Pith Number

pith:RFOFDEYB

pith:2010:RFOFDEYBDJI7AGT3AXN2VNOGX5

not attested not anchored not stored refs pending

Critical sets of random smooth functions on products of spheres

Liviu I. Nicolaescu

arxiv:1008.5085 v4 · 2010-08-30 · math.DG · math-ph · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RFOFDEYBDJI7AGT3AXN2VNOGX5}

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	2026-05-18T02:56:12.889050Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

895c5193011a51f01a7b05dbaab5c6bf6b5bf437b2a0a5b119a86561239f81e9

Aliases

arxiv: 1008.5085 · arxiv_version: 1008.5085v4 · doi: 10.48550/arxiv.1008.5085 · pith_short_12: RFOFDEYBDJI7 · pith_short_16: RFOFDEYBDJI7AGT3 · pith_short_8: RFOFDEYB

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/RFOFDEYBDJI7AGT3AXN2VNOGX5 \
  | 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: 895c5193011a51f01a7b05dbaab5c6bf6b5bf437b2a0a5b119a86561239f81e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb6c23a46b035c76ef61c9d8f34547aaf0db3c3f7de4c5e4ce28a016cc4277ac",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-08-30T14:01:03Z",
    "title_canon_sha256": "91a95d7b80d982f513928f82e24262281f8431b271d48c49e0e27b887c367034"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.5085",
    "kind": "arxiv",
    "version": 4
  }
}