Pith Number

pith:LSHA75F6

pith:2008:LSHA75F6S3YMDFUSHJBKGVRMJH

not attested not anchored not stored refs pending

Average growth of the spectral function on a Riemannian manifold

Hugues Lapointe, Iosif Polterovich, Yuri Safarov

arxiv:0803.4171 v2 · 2008-03-28 · math.SP · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LSHA75F6S3YMDFUSHJBKGVRMJH}

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	2026-07-04T15:14:29.288101Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5c8e0ff4be96f0c196923a42a3562c49e2c93d679925cbf54a71ee92e6f5782d

Aliases

arxiv: 0803.4171 · arxiv_version: 0803.4171v2 · doi: 10.48550/arxiv.0803.4171 · pith_short_12: LSHA75F6S3YM · pith_short_16: LSHA75F6S3YMDFUS · pith_short_8: LSHA75F6

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/LSHA75F6S3YMDFUSHJBKGVRMJH \
  | 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: 5c8e0ff4be96f0c196923a42a3562c49e2c93d679925cbf54a71ee92e6f5782d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e3637c61a3b0d68b406fb6ab2df83ba44037b96ce40df2feac1f1c1a7548c95e",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2008-03-28T17:23:05Z",
    "title_canon_sha256": "373858454f56a92ed47e0254fc3227bbef1027d4910795cd7d786e33bd2319cf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0803.4171",
    "kind": "arxiv",
    "version": 2
  }
}