Pith Number

pith:KGHSW6MZ

pith:2012:KGHSW6MZ4A3ORBX23PBVGTN7CU

not attested not anchored not stored refs pending

On the Hopf Conjecture with Symmetry

Lee Kennard

arxiv:1203.3808 v1 · 2012-03-16 · 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{KGHSW6MZ4A3ORBX23PBVGTN7CU}

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	2026-05-18T01:22:26.793264Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

518f2b7999e036e886fadbc3534dbf15390cab006e93b543fefb30a60a1a8ca9

Aliases

arxiv: 1203.3808 · arxiv_version: 1203.3808v1 · doi: 10.48550/arxiv.1203.3808 · pith_short_12: KGHSW6MZ4A3O · pith_short_16: KGHSW6MZ4A3ORBX2 · pith_short_8: KGHSW6MZ

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/KGHSW6MZ4A3ORBX23PBVGTN7CU \
  | 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: 518f2b7999e036e886fadbc3534dbf15390cab006e93b543fefb30a60a1a8ca9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e6d717b79d8cb66e3d6aebc796f25aaab11adcf3a09b9fe26b3ce2cd47e5da0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-03-16T20:13:22Z",
    "title_canon_sha256": "83e7b45241b4254f08d35c3754de3d4d2c56ee7145831daeb363268e95d3e944"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.3808",
    "kind": "arxiv",
    "version": 1
  }
}