Pith Number

pith:MW5RD63K

pith:2013:MW5RD63K3N4XZZDMX7KTOICC3B

not attested not anchored not stored refs pending

Self similar sets, entropy and additive combinatorics

Michael Hochman

arxiv:1307.6399 v5 · 2013-07-24 · math.CA · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MW5RD63K3N4XZZDMX7KTOICC3B}

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	2026-05-18T02:41:42.272242Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65bb11fb6adb797ce46cbfd5372042d878ff22d3efd9a4172e8b16c02e405181

Aliases

arxiv: 1307.6399 · arxiv_version: 1307.6399v5 · doi: 10.48550/arxiv.1307.6399 · pith_short_12: MW5RD63K3N4X · pith_short_16: MW5RD63K3N4XZZDM · pith_short_8: MW5RD63K

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/MW5RD63K3N4XZZDMX7KTOICC3B \
  | 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: 65bb11fb6adb797ce46cbfd5372042d878ff22d3efd9a4172e8b16c02e405181

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f567a4aba6f3b8bbef6fe8c2c7127b8b45f39c652752141609e071c24f8ef69",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-07-24T12:18:54Z",
    "title_canon_sha256": "401042864fbcb8895636c8c54ba0efd267f56c51af6503f7e88062bf768b8219"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.6399",
    "kind": "arxiv",
    "version": 5
  }
}