Pith Number

pith:4TDNTP32

pith:2011:4TDNTP32O4UOEGHXBJVGMB5KFK

not attested not anchored not stored refs pending

Lower bounds for volumes of nodal sets: an improvement of a result of Sogge-Zelditch

Hamid Hezari, Zuoqin Wang

arxiv:1107.0092 v2 · 2011-07-01 · math.AP · math.DG · 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{4TDNTP32O4UOEGHXBJVGMB5KFK}

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	2026-05-18T04:18:23.123192Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4c6d9bf7a7728e218f70a6a6607aa2aa2bf19edb7dd4988c16b55ab623fefea

Aliases

arxiv: 1107.0092 · arxiv_version: 1107.0092v2 · doi: 10.48550/arxiv.1107.0092 · pith_short_12: 4TDNTP32O4UO · pith_short_16: 4TDNTP32O4UOEGHX · pith_short_8: 4TDNTP32

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/4TDNTP32O4UOEGHXBJVGMB5KFK \
  | 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: e4c6d9bf7a7728e218f70a6a6607aa2aa2bf19edb7dd4988c16b55ab623fefea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f11f05553687694a6560208bf5a656af1c29358a08689aff89f70702aa0086db",
    "cross_cats_sorted": [
      "math.DG",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-07-01T01:49:12Z",
    "title_canon_sha256": "47cba4d2ea1c2c19c26c95e5f369d30b319f415ae8e8fce1060d67524fc0c444"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.0092",
    "kind": "arxiv",
    "version": 2
  }
}