Pith Number

pith:YWHNZN4P

pith:2012:YWHNZN4PQSCW4VCYZZV6K7NO2R

not attested not anchored not stored refs pending

On $L^p$-resolvent estimates and the density of eigenvalues for compact Riemannian manifolds

Christopher D. Sogge, Jean Bourgain, Peng Shao, Xiaohua Yao

arxiv:1204.3927 v3 · 2012-04-17 · math.AP · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YWHNZN4PQSCW4VCYZZV6K7NO2R}

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	2026-05-18T03:07:41.393115Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c58edcb78f84856e5458ce6be57daed452f72d86c1a8fa284d387b3a86f705d9

Aliases

arxiv: 1204.3927 · arxiv_version: 1204.3927v3 · doi: 10.48550/arxiv.1204.3927 · pith_short_12: YWHNZN4PQSCW · pith_short_16: YWHNZN4PQSCW4VCY · pith_short_8: YWHNZN4P

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/YWHNZN4PQSCW4VCYZZV6K7NO2R \
  | 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: c58edcb78f84856e5458ce6be57daed452f72d86c1a8fa284d387b3a86f705d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b22ddb03354b9134e095d4a6891d4d8b65f2db0c9c727c57c15715bf6cda12c1",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-04-17T21:46:17Z",
    "title_canon_sha256": "c5972f6dece4537562ddc046527b30d38d0a43fac7381215ff053800f7b664eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.3927",
    "kind": "arxiv",
    "version": 3
  }
}