Pith Number

pith:SIFV5MA5

pith:2012:SIFV5MA57VMZSGKTJ6M3HI6OT2

not attested not anchored not stored refs pending

The Hopf conjecture for manifolds with low cohomogeneity or high symmetry rank

Catherine Searle, Thomas Puettmann

arxiv:1207.4086 v1 · 2012-07-17 · 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{SIFV5MA57VMZSGKTJ6M3HI6OT2}

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	2026-05-18T03:50:49.057634Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

920b5eb01dfd599919534f99b3a3ce9e89a3622d6cd02f94eecf8efc49d19033

Aliases

arxiv: 1207.4086 · arxiv_version: 1207.4086v1 · doi: 10.48550/arxiv.1207.4086 · pith_short_12: SIFV5MA57VMZ · pith_short_16: SIFV5MA57VMZSGKT · pith_short_8: SIFV5MA5

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/SIFV5MA57VMZSGKTJ6M3HI6OT2 \
  | 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: 920b5eb01dfd599919534f99b3a3ce9e89a3622d6cd02f94eecf8efc49d19033

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e013d53d3e4947c2b3c197084527e04001d9facc229e806515a1439753fe19c7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-07-17T18:55:12Z",
    "title_canon_sha256": "c2ff074b07df8dfd086045fedd4c1a5956864fda524544d16e9829e44f172c27"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.4086",
    "kind": "arxiv",
    "version": 1
  }
}