Pith Number

pith:YBHLMBIV

pith:2015:YBHLMBIVX6I5HNPI2DD2VOKRW7

not attested not anchored not stored refs pending

A short proof of a Theorem by Hopf

Daniel Cibotaru

arxiv:1507.07018 v1 · 2015-07-24 · 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{YBHLMBIVX6I5HNPI2DD2VOKRW7}

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	2026-05-18T01:36:17.519842Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c04eb60515bf91d3b5e8d0c7aab951b7ffb52054ab8c9e7e4af843ed2b8dfc36

Aliases

arxiv: 1507.07018 · arxiv_version: 1507.07018v1 · doi: 10.48550/arxiv.1507.07018 · pith_short_12: YBHLMBIVX6I5 · pith_short_16: YBHLMBIVX6I5HNPI · pith_short_8: YBHLMBIV

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/YBHLMBIVX6I5HNPI2DD2VOKRW7 \
  | 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: c04eb60515bf91d3b5e8d0c7aab951b7ffb52054ab8c9e7e4af843ed2b8dfc36

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b764aa2ef565f536e329d064f8f7bbcc823a7504e6ade45a54f6fda39739e73",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-07-24T21:17:26Z",
    "title_canon_sha256": "812efd86f612e43fa3354a4e7a5bd52bd5419a59d5eb52062d8cc123300f5202"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.07018",
    "kind": "arxiv",
    "version": 1
  }
}