Pith Number

pith:AV37ZXAT

pith:2016:AV37ZXATAI7YX2BQBJDXROT5OM

not attested not anchored not stored refs pending

Some problems on the boundary of fractal geometry and additive combinatorics

Michael Hochman

arxiv:1608.02711 v3 · 2016-08-09 · math.DS · 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{AV37ZXATAI7YX2BQBJDXROT5OM}

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	2026-05-18T00:43:02.457792Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0577fcdc13023f8be8300a4778ba7d731b2169f1d4d8fef5d97e86c360679a58

Aliases

arxiv: 1608.02711 · arxiv_version: 1608.02711v3 · doi: 10.48550/arxiv.1608.02711 · pith_short_12: AV37ZXATAI7Y · pith_short_16: AV37ZXATAI7YX2BQ · pith_short_8: AV37ZXAT

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/AV37ZXATAI7YX2BQBJDXROT5OM \
  | 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: 0577fcdc13023f8be8300a4778ba7d731b2169f1d4d8fef5d97e86c360679a58

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa06ff9303c64c0ed4f00431b3408f4b73c4ee21af43313ceceacac9d3cc0241",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-08-09T07:48:01Z",
    "title_canon_sha256": "f088a88440712e386a61fdb163dd459f27ab9630dd3448dfe0c58c73fe19903e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.02711",
    "kind": "arxiv",
    "version": 3
  }
}