Pith Number

pith:SWUPPVZ4

pith:2010:SWUPPVZ4YS2KKGN7WDZJLJHVVS

not attested not anchored not stored refs pending

Lipschitz minimality of Hopf fibrations and Hopf vector fields

Dennis DeTurck, Herman Gluck, Peter A. Storm

arxiv:1009.5439 v1 · 2010-09-28 · 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{SWUPPVZ4YS2KKGN7WDZJLJHVVS}

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	2026-05-18T02:41:50.725189Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

95a8f7d73cc4b4a519bfb0f295a4f5ac8b6e0338a55d9692ee8e2eecbd426556

Aliases

arxiv: 1009.5439 · arxiv_version: 1009.5439v1 · doi: 10.48550/arxiv.1009.5439 · pith_short_12: SWUPPVZ4YS2K · pith_short_16: SWUPPVZ4YS2KKGN7 · pith_short_8: SWUPPVZ4

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/SWUPPVZ4YS2KKGN7WDZJLJHVVS \
  | 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: 95a8f7d73cc4b4a519bfb0f295a4f5ac8b6e0338a55d9692ee8e2eecbd426556

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "20f08712faf46684658f624d1be9d538f95ef968adc6fe3f5bf87c13d1b3f797",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-09-28T04:30:28Z",
    "title_canon_sha256": "f14201740d2b8824fa32f030697c80a8a098d575991c84ea0f658d89eb74979f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.5439",
    "kind": "arxiv",
    "version": 1
  }
}