Pith Number

pith:F77LIBIF

pith:2016:F77LIBIFUN3AVFNUUNZWUWI62O

not attested not anchored not stored refs pending

On Tsirelson's theorem about triple points for harmonic measure

Alexander Volberg, Xavier Tolsa

arxiv:1608.04022 v4 · 2016-08-13 · math.CA · 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{F77LIBIFUN3AVFNUUNZWUWI62O}

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	2026-05-18T00:55:12.560300Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ffeb40505a3760a95b4a3736a591ed3a48410124ce9d8b38ddb972127c68bda

Aliases

arxiv: 1608.04022 · arxiv_version: 1608.04022v4 · doi: 10.48550/arxiv.1608.04022 · pith_short_12: F77LIBIFUN3A · pith_short_16: F77LIBIFUN3AVFNU · pith_short_8: F77LIBIF

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/F77LIBIFUN3AVFNUUNZWUWI62O \
  | 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: 2ffeb40505a3760a95b4a3736a591ed3a48410124ce9d8b38ddb972127c68bda

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "05781a9d78a31e85c585494905bb452c64056dc1eed5bf78f30ae789c69f4e29",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-08-13T19:48:14Z",
    "title_canon_sha256": "18e48ff2f8707d71ea9e593464deed03540cdb492a5715439d266da281503b33"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.04022",
    "kind": "arxiv",
    "version": 4
  }
}