Pith Number

pith:LQS4SOXP

pith:2011:LQS4SOXPZ45NZGHNOUA6LZ7TOV

not attested not anchored not stored refs pending

A natural lower bound for the size of nodal sets

Christopher D. Sogge, Hamid Hezari

arxiv:1107.3440 v3 · 2011-07-18 · math.AP · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LQS4SOXPZ45NZGHNOUA6LZ7TOV}

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	2026-05-18T03:35:26.359469Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5c25c93aefcf3adc98ed7501e5e7f3756c2deecc1e996b3d28cef5c3889ffe0d

Aliases

arxiv: 1107.3440 · arxiv_version: 1107.3440v3 · doi: 10.48550/arxiv.1107.3440 · pith_short_12: LQS4SOXPZ45N · pith_short_16: LQS4SOXPZ45NZGHN · pith_short_8: LQS4SOXP

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/LQS4SOXPZ45NZGHNOUA6LZ7TOV \
  | 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: 5c25c93aefcf3adc98ed7501e5e7f3756c2deecc1e996b3d28cef5c3889ffe0d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "792811783dceb8df08f6b26c4ec30db498e8689998aa039673e91cec9cb06986",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-07-18T14:06:09Z",
    "title_canon_sha256": "7968059797c575e3792888625b558a8c26361e713ab5cca08272cd9a1205a837"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.3440",
    "kind": "arxiv",
    "version": 3
  }
}