Pith Number

pith:FZQJV52F

pith:2012:FZQJV52FCLWVUQM7UFMN76AJQH

not attested not anchored not stored refs pending

Weighted Plancherel estimates and sharp spectral multipliers for the Grushin operators

Adam Sikora, Alessio Martini

arxiv:1204.1159 v1 · 2012-04-05 · 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{FZQJV52FCLWVUQM7UFMN76AJQH}

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	2026-05-18T03:30:53.836402Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2e609af74512ed5a419fa158dff80981f2b6f0f6c3a7b5cf406062b2c651cb57

Aliases

arxiv: 1204.1159 · arxiv_version: 1204.1159v1 · doi: 10.48550/arxiv.1204.1159 · pith_short_12: FZQJV52FCLWV · pith_short_16: FZQJV52FCLWVUQM7 · pith_short_8: FZQJV52F

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/FZQJV52FCLWVUQM7UFMN76AJQH \
  | 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: 2e609af74512ed5a419fa158dff80981f2b6f0f6c3a7b5cf406062b2c651cb57

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb9b0e3d178eb837a9115a6465ef9b8bea49f1bef197a232e269ab13c49281d7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-04-05T09:27:49Z",
    "title_canon_sha256": "2027b0918e2a31ddb367025a34b589df4fd2d88c6e24fd7a71bf382f52eec3ba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.1159",
    "kind": "arxiv",
    "version": 1
  }
}