Pith Number

pith:P2JQ7QNS

pith:2021:P2JQ7QNSNOCB42T7733S75HTKT

not attested not anchored not stored refs pending

A $p$-specific spectral multiplier theorem with sharp regularity bound for Grushin operators

Lars Niedorf

arxiv:2110.10058 v3 · 2021-10-19 · math.AP · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P2JQ7QNSNOCB42T7733S75HTKT}

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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	2026-07-05T10:11:54.869472Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e930fc1b26b841e6a7ffef72ff4f354d17b683dfab51ae5c3c9ac0408b2fd23

Aliases

arxiv: 2110.10058 · arxiv_version: 2110.10058v3 · doi: 10.48550/arxiv.2110.10058 · pith_short_12: P2JQ7QNSNOCB · pith_short_16: P2JQ7QNSNOCB42T7 · pith_short_8: P2JQ7QNS

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/P2JQ7QNSNOCB42T7733S75HTKT \
  | 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: 7e930fc1b26b841e6a7ffef72ff4f354d17b683dfab51ae5c3c9ac0408b2fd23

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c01280d6f0c4019ec74b630d2757ec81e581ede3d273565879c505a3d44dbcbf",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2021-10-19T15:35:05Z",
    "title_canon_sha256": "0b876e46265be2fdaf580cdd5def4cfd7976b8ba3eb2465bd78be5e921245ad8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2110.10058",
    "kind": "arxiv",
    "version": 3
  }
}