Pith Number

pith:VKP4XRX6

pith:2010:VKP4XRX6ORQOF2NUGY2XVSP7NX

not attested not anchored not stored refs pending

A Remark on Recent Lower Bounds for Nodal Sets

Dan Mangoubi

arxiv:1010.4579 v2 · 2010-10-21 · 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{VKP4XRX6ORQOF2NUGY2XVSP7NX}

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	2026-05-18T04:10:12.541865Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa9fcbc6fe7460e2e9b436357ac9ff6df0b46c82ad5a6d1aa4d388558682507b

Aliases

arxiv: 1010.4579 · arxiv_version: 1010.4579v2 · doi: 10.48550/arxiv.1010.4579 · pith_short_12: VKP4XRX6ORQO · pith_short_16: VKP4XRX6ORQOF2NU · pith_short_8: VKP4XRX6

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/VKP4XRX6ORQOF2NUGY2XVSP7NX \
  | 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: aa9fcbc6fe7460e2e9b436357ac9ff6df0b46c82ad5a6d1aa4d388558682507b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "39eddcdc4c3ef1ba46b85f4622ecfe3c7c38c9c7d3ee82140658ab8d2358243b",
    "cross_cats_sorted": [
      "math.DG",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-10-21T20:34:02Z",
    "title_canon_sha256": "07a0918a21489ab69ab579d6ca1ef8c5a6d63b2cb307a5daaf15c3a6a4b5d1e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.4579",
    "kind": "arxiv",
    "version": 2
  }
}