Pith Number

pith:M6SLLR2R

pith:2014:M6SLLR2RKNO2JWHC2OMLN2UJ23

not attested not anchored not stored refs pending

L^{p}(\mu)-L^{q}(\nu) characterization for well localized operators

Emil Vuorinen

arxiv:1412.2127 v2 · 2014-12-05 · 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{M6SLLR2RKNO2JWHC2OMLN2UJ23}

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	2026-05-18T01:22:03.269354Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67a4b5c751535da4d8e2d398b6ea89d6e73ef9dfa7a3f93b7ba45908b97eac31

Aliases

arxiv: 1412.2127 · arxiv_version: 1412.2127v2 · doi: 10.48550/arxiv.1412.2127 · pith_short_12: M6SLLR2RKNO2 · pith_short_16: M6SLLR2RKNO2JWHC · pith_short_8: M6SLLR2R

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/M6SLLR2RKNO2JWHC2OMLN2UJ23 \
  | 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: 67a4b5c751535da4d8e2d398b6ea89d6e73ef9dfa7a3f93b7ba45908b97eac31

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9442fbf3cda0d8d73ab155973dae6617957a696e14b83751c34ffcfca31bb478",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2014-12-05T20:39:07Z",
    "title_canon_sha256": "485abac7494bd7835405757789408461eb0cbc59f7868db17a7f137d014a2766"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.2127",
    "kind": "arxiv",
    "version": 2
  }
}