013d58337d7886de2e616258b46d",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-09-12T16:31:06Z",
    "title_canon_sha256": "7377ea044c30031292a47a23c7a21ea831af7a5fe5ff2a527d20c43294b1b11a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.2653",
    "kind": "arxiv",
    "version": 2
  }
}