Pith Number

pith:W4IGWFOS

pith:2019:W4IGWFOSCSQJDJA2EGR3QWSMHC

not attested not anchored not stored refs pending

A New Proof of Hopf's Inequality Using a Complex Extension of the Hilbert Metric

Guangyue Han, Wendi Han

arxiv:1906.04875 v3 · 2019-06-12 · math.SP · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W4IGWFOSCSQJDJA2EGR3QWSMHC}

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	2026-05-17T23:40:30.170472Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7106b15d214a091a41a21a3b85a4c3899b5d15f89a7f45fdf33a9c40d37ffba

Aliases

arxiv: 1906.04875 · arxiv_version: 1906.04875v3 · doi: 10.48550/arxiv.1906.04875 · pith_short_12: W4IGWFOSCSQJ · pith_short_16: W4IGWFOSCSQJDJA2 · pith_short_8: W4IGWFOS

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/W4IGWFOSCSQJDJA2EGR3QWSMHC \
  | 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: b7106b15d214a091a41a21a3b85a4c3899b5d15f89a7f45fdf33a9c40d37ffba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce770a3fa44a00d5d45591dfbc076bfa7ba59044f82d9d42bf745f4cbc9c53b7",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2019-06-12T01:25:12Z",
    "title_canon_sha256": "ba7f7f05b08c93a2ad868ba0ce3427f0dd981183f49840252f4df1842154d0be"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.04875",
    "kind": "arxiv",
    "version": 3
  }
}