Pith Number

pith:QRPFIZD7

pith:2010:QRPFIZD7O2TYXXYFDUMHGHRXE7

not attested not anchored not stored refs pending

On stable compact minimal submanifolds

Francisco Torralbo, Francisco Urbano

arxiv:1012.0679 v1 · 2010-12-03 · 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{QRPFIZD7O2TYXXYFDUMHGHRXE7}

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	2026-05-18T04:34:09.614218Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

845e54647f76a78bdf051d18731e3727eb10420a93ec99f1afa35af6d647f18e

Aliases

arxiv: 1012.0679 · arxiv_version: 1012.0679v1 · doi: 10.48550/arxiv.1012.0679 · pith_short_12: QRPFIZD7O2TY · pith_short_16: QRPFIZD7O2TYXXYF · pith_short_8: QRPFIZD7

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/QRPFIZD7O2TYXXYFDUMHGHRXE7 \
  | 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: 845e54647f76a78bdf051d18731e3727eb10420a93ec99f1afa35af6d647f18e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "46de931be6b5f6990f62564e71cf2113537d5ad19e5463061ef0218abfe780a8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-12-03T10:00:44Z",
    "title_canon_sha256": "08b91301c9b8133b561acb303c5d1e30a5e2f7b33716c8e687b62731b39c82f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.0679",
    "kind": "arxiv",
    "version": 1
  }
}