Pith Number

pith:6JW6LOZF

pith:2012:6JW6LOZF55ZRHBKL5CEJJHQNLF

not attested not anchored not stored refs pending

Complexity of random smooth functions on compact manifolds

Liviu I. Nicolaescu

arxiv:1201.4972 v4 · 2012-01-24 · math.DG · 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{6JW6LOZF55ZRHBKL5CEJJHQNLF}

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	2026-05-18T02:56:12.863643Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f26de5bb25ef7313854be888949e0d5947d397bd0b27d32464bb27544f86f6d9

Aliases

arxiv: 1201.4972 · arxiv_version: 1201.4972v4 · doi: 10.48550/arxiv.1201.4972 · pith_short_12: 6JW6LOZF55ZR · pith_short_16: 6JW6LOZF55ZRHBKL · pith_short_8: 6JW6LOZF

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/6JW6LOZF55ZRHBKL5CEJJHQNLF \
  | 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: f26de5bb25ef7313854be888949e0d5947d397bd0b27d32464bb27544f86f6d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b2dd685a8a8dff6847373225b4e7e2a51d0f5cf2f3dd2b3fc7ba8cd641c7f042",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-01-24T13:14:59Z",
    "title_canon_sha256": "020995490a3c715511302ad383b4797240c0d4dfeecd0ccffb73bd950d6202a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.4972",
    "kind": "arxiv",
    "version": 4
  }
}