Pith Number

pith:MWYILRIP

pith:2012:MWYILRIP6YTC7ZG7F7EMVMKGUW

not attested not anchored not stored refs pending

Height functions on Whitney umbrellas

Masaru Hasegawa, Toshizumi Fukui

arxiv:1205.3044 v4 · 2012-05-14 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MWYILRIP6YTC7ZG7F7EMVMKGUW}

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	2026-05-18T03:39:03.662704Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65b085c50ff6262fe4df2fc8cab146a5b8ae24a608681652d82255e5be7c54ad

Aliases

arxiv: 1205.3044 · arxiv_version: 1205.3044v4 · doi: 10.48550/arxiv.1205.3044 · pith_short_12: MWYILRIP6YTC · pith_short_16: MWYILRIP6YTC7ZG7 · pith_short_8: MWYILRIP

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/MWYILRIP6YTC7ZG7F7EMVMKGUW \
  | 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: 65b085c50ff6262fe4df2fc8cab146a5b8ae24a608681652d82255e5be7c54ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "303c35ca4430b08f40e3f2f6ca95acef67f553fd989ef8a24b5fad27953f0dae",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-05-14T14:43:39Z",
    "title_canon_sha256": "1de84a0981af00e8cbfe3a2ccfd4bee0675100468a5532f96f12cce3b127a67a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.3044",
    "kind": "arxiv",
    "version": 4
  }
}