Pith Number

pith:ENZK4MLU

pith:2015:ENZK4MLUMN2D4DAQGVFO3O5TMR

not attested not anchored not stored refs pending

On the parity of the number of nodal domains for an eigenfunction of the Laplacian on tori

Corentin L\'ena

arxiv:1504.03944 v2 · 2015-04-15 · math.AP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ENZK4MLUMN2D4DAQGVFO3O5TMR}

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	2026-05-18T01:36:58.020124Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2372ae317463743e0c10354aedbbb36448d5ec95b6e74d8aecda717022df8b17

Aliases

arxiv: 1504.03944 · arxiv_version: 1504.03944v2 · doi: 10.48550/arxiv.1504.03944 · pith_short_12: ENZK4MLUMN2D · pith_short_16: ENZK4MLUMN2D4DAQ · pith_short_8: ENZK4MLU

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/ENZK4MLUMN2D4DAQGVFO3O5TMR \
  | 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: 2372ae317463743e0c10354aedbbb36448d5ec95b6e74d8aecda717022df8b17

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d266fc59f6787617239b143536fa21cb35f9ac9c5561d034daa1c1bc1d046bef",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-04-15T15:29:14Z",
    "title_canon_sha256": "13adf4879acb7f217dca061955d89e6a59a664bf5b5df1f8837dcb6303d87413"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.03944",
    "kind": "arxiv",
    "version": 2
  }
}