Pith Number

pith:2GLMH6C6

pith:2013:2GLMH6C6NTQBODZ7BV2NVXY7UI

not attested not anchored not stored refs pending

Lower estimates for the expected Betti numbers of random real hypersurfaces

Damien Gayet (ICJ), Jean-Yves Welschinger (ICJ)

arxiv:1303.3035 v1 · 2013-03-12 · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2GLMH6C6NTQBODZ7BV2NVXY7UI}

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	2026-05-18T00:44:29.969469Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d196c3f85e6ce0170f3f0d74dadf1fa21c93709a45636469e583fc55d83e3c1e

Aliases

arxiv: 1303.3035 · arxiv_version: 1303.3035v1 · doi: 10.48550/arxiv.1303.3035 · pith_short_12: 2GLMH6C6NTQB · pith_short_16: 2GLMH6C6NTQBODZ7 · pith_short_8: 2GLMH6C6

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/2GLMH6C6NTQBODZ7BV2NVXY7UI \
  | 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: d196c3f85e6ce0170f3f0d74dadf1fa21c93709a45636469e583fc55d83e3c1e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69b060a299750402448dc0e499154c2142f5df1745811b7fe24f7f9f922b0e0e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2013-03-12T21:05:52Z",
    "title_canon_sha256": "6fdac09d02150988457454606060b32a61768260ace41d2c6f8e8bb04d7cc982"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.3035",
    "kind": "arxiv",
    "version": 1
  }
}