Pith Number

pith:AXYCDFER

pith:2017:AXYCDFER37WPLMAUIRI66NQRPK

not attested not anchored not stored refs pending

Semi-uniform domains and the $A_{\infty}$ property for harmonic measure

Jonas Azzam

arxiv:1711.03088 v4 · 2017-11-08 · math.AP · math.CA · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AXYCDFER37WPLMAUIRI66NQRPK}

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	2026-05-18T00:07:11.606693Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

05f0219491dfecf5b0144451ef36117a9c8fbe891d564d757ea649a46625338f

Aliases

arxiv: 1711.03088 · arxiv_version: 1711.03088v4 · doi: 10.48550/arxiv.1711.03088 · pith_short_12: AXYCDFER37WP · pith_short_16: AXYCDFER37WPLMAU · pith_short_8: AXYCDFER

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/AXYCDFER37WPLMAUIRI66NQRPK \
  | 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: 05f0219491dfecf5b0144451ef36117a9c8fbe891d564d757ea649a46625338f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1bd1940c937a45da347ae39a056025a6a33a08f23da309d5cb280ad80f966b00",
    "cross_cats_sorted": [
      "math.CA",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-11-08T18:40:08Z",
    "title_canon_sha256": "bdecc1a2d6f4b1b354ecfd6792485c9821c0e35443a2205b047045c63306bd01"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.03088",
    "kind": "arxiv",
    "version": 4
  }
}