Pith Number

pith:G2IYCI4C

pith:2015:G2IYCI4CVAQXMJ5PFHEAXPW6SN

not attested not anchored not stored refs pending

Commutators in the Two-Weight Setting

Brett D. Wick, Irina Holmes, Michael T. Lacey

arxiv:1506.05747 v4 · 2015-06-18 · 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{G2IYCI4CVAQXMJ5PFHEAXPW6SN}

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	2026-05-18T00:43:36.101749Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3691812382a8217627af29c80bbede935937868638d77e45973072090268d3b3

Aliases

arxiv: 1506.05747 · arxiv_version: 1506.05747v4 · doi: 10.48550/arxiv.1506.05747 · pith_short_12: G2IYCI4CVAQX · pith_short_16: G2IYCI4CVAQXMJ5P · pith_short_8: G2IYCI4C

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/G2IYCI4CVAQXMJ5PFHEAXPW6SN \
  | 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: 3691812382a8217627af29c80bbede935937868638d77e45973072090268d3b3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "68b30a556814b5a72dfafbb42843bf29127ffb3a1983692cc819ab6116cbadd0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-06-18T16:46:24Z",
    "title_canon_sha256": "2c79314978653feb45c988d9c37b46bfd7a9576b4265256017570e1a6810ccf8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.05747",
    "kind": "arxiv",
    "version": 4
  }
}