Pith Number

pith:3FCPBT5I

pith:2015:3FCPBT5IMQQ2AIRIAUOOALGX24

not attested not anchored not stored refs pending

On self-similar sets with overlaps and inverse theorems for entropy in $\mathbb{R}^d$

Michael Hochman

arxiv:1503.09043 v2 · 2015-03-31 · math.CA · 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{3FCPBT5IMQQ2AIRIAUOOALGX24}

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.

Cited by

1 paper in Pith

Weakly separated self-affine carpets

Receipt and verification

First computed	2026-05-18T00:43:03.300496Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d944f0cfa86421a02228051ce02cd7d7052ab5fcba459503b3e4021b79f67293

Aliases

arxiv: 1503.09043 · arxiv_version: 1503.09043v2 · doi: 10.48550/arxiv.1503.09043 · pith_short_12: 3FCPBT5IMQQ2 · pith_short_16: 3FCPBT5IMQQ2AIRI · pith_short_8: 3FCPBT5I

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/3FCPBT5IMQQ2AIRIAUOOALGX24 \
  | 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: d944f0cfa86421a02228051ce02cd7d7052ab5fcba459503b3e4021b79f67293

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "450540f57023af175149dda78accf03ecc5f81ff9ffa9fa74d610a2611f108ee",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-03-31T13:46:44Z",
    "title_canon_sha256": "8faeb1f7fd9c420790576d0b0e56493ad4e5482fce6a637d81edd1a7e79eb527"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.09043",
    "kind": "arxiv",
    "version": 2
  }
}