Pith Number

pith:3KRB3RUE

pith:2011:3KRB3RUEZMB32PGFLWRBMGXSLH

not attested not anchored not stored refs pending

Stability of nodal structures in graph eigenfunctions and its relation to the nodal domain count

Gregory Berkolaiko, Hillel Raz, Uzy Smilansky

arxiv:1110.3802 v1 · 2011-10-17 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3KRB3RUEZMB32PGFLWRBMGXSLH}

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	2026-05-18T03:31:54.421265Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

daa21dc684cb03bd3cc55da2161af259d9759b5b17be9240e1bdf73d082c3986

Aliases

arxiv: 1110.3802 · arxiv_version: 1110.3802v1 · doi: 10.48550/arxiv.1110.3802 · pith_short_12: 3KRB3RUEZMB3 · pith_short_16: 3KRB3RUEZMB32PGF · pith_short_8: 3KRB3RUE

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/3KRB3RUEZMB32PGFLWRBMGXSLH \
  | 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: daa21dc684cb03bd3cc55da2161af259d9759b5b17be9240e1bdf73d082c3986

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9076aecf1bd2e71e9141e35f33c5ab4edd8d2182cccf04e79e161c7da00d8886",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-10-17T20:04:50Z",
    "title_canon_sha256": "3fc4c31ef5c805213cecd7179956844d44f5e185f6209876b503373cf6a945d4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.3802",
    "kind": "arxiv",
    "version": 1
  }
}