Pith Number

pith:ZPRAE5PU

pith:2009:ZPRAE5PUQO3JXFGPIMUAVQB3HB

not attested not anchored not stored refs pending

Four-manifolds with shadow-complexity zero

Bruno Martelli

arxiv:0909.0168 v1 · 2009-09-01 · 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{ZPRAE5PUQO3JXFGPIMUAVQB3HB}

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	2026-05-18T04:14:15.235132Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbe20275f483b69b94cf43280ac03b386d561253a3cdfca46b027b54bd577779

Aliases

arxiv: 0909.0168 · arxiv_version: 0909.0168v1 · doi: 10.48550/arxiv.0909.0168 · pith_short_12: ZPRAE5PUQO3J · pith_short_16: ZPRAE5PUQO3JXFGP · pith_short_8: ZPRAE5PU

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/ZPRAE5PUQO3JXFGPIMUAVQB3HB \
  | 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: cbe20275f483b69b94cf43280ac03b386d561253a3cdfca46b027b54bd577779

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "30e2d035eeb35c4b977bf61461fe50863836583ba43250298f0a247741faa51c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2009-09-01T12:42:18Z",
    "title_canon_sha256": "4dfec3790d7fe211c77b84a4c8f8f8d968cb224ca0cdda44444361d5627f8b5a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.0168",
    "kind": "arxiv",
    "version": 1
  }
}