Pith Number

pith:HP5KJD74

pith:2016:HP5KJD74OFHWZY3GKFLL6ZU3WW

not attested not anchored not stored refs pending

Mutual absolute continuity of interior and exterior harmonic measure implies rectifiability

Jonas Azzam, Mihalis Mourgoglou, Xavier Tolsa

arxiv:1602.01397 v2 · 2016-02-03 · math.CA · math.AP · 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{HP5KJD74OFHWZY3GKFLL6ZU3WW}

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	2026-05-18T01:13:15.415714Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3bfaa48ffc714f6ce3665156bf669bb5914d42dfdf27d03e499429680fa6f8b2

Aliases

arxiv: 1602.01397 · arxiv_version: 1602.01397v2 · doi: 10.48550/arxiv.1602.01397 · pith_short_12: HP5KJD74OFHW · pith_short_16: HP5KJD74OFHWZY3G · pith_short_8: HP5KJD74

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/HP5KJD74OFHWZY3GKFLL6ZU3WW \
  | 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: 3bfaa48ffc714f6ce3665156bf669bb5914d42dfdf27d03e499429680fa6f8b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18e44b59c441f04fd5371d1fc45c0bb89c8d071b013c988a3fbe6fedf8e6109b",
    "cross_cats_sorted": [
      "math.AP",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-02-03T18:08:51Z",
    "title_canon_sha256": "d030b669b7634e4ea53bff1448139e2c8c450998845c45ce11e69bf45102c0fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.01397",
    "kind": "arxiv",
    "version": 2
  }
}