Pith Number

pith:DCG3HLVY

pith:2019:DCG3HLVYDUBU7IIP4HNNMESNH2

not attested not anchored not stored refs pending

Three examples of Sharp Commutator Estimates via Harmonic Extensions

Armin Schikorra

arxiv:1902.08778 v1 · 2019-02-23 · 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{DCG3HLVYDUBU7IIP4HNNMESNH2}

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	2026-05-17T23:52:49.967782Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

188db3aeb81d034fa10fe1dad6124d3ea7f53d666589c5be0209c81baf27af54

Aliases

arxiv: 1902.08778 · arxiv_version: 1902.08778v1 · doi: 10.48550/arxiv.1902.08778 · pith_short_12: DCG3HLVYDUBU · pith_short_16: DCG3HLVYDUBU7IIP · pith_short_8: DCG3HLVY

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/DCG3HLVYDUBU7IIP4HNNMESNH2 \
  | 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: 188db3aeb81d034fa10fe1dad6124d3ea7f53d666589c5be0209c81baf27af54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b3892df26363f793cf2ca54673ae1b1f5c393da1b8cbceb23806e559f01fdfc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-02-23T11:37:13Z",
    "title_canon_sha256": "5922bee1efd7a8b9dfbcc24ca2e9eeb5665daf73caa6a9e1c8ef58f71981d224"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1902.08778",
    "kind": "arxiv",
    "version": 1
  }
}