Pith Number

pith:D2OHRRGF

pith:2012:D2OHRRGFJPJFFBYRDZZYROCIE2

not attested not anchored not stored refs pending

Random Morse functions and spectral geometry

Liviu I. Nicolaescu

arxiv:1209.0639 v3 · 2012-09-04 · math.DG · math.AP · 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{D2OHRRGFJPJFFBYRDZZYROCIE2}

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	2026-05-18T02:56:44.497843Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1e9c78c4c54bd25287111e7388b848268cac04ef08a706dc057e49399d015313

Aliases

arxiv: 1209.0639 · arxiv_version: 1209.0639v3 · doi: 10.48550/arxiv.1209.0639 · pith_short_12: D2OHRRGFJPJF · pith_short_16: D2OHRRGFJPJFFBYR · pith_short_8: D2OHRRGF

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/D2OHRRGFJPJFFBYRDZZYROCIE2 \
  | 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: 1e9c78c4c54bd25287111e7388b848268cac04ef08a706dc057e49399d015313

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc34f716213ee0a52d3d1ebc271461591136e94372af7263ae8a3482c133f5f3",
    "cross_cats_sorted": [
      "math.AP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-09-04T13:29:31Z",
    "title_canon_sha256": "c12fff9a732fc7bc249cd483950dc6727d8fd16aae18d45f0b44685cbe1962dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.0639",
    "kind": "arxiv",
    "version": 3
  }
}