Pith Number

pith:DWBRR5OE

pith:2014:DWBRR5OE2CT4JE7226LXS7OXKZ

not attested not anchored not stored refs pending

Lin-Wang type formula for the Haefliger invariant

Keiichi Sakai

arxiv:1405.1947 v2 · 2014-05-08 · math.GT · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DWBRR5OE2CT4JE7226LXS7OXKZ}

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	2026-05-18T01:25:16.250967Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1d8318f5c4d0a7c493fad797797dd75666c9197107261daf5954e12c574f6890

Aliases

arxiv: 1405.1947 · arxiv_version: 1405.1947v2 · doi: 10.48550/arxiv.1405.1947 · pith_short_12: DWBRR5OE2CT4 · pith_short_16: DWBRR5OE2CT4JE72 · pith_short_8: DWBRR5OE

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/DWBRR5OE2CT4JE7226LXS7OXKZ \
  | 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: 1d8318f5c4d0a7c493fad797797dd75666c9197107261daf5954e12c574f6890

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eeedbe5fb97e6fb4033e2d514008b4c4deb6938f07ad9a554803a2efd826d755",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2014-05-08T14:43:07Z",
    "title_canon_sha256": "1abff8736409b36f3aa989896c5bae489afca5197953c3435975a855bcec3628"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1405.1947",
    "kind": "arxiv",
    "version": 2
  }
}