Pith Number

pith:ASOAXS6Q

pith:2016:ASOAXS6QDRELSGYAZCJNZTMHV3

not attested not anchored not stored refs pending

Sharp commutator estimates via harmonic extensions

Armin Schikorra, Enno Lenzmann

arxiv:1609.08547 v2 · 2016-09-27 · 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{ASOAXS6QDRELSGYAZCJNZTMHV3}

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	2026-05-17T23:59:44.027438Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

049c0bcbd01c48b91b00c892dccd87aef9f6ee548556b5c3f26ff110bbd5b26f

Aliases

arxiv: 1609.08547 · arxiv_version: 1609.08547v2 · doi: 10.48550/arxiv.1609.08547 · pith_short_12: ASOAXS6QDREL · pith_short_16: ASOAXS6QDRELSGYA · pith_short_8: ASOAXS6Q

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/ASOAXS6QDRELSGYAZCJNZTMHV3 \
  | 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: 049c0bcbd01c48b91b00c892dccd87aef9f6ee548556b5c3f26ff110bbd5b26f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "91edbb0d53e1879915e45c832f6a89ba104bbff8753613b4d5d45ac1a2701a11",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-09-27T17:45:33Z",
    "title_canon_sha256": "7fed61ce4614600028834199a3f018438e3c06c14f137c5f7509124cea74e2f2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.08547",
    "kind": "arxiv",
    "version": 2
  }
}