Pith Number

pith:7Y7H5CTK

pith:2011:7Y7H5CTKNHHVYV3QKHBMIJZCCU

not attested not anchored not stored refs pending

Topology of steady and expanding gradient Ricci solitons via f-harmonic maps

Giona Veronelli, Michele Rimoldi

arxiv:1112.3637 v2 · 2011-12-15 · math.DG · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7Y7H5CTKNHHVYV3QKHBMIJZCCU}

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	2026-05-18T00:00:45.586053Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe3e7e8a6a69cf5c577051c2c42722150b2ad82a411c3a93bc62a6bf26752917

Aliases

arxiv: 1112.3637 · arxiv_version: 1112.3637v2 · doi: 10.48550/arxiv.1112.3637 · pith_short_12: 7Y7H5CTKNHHV · pith_short_16: 7Y7H5CTKNHHVYV3Q · pith_short_8: 7Y7H5CTK

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/7Y7H5CTKNHHVYV3QKHBMIJZCCU \
  | 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: fe3e7e8a6a69cf5c577051c2c42722150b2ad82a411c3a93bc62a6bf26752917

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a85bfa7af6c5ed03273c65658bae0e5b82dd36b83aefa2e4b932cd92fd22947",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-12-15T20:24:42Z",
    "title_canon_sha256": "c079b8b213010335c17ea178b1868f73fd477c4e1da2f9a802b82fc6a0b2f3a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.3637",
    "kind": "arxiv",
    "version": 2
  }
}