Pith Number

pith:PWMBLDLD

pith:2012:PWMBLDLDPN6DKFIXFQAEHMNW3N

not attested not anchored not stored refs pending

On self-similar sets with overlaps and inverse theorems for entropy

Michael Hochman

arxiv:1212.1873 v6 · 2012-12-09 · math.CA · math.DS · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PWMBLDLDPN6DKFIXFQAEHMNW3N}

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	2026-05-18T02:42:15.232037Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d98158d637b7c3515172c0043b1b6db40f8f3a6d620e847dca5f69459edcd56

Aliases

arxiv: 1212.1873 · arxiv_version: 1212.1873v6 · doi: 10.48550/arxiv.1212.1873 · pith_short_12: PWMBLDLDPN6D · pith_short_16: PWMBLDLDPN6DKFIX · pith_short_8: PWMBLDLD

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/PWMBLDLDPN6DKFIXFQAEHMNW3N \
  | 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: 7d98158d637b7c3515172c0043b1b6db40f8f3a6d620e847dca5f69459edcd56

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73ca956a8fc1f06df1c6b9cbb1fffb7f0d95d432d4f0019c88892d03cf349b8e",
    "cross_cats_sorted": [
      "math.DS",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-12-09T10:12:37Z",
    "title_canon_sha256": "e6ecdf34605683a7d8f6edefda6b7c43b29ca15f2bc7c23fc8daaaee618f391b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.1873",
    "kind": "arxiv",
    "version": 6
  }
}